premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is not old or not kind then someone is not generous. Everyone who is either not strong or creative is either not wise or funny. Everyone who is either not rich or generous is happy or not old. Everyone who is both tall and not brave is generous and vice versa. If mary is both curious and old then someone is not brave or kind. If someone is not calm then someone is creative and vice versa. Everyone who is not funny or not humble is both creative and strong and vice versa. Everyone who is calm or patient is not strong or funny and vice versa. Everyone who is not patient is kind. Everyone who is either strong or not strong is either not funny or patient and vice versa. If someone is either not creative or not funny then someone is not brave or not happy and vice versa. If someone is both not tall and not patient then someone is not calm and vice versa. If mary is not kind or not creative then mary is not funny or strong and vice versa. If john is not wise or not calm then someone is either curious or not funny and vice versa. Everyone who is not generous is wise. If paul is both creative and patient then someone is either not wise or old. Someone is both not old and not happy. Lucy is tall. Someone is either wise or not wise. John is not tall or rich. Someone is both curious and not kind. Fred is not strong. Someone is either strong or not happy. | Lucy is creative. | contradiction | ((?[X]:((~old(X)|~kind(X))))=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)<~>creative(X))=>(~wise(X)<~>funny(X))))&
(![X]:((~rich(X)<~>generous(X))=>(happy(X)|~old(X))))&
(![X]:((tall(X)&~brave(X))<=>generous(X)))&
(((curious(mary)&old(mary)))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(creative(X))))&
(![X]:((~funny(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((calm(X)|patient(X))<=>(~strong(X)|funny(X))))&
(![X]:(~patient(X)=>kind(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~calm(X))))&
(((~kind(mary)|~creative(mary)))<=>((~funny(mary)|strong(mary))))&
(((~wise(john)|~calm(john)))<=>(?[X]:((curious(X)<~>~funny(X)))))&
(![X]:(~generous(X)=>wise(X)))&
(((creative(paul)&patient(paul)))=>(?[X]:((~wise(X)<~>old(X)))))&
(?[X]:((~old(X)&~happy(X))))&
(tall(lucy))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(john)|rich(john)))&
(?[X]:((curious(X)&~kind(X))))&
(~strong(fred))&
(?[X]:((strong(X)<~>~happy(X)))) | creative(lucy) | [
"p1",
"p3",
"p5",
"p6",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8811485112314348144936168
% SZS output start Proof for 8811485112314348144936168
2. ! [X0] : ((~strong(X0) <~> creative(X0)) => (~wise(X0) <~> funny(X0))) [input p1]
4. ! [X0] : ((~brave(X0) & tall(X0)) <=> generous(X0)) [input p3]
6. ? [X0] : ~calm(X0) <=> ? [X0] : creative(X0) [input p5]
7. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (strong(X0) & creative(X0))) [input p6]
10. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p9]
12. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X0] : ~calm(X0) [input p11]
15. ! [X0] : (~generous(X0) => wise(X0)) [input p14]
24. creative(lucy) [input hypothesis]
26. ? [X0] : ~calm(X0) <=> ? [X1] : creative(X1) [rectify 6]
28. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X1] : ~calm(X1) [rectify 12]
30. ! [X0] : ((~wise(X0) <~> funny(X0)) | (~strong(X0) <=> creative(X0))) [ennf transformation 2]
36. ! [X0] : (wise(X0) | generous(X0)) [ennf transformation 15]
42. ! [X0] : (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) [nnf transformation 30]
44. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 4]
45. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | brave(X0) | ~tall(X0))) [flattening 44]
48. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : calm(X0)) [nnf transformation 26]
49. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : calm(X3)) [rectify 48]
50. ? [X0] : ~calm(X0) => ~calm(sK2) [choice axiom]
51. ? [X2] : creative(X2) => creative(sK3) [choice axiom]
52. (~calm(sK2) | ! [X1] : ~creative(X1)) & (creative(sK3) | ! [X3] : calm(X3)) [skolemisation 49,51,50]
53. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 7]
54. ! [X0] : ((~humble(X0) | ~funny(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [flattening 53]
57. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 10]
63. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (patient(X0) | tall(X0))) [nnf transformation 28]
64. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (patient(X3) | tall(X3))) [rectify 63]
65. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK6) & ~tall(sK6)) [choice axiom]
66. ? [X2] : ~calm(X2) => ~calm(sK7) [choice axiom]
67. ((~patient(sK6) & ~tall(sK6)) | ! [X1] : calm(X1)) & (~calm(sK7) | ! [X3] : (patient(X3) | tall(X3))) [skolemisation 64,66,65]
91. ~wise(X0) | funny(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 42]
97. ~generous(X0) | tall(X0) [cnf transformation 45]
101. ~calm(sK2) | ~creative(X1) [cnf transformation 52]
102. funny(X0) | creative(X0) [cnf transformation 54]
104. funny(X0) | strong(X0) [cnf transformation 54]
112. patient(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 57]
113. patient(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 57]
127. ~tall(sK6) | calm(X1) [cnf transformation 67]
128. ~patient(sK6) | calm(X1) [cnf transformation 67]
139. wise(X0) | generous(X0) [cnf transformation 36]
153. creative(lucy) [cnf transformation 24]
154. patient(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 112]
155. patient(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 113]
188. 8 <=> ! [X1] : ~creative(X1) [avatar definition]
189. ~creative(X1) <- (8) [avatar component clause 188]
191. 9 <=> calm(sK2) [avatar definition]
193. ~calm(sK2) <- (~9) [avatar component clause 191]
194. 8 | ~9 [avatar split clause 101,191,188]
196. 10 <=> ! [X3] : calm(X3) [avatar definition]
197. calm(X3) <- (10) [avatar component clause 196]
205. patient(X0) | strong(X0) [subsumption resolution 155,104]
206. ~funny(X0) | patient(X0) [subsumption resolution 154,205]
242. 20 <=> patient(sK6) [avatar definition]
244. ~patient(sK6) <- (~20) [avatar component clause 242]
245. 10 | ~20 [avatar split clause 128,242,196]
247. 21 <=> tall(sK6) [avatar definition]
249. ~tall(sK6) <- (~21) [avatar component clause 247]
250. 10 | ~21 [avatar split clause 127,247,196]
347. $false <- (~9, 10) [subsumption resolution 193,197]
348. 9 | ~10 [avatar contradiction clause 347]
349. $false <- (8) [resolution 189,153]
350. ~8 [avatar contradiction clause 349]
387. funny(X0) | ~strong(X0) | ~creative(X0) | generous(X0) [resolution 91,139]
389. funny(X0) | ~creative(X0) | generous(X0) [subsumption resolution 387,104]
390. funny(X0) | generous(X0) [subsumption resolution 389,102]
414. patient(X3) | generous(X3) [resolution 390,206]
422. generous(sK6) <- (~20) [resolution 414,244]
431. tall(sK6) <- (~20) [resolution 422,97]
432. $false <- (~20, ~21) [subsumption resolution 431,249]
433. 20 | 21 [avatar contradiction clause 432]
434. $false [avatar sat refutation 194,245,250,348,350,433]
% SZS output end Proof for 8811485112314348144936168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is creative or rich then someone is either not tall or not wise and vice versa.
Everyone who is either happy or old is either quiet or wise and vice versa.
Everyone who is both not patient and not brave is not calm.
Everyone who is rich or curious is both not quiet and kind and vice versa.
If someone is not quiet then mary is wise and vice versa.
If someone is old then someone is both not brave and not quiet and vice versa.
Everyone who is brave or not rich is not brave.
Everyone who is both not brave and humble is brave and vice versa.
Everyone who is both strong and curious is not generous or not curious.
If mary is either not tall or curious then someone is either funny or not calm.
If someone is either wise or brave then fred is not wise or not rich.
Everyone who is not calm is either curious or not wise and vice versa.
If someone is either not funny or not creative then someone is both not creative and not tall.
Everyone who is both not happy and calm is strong.
If someone is not creative or not brave then someone is not wise or not rich.
If john is either not humble or funny then lucy is both humble and kind and vice versa.
Someone is either creative or tall.
Lucy is creative.
Alice is happy or not brave.
Someone is not happy.
Someone is happy.
Someone is either funny or brave.
Someone is not funny or not happy.
Someone is patient. | Lucy is brave. | contradiction | (((creative(john)|rich(john)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>old(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((~patient(X)&~brave(X))=>~calm(X)))&
(![X]:((rich(X)|curious(X))<=>(~quiet(X)&kind(X))))&
((?[X]:(~quiet(X)))<=>(wise(mary)))&
((?[X]:(old(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:((~brave(X)&humble(X))<=>brave(X)))&
(![X]:((strong(X)&curious(X))=>(~generous(X)|~curious(X))))&
(((~tall(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>~calm(X)))))&
((?[X]:((wise(X)<~>brave(X))))=>((~wise(fred)|~rich(fred))))&
(![X]:(~calm(X)<=>(curious(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~happy(X)&calm(X))=>strong(X)))&
((?[X]:((~creative(X)|~brave(X))))=>(?[X]:((~wise(X)|~rich(X)))))&
(((~humble(john)<~>funny(john)))<=>((humble(lucy)&kind(lucy))))&
(?[X]:((creative(X)<~>tall(X))))&
(creative(lucy))&
((happy(alice)|~brave(alice)))&
(?[X]:(~happy(X)))&
(?[X]:(happy(X)))&
(?[X]:((funny(X)<~>brave(X))))&
(?[X]:((~funny(X)|~happy(X))))&
(?[X]:(patient(X))) | brave(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8522538984806230350117639
% SZS output start Proof for 8522538984806230350117639
7. ! [X0] : ((~rich(X0) | brave(X0)) => ~brave(X0)) [input p6]
25. brave(lucy) [input hypothesis]
33. ! [X0] : (~brave(X0) | (rich(X0) & ~brave(X0))) [ennf transformation 7]
108. ~brave(X0) | ~brave(X0) [cnf transformation 33]
144. brave(lucy) [cnf transformation 25]
147. ~brave(X0) [duplicate literal removal 108]
309. $false [subsumption resolution 144,147]
% SZS output end Proof for 8522538984806230350117639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not humble or rich then alice is either wise or not kind and vice versa. Everyone who is either not curious or curious is both not happy and curious and vice versa. Everyone who is generous or kind is both strong and not curious. Everyone who is humble is either rich or not humble. If someone is either not curious or not old then someone is not patient. Everyone who is not brave is either tall or curious. Everyone who is not old or not wise is not wise. Everyone who is not calm is both creative and not kind and vice versa. Everyone who is wise is either calm or old. Everyone who is either not funny or kind is either not curious or not brave. Everyone who is not tall is not rich and vice versa. Everyone who is both tall and brave is either not generous or creative and vice versa. Everyone who is either rich or not generous is both not happy and not old and vice versa. If fred is not brave or not patient then someone is either patient or not strong and vice versa. Everyone who is kind is both not calm and not old. Everyone who is either not old or old is creative. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. Alice is tall or not quiet. Someone is either not brave or curious. Fred is wise or not patient. Paul is either calm or not humble. | Paul is wise. | contradiction | (((~humble(fred)|rich(fred)))<=>((wise(alice)<~>~kind(alice))))&
(![X]:((~curious(X)<~>curious(X))<=>(~happy(X)&curious(X))))&
(![X]:((generous(X)|kind(X))=>(strong(X)&~curious(X))))&
(![X]:(humble(X)=>(rich(X)<~>~humble(X))))&
((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)=>(tall(X)<~>curious(X))))&
(![X]:((~old(X)|~wise(X))=>~wise(X)))&
(![X]:(~calm(X)<=>(creative(X)&~kind(X))))&
(![X]:(wise(X)=>(calm(X)<~>old(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~curious(X)<~>~brave(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:((tall(X)&brave(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(~happy(X)&~old(X))))&
(((~brave(fred)|~patient(fred)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:(kind(X)=>(~calm(X)&~old(X))))&
(![X]:((~old(X)<~>old(X))=>creative(X)))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy)))&
((tall(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>curious(X))))&
((wise(fred)|~patient(fred)))&
((calm(paul)<~>~humble(paul))) | wise(paul) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p10",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1715005989959675234318618
% SZS output start Proof for 1715005989959675234318618
2. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> (curious(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((kind(X0) | generous(X0)) => (~curious(X0) & strong(X0))) [input p2]
6. ! [X0] : (~brave(X0) => (tall(X0) <~> curious(X0))) [input p5]
7. ! [X0] : ((~wise(X0) | ~old(X0)) => ~wise(X0)) [input p6]
8. ! [X0] : (~calm(X0) <=> (~kind(X0) & creative(X0))) [input p7]
11. ! [X0] : (~tall(X0) <=> ~rich(X0)) [input p10]
12. ! [X0] : ((brave(X0) & tall(X0)) <=> (~generous(X0) <~> creative(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~old(X0) & ~happy(X0))) [input p12]
16. ! [X0] : ((~old(X0) <~> old(X0)) => creative(X0)) [input p15]
24. wise(paul) [input hypothesis]
27. ! [X0] : ((~curious(X0) & strong(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 3]
30. ! [X0] : ((tall(X0) <~> curious(X0)) | brave(X0)) [ennf transformation 6]
31. ! [X0] : (~wise(X0) | (wise(X0) & old(X0))) [ennf transformation 7]
35. ! [X0] : (creative(X0) | (~old(X0) <=> old(X0))) [ennf transformation 16]
38. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [flattening 38]
45. ! [X0] : (((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | brave(X0)) [nnf transformation 30]
46. ! [X0] : ((~calm(X0) | (kind(X0) | ~creative(X0))) & ((~kind(X0) & creative(X0)) | calm(X0))) [nnf transformation 8]
47. ! [X0] : ((~calm(X0) | kind(X0) | ~creative(X0)) & ((~kind(X0) & creative(X0)) | calm(X0))) [flattening 46]
50. ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 11]
51. ! [X0] : (((brave(X0) & tall(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~brave(X0) | ~tall(X0)))) [nnf transformation 12]
52. ! [X0] : (((brave(X0) & tall(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~brave(X0) | ~tall(X0))) [flattening 51]
53. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 13]
54. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 53]
60. ! [X0] : (creative(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 35]
78. curious(X0) | curious(X0) | curious(X0) [cnf transformation 39]
84. ~curious(X0) | ~generous(X0) [cnf transformation 27]
85. ~curious(X0) | ~kind(X0) [cnf transformation 27]
91. ~curious(X0) | ~tall(X0) | brave(X0) [cnf transformation 45]
92. ~wise(X0) | old(X0) [cnf transformation 31]
94. creative(X0) | calm(X0) [cnf transformation 47]
96. ~calm(X0) | kind(X0) | ~creative(X0) [cnf transformation 47]
103. ~rich(X0) | tall(X0) [cnf transformation 50]
106. ~creative(X0) | generous(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 52]
114. ~old(X0) | rich(X0) | generous(X0) [cnf transformation 54]
125. creative(X0) | old(X0) | old(X0) [cnf transformation 60]
126. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 60]
136. wise(paul) [cnf transformation 24]
137. creative(X0) | old(X0) [duplicate literal removal 125]
138. ~old(X0) | creative(X0) [duplicate literal removal 126]
142. curious(X0) [duplicate literal removal 78]
169. ~kind(X0) [subsumption resolution 85,142]
170. ~generous(X0) [subsumption resolution 84,142]
180. ~tall(X0) | brave(X0) [subsumption resolution 91,142]
181. ~creative(X0) | ~calm(X0) [subsumption resolution 96,169]
187. ~creative(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 106,170]
188. ~creative(X0) | ~tall(X0) [subsumption resolution 187,180]
191. ~old(X0) | rich(X0) [subsumption resolution 114,170]
220. creative(X0) [subsumption resolution 137,138]
248. old(paul) [resolution 92,136]
251. ~calm(X1) [resolution 181,220]
257. ~tall(X2) | calm(X2) [resolution 188,94]
259. ~tall(X2) [subsumption resolution 257,251]
260. rich(paul) [resolution 191,248]
262. tall(paul) [resolution 260,103]
263. $false [subsumption resolution 262,259]
% SZS output end Proof for 1715005989959675234318618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not kind is not curious. Everyone who is not humble or humble is creative or not quiet and vice versa. Everyone who is either calm or not tall is both wise and kind. Everyone who is old or patient is either curious or quiet and vice versa. If fred is both rich and not generous then someone is rich or not brave. Everyone who is not patient is both creative and not rich and vice versa. Everyone who is either happy or not happy is not happy or not rich. If paul is both not creative and funny then someone is not kind and vice versa. If someone is both patient and old then someone is funny or not generous and vice versa. If someone is not rich then someone is patient. If paul is not generous then someone is not wise. If alice is both not kind and not patient then someone is either old or not old. If someone is either not creative or not generous then alice is humble or not wise and vice versa. Everyone who is not happy is old. If someone is kind or rich then someone is not wise or not funny and vice versa. Everyone who is not humble is generous. Susan is either generous or quiet. Someone is not funny. Someone is either funny or not wise. Someone is tall. Susan is both kind and not humble. Someone is not tall or tall. Someone is both not humble and calm. Lucy is both not old and wise. | Lucy is not quiet. | entailment | (![X]:((curious(X)|~kind(X))=>~curious(X)))&
(![X]:((~humble(X)|humble(X))<=>(creative(X)|~quiet(X))))&
(![X]:((calm(X)<~>~tall(X))=>(wise(X)&kind(X))))&
(![X]:((old(X)|patient(X))<=>(curious(X)<~>quiet(X))))&
(((rich(fred)&~generous(fred)))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:(~patient(X)<=>(creative(X)&~rich(X))))&
(![X]:((happy(X)<~>~happy(X))=>(~happy(X)|~rich(X))))&
(((~creative(paul)&funny(paul)))<=>(?[X]:(~kind(X))))&
((?[X]:((patient(X)&old(X))))<=>(?[X]:((funny(X)|~generous(X)))))&
((?[X]:(~rich(X)))=>(?[X]:(patient(X))))&
((~generous(paul))=>(?[X]:(~wise(X))))&
(((~kind(alice)&~patient(alice)))=>(?[X]:((old(X)<~>~old(X)))))&
((?[X]:((~creative(X)<~>~generous(X))))<=>((humble(alice)|~wise(alice))))&
(![X]:(~happy(X)=>old(X)))&
((?[X]:((kind(X)|rich(X))))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(~humble(X)=>generous(X)))&
((generous(susan)<~>quiet(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:(tall(X)))&
((kind(susan)&~humble(susan)))&
(?[X]:((~tall(X)|tall(X))))&
(?[X]:((~humble(X)&calm(X))))&
((~old(lucy)&wise(lucy))) | ~quiet(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p6",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8161771501211043755645845
% SZS output start Proof for 8161771501211043755645845
1. ! [X0] : ((~kind(X0) | curious(X0)) => ~curious(X0)) [input p0]
2. ! [X0] : ((humble(X0) | ~humble(X0)) <=> (~quiet(X0) | creative(X0))) [input p1]
4. ! [X0] : ((patient(X0) | old(X0)) <=> (curious(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : (~patient(X0) <=> (~rich(X0) & creative(X0))) [input p5]
7. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (~rich(X0) | ~happy(X0))) [input p6]
14. ! [X0] : (~happy(X0) => old(X0)) [input p13]
24. wise(lucy) & ~old(lucy) [input p23]
25. quiet(lucy) [input hypothesis]
30. ! [X0] : (~curious(X0) | (kind(X0) & ~curious(X0))) [ennf transformation 1]
32. ! [X0] : ((~rich(X0) | ~happy(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 7]
33. ! [X0] : (~rich(X0) | ~happy(X0) | (happy(X0) <=> ~happy(X0))) [flattening 32]
38. ! [X0] : (old(X0) | happy(X0)) [ennf transformation 14]
40. ! [X0] : (((humble(X0) | ~humble(X0)) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | (~humble(X0) & humble(X0)))) [nnf transformation 2]
41. ! [X0] : ((humble(X0) | ~humble(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | (~humble(X0) & humble(X0)))) [flattening 40]
43. ! [X0] : (((patient(X0) | old(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~patient(X0) & ~old(X0)))) [nnf transformation 4]
44. ! [X0] : ((patient(X0) | old(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~patient(X0) & ~old(X0)))) [flattening 43]
45. ! [X0] : ((~patient(X0) | (rich(X0) | ~creative(X0))) & ((~rich(X0) & creative(X0)) | patient(X0))) [nnf transformation 6]
46. ! [X0] : ((~patient(X0) | rich(X0) | ~creative(X0)) & ((~rich(X0) & creative(X0)) | patient(X0))) [flattening 45]
47. ! [X0] : (~rich(X0) | ~happy(X0) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 33]
88. ~curious(X0) | ~curious(X0) [cnf transformation 30]
90. ~quiet(X0) | creative(X0) | humble(X0) [cnf transformation 41]
91. ~quiet(X0) | creative(X0) | ~humble(X0) [cnf transformation 41]
103. patient(X0) | old(X0) | curious(X0) | ~quiet(X0) [cnf transformation 44]
106. ~patient(X0) | rich(X0) | ~creative(X0) [cnf transformation 46]
107. ~rich(X0) | ~happy(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 47]
127. happy(X0) | old(X0) [cnf transformation 38]
144. ~old(lucy) [cnf transformation 24]
146. quiet(lucy) [cnf transformation 25]
147. ~happy(X0) | ~rich(X0) [duplicate literal removal 107]
149. ~curious(X0) [duplicate literal removal 88]
150. ~quiet(X0) | creative(X0) [subsumption resolution 90,91]
151. ~quiet(X0) | old(X0) | patient(X0) [subsumption resolution 103,149]
310. ~rich(X0) | old(X0) [resolution 147,127]
312. creative(lucy) [resolution 150,146]
377. old(lucy) | patient(lucy) [resolution 151,146]
380. patient(lucy) [subsumption resolution 377,144]
382. rich(lucy) | ~creative(lucy) [resolution 380,106]
384. rich(lucy) [subsumption resolution 382,312]
388. old(lucy) [resolution 310,384]
389. $false [subsumption resolution 388,144]
% SZS output end Proof for 8161771501211043755645845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or generous is rich and vice versa.
Everyone who is brave is not patient and vice versa.
Everyone who is rich or brave is both funny and brave and vice versa.
Everyone who is both not happy and wise is tall.
If someone is both not curious and not patient then paul is not rich.
Everyone who is either kind or not funny is creative.
Everyone who is happy or funny is either not old or humble.
If someone is not brave or not calm then susan is not humble or wise.
Everyone who is both not kind and generous is brave or not generous.
Everyone who is both tall and humble is both quiet and not creative and vice versa.
Everyone who is either not quiet or not brave is wise and vice versa.
Everyone who is both not creative and not strong is both not patient and not generous and vice versa.
Everyone who is either humble or not quiet is both humble and not happy.
Everyone who is both generous and kind is both not rich and curious and vice versa.
If someone is both creative and happy then susan is either not rich or not curious.
Everyone who is either not rich or humble is either curious or strong and vice versa.
Paul is either rich or humble.
Someone is both not strong and calm.
Susan is either tall or strong.
Alice is both quiet and kind.
Lucy is wise or not happy.
Someone is quiet or not quiet.
Someone is both kind and old. | Paul is not generous. | entailment | (![X]:((~happy(X)|generous(X))<=>rich(X)))&
(![X]:(brave(X)<=>~patient(X)))&
(![X]:((rich(X)|brave(X))<=>(funny(X)&brave(X))))&
(![X]:((~happy(X)&wise(X))=>tall(X)))&
((?[X]:((~curious(X)&~patient(X))))=>(~rich(paul)))&
(![X]:((kind(X)<~>~funny(X))=>creative(X)))&
(![X]:((happy(X)|funny(X))=>(~old(X)<~>humble(X))))&
((?[X]:((~brave(X)|~calm(X))))=>((~humble(susan)|wise(susan))))&
(![X]:((~kind(X)&generous(X))=>(brave(X)|~generous(X))))&
(![X]:((tall(X)&humble(X))<=>(quiet(X)&~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:((~creative(X)&~strong(X))<=>(~patient(X)&~generous(X))))&
(![X]:((humble(X)<~>~quiet(X))=>(humble(X)&~happy(X))))&
(![X]:((generous(X)&kind(X))<=>(~rich(X)&curious(X))))&
((?[X]:((creative(X)&happy(X))))=>((~rich(susan)<~>~curious(susan))))&
(![X]:((~rich(X)<~>humble(X))<=>(curious(X)<~>strong(X))))&
((rich(paul)<~>humble(paul)))&
(?[X]:((~strong(X)&calm(X))))&
((tall(susan)<~>strong(susan)))&
((quiet(alice)&kind(alice)))&
((wise(lucy)|~happy(lucy)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((kind(X)&old(X)))) | ~generous(paul) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p9",
"p11",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6520696883019505668246149
% SZS output start Proof for 6520696883019505668246149
1. ! [X0] : ((generous(X0) | ~happy(X0)) <=> rich(X0)) [input p0]
2. ! [X0] : (brave(X0) <=> ~patient(X0)) [input p1]
3. ! [X0] : ((brave(X0) | rich(X0)) <=> (brave(X0) & funny(X0))) [input p2]
5. ? [X0] : (~patient(X0) & ~curious(X0)) => ~rich(paul) [input p4]
6. ! [X0] : ((kind(X0) <~> ~funny(X0)) => creative(X0)) [input p5]
10. ! [X0] : ((humble(X0) & tall(X0)) <=> (~creative(X0) & quiet(X0))) [input p9]
12. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (~generous(X0) & ~patient(X0))) [input p11]
13. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => (~happy(X0) & humble(X0))) [input p12]
14. ! [X0] : ((kind(X0) & generous(X0)) <=> (curious(X0) & ~rich(X0))) [input p13]
15. ? [X0] : (happy(X0) & creative(X0)) => (~rich(susan) <~> ~curious(susan)) [input p14]
20. kind(alice) & quiet(alice) [input p19]
24. generous(paul) [input hypothesis]
29. ~rich(paul) | ! [X0] : (patient(X0) | curious(X0)) [ennf transformation 5]
30. ! [X0] : (creative(X0) | (kind(X0) <=> ~funny(X0))) [ennf transformation 6]
36. ! [X0] : ((~happy(X0) & humble(X0)) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 13]
37. (~rich(susan) <~> ~curious(susan)) | ! [X0] : (~happy(X0) | ~creative(X0)) [ennf transformation 15]
38. ! [X0] : (((generous(X0) | ~happy(X0)) | ~rich(X0)) & (rich(X0) | (~generous(X0) & happy(X0)))) [nnf transformation 1]
39. ! [X0] : ((generous(X0) | ~happy(X0) | ~rich(X0)) & (rich(X0) | (~generous(X0) & happy(X0)))) [flattening 38]
40. ! [X0] : ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0))) [nnf transformation 2]
41. ! [X0] : (((brave(X0) | rich(X0)) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | (~brave(X0) & ~rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((brave(X0) | rich(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | (~brave(X0) & ~rich(X0)))) [flattening 41]
43. ! [X0] : (creative(X0) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) [nnf transformation 30]
45. ! [X0] : (((humble(X0) & tall(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (~humble(X0) | ~tall(X0)))) [nnf transformation 10]
46. ! [X0] : (((humble(X0) & tall(X0)) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | ~humble(X0) | ~tall(X0))) [flattening 45]
48. ! [X0] : (((~strong(X0) & ~creative(X0)) | (generous(X0) | patient(X0))) & ((~generous(X0) & ~patient(X0)) | (strong(X0) | creative(X0)))) [nnf transformation 12]
49. ! [X0] : (((~strong(X0) & ~creative(X0)) | generous(X0) | patient(X0)) & ((~generous(X0) & ~patient(X0)) | strong(X0) | creative(X0))) [flattening 48]
50. ! [X0] : ((~happy(X0) & humble(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 36]
51. ! [X0] : (((kind(X0) & generous(X0)) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | (~kind(X0) | ~generous(X0)))) [nnf transformation 14]
52. ! [X0] : (((kind(X0) & generous(X0)) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | ~kind(X0) | ~generous(X0))) [flattening 51]
53. ((curious(susan) | rich(susan)) & (~curious(susan) | ~rich(susan))) | ! [X0] : (~happy(X0) | ~creative(X0)) [nnf transformation 37]
63. rich(X0) | happy(X0) [cnf transformation 39]
64. ~generous(X0) | rich(X0) [cnf transformation 39]
66. ~patient(X0) | ~brave(X0) [cnf transformation 40]
68. ~rich(X0) | funny(X0) [cnf transformation 42]
70. ~rich(X0) | brave(X0) [cnf transformation 42]
74. ~rich(paul) | patient(X0) | curious(X0) [cnf transformation 29]
75. ~kind(X0) | ~funny(X0) | creative(X0) [cnf transformation 43]
86. ~quiet(X0) | creative(X0) | humble(X0) [cnf transformation 46]
93. ~creative(X0) | generous(X0) | patient(X0) [cnf transformation 49]
96. humble(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
97. ~quiet(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 50]
99. ~rich(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 52]
101. generous(X0) | ~curious(X0) | rich(X0) [cnf transformation 52]
103. ~curious(susan) | ~rich(susan) | ~happy(X0) | ~creative(X0) [cnf transformation 53]
104. curious(susan) | rich(susan) | ~happy(X0) | ~creative(X0) [cnf transformation 53]
118. quiet(alice) [cnf transformation 20]
119. kind(alice) [cnf transformation 20]
124. generous(paul) [cnf transformation 24]
125. quiet(X0) | humble(X0) [duplicate literal removal 96]
128. 1 <=> ! [X0] : (patient(X0) | curious(X0)) [avatar definition]
129. curious(X0) | patient(X0) <- (1) [avatar component clause 128]
131. 2 <=> rich(paul) [avatar definition]
134. 1 | ~2 [avatar split clause 74,131,128]
147. ~curious(X0) | rich(X0) [subsumption resolution 101,64]
148. ~kind(X0) | ~generous(X0) [subsumption resolution 99,64]
149. rich(susan) | ~happy(X0) | ~creative(X0) [subsumption resolution 104,147]
151. 6 <=> ! [X0] : (~happy(X0) | ~creative(X0)) [avatar definition]
152. ~creative(X0) | ~happy(X0) <- (6) [avatar component clause 151]
154. 7 <=> rich(susan) [avatar definition]
156. rich(susan) <- (7) [avatar component clause 154]
157. 6 | 7 [avatar split clause 149,154,151]
158. ~curious(susan) | ~happy(X0) | ~creative(X0) [subsumption resolution 103,147]
160. 8 <=> curious(susan) [avatar definition]
162. ~curious(susan) <- (~8) [avatar component clause 160]
163. 6 | ~8 [avatar split clause 158,160,151]
194. rich(paul) [resolution 64,124]
197. 2 [avatar split clause 194,131]
199. funny(X0) | happy(X0) [resolution 68,63]
201. brave(X0) | happy(X0) [resolution 70,63]
205. ~generous(alice) [resolution 148,119]
209. ~funny(alice) | creative(alice) [resolution 75,119]
212. 14 <=> creative(alice) [avatar definition]
214. creative(alice) <- (14) [avatar component clause 212]
216. 15 <=> funny(alice) [avatar definition]
218. ~funny(alice) <- (~15) [avatar component clause 216]
219. 14 | ~15 [avatar split clause 209,216,212]
262. creative(X0) | humble(X0) | humble(X0) [resolution 86,125]
263. humble(X0) | creative(X0) [duplicate literal removal 262]
278. 23 <=> brave(alice) [avatar definition]
279. ~brave(alice) <- (~23) [avatar component clause 278]
280. brave(alice) <- (23) [avatar component clause 278]
323. generous(alice) | patient(alice) <- (14) [resolution 93,214]
324. patient(alice) <- (14) [subsumption resolution 323,205]
326. ~brave(alice) <- (14) [resolution 324,66]
327. $false <- (14, 23) [subsumption resolution 326,280]
328. ~14 | ~23 [avatar contradiction clause 327]
331. ~happy(alice) | ~humble(alice) [resolution 97,118]
335. 28 <=> humble(alice) [avatar definition]
337. ~humble(alice) <- (~28) [avatar component clause 335]
339. 29 <=> happy(alice) [avatar definition]
342. ~28 | ~29 [avatar split clause 331,339,335]
345. happy(alice) <- (~15) [resolution 218,199]
346. 29 | 15 [avatar split clause 345,216,339]
350. happy(alice) <- (~23) [resolution 279,201]
379. brave(susan) <- (7) [resolution 156,70]
477. creative(alice) <- (~28) [resolution 263,337]
484. 14 | 28 [avatar split clause 477,335,212]
485. patient(susan) <- (1, ~8) [resolution 162,129]
489. ~brave(susan) <- (1, ~8) [resolution 485,66]
490. $false <- (1, 7, ~8) [subsumption resolution 489,379]
491. ~1 | ~7 | 8 [avatar contradiction clause 490]
501. ~happy(alice) <- (6, 14) [resolution 152,214]
505. ~29 | ~6 | ~14 [avatar split clause 501,212,151,339]
506. 29 | 23 [avatar split clause 350,278,339]
507. $false [avatar sat refutation 134,157,163,197,219,328,342,346,484,491,505,506]
% SZS output end Proof for 6520696883019505668246149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both not brave and tall and vice versa.
If fred is either brave or not patient then someone is brave or not patient.
Everyone who is brave or not kind is not patient and vice versa.
Everyone who is either not generous or not curious is not tall or not strong.
If someone is not brave or patient then someone is not rich or not generous.
If someone is either brave or not kind then paul is both not creative and not funny and vice versa.
If someone is not wise then fred is either kind or not strong.
If fred is either old or not tall then someone is wise or not old and vice versa.
Everyone who is both not brave and humble is either generous or strong and vice versa.
Everyone who is either quiet or rich is not tall.
If someone is either not strong or not wise then someone is either not strong or not patient and vice versa.
If alice is either not patient or wise then someone is not creative or not brave.
Everyone who is either not kind or creative is both happy and not wise and vice versa.
If someone is either not rich or funny then someone is either patient or not curious and vice versa.
Everyone who is calm is not strong.
If john is calm then mary is rich and vice versa.
Susan is both not humble and funny.
Someone is not humble.
John is rich.
Someone is either patient or quiet.
Someone is both curious and not creative.
Someone is rich.
John is either wise or creative. | Susan is patient. | contradiction | (![X]:(~tall(X)<=>(~brave(X)&tall(X))))&
(((brave(fred)<~>~patient(fred)))=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:((brave(X)|~kind(X))<=>~patient(X)))&
(![X]:((~generous(X)<~>~curious(X))=>(~tall(X)|~strong(X))))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
((?[X]:((brave(X)<~>~kind(X))))<=>((~creative(paul)&~funny(paul))))&
((?[X]:(~wise(X)))=>((kind(fred)<~>~strong(fred))))&
(((old(fred)<~>~tall(fred)))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~brave(X)&humble(X))<=>(generous(X)<~>strong(X))))&
(![X]:((quiet(X)<~>rich(X))=>~tall(X)))&
((?[X]:((~strong(X)<~>~wise(X))))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
(((~patient(alice)<~>wise(alice)))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((~kind(X)<~>creative(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:(calm(X)=>~strong(X)))&
((calm(john))<=>(rich(mary)))&
((~humble(susan)&funny(susan)))&
(?[X]:(~humble(X)))&
(rich(john))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:(rich(X)))&
((wise(john)<~>creative(john))) | patient(susan) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 699067719922958331743482
% SZS output start Proof for 699067719922958331743482
1. ! [X0] : (~tall(X0) <=> (tall(X0) & ~brave(X0))) [input p0]
3. ! [X0] : ((~kind(X0) | brave(X0)) <=> ~patient(X0)) [input p2]
24. patient(susan) [input hypothesis]
36. ! [X0] : ((~tall(X0) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | tall(X0))) [nnf transformation 1]
37. ! [X0] : ((~tall(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | tall(X0))) [flattening 36]
41. ! [X0] : (((~kind(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [nnf transformation 3]
42. ! [X0] : ((~kind(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [flattening 41]
87. tall(X0) | tall(X0) [cnf transformation 37]
88. ~tall(X0) | ~tall(X0) | brave(X0) [cnf transformation 37]
91. ~patient(X0) | ~brave(X0) [cnf transformation 42]
158. patient(susan) [cnf transformation 24]
159. tall(X0) [duplicate literal removal 87]
160. ~tall(X0) | brave(X0) [duplicate literal removal 88]
194. 8 <=> ! [X1] : brave(X1) [avatar definition]
195. brave(X1) <- (8) [avatar component clause 194]
384. ~brave(susan) [resolution 91,158]
388. brave(X0) [resolution 160,159]
389. 8 [avatar split clause 388,194]
391. $false <- (8) [resolution 195,384]
394. ~8 [avatar contradiction clause 391]
396. $false [avatar sat refutation 389,394]
% SZS output end Proof for 699067719922958331743482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not curious then someone is strong or curious.
If lucy is both not curious and generous then alice is strong or rich and vice versa.
Everyone who is either wise or not strong is either calm or not calm.
If lucy is humble or not wise then susan is not funny or strong.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
If someone is either quiet or not tall then someone is both not creative and not curious and vice versa.
If someone is either wise or not old then someone is either not tall or not happy and vice versa.
Everyone who is not brave or not old is both kind and not generous.
Everyone who is brave or happy is both humble and strong and vice versa.
Everyone who is both not generous and tall is both not patient and brave.
If someone is either quiet or not tall then fred is not old and vice versa.
Someone is kind or brave.
Someone is not happy or not brave.
Someone is funny.
Someone is either not brave or kind.
Paul is either not curious or tall. | Fred is kind. | neutral | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|curious(X)))))&
(((~curious(lucy)&generous(lucy)))<=>((strong(alice)|rich(alice))))&
(![X]:((wise(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(((humble(lucy)|~wise(lucy)))=>((~funny(susan)|strong(susan))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((brave(X)|happy(X))<=>(humble(X)&strong(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~curious(paul)<~>tall(paul))) | kind(fred) | [] | null | 0 |
Everyone who is both not kind and not wise is either not creative or funny and vice versa.
If someone is tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Someone is not old or not generous.
Alice is not generous or not kind.
Someone is not humble. | Mary is curious. | contradiction | (![X]:((~kind(X)&~wise(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:(tall(X)))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
(?[X]:((~old(X)|~generous(X))))&
((~generous(alice)|~kind(alice)))&
(?[X]:(~humble(X))) | curious(mary) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1772189592979946513105177
% SZS output start Proof for 1772189592979946513105177
1. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~creative(X0) <~> funny(X0))) [input p0]
2. ? [X0] : tall(X0) <=> ~rich(lucy) [input p1]
5. ? [X0] : (~wise(X0) | ~creative(X0)) => (patient(lucy) & ~curious(lucy)) [input p4]
7. ! [X0] : ((~happy(X0) | tall(X0)) <=> (curious(X0) <~> wise(X0))) [input p6]
8. ! [X0] : ((wise(X0) & ~creative(X0)) <=> strong(X0)) [input p7]
9. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p8]
11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10]
13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13]
15. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p14]
16. (~rich(mary) | ~generous(mary)) => ? [X0] : wise(X0) [input p15]
20. curious(mary) [input hypothesis]
23. (patient(lucy) & ~curious(lucy)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 5]
26. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11]
28. ? [X0] : wise(X0) | (rich(mary) & generous(mary)) [ennf transformation 16]
29. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 1]
30. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | wise(X0) | kind(X0))) [flattening 29]
31. (? [X0] : tall(X0) | rich(lucy)) & (~rich(lucy) | ! [X0] : ~tall(X0)) [nnf transformation 2]
32. (? [X0] : tall(X0) | rich(lucy)) & (~rich(lucy) | ! [X1] : ~tall(X1)) [rectify 31]
33. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
34. (tall(sK0) | rich(lucy)) & (~rich(lucy) | ! [X1] : ~tall(X1)) [skolemisation 32,33]
38. ! [X0] : (((~happy(X0) | tall(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [nnf transformation 7]
39. ! [X0] : ((~happy(X0) | tall(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [flattening 38]
40. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | (~wise(X0) | creative(X0)))) [nnf transformation 8]
41. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | ~wise(X0) | creative(X0))) [flattening 40]
42. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 9]
43. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 42]
47. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13]
48. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 47]
49. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14]
50. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 49]
51. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 15]
52. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 51]
53. ? [X0] : wise(X0) => wise(sK1) [choice axiom]
54. wise(sK1) | (rich(mary) & generous(mary)) [skolemisation 28,53]
61. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 30]
62. ~funny(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 30]
63. ~wise(X0) | funny(X0) | creative(X0) [cnf transformation 30]
64. ~funny(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 30]
65. ~rich(lucy) | ~tall(X1) [cnf transformation 34]
72. ~curious(lucy) | wise(X0) [cnf transformation 23]
78. curious(X0) | wise(X0) | happy(X0) [cnf transformation 39]
80. ~curious(X0) | ~wise(X0) | happy(X0) [cnf transformation 39]
81. ~curious(X0) | tall(X0) | wise(X0) | ~happy(X0) [cnf transformation 39]
83. ~wise(X0) | strong(X0) | creative(X0) [cnf transformation 41]
84. ~strong(X0) | ~creative(X0) [cnf transformation 41]
86. ~rich(X0) | funny(X0) [cnf transformation 43]
87. ~rich(X0) | happy(X0) [cnf transformation 43]
89. ~strong(X0) | happy(X0) [cnf transformation 43]
90. ~happy(X0) | ~funny(X0) | strong(X0) | rich(X0) [cnf transformation 43]
95. ~happy(X0) | funny(X0) [cnf transformation 26]
96. ~old(X0) | ~happy(X0) [cnf transformation 26]
102. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 48]
103. ~brave(X0) | happy(X0) | old(X0) [cnf transformation 48]
106. brave(X0) | wise(X0) | kind(X0) | old(X0) [cnf transformation 50]
109. ~brave(X0) | old(X0) | ~wise(X0) [cnf transformation 50]
111. ~funny(X0) | creative(X0) | rich(X0) [cnf transformation 52]
112. rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 52]
118. wise(sK1) | rich(mary) [cnf transformation 54]
122. curious(mary) [cnf transformation 20]
124. 1 <=> rich(lucy) [avatar definition]
125. ~rich(lucy) <- (~1) [avatar component clause 124]
133. 3 <=> ! [X1] : ~tall(X1) [avatar definition]
134. ~tall(X1) <- (3) [avatar component clause 133]
135. 3 | ~1 [avatar split clause 65,124,133]
152. 7 <=> ! [X0] : wise(X0) [avatar definition]
153. wise(X0) <- (7) [avatar component clause 152]
164. 10 <=> curious(lucy) [avatar definition]
166. ~curious(lucy) <- (~10) [avatar component clause 164]
167. 7 | ~10 [avatar split clause 72,164,152]
189. ~happy(X0) | brave(X0) [subsumption resolution 102,95]
192. ~creative(X0) | funny(X0) [subsumption resolution 112,86]
194. 15 <=> rich(mary) [avatar definition]
195. ~rich(mary) <- (~15) [avatar component clause 194]
196. rich(mary) <- (15) [avatar component clause 194]
198. 16 <=> wise(sK1) [avatar definition]
200. wise(sK1) <- (16) [avatar component clause 198]
201. 15 | 16 [avatar split clause 118,198,194]
225. funny(sK1) | creative(sK1) <- (16) [resolution 63,200]
226. funny(sK1) <- (16) [subsumption resolution 225,192]
233. 23 <=> creative(sK1) [avatar definition]
235. ~creative(sK1) <- (~23) [avatar component clause 233]
237. ~creative(sK1) | ~wise(sK1) <- (16) [resolution 64,226]
238. ~creative(sK1) <- (16) [subsumption resolution 237,200]
239. ~23 | ~16 [avatar split clause 238,198,233]
254. wise(lucy) | happy(lucy) <- (~10) [resolution 78,166]
258. 26 <=> wise(lucy) [avatar definition]
259. wise(lucy) <- (26) [avatar component clause 258]
260. ~wise(lucy) <- (~26) [avatar component clause 258]
262. 27 <=> creative(lucy) [avatar definition]
273. ~wise(mary) | happy(mary) [resolution 80,122]
277. 29 <=> happy(mary) [avatar definition]
278. ~happy(mary) <- (~29) [avatar component clause 277]
279. happy(mary) <- (29) [avatar component clause 277]
281. 30 <=> wise(mary) [avatar definition]
283. ~wise(mary) <- (~30) [avatar component clause 281]
284. 29 | ~30 [avatar split clause 273,281,277]
333. happy(lucy) <- (~10, ~26) [subsumption resolution 254,260]
353. tall(mary) | wise(mary) | ~happy(mary) [resolution 81,122]
374. happy(mary) <- (15) [resolution 196,87]
378. 29 | ~15 [avatar split clause 374,194,277]
382. brave(mary) <- (29) [resolution 279,189]
384. ~funny(lucy) | strong(lucy) | rich(lucy) <- (~10, ~26) [resolution 333,90]
387. funny(lucy) <- (~10, ~26) [resolution 333,95]
388. ~funny(lucy) | strong(lucy) <- (~1, ~10, ~26) [subsumption resolution 384,125]
390. 37 <=> strong(lucy) [avatar definition]
392. strong(lucy) <- (37) [avatar component clause 390]
394. 38 <=> funny(lucy) [avatar definition]
395. funny(lucy) <- (38) [avatar component clause 394]
397. 37 | ~38 | 1 | 10 | 26 [avatar split clause 388,258,164,124,394,390]
398. 38 | 10 | 26 [avatar split clause 387,258,164,394]
403. wise(X4) | kind(X4) | old(X4) | happy(X4) | old(X4) [resolution 106,103]
404. old(X4) | kind(X4) | wise(X4) | happy(X4) [duplicate literal removal 403]
416. 39 <=> kind(mary) [avatar definition]
418. kind(mary) <- (39) [avatar component clause 416]
420. 40 <=> creative(mary) [avatar definition]
432. old(mary) | ~wise(mary) <- (29) [resolution 382,109]
469. ~creative(lucy) <- (37) [resolution 392,84]
474. funny(lucy) | creative(lucy) <- (26) [resolution 259,63]
488. funny(lucy) <- (26) [subsumption resolution 474,192]
489. 38 | ~26 [avatar split clause 488,258,394]
490. ~27 | ~37 [avatar split clause 469,390,262]
493. $false <- (7, ~30) [resolution 153,283]
498. ~7 | 30 [avatar contradiction clause 493]
616. wise(mary) | ~happy(mary) <- (3) [subsumption resolution 353,134]
622. wise(mary) <- (3, 29) [subsumption resolution 616,279]
623. 30 | ~3 | ~29 [avatar split clause 622,277,133,281]
626. 49 <=> old(mary) [avatar definition]
627. old(mary) <- (49) [avatar component clause 626]
628. ~old(mary) <- (~49) [avatar component clause 626]
630. ~30 | 49 | ~29 [avatar split clause 432,277,626,281]
703. creative(lucy) | rich(lucy) <- (38) [resolution 395,111]
704. ~creative(lucy) | ~wise(lucy) <- (38) [resolution 395,64]
842. ~happy(mary) <- (49) [resolution 627,96]
843. $false <- (29, 49) [subsumption resolution 842,279]
844. ~29 | ~49 [avatar contradiction clause 843]
860. 65 <=> happy(sK1) [avatar definition]
861. happy(sK1) <- (65) [avatar component clause 860]
879. 1 | 27 | ~38 [avatar split clause 703,394,262,124]
897. strong(sK1) | creative(sK1) <- (16) [resolution 200,83]
899. strong(sK1) <- (16, ~23) [subsumption resolution 897,235]
906. happy(sK1) <- (16, ~23) [resolution 899,89]
947. ~26 | ~27 | ~38 [avatar split clause 704,394,262,258]
952. kind(mary) | wise(mary) | happy(mary) <- (~49) [resolution 628,404]
953. kind(mary) | happy(mary) <- (~30, ~49) [subsumption resolution 952,283]
954. kind(mary) <- (~29, ~30, ~49) [subsumption resolution 953,278]
955. 39 | 29 | 30 | 49 [avatar split clause 954,626,281,277,416]
956. funny(mary) | creative(mary) <- (39) [resolution 418,61]
957. funny(mary) <- (39) [subsumption resolution 956,192]
992. creative(mary) | rich(mary) <- (39) [resolution 957,111]
994. ~creative(mary) | ~kind(mary) <- (39) [resolution 957,62]
995. creative(mary) <- (~15, 39) [subsumption resolution 992,195]
996. 40 | 15 | ~39 [avatar split clause 995,416,194,420]
997. ~creative(mary) <- (39) [subsumption resolution 994,418]
998. ~40 | ~39 [avatar split clause 997,416,420]
1044. brave(sK1) <- (65) [resolution 861,189]
1079. old(sK1) | ~wise(sK1) <- (65) [resolution 1044,109]
1082. old(sK1) <- (16, 65) [subsumption resolution 1079,200]
1095. ~happy(sK1) <- (16, 65) [resolution 1082,96]
1097. $false <- (16, 65) [subsumption resolution 1095,861]
1098. ~16 | ~65 [avatar contradiction clause 1097]
1100. 65 | ~16 | 23 [avatar split clause 906,233,198,860]
1103. $false [avatar sat refutation 135,167,201,239,284,378,397,398,489,490,498,623,630,844,879,947,955,996,998,1098,1100]
% SZS output end Proof for 1772189592979946513105177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is not happy. Everyone who is not creative is generous and vice versa. Everyone who is wise or old is both not kind and not wise and vice versa. If lucy is both not brave and not tall then someone is both not funny and not quiet and vice versa. Everyone who is humble is both not calm and not quiet. If someone is not rich or happy then susan is quiet and vice versa. If john is not old or strong then someone is either not old or not humble. Everyone who is not rich is wise or old and vice versa. Everyone who is not wise is humble. If alice is both not humble and not brave then paul is both not old and not brave and vice versa. If someone is tall then someone is curious. Everyone who is creative or wise is either generous or quiet. Everyone who is wise or old is funny and vice versa. If paul is not rich or wise then someone is not wise or calm. If someone is kind or not wise then someone is brave or not funny. Lucy is not quiet or not generous. Lucy is not happy. Someone is not curious. Someone is not tall. Mary is not brave. | Alice is creative. | contradiction | ((?[X]:(funny(X)))=>(?[X]:(~happy(X))))&
(![X]:(~creative(X)<=>generous(X)))&
(![X]:((wise(X)|old(X))<=>(~kind(X)&~wise(X))))&
(((~brave(lucy)&~tall(lucy)))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(humble(X)=>(~calm(X)&~quiet(X))))&
((?[X]:((~rich(X)|happy(X))))<=>(quiet(susan)))&
(((~old(john)|strong(john)))=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:(~rich(X)<=>(wise(X)|old(X))))&
(![X]:(~wise(X)=>humble(X)))&
(((~humble(alice)&~brave(alice)))<=>((~old(paul)&~brave(paul))))&
((?[X]:(tall(X)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|wise(X))=>(generous(X)<~>quiet(X))))&
(![X]:((wise(X)|old(X))<=>funny(X)))&
(((~rich(paul)|wise(paul)))=>(?[X]:((~wise(X)|calm(X)))))&
((?[X]:((kind(X)|~wise(X))))=>(?[X]:((brave(X)|~funny(X)))))&
((~quiet(lucy)|~generous(lucy)))&
(~happy(lucy))&
(?[X]:(~curious(X)))&
(?[X]:(~tall(X)))&
(~brave(mary)) | creative(alice) | [
"p1",
"p2",
"p4",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8074944694706962301727010
% SZS output start Proof for 8074944694706962301727010
2. ! [X0] : (~creative(X0) <=> generous(X0)) [input p1]
3. ! [X0] : ((old(X0) | wise(X0)) <=> (~wise(X0) & ~kind(X0))) [input p2]
5. ! [X0] : (humble(X0) => (~quiet(X0) & ~calm(X0))) [input p4]
9. ! [X0] : (~wise(X0) => humble(X0)) [input p8]
12. ! [X0] : ((wise(X0) | creative(X0)) => (generous(X0) <~> quiet(X0))) [input p11]
21. creative(alice) [input hypothesis]
27. ! [X0] : ((~quiet(X0) & ~calm(X0)) | ~humble(X0)) [ennf transformation 5]
29. ! [X0] : (humble(X0) | wise(X0)) [ennf transformation 9]
31. ! [X0] : ((generous(X0) <~> quiet(X0)) | (~wise(X0) & ~creative(X0))) [ennf transformation 12]
37. ! [X0] : ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))) [nnf transformation 2]
38. ! [X0] : (((old(X0) | wise(X0)) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | (~old(X0) & ~wise(X0)))) [nnf transformation 3]
39. ! [X0] : ((old(X0) | wise(X0) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | (~old(X0) & ~wise(X0)))) [flattening 38]
59. ! [X0] : (((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | (~wise(X0) & ~creative(X0))) [nnf transformation 31]
72. generous(X0) | creative(X0) [cnf transformation 37]
73. ~generous(X0) | ~creative(X0) [cnf transformation 37]
76. ~wise(X0) | ~wise(X0) [cnf transformation 39]
84. ~humble(X0) | ~quiet(X0) [cnf transformation 27]
93. humble(X0) | wise(X0) [cnf transformation 29]
99. quiet(X0) | generous(X0) | ~creative(X0) [cnf transformation 59]
115. creative(alice) [cnf transformation 21]
116. ~wise(X0) [duplicate literal removal 76]
185. humble(X0) [subsumption resolution 93,116]
209. quiet(X0) | generous(X0) [subsumption resolution 99,72]
238. ~quiet(X0) [resolution 84,185]
256. generous(X0) [resolution 209,238]
259. ~creative(X0) [resolution 256,73]
262. $false [resolution 259,115]
% SZS output end Proof for 8074944694706962301727010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave then susan is both not funny and wise and vice versa. If someone is calm or rich then alice is either rich or not patient. If someone is quiet or tall then paul is not curious. If someone is strong then mary is both not old and not kind and vice versa. Everyone who is rich or old is both curious and tall and vice versa. If paul is not patient then someone is humble or not patient and vice versa. If alice is not tall or not old then paul is not old. Everyone who is not wise is both strong and not wise and vice versa. If paul is either not humble or not creative then fred is creative or not generous. If mary is not old or not quiet then susan is not funny or tall and vice versa. If someone is curious then someone is both kind and not kind and vice versa. Everyone who is old or funny is not tall. If someone is both not generous and curious then susan is either funny or quiet. If someone is not old then someone is not generous. If mary is both not happy and funny then paul is not patient or curious and vice versa. Everyone who is rich is creative and vice versa. Fred is quiet. Someone is kind or creative. Susan is both not kind and not wise. Fred is tall. John is quiet or not humble. Susan is either brave or patient. Someone is not calm or not funny. Lucy is both not tall and humble. | Susan is patient. | contradiction | ((?[X]:((old(X)|~brave(X))))<=>((~funny(susan)&wise(susan))))&
((?[X]:((calm(X)|rich(X))))=>((rich(alice)<~>~patient(alice))))&
((?[X]:((quiet(X)|tall(X))))=>(~curious(paul)))&
((?[X]:(strong(X)))<=>((~old(mary)&~kind(mary))))&
(![X]:((rich(X)|old(X))<=>(curious(X)&tall(X))))&
((~patient(paul))<=>(?[X]:((humble(X)|~patient(X)))))&
(((~tall(alice)|~old(alice)))=>(~old(paul)))&
(![X]:(~wise(X)<=>(strong(X)&~wise(X))))&
(((~humble(paul)<~>~creative(paul)))=>((creative(fred)|~generous(fred))))&
(((~old(mary)|~quiet(mary)))<=>((~funny(susan)|tall(susan))))&
((?[X]:(curious(X)))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((old(X)|funny(X))=>~tall(X)))&
((?[X]:((~generous(X)&curious(X))))=>((funny(susan)<~>quiet(susan))))&
((?[X]:(~old(X)))=>(?[X]:(~generous(X))))&
(((~happy(mary)&funny(mary)))<=>((~patient(paul)|curious(paul))))&
(![X]:(rich(X)<=>creative(X)))&
(quiet(fred))&
(?[X]:((kind(X)|creative(X))))&
((~kind(susan)&~wise(susan)))&
(tall(fred))&
((quiet(john)|~humble(john)))&
((brave(susan)<~>patient(susan)))&
(?[X]:((~calm(X)|~funny(X))))&
((~tall(lucy)&humble(lucy))) | patient(susan) | [
"p0",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4658353857849714183599537
% SZS output start Proof for 4658353857849714183599537
1. ? [X0] : (~brave(X0) | old(X0)) <=> (wise(susan) & ~funny(susan)) [input p0]
19. ~wise(susan) & ~kind(susan) [input p18]
22. brave(susan) <~> patient(susan) [input p21]
25. patient(susan) [input hypothesis]
38. (? [X0] : (~brave(X0) | old(X0)) | (~wise(susan) | funny(susan))) & ((wise(susan) & ~funny(susan)) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 1]
39. (? [X0] : (~brave(X0) | old(X0)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X0] : (brave(X0) & ~old(X0))) [flattening 38]
40. (? [X0] : (~brave(X0) | old(X0)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 39]
41. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK0) | old(sK0)) [choice axiom]
42. ((~brave(sK0) | old(sK0)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 40,41]
74. (~patient(susan) | ~brave(susan)) & (patient(susan) | brave(susan)) [nnf transformation 22]
78. wise(susan) | brave(X1) [cnf transformation 42]
124. ~wise(susan) [cnf transformation 19]
128. ~patient(susan) | ~brave(susan) [cnf transformation 74]
131. patient(susan) [cnf transformation 25]
137. 2 <=> wise(susan) [avatar definition]
150. 5 <=> ! [X1] : brave(X1) [avatar definition]
151. brave(X1) <- (5) [avatar component clause 150]
152. 5 | 2 [avatar split clause 78,137,150]
317. ~2 [avatar split clause 124,137]
328. 43 <=> brave(susan) [avatar definition]
330. ~brave(susan) <- (~43) [avatar component clause 328]
332. 44 <=> patient(susan) [avatar definition]
335. ~43 | ~44 [avatar split clause 128,332,328]
337. 44 [avatar split clause 131,332]
346. $false <- (5, ~43) [resolution 330,151]
347. ~5 | 43 [avatar contradiction clause 346]
348. $false [avatar sat refutation 152,317,335,337,347]
% SZS output end Proof for 4658353857849714183599537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then susan is both not tall and not generous. Everyone who is generous is both creative and old. If someone is either tall or not happy then someone is not strong or kind. Everyone who is not quiet or not brave is both not patient and not strong and vice versa. Everyone who is not tall or not strong is either calm or generous. Everyone who is both not brave and not funny is happy and vice versa. If john is either kind or funny then lucy is not patient or not tall. If paul is not quiet or not humble then someone is brave or not happy. Everyone who is both quiet and not kind is either not brave or not rich and vice versa. If alice is not rich or creative then someone is either generous or funny and vice versa. If someone is not wise or creative then someone is either not brave or not funny and vice versa. Everyone who is calm is not brave and vice versa. If paul is either not rich or not quiet then john is funny and vice versa. Everyone who is curious is happy. Everyone who is either generous or not curious is curious and vice versa. Everyone who is either not wise or not brave is not creative or not kind. Alice is humble. Someone is calm or old. Fred is both patient and strong. Someone is both tall and rich. Someone is not funny or not humble. | Lucy is generous. | entailment | ((?[X]:(~patient(X)))=>((~tall(susan)&~generous(susan))))&
(![X]:(generous(X)=>(creative(X)&old(X))))&
((?[X]:((tall(X)<~>~happy(X))))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>(~patient(X)&~strong(X))))&
(![X]:((~tall(X)|~strong(X))=>(calm(X)<~>generous(X))))&
(![X]:((~brave(X)&~funny(X))<=>happy(X)))&
(((kind(john)<~>funny(john)))=>((~patient(lucy)|~tall(lucy))))&
(((~quiet(paul)|~humble(paul)))=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~brave(X)<~>~rich(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:(calm(X)<=>~brave(X)))&
(((~rich(paul)<~>~quiet(paul)))<=>(funny(john)))&
(![X]:(curious(X)=>happy(X)))&
(![X]:((generous(X)<~>~curious(X))<=>curious(X)))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)|~kind(X))))&
(humble(alice))&
(?[X]:((calm(X)|old(X))))&
((patient(fred)&strong(fred)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((~funny(X)|~humble(X)))) | generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8073256461925992391212744
% SZS output start Proof for 8073256461925992391212744
15. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> curious(X0)) [input p14]
22. ~generous(lucy) [input hypothesis]
63. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | ~curious(X0)) & (curious(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 15]
116. curious(X0) | generous(X0) | curious(X0) [cnf transformation 63]
117. ~curious(X0) | generous(X0) | ~curious(X0) [cnf transformation 63]
127. ~generous(lucy) [cnf transformation 22]
128. curious(X0) | generous(X0) [duplicate literal removal 116]
129. ~curious(X0) | generous(X0) [duplicate literal removal 117]
263. generous(X0) [subsumption resolution 128,129]
273. $false [subsumption resolution 127,263]
% SZS output end Proof for 8073256461925992391212744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is generous or not patient then someone is not strong or happy and vice versa.
If john is both not wise and tall then someone is not kind or patient and vice versa.
Everyone who is brave is not wise.
Everyone who is brave is both not generous and not happy.
If someone is not patient then someone is humble or curious.
Everyone who is not quiet is tall.
If paul is either not strong or quiet then someone is both not wise and not tall and vice versa.
If someone is not rich then susan is both curious and strong.
If alice is both not rich and not wise then lucy is creative and vice versa.
If paul is not wise then susan is not patient or brave.
Everyone who is generous or not humble is funny or not patient.
Everyone who is not tall is not funny and vice versa.
If fred is quiet or not strong then someone is strong or not funny and vice versa.
Everyone who is not old or tall is not funny or generous.
If someone is generous then someone is either not wise or calm.
Everyone who is not calm is not rich.
Lucy is not calm.
Someone is both not quiet and tall.
Paul is not generous or not curious.
Someone is creative.
Mary is either not patient or not tall.
Someone is patient.
John is not kind or not rich.
John is not humble or not generous. | John is not wise. | entailment | (((generous(alice)|~patient(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(((~wise(john)&tall(john)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:(brave(X)=>(~generous(X)&~happy(X))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:(~quiet(X)=>tall(X)))&
(((~strong(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))=>((curious(susan)&strong(susan))))&
(((~rich(alice)&~wise(alice)))<=>(creative(lucy)))&
((~wise(paul))=>((~patient(susan)|brave(susan))))&
(![X]:((generous(X)|~humble(X))=>(funny(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((quiet(fred)|~strong(fred)))<=>(?[X]:((strong(X)|~funny(X)))))&
(![X]:((~old(X)|tall(X))=>(~funny(X)|generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(~calm(X)=>~rich(X)))&
(~calm(lucy))&
(?[X]:((~quiet(X)&tall(X))))&
((~generous(paul)|~curious(paul)))&
(?[X]:(creative(X)))&
((~patient(mary)<~>~tall(mary)))&
(?[X]:(patient(X)))&
((~kind(john)|~rich(john)))&
((~humble(john)|~generous(john))) | ~wise(john) | [
"p1",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6753537043080992395472390
% SZS output start Proof for 6753537043080992395472390
2. (tall(john) & ~wise(john)) <=> ? [X0] : (patient(X0) | ~kind(X0)) [input p1]
22. ? [X0] : patient(X0) [input p21]
25. wise(john) [input hypothesis]
47. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | (~tall(john) | wise(john))) [nnf transformation 2]
48. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | ~tall(john) | wise(john)) [flattening 47]
49. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X1] : (patient(X1) | ~kind(X1)) | ~tall(john) | wise(john)) [rectify 48]
50. ? [X1] : (patient(X1) | ~kind(X1)) => (patient(sK1) | ~kind(sK1)) [choice axiom]
51. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & ((patient(sK1) | ~kind(sK1)) | ~tall(john) | wise(john)) [skolemisation 49,50]
76. ? [X0] : patient(X0) => patient(sK8) [choice axiom]
77. patient(sK8) [skolemisation 22,76]
84. ~wise(john) | ~patient(X0) [cnf transformation 51]
123. patient(sK8) [cnf transformation 77]
126. wise(john) [cnf transformation 25]
154. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
155. ~patient(X0) <- (7) [avatar component clause 154]
166. 10 <=> wise(john) [avatar definition]
169. 7 | ~10 [avatar split clause 84,166,154]
335. 10 [avatar split clause 126,166]
340. $false <- (7) [resolution 155,123]
341. ~7 [avatar contradiction clause 340]
342. $false [avatar sat refutation 169,335,341]
% SZS output end Proof for 6753537043080992395472390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is kind. Everyone who is both not old and not brave is both not quiet and not kind. Everyone who is either not rich or tall is both not rich and not creative. Everyone who is not funny or not happy is not wise. If someone is not old or not creative then someone is not creative or not curious. Everyone who is calm or not curious is either funny or tall. If someone is not wise or not calm then someone is both not tall and not old. If alice is brave then someone is not quiet and vice versa. If someone is both rich and quiet then alice is strong or brave and vice versa. Everyone who is not old or not funny is both tall and not humble. If susan is rich then someone is either not brave or not rich. If alice is both quiet and not wise then fred is not calm. Everyone who is both curious and calm is not patient and vice versa. Everyone who is not wise is both strong and not quiet and vice versa. Everyone who is generous or rich is either not generous or not old. If someone is both not old and happy then someone is both not kind and curious and vice versa. Mary is not quiet or not strong. Someone is happy or not kind. Someone is both not rich and strong. Paul is creative. Fred is both curious and creative. Someone is both wise and curious. Someone is not humble. Someone is not strong or not quiet. | Fred is calm. | entailment | (![X]:(~strong(X)=>kind(X)))&
(![X]:((~old(X)&~brave(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~rich(X)<~>tall(X))=>(~rich(X)&~creative(X))))&
(![X]:((~funny(X)|~happy(X))=>~wise(X)))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((calm(X)|~curious(X))=>(funny(X)<~>tall(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((~tall(X)&~old(X)))))&
((brave(alice))<=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)&quiet(X))))<=>((strong(alice)|brave(alice))))&
(![X]:((~old(X)|~funny(X))=>(tall(X)&~humble(X))))&
((rich(susan))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(((quiet(alice)&~wise(alice)))=>(~calm(fred)))&
(![X]:((curious(X)&calm(X))<=>~patient(X)))&
(![X]:(~wise(X)<=>(strong(X)&~quiet(X))))&
(![X]:((generous(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
((~quiet(mary)|~strong(mary)))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((~rich(X)&strong(X))))&
(creative(paul))&
((curious(fred)&creative(fred)))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)|~quiet(X)))) | calm(fred) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4292944421189182821201190
% SZS output start Proof for 4292944421189182821201190
7. ? [X0] : (~calm(X0) | ~wise(X0)) => ? [X0] : (~old(X0) & ~tall(X0)) [input p6]
10. ! [X0] : ((~funny(X0) | ~old(X0)) => (~humble(X0) & tall(X0))) [input p9]
25. ~calm(fred) [input hypothesis]
27. ? [X0] : (~calm(X0) | ~wise(X0)) => ? [X1] : (~old(X1) & ~tall(X1)) [rectify 7]
29. ! [X0] : ((~funny(X0) | ~old(X0)) => tall(X0)) [pure predicate removal 10]
38. ? [X1] : (~old(X1) & ~tall(X1)) | ! [X0] : (calm(X0) & wise(X0)) [ennf transformation 27]
39. ! [X0] : (tall(X0) | (funny(X0) & old(X0))) [ennf transformation 29]
49. ? [X0] : (~old(X0) & ~tall(X0)) | ! [X1] : (calm(X1) & wise(X1)) [rectify 38]
50. ? [X0] : (~old(X0) & ~tall(X0)) => (~old(sK1) & ~tall(sK1)) [choice axiom]
51. (~old(sK1) & ~tall(sK1)) | ! [X1] : (calm(X1) & wise(X1)) [skolemisation 49,50]
96. ~tall(sK1) | calm(X1) [cnf transformation 51]
98. ~old(sK1) | calm(X1) [cnf transformation 51]
106. tall(X0) | old(X0) [cnf transformation 39]
132. ~calm(fred) [cnf transformation 25]
152. 5 <=> ! [X1] : calm(X1) [avatar definition]
153. calm(X1) <- (5) [avatar component clause 152]
155. 6 <=> old(sK1) [avatar definition]
157. ~old(sK1) <- (~6) [avatar component clause 155]
158. 5 | ~6 [avatar split clause 98,155,152]
164. 8 <=> tall(sK1) [avatar definition]
166. ~tall(sK1) <- (~8) [avatar component clause 164]
167. 5 | ~8 [avatar split clause 96,164,152]
225. 21 <=> calm(fred) [avatar definition]
227. ~calm(fred) <- (~21) [avatar component clause 225]
282. ~21 [avatar split clause 132,225]
286. old(sK1) <- (~8) [resolution 106,166]
287. $false <- (~6, ~8) [subsumption resolution 286,157]
288. 6 | 8 [avatar contradiction clause 287]
289. $false <- (5, ~21) [resolution 153,227]
290. ~5 | 21 [avatar contradiction clause 289]
291. $false [avatar sat refutation 158,167,282,288,290]
% SZS output end Proof for 4292944421189182821201190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either brave or funny then john is tall and vice versa.
Everyone who is happy or patient is either not patient or not kind.
If susan is curious or old then someone is not quiet and vice versa.
Everyone who is not creative or not old is creative or humble and vice versa.
Everyone who is not old or not funny is both not patient and rich and vice versa.
If john is quiet then someone is both strong and humble and vice versa.
Everyone who is either tall or rich is either not creative or creative and vice versa.
If susan is not curious then someone is both not tall and not kind.
Everyone who is strong is both not strong and tall.
Everyone who is not curious is both not humble and not tall.
If susan is patient then alice is both not curious and not patient.
If someone is both brave and not calm then someone is not calm or happy and vice versa.
If lucy is wise or strong then someone is not strong.
Everyone who is strong is not patient or not funny.
If someone is funny then susan is both rich and not brave and vice versa.
Everyone who is kind is not kind.
Someone is curious.
Someone is either not calm or not strong.
Mary is creative or strong.
Someone is not quiet or creative.
Lucy is both not tall and not strong.
Paul is either not generous or humble.
John is not rich or not funny. | John is rich. | neutral | (((brave(john)<~>funny(john)))<=>(tall(john)))&
(![X]:((happy(X)|patient(X))=>(~patient(X)<~>~kind(X))))&
(((curious(susan)|old(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)|~old(X))<=>(creative(X)|humble(X))))&
(![X]:((~old(X)|~funny(X))<=>(~patient(X)&rich(X))))&
((quiet(john))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((tall(X)<~>rich(X))<=>(~creative(X)<~>creative(X))))&
((~curious(susan))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(strong(X)=>(~strong(X)&tall(X))))&
(![X]:(~curious(X)=>(~humble(X)&~tall(X))))&
((patient(susan))=>((~curious(alice)&~patient(alice))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(((wise(lucy)|strong(lucy)))=>(?[X]:(~strong(X))))&
(![X]:(strong(X)=>(~patient(X)|~funny(X))))&
((?[X]:(funny(X)))<=>((rich(susan)&~brave(susan))))&
(![X]:(kind(X)=>~kind(X)))&
(?[X]:(curious(X)))&
(?[X]:((~calm(X)<~>~strong(X))))&
((creative(mary)|strong(mary)))&
(?[X]:((~quiet(X)|creative(X))))&
((~tall(lucy)&~strong(lucy)))&
((~generous(paul)<~>humble(paul)))&
((~rich(john)|~funny(john))) | rich(john) | [] | 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. | Paul is wise. | 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)))) | wise(paul) | [
"p1",
"p2",
"p4",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 456927108070247390658332
% SZS output start Proof for 456927108070247390658332
2. ! [X0] : ((~kind(X0) | ~tall(X0)) => (~strong(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((brave(X0) | strong(X0)) => (creative(X0) & ~strong(X0))) [input p2]
5. ! [X0] : ((wise(X0) & ~generous(X0)) <=> ~calm(X0)) [input p4]
8. ! [X0] : ((rich(X0) & ~strong(X0)) => strong(X0)) [input p7]
12. ! [X0] : ((~rich(X0) | ~quiet(X0)) => (~tall(X0) <~> rich(X0))) [input p11]
17. ~generous(paul) [input p16]
22. wise(paul) [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]
35. ! [X0] : (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | tall(X0)) [nnf transformation 27]
36. ! [X0] : (((wise(X0) & ~generous(X0)) | calm(X0)) & (~calm(X0) | (~wise(X0) | generous(X0)))) [nnf transformation 5]
37. ! [X0] : (((wise(X0) & ~generous(X0)) | calm(X0)) & (~calm(X0) | ~wise(X0) | generous(X0))) [flattening 36]
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]
77. ~wise(X0) | ~calm(X0) | generous(X0) [cnf transformation 37]
87. strong(X0) | ~rich(X0) | strong(X0) [cnf transformation 31]
100. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 50]
120. ~generous(paul) [cnf transformation 17]
127. wise(paul) [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]
182. ~rich(X0) [subsumption resolution 129,130]
183. ~tall(X0) [subsumption resolution 128,182]
248. ~calm(paul) | generous(paul) [resolution 77,127]
250. ~calm(paul) [subsumption resolution 248,120]
251. strong(paul) | tall(paul) [resolution 250,70]
252. tall(paul) [subsumption resolution 251,130]
253. $false [subsumption resolution 252,183]
% SZS output end Proof for 456927108070247390658332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or brave is not old or strong. If someone is not quiet then someone is both not old and generous. If lucy is either not generous or not humble then mary is rich or not brave and vice versa. If someone is curious then fred is not wise and vice versa. If someone is either not tall or not creative then lucy is either patient or not happy and vice versa. If paul is either not old or not creative then someone is not tall or kind. Everyone who is either not generous or kind is humble and vice versa. Everyone who is not rich or not happy is either generous or curious. If someone is either not humble or happy then someone is either not curious or kind and vice versa. If someone is not kind then someone is not tall or not generous. Everyone who is not creative or patient is not generous or happy. If someone is not generous or not tall then someone is generous or brave. Everyone who is not funny is not rich. Everyone who is rich is tall. Everyone who is not happy is both rich and strong. If paul is not quiet then fred is either funny or curious. Paul is not old or not calm. Alice is not generous or not creative. Lucy is kind. Paul is either rich or tall. Someone is not rich. Someone is old. Someone is creative or not old. Someone is not strong or not happy. | Fred is not wise. | neutral | (![X]:((kind(X)<~>brave(X))=>(~old(X)|strong(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~old(X)&generous(X)))))&
(((~generous(lucy)<~>~humble(lucy)))<=>((rich(mary)|~brave(mary))))&
((?[X]:(curious(X)))<=>(~wise(fred)))&
((?[X]:((~tall(X)<~>~creative(X))))<=>((patient(lucy)<~>~happy(lucy))))&
(((~old(paul)<~>~creative(paul)))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~generous(X)<~>kind(X))<=>humble(X)))&
(![X]:((~rich(X)|~happy(X))=>(generous(X)<~>curious(X))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((~creative(X)|patient(X))=>(~generous(X)|happy(X))))&
((?[X]:((~generous(X)|~tall(X))))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:(rich(X)=>tall(X)))&
(![X]:(~happy(X)=>(rich(X)&strong(X))))&
((~quiet(paul))=>((funny(fred)<~>curious(fred))))&
((~old(paul)|~calm(paul)))&
((~generous(alice)|~creative(alice)))&
(kind(lucy))&
((rich(paul)<~>tall(paul)))&
(?[X]:(~rich(X)))&
(?[X]:(old(X)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~strong(X)|~happy(X)))) | ~wise(fred) | [] | null | 0 |
Everyone who is either not tall or patient is quiet. If mary is either rich or not generous then john is both not strong and rich and vice versa. Everyone who is patient or strong is either not patient or not old and vice versa. Everyone who is either not happy or humble is not generous or generous. Everyone who is creative is not rich and vice versa. Everyone who is either strong or not tall is tall and vice versa. If john is either generous or funny then someone is not rich or not quiet. Everyone who is calm or not patient is not quiet or not old and vice versa. If alice is not quiet then someone is not quiet and vice versa. Everyone who is either curious or not old is both happy and tall. Everyone who is both patient and strong is either not patient or not brave. If someone is strong then someone is rich. Everyone who is not generous or funny is not funny or not tall. If someone is both not curious and not tall then lucy is both wise and not curious and vice versa. Everyone who is not quiet is both not rich and quiet. Everyone who is both not brave and not curious is humble. Mary is happy or not curious. Someone is strong or calm. Mary is both not funny and not humble. Someone is both curious and generous. John is not wise. Paul is not rich or funny. Someone is either not kind or funny. Someone is both calm and strong. | Mary is brave. | contradiction | (![X]:((~tall(X)<~>patient(X))=>quiet(X)))&
(((rich(mary)<~>~generous(mary)))<=>((~strong(john)&rich(john))))&
(![X]:((patient(X)|strong(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((~happy(X)<~>humble(X))=>(~generous(X)|generous(X))))&
(![X]:(creative(X)<=>~rich(X)))&
(![X]:((strong(X)<~>~tall(X))<=>tall(X)))&
(((generous(john)<~>funny(john)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((calm(X)|~patient(X))<=>(~quiet(X)|~old(X))))&
((~quiet(alice))<=>(?[X]:(~quiet(X))))&
(![X]:((curious(X)<~>~old(X))=>(happy(X)&tall(X))))&
(![X]:((patient(X)&strong(X))=>(~patient(X)<~>~brave(X))))&
((?[X]:(strong(X)))=>(?[X]:(rich(X))))&
(![X]:((~generous(X)|funny(X))=>(~funny(X)|~tall(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>((wise(lucy)&~curious(lucy))))&
(![X]:(~quiet(X)=>(~rich(X)&quiet(X))))&
(![X]:((~brave(X)&~curious(X))=>humble(X)))&
((happy(mary)|~curious(mary)))&
(?[X]:((strong(X)|calm(X))))&
((~funny(mary)&~humble(mary)))&
(?[X]:((curious(X)&generous(X))))&
(~wise(john))&
((~rich(paul)|funny(paul)))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:((calm(X)&strong(X)))) | brave(mary) | [
"p2",
"p5",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5279996401263941912508812
% SZS output start Proof for 5279996401263941912508812
3. ! [X0] : ((strong(X0) | patient(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p2]
6. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> tall(X0)) [input p5]
8. ! [X0] : ((~patient(X0) | calm(X0)) <=> (~old(X0) | ~quiet(X0))) [input p7]
11. ! [X0] : ((strong(X0) & patient(X0)) => (~patient(X0) <~> ~brave(X0))) [input p10]
15. ! [X0] : (~quiet(X0) => (quiet(X0) & ~rich(X0))) [input p14]
25. brave(mary) [input hypothesis]
32. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (~strong(X0) | ~patient(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | ~strong(X0) | ~patient(X0)) [flattening 32]
37. ! [X0] : ((quiet(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 15]
43. ! [X0] : (((strong(X0) | patient(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~strong(X0) & ~patient(X0)))) [nnf transformation 3]
44. ! [X0] : ((strong(X0) | patient(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~strong(X0) & ~patient(X0)))) [flattening 43]
46. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | ~tall(X0)) & (tall(X0) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 6]
50. ! [X0] : (((~patient(X0) | calm(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 8]
51. ! [X0] : ((~patient(X0) | calm(X0) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | (patient(X0) & ~calm(X0)))) [flattening 50]
57. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ~strong(X0) | ~patient(X0)) [nnf transformation 33]
83. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 44]
86. ~strong(X0) | patient(X0) | old(X0) [cnf transformation 44]
92. tall(X0) | strong(X0) | tall(X0) [cnf transformation 46]
93. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 46]
98. ~old(X0) | ~quiet(X0) | patient(X0) [cnf transformation 51]
107. ~brave(X0) | ~patient(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57]
117. quiet(X0) | quiet(X0) [cnf transformation 37]
131. brave(mary) [cnf transformation 25]
132. quiet(X0) [duplicate literal removal 117]
134. ~brave(X0) | ~patient(X0) | ~strong(X0) [duplicate literal removal 107]
135. tall(X0) | strong(X0) [duplicate literal removal 92]
136. ~tall(X0) | strong(X0) [duplicate literal removal 93]
137. ~old(X0) | ~patient(X0) [duplicate literal removal 83]
161. strong(X0) [subsumption resolution 135,136]
181. ~old(X0) | ~quiet(X0) [subsumption resolution 98,137]
183. 9 <=> ! [X0] : quiet(X0) [avatar definition]
184. quiet(X0) <- (9) [avatar component clause 183]
195. ~brave(X0) | ~patient(X0) [subsumption resolution 134,161]
220. 9 [avatar split clause 132,183]
258. ~patient(mary) [resolution 195,131]
259. old(X0) | patient(X0) [resolution 86,161]
317. patient(X1) | ~quiet(X1) [resolution 259,181]
322. patient(X1) <- (9) [subsumption resolution 317,184]
327. $false <- (9) [resolution 322,258]
328. ~9 [avatar contradiction clause 327]
329. $false [avatar sat refutation 220,328]
% SZS output end Proof for 5279996401263941912508812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not curious or not rich then someone is funny or quiet.
Everyone who is either not happy or not tall is either calm or not patient and vice versa.
Everyone who is both not creative and not quiet is tall or not strong and vice versa.
Everyone who is both wise and not creative is rich or patient.
If someone is either not happy or curious then someone is tall and vice versa.
If someone is both quiet and generous then someone is either kind or generous.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Everyone who is not quiet or not rich is both not happy and not patient.
Everyone who is not old or not wise is either rich or not tall and vice versa.
If someone is both brave and tall then someone is both not wise and not creative and vice versa.
Everyone who is curious is not happy and vice versa.
Everyone who is both not generous and quiet is not generous or not kind.
Everyone who is either not kind or happy is both not curious and creative.
Everyone who is not generous is not kind or not tall and vice versa.
Someone is either not curious or curious.
Paul is not kind or happy.
Someone is not funny. | Paul is not creative. | neutral | (((~curious(alice)|~rich(alice)))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(calm(X)<~>~patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(tall(X)|~strong(X))))&
(![X]:((wise(X)&~creative(X))=>(rich(X)|patient(X))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~curious(X)&creative(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~tall(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
((~kind(paul)|happy(paul)))&
(?[X]:(~funny(X))) | ~creative(paul) | [] | null | 0 |
Everyone who is funny is both not old and funny and vice versa.
If someone is either not tall or not old then paul is funny and vice versa.
Everyone who is both tall and funny is not tall or not curious and vice versa.
If someone is both patient and funny then paul is either humble or not curious and vice versa.
If lucy is not creative then mary is both not rich and tall and vice versa.
Everyone who is both strong and not kind is kind or tall and vice versa.
Everyone who is not tall is creative or humble and vice versa.
Everyone who is both wise and not calm is either generous or tall.
Everyone who is both wise and not calm is both old and not strong.
Everyone who is either calm or not funny is either not funny or not tall.
If mary is both not old and funny then fred is funny or not generous and vice versa.
Everyone who is not quiet is not happy and vice versa.
Everyone who is both not humble and quiet is happy.
Everyone who is generous is either kind or not strong.
If someone is either not generous or calm then someone is not brave.
If susan is strong then someone is not generous or not rich and vice versa.
Alice is either calm or generous.
John is not curious or kind.
Lucy is old or not strong.
Susan is not brave.
John is either not quiet or tall.
Someone is humble or calm.
Someone is either funny or not old. | Alice is funny. | contradiction | (![X]:(funny(X)<=>(~old(X)&funny(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>(funny(paul)))&
(![X]:((tall(X)&funny(X))<=>(~tall(X)|~curious(X))))&
((?[X]:((patient(X)&funny(X))))<=>((humble(paul)<~>~curious(paul))))&
((~creative(lucy))<=>((~rich(mary)&tall(mary))))&
(![X]:((strong(X)&~kind(X))<=>(kind(X)|tall(X))))&
(![X]:(~tall(X)<=>(creative(X)|humble(X))))&
(![X]:((wise(X)&~calm(X))=>(generous(X)<~>tall(X))))&
(![X]:((wise(X)&~calm(X))=>(old(X)&~strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~funny(X)<~>~tall(X))))&
(((~old(mary)&funny(mary)))<=>((funny(fred)|~generous(fred))))&
(![X]:(~quiet(X)<=>~happy(X)))&
(![X]:((~humble(X)&quiet(X))=>happy(X)))&
(![X]:(generous(X)=>(kind(X)<~>~strong(X))))&
((?[X]:((~generous(X)<~>calm(X))))=>(?[X]:(~brave(X))))&
((strong(susan))<=>(?[X]:((~generous(X)|~rich(X)))))&
((calm(alice)<~>generous(alice)))&
((~curious(john)|kind(john)))&
((old(lucy)|~strong(lucy)))&
(~brave(susan))&
((~quiet(john)<~>tall(john)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:((funny(X)<~>~old(X)))) | funny(alice) | [
"p2",
"p5",
"p9",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5561474871774038299699812
% SZS output start Proof for 5561474871774038299699812
3. ! [X0] : ((funny(X0) & tall(X0)) <=> (~curious(X0) | ~tall(X0))) [input p2]
6. ! [X0] : ((~kind(X0) & strong(X0)) <=> (tall(X0) | kind(X0))) [input p5]
10. ! [X0] : ((calm(X0) <~> ~funny(X0)) => (~funny(X0) <~> ~tall(X0))) [input p9]
14. ! [X0] : (generous(X0) => (kind(X0) <~> ~strong(X0))) [input p13]
17. calm(alice) <~> generous(alice) [input p16]
24. funny(alice) [input hypothesis]
30. ! [X0] : ((~funny(X0) <~> ~tall(X0)) | (calm(X0) <=> ~funny(X0))) [ennf transformation 10]
33. ! [X0] : ((kind(X0) <~> ~strong(X0)) | ~generous(X0)) [ennf transformation 14]
40. ! [X0] : (((funny(X0) & tall(X0)) | (curious(X0) & tall(X0))) & ((~curious(X0) | ~tall(X0)) | (~funny(X0) | ~tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((funny(X0) & tall(X0)) | (curious(X0) & tall(X0))) & (~curious(X0) | ~tall(X0) | ~funny(X0) | ~tall(X0))) [flattening 40]
48. ! [X0] : (((~kind(X0) & strong(X0)) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | (kind(X0) | ~strong(X0)))) [nnf transformation 6]
49. ! [X0] : (((~kind(X0) & strong(X0)) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | kind(X0) | ~strong(X0))) [flattening 48]
52. ! [X0] : (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) [nnf transformation 30]
56. ! [X0] : (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ~generous(X0)) [nnf transformation 33]
61. (~generous(alice) | ~calm(alice)) & (generous(alice) | calm(alice)) [nnf transformation 17]
76. tall(X0) | tall(X0) [cnf transformation 41]
91. strong(X0) | ~tall(X0) [cnf transformation 49]
93. ~kind(X0) | ~tall(X0) [cnf transformation 49]
97. ~tall(X0) | ~funny(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 52]
109. ~strong(X0) | kind(X0) | ~generous(X0) [cnf transformation 56]
114. generous(alice) | calm(alice) [cnf transformation 61]
123. funny(alice) [cnf transformation 24]
124. ~tall(X0) | ~funny(X0) | ~calm(X0) [duplicate literal removal 97]
129. tall(X0) [duplicate literal removal 76]
189. ~kind(X0) [subsumption resolution 93,129]
190. strong(X0) [subsumption resolution 91,129]
193. ~calm(X0) | ~funny(X0) [subsumption resolution 124,129]
216. kind(X0) | ~generous(X0) [subsumption resolution 109,190]
217. ~generous(X0) [subsumption resolution 216,189]
218. calm(alice) [subsumption resolution 114,217]
243. ~funny(alice) [resolution 193,218]
245. $false [subsumption resolution 243,123]
% SZS output end Proof for 5561474871774038299699812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and humble then paul is either not curious or funny.
If someone is not humble or not happy then someone is happy or not quiet and vice versa.
Everyone who is patient is both not tall and not strong.
If someone is not tall then someone is both strong and not brave.
If someone is generous then lucy is either curious or creative.
Everyone who is both not kind and not tall is not calm or old and vice versa.
If lucy is both generous and not rich then someone is both generous and happy and vice versa.
Everyone who is both not kind and not wise is not generous.
Everyone who is both not tall and calm is either not patient or not calm and vice versa.
Everyone who is either kind or not old is either curious or tall.
Everyone who is either rich or curious is not kind or not patient and vice versa.
Everyone who is not kind or not brave is not kind or funny and vice versa.
If alice is generous then someone is tall.
If susan is either not quiet or not brave then susan is both not kind and calm and vice versa.
Everyone who is kind is both patient and not rich.
If alice is calm then someone is brave or not old.
Someone is not tall or funny.
Lucy is either quiet or patient.
Fred is either not happy or not generous.
Alice is humble.
Mary is both generous and not happy.
Someone is not patient.
John is both not funny and not tall.
Fred is not funny. | John is not kind. | entailment | ((?[X]:((~kind(X)&humble(X))))=>((~curious(paul)<~>funny(paul))))&
((?[X]:((~humble(X)|~happy(X))))<=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:(patient(X)=>(~tall(X)&~strong(X))))&
((?[X]:(~tall(X)))=>(?[X]:((strong(X)&~brave(X)))))&
((?[X]:(generous(X)))=>((curious(lucy)<~>creative(lucy))))&
(![X]:((~kind(X)&~tall(X))<=>(~calm(X)|old(X))))&
(((generous(lucy)&~rich(lucy)))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((~kind(X)&~wise(X))=>~generous(X)))&
(![X]:((~tall(X)&calm(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>tall(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~kind(X)|funny(X))))&
((generous(alice))=>(?[X]:(tall(X))))&
(((~quiet(susan)<~>~brave(susan)))<=>((~kind(susan)&calm(susan))))&
(![X]:(kind(X)=>(patient(X)&~rich(X))))&
((calm(alice))=>(?[X]:((brave(X)|~old(X)))))&
(?[X]:((~tall(X)|funny(X))))&
((quiet(lucy)<~>patient(lucy)))&
((~happy(fred)<~>~generous(fred)))&
(humble(alice))&
((generous(mary)&~happy(mary)))&
(?[X]:(~patient(X)))&
((~funny(john)&~tall(john)))&
(~funny(fred)) | ~kind(john) | [
"p2",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8881978818100231542168491
% SZS output start Proof for 8881978818100231542168491
3. ! [X0] : (patient(X0) => (~strong(X0) & ~tall(X0))) [input p2]
6. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (old(X0) | ~calm(X0))) [input p5]
9. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p8]
15. ! [X0] : (kind(X0) => (~rich(X0) & patient(X0))) [input p14]
25. kind(john) [input hypothesis]
30. ! [X0] : ((~strong(X0) & ~tall(X0)) | ~patient(X0)) [ennf transformation 3]
35. ! [X0] : ((~rich(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 15]
47. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 6]
48. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | tall(X0) | kind(X0))) [flattening 47]
54. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) | tall(X0)))) [nnf transformation 9]
55. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~calm(X0) | tall(X0))) [flattening 54]
79. ~tall(X0) | ~patient(X0) [cnf transformation 30]
88. ~tall(X0) | calm(X0) [cnf transformation 48]
94. ~calm(X0) | ~patient(X0) | ~calm(X0) | tall(X0) [cnf transformation 55]
96. ~tall(X0) | ~calm(X0) | patient(X0) [cnf transformation 55]
99. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 55]
121. patient(X0) | ~kind(X0) [cnf transformation 35]
136. kind(john) [cnf transformation 25]
137. ~calm(X0) | ~patient(X0) | tall(X0) [duplicate literal removal 94]
138. calm(X0) | ~patient(X0) [duplicate literal removal 99]
233. ~tall(X0) | patient(X0) [subsumption resolution 96,88]
234. ~tall(X0) [subsumption resolution 233,79]
235. ~calm(X0) | ~patient(X0) [subsumption resolution 137,234]
236. ~patient(X0) [subsumption resolution 235,138]
263. ~kind(X0) [subsumption resolution 121,236]
288. $false [subsumption resolution 136,263]
% SZS output end Proof for 8881978818100231542168491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not tall then someone is both strong and not wise and vice versa.
Everyone who is not quiet or wise is curious and vice versa.
If someone is both kind and not wise then someone is strong or not patient.
If susan is either patient or funny then someone is both wise and not strong and vice versa.
Everyone who is either generous or curious is both kind and not generous and vice versa.
If someone is either calm or brave then alice is creative or wise and vice versa.
Everyone who is not curious is not kind or creative and vice versa.
Everyone who is curious is both funny and rich and vice versa.
Everyone who is not strong or creative is happy and vice versa.
If alice is both creative and not quiet then someone is not strong.
If susan is not calm then alice is not funny and vice versa.
Everyone who is either kind or brave is both strong and not brave and vice versa.
Everyone who is either funny or brave is rich or not tall and vice versa.
Everyone who is not wise or wise is strong or not tall and vice versa.
If john is not humble or kind then mary is either not kind or generous and vice versa.
Everyone who is both quiet and curious is either not rich or humble.
Lucy is not calm.
Someone is not strong.
Someone is curious.
Fred is both calm and not curious.
Paul is not strong or rich.
Someone is not creative or not wise.
Someone is humble. | Paul is brave. | contradiction | ((~tall(susan))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:((~quiet(X)|wise(X))<=>curious(X)))&
((?[X]:((kind(X)&~wise(X))))=>(?[X]:((strong(X)|~patient(X)))))&
(((patient(susan)<~>funny(susan)))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((generous(X)<~>curious(X))<=>(kind(X)&~generous(X))))&
((?[X]:((calm(X)<~>brave(X))))<=>((creative(alice)|wise(alice))))&
(![X]:(~curious(X)<=>(~kind(X)|creative(X))))&
(![X]:(curious(X)<=>(funny(X)&rich(X))))&
(![X]:((~strong(X)|creative(X))<=>happy(X)))&
(((creative(alice)&~quiet(alice)))=>(?[X]:(~strong(X))))&
((~calm(susan))<=>(~funny(alice)))&
(![X]:((kind(X)<~>brave(X))<=>(strong(X)&~brave(X))))&
(![X]:((funny(X)<~>brave(X))<=>(rich(X)|~tall(X))))&
(![X]:((~wise(X)|wise(X))<=>(strong(X)|~tall(X))))&
(((~humble(john)|kind(john)))<=>((~kind(mary)<~>generous(mary))))&
(![X]:((quiet(X)&curious(X))=>(~rich(X)<~>humble(X))))&
(~calm(lucy))&
(?[X]:(~strong(X)))&
(?[X]:(curious(X)))&
((calm(fred)&~curious(fred)))&
((~strong(paul)|rich(paul)))&
(?[X]:((~creative(X)|~wise(X))))&
(?[X]:(humble(X))) | brave(paul) | [
"p4",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7452252181275103858967910
% SZS output start Proof for 7452252181275103858967910
5. ! [X0] : ((generous(X0) <~> curious(X0)) <=> (~generous(X0) & kind(X0))) [input p4]
8. ! [X0] : (curious(X0) <=> (rich(X0) & funny(X0))) [input p7]
12. ! [X0] : ((kind(X0) <~> brave(X0)) <=> (~brave(X0) & strong(X0))) [input p11]
13. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (~tall(X0) | rich(X0))) [input p12]
24. brave(paul) [input hypothesis]
44. ! [X0] : ((((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))))) [flattening 44]
53. ! [X0] : ((curious(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ~curious(X0))) [nnf transformation 8]
54. ! [X0] : ((curious(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ~curious(X0))) [flattening 53]
58. ! [X0] : ((((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (brave(X0) | ~strong(X0))) & ((~brave(X0) & strong(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | brave(X0) | ~strong(X0)) & ((~brave(X0) & strong(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 60]
90. ~generous(X0) | curious(X0) | ~generous(X0) [cnf transformation 45]
92. curious(X0) | generous(X0) | generous(X0) | ~kind(X0) [cnf transformation 45]
103. ~curious(X0) | funny(X0) [cnf transformation 54]
104. ~curious(X0) | rich(X0) [cnf transformation 54]
112. ~brave(X0) | kind(X0) | ~brave(X0) [cnf transformation 59]
119. ~rich(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 61]
141. brave(paul) [cnf transformation 24]
142. ~brave(X0) | kind(X0) [duplicate literal removal 112]
144. ~generous(X0) | curious(X0) [duplicate literal removal 90]
145. ~kind(X0) | generous(X0) | curious(X0) [duplicate literal removal 92]
277. 28 <=> rich(paul) [avatar definition]
279. rich(paul) <- (28) [avatar component clause 277]
303. kind(paul) [resolution 142,141]
330. 33 <=> curious(paul) [avatar definition]
331. ~curious(paul) <- (~33) [avatar component clause 330]
332. curious(paul) <- (33) [avatar component clause 330]
343. rich(paul) <- (33) [resolution 332,104]
344. funny(paul) <- (33) [resolution 332,103]
355. 28 | ~33 [avatar split clause 343,330,277]
390. ~funny(paul) | ~brave(paul) <- (28) [resolution 119,279]
393. ~brave(paul) <- (28, 33) [subsumption resolution 390,344]
394. $false <- (28, 33) [subsumption resolution 393,141]
395. ~28 | ~33 [avatar contradiction clause 394]
448. generous(paul) | curious(paul) [resolution 145,303]
451. generous(paul) <- (~33) [subsumption resolution 448,331]
536. curious(paul) <- (~33) [resolution 451,144]
537. $false <- (~33) [subsumption resolution 536,331]
538. 33 [avatar contradiction clause 537]
539. $false [avatar sat refutation 355,395,538]
% SZS output end Proof for 7452252181275103858967910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or not generous then mary is generous and vice versa.
Everyone who is both creative and humble is either not wise or not humble and vice versa.
Everyone who is either quiet or funny is either curious or not kind.
If someone is either humble or not old then someone is either tall or not patient.
If someone is not kind or not brave then someone is both brave and not kind.
If someone is tall or curious then someone is not wise.
If someone is happy or not brave then someone is either funny or strong.
If someone is both tall and not strong then someone is either not wise or not happy.
Everyone who is both patient and not humble is not curious or not creative.
Everyone who is both not tall and not happy is both old and not happy and vice versa.
Everyone who is both not old and not calm is calm and vice versa.
If susan is strong then alice is not patient and vice versa.
Everyone who is either not humble or not patient is quiet or tall and vice versa.
If susan is not quiet then someone is both not funny and not creative.
Everyone who is old is both funny and brave and vice versa.
If someone is either patient or not calm then mary is both creative and not brave and vice versa.
Mary is brave or calm.
Alice is not curious.
Someone is patient or not strong.
Someone is creative or old.
Someone is patient.
Someone is not strong.
Someone is old. | Susan is not brave. | contradiction | ((?[X]:((~creative(X)|~generous(X))))<=>(generous(mary)))&
(![X]:((creative(X)&humble(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>funny(X))=>(curious(X)<~>~kind(X))))&
((?[X]:((humble(X)<~>~old(X))))=>(?[X]:((tall(X)<~>~patient(X)))))&
((?[X]:((~kind(X)|~brave(X))))=>(?[X]:((brave(X)&~kind(X)))))&
((?[X]:((tall(X)|curious(X))))=>(?[X]:(~wise(X))))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((funny(X)<~>strong(X)))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:((patient(X)&~humble(X))=>(~curious(X)|~creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>(old(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>calm(X)))&
((strong(susan))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~patient(X))<=>(quiet(X)|tall(X))))&
((~quiet(susan))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(old(X)<=>(funny(X)&brave(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((creative(mary)&~brave(mary))))&
((brave(mary)|calm(mary)))&
(~curious(alice))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((creative(X)|old(X))))&
(?[X]:(patient(X)))&
(?[X]:(~strong(X)))&
(?[X]:(old(X))) | ~brave(susan) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7824670026837779850581913
% SZS output start Proof for 7824670026837779850581913
11. ! [X0] : ((~calm(X0) & ~old(X0)) <=> calm(X0)) [input p10]
15. ! [X0] : (old(X0) <=> (brave(X0) & funny(X0))) [input p14]
24. ~brave(susan) [input hypothesis]
66. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | old(X0)))) [nnf transformation 11]
67. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | old(X0))) [flattening 66]
73. ! [X0] : ((old(X0) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | ~old(X0))) [nnf transformation 15]
74. ! [X0] : ((old(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | ~old(X0))) [flattening 73]
124. calm(X0) | calm(X0) | old(X0) [cnf transformation 67]
126. ~calm(X0) | ~calm(X0) [cnf transformation 67]
138. brave(X0) | ~old(X0) [cnf transformation 74]
153. ~brave(susan) [cnf transformation 24]
154. calm(X0) | old(X0) [duplicate literal removal 124]
155. ~calm(X0) [duplicate literal removal 126]
199. 10 <=> ! [X1] : brave(X1) [avatar definition]
200. brave(X1) <- (10) [avatar component clause 199]
256. old(X0) [subsumption resolution 154,155]
281. brave(X0) [subsumption resolution 138,256]
282. 10 [avatar split clause 281,199]
322. $false <- (10) [resolution 200,153]
323. ~10 [avatar contradiction clause 322]
324. $false [avatar sat refutation 282,323]
% SZS output end Proof for 7824670026837779850581913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or calm is funny.
Everyone who is not happy or happy is both not tall and creative.
Everyone who is either rich or not wise is calm or rich and vice versa.
Everyone who is both not brave and not wise is both calm and not wise.
If someone is humble then someone is both calm and patient.
If paul is both not patient and not wise then someone is not wise and vice versa.
Everyone who is both calm and patient is either not happy or not creative and vice versa.
Everyone who is either humble or not funny is happy or patient and vice versa.
If fred is either not creative or not patient then alice is either generous or not happy.
If someone is either not creative or quiet then susan is generous or not happy and vice versa.
If fred is either not patient or kind then mary is both generous and old.
If alice is brave then alice is either not strong or generous and vice versa.
Everyone who is both not patient and quiet is either calm or strong and vice versa.
If someone is either not generous or old then someone is old or strong and vice versa.
Paul is happy.
Someone is either not rich or not wise.
Someone is rich or not happy.
Alice is not old.
Fred is not generous or not curious.
Alice is not calm. | Mary is not generous. | neutral | (![X]:((~funny(X)|calm(X))=>funny(X)))&
(![X]:((~happy(X)|happy(X))=>(~tall(X)&creative(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(calm(X)|rich(X))))&
(![X]:((~brave(X)&~wise(X))=>(calm(X)&~wise(X))))&
((?[X]:(humble(X)))=>(?[X]:((calm(X)&patient(X)))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(happy(X)|patient(X))))&
(((~creative(fred)<~>~patient(fred)))=>((generous(alice)<~>~happy(alice))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((generous(susan)|~happy(susan))))&
(((~patient(fred)<~>kind(fred)))=>((generous(mary)&old(mary))))&
((brave(alice))<=>((~strong(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(calm(X)<~>strong(X))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((old(X)|strong(X)))))&
(happy(paul))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:((rich(X)|~happy(X))))&
(~old(alice))&
((~generous(fred)|~curious(fred)))&
(~calm(alice)) | ~generous(mary) | [] | null | 0 |
Everyone who is not rich or not generous is not happy or not old.
If paul is both brave and not kind then paul is not kind.
Everyone who is both not generous and funny is generous or not brave and vice versa.
If someone is not old or tall then someone is both not kind and not humble.
Everyone who is both calm and not calm is not funny or not old and vice versa.
If john is either not rich or not quiet then someone is both calm and not strong and vice versa.
If someone is humble or not patient then someone is both happy and not old.
Everyone who is either wise or generous is not curious.
Everyone who is either humble or quiet is not tall.
Everyone who is calm or humble is humble or not strong.
If fred is both strong and brave then mary is rich and vice versa.
If mary is not funny or not generous then susan is either humble or not generous.
Everyone who is either not kind or not humble is either not rich or not funny and vice versa.
Everyone who is both not tall and not brave is happy.
Lucy is either not quiet or not creative.
Someone is both funny and old.
Someone is kind.
Paul is funny or not calm.
Mary is calm or not patient. | John is not patient. | contradiction | (![X]:((~rich(X)|~generous(X))=>(~happy(X)|~old(X))))&
(((brave(paul)&~kind(paul)))=>(~kind(paul)))&
(![X]:((~generous(X)&funny(X))<=>(generous(X)|~brave(X))))&
((?[X]:((~old(X)|tall(X))))=>(?[X]:((~kind(X)&~humble(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|~old(X))))&
(((~rich(john)<~>~quiet(john)))<=>(?[X]:((calm(X)&~strong(X)))))&
((?[X]:((humble(X)|~patient(X))))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((wise(X)<~>generous(X))=>~curious(X)))&
(![X]:((humble(X)<~>quiet(X))=>~tall(X)))&
(![X]:((calm(X)|humble(X))=>(humble(X)|~strong(X))))&
(((strong(fred)&brave(fred)))<=>(rich(mary)))&
(((~funny(mary)|~generous(mary)))=>((humble(susan)<~>~generous(susan))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((~tall(X)&~brave(X))=>happy(X)))&
((~quiet(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:(kind(X)))&
((funny(paul)|~calm(paul)))&
((calm(mary)|~patient(mary))) | ~patient(john) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2885065896642675430627255
% SZS output start Proof for 2885065896642675430627255
5. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~old(X0) | ~funny(X0))) [input p4]
7. ? [X0] : (~patient(X0) | humble(X0)) => ? [X0] : (~old(X0) & happy(X0)) [input p6]
20. ~patient(john) [input hypothesis]
22. ? [X0] : (~patient(X0) | humble(X0)) => ? [X1] : (~old(X1) & happy(X1)) [rectify 7]
29. ? [X1] : (~old(X1) & happy(X1)) | ! [X0] : (patient(X0) & ~humble(X0)) [ennf transformation 22]
41. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & ((~old(X0) | ~funny(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 5]
42. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & (~old(X0) | ~funny(X0) | calm(X0) | ~calm(X0))) [flattening 41]
47. ? [X0] : (~old(X0) & happy(X0)) | ! [X1] : (patient(X1) & ~humble(X1)) [rectify 29]
48. ? [X0] : (~old(X0) & happy(X0)) => (~old(sK2) & happy(sK2)) [choice axiom]
49. (~old(sK2) & happy(sK2)) | ! [X1] : (patient(X1) & ~humble(X1)) [skolemisation 47,48]
74. calm(X0) | old(X0) [cnf transformation 42]
76. ~calm(X0) | old(X0) [cnf transformation 42]
86. ~old(sK2) | patient(X1) [cnf transformation 49]
114. ~patient(john) [cnf transformation 20]
127. 3 <=> ! [X1] : old(X1) [avatar definition]
128. old(X1) <- (3) [avatar component clause 127]
136. old(X0) [subsumption resolution 74,76]
137. 3 [avatar split clause 136,127]
165. 10 <=> ! [X1] : patient(X1) [avatar definition]
166. patient(X1) <- (10) [avatar component clause 165]
168. 11 <=> old(sK2) [avatar definition]
170. ~old(sK2) <- (~11) [avatar component clause 168]
171. 10 | ~11 [avatar split clause 86,168,165]
222. $false <- (10) [resolution 166,114]
223. ~10 [avatar contradiction clause 222]
224. $false <- (3, ~11) [resolution 170,128]
225. ~3 | 11 [avatar contradiction clause 224]
226. $false [avatar sat refutation 137,171,223,225]
% SZS output end Proof for 2885065896642675430627255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not patient is tall.
Everyone who is either not generous or not happy is both creative and calm.
Everyone who is not funny or brave is either not quiet or not humble.
Everyone who is funny is both not old and generous and vice versa.
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 both patient and not humble is humble and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
If fred is either not funny or patient then mary is not calm or not happy.
Everyone who is either not patient or kind is not creative or not patient and vice versa.
Everyone who is not creative is wise and vice versa.
If someone is creative then paul is not curious and vice versa.
Everyone who is either not quiet or not creative is not generous or not wise.
Someone is both not brave and not kind.
Someone is both not calm and not old.
Someone is both not patient and generous.
Someone is either not curious or not generous.
Someone is either quiet or not humble.
Alice is curious or patient.
Someone is humble or quiet. | John is kind. | contradiction | (![X]:((brave(X)&~patient(X))=>tall(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(creative(X)&calm(X))))&
(![X]:((~funny(X)|brave(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:(funny(X)<=>(~old(X)&generous(X))))&
(![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]:((patient(X)&~humble(X))<=>humble(X)))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
(((~funny(fred)<~>patient(fred)))=>((~calm(mary)|~happy(mary))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~patient(X))))&
(![X]:(~creative(X)<=>wise(X)))&
((?[X]:(creative(X)))<=>(~curious(paul)))&
(![X]:((~quiet(X)<~>~creative(X))=>(~generous(X)|~wise(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((~patient(X)&generous(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
((curious(alice)|patient(alice)))&
(?[X]:((humble(X)|quiet(X)))) | kind(john) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3608993884436752453974779
% SZS output start Proof for 3608993884436752453974779
10. ! [X0] : ((~humble(X0) & patient(X0)) <=> humble(X0)) [input p9]
13. ! [X0] : ((~patient(X0) <~> kind(X0)) <=> (~patient(X0) | ~creative(X0))) [input p12]
24. kind(john) [input hypothesis]
50. ! [X0] : (((~humble(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) | ~patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~humble(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | humble(X0) | ~patient(X0))) [flattening 50]
54. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (patient(X0) & creative(X0))) & ((~patient(X0) | ~creative(X0)) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (patient(X0) & creative(X0))) & (~patient(X0) | ~creative(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [flattening 54]
100. humble(X0) | humble(X0) | ~patient(X0) [cnf transformation 51]
102. ~humble(X0) | ~humble(X0) [cnf transformation 51]
118. ~kind(X0) | patient(X0) | patient(X0) [cnf transformation 55]
137. kind(john) [cnf transformation 24]
139. ~kind(X0) | patient(X0) [duplicate literal removal 118]
140. humble(X0) | ~patient(X0) [duplicate literal removal 100]
141. ~humble(X0) [duplicate literal removal 102]
173. ~patient(X0) [subsumption resolution 140,141]
174. ~kind(X0) [subsumption resolution 139,173]
202. $false [subsumption resolution 137,174]
% SZS output end Proof for 3608993884436752453974779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either brave or not strong then someone is both brave and not kind and vice versa.
Everyone who is both not old and wise is both funny and not happy and vice versa.
Everyone who is not tall or not humble is both not creative and wise.
Everyone who is both not brave and not generous is not happy or calm.
Everyone who is wise or patient is not quiet and vice versa.
If someone is both not kind and happy then someone is not strong.
Everyone who is creative or not quiet is both not quiet and funny and vice versa.
Everyone who is either patient or quiet is not old and vice versa.
Everyone who is both happy and not creative is calm or brave and vice versa.
Everyone who is not creative is brave or not strong.
If john is either not creative or not quiet then fred is either calm or curious.
Everyone who is both not brave and not quiet is tall or patient and vice versa.
If someone is calm then lucy is tall or not old.
If paul is both not curious and kind then someone is both not wise and brave.
Everyone who is tall is either not creative or not humble and vice versa.
Everyone who is either not rich or happy is strong or not brave.
Paul is calm or old.
Someone is kind.
Someone is not brave or not wise.
Fred is generous or not calm.
Someone is not brave or not strong.
Susan is not patient or not curious.
Fred is both generous and kind.
Someone is either generous or kind. | Fred is not creative. | entailment | (((brave(paul)<~>~strong(paul)))<=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~old(X)&wise(X))<=>(funny(X)&~happy(X))))&
(![X]:((~tall(X)|~humble(X))=>(~creative(X)&wise(X))))&
(![X]:((~brave(X)&~generous(X))=>(~happy(X)|calm(X))))&
(![X]:((wise(X)|patient(X))<=>~quiet(X)))&
((?[X]:((~kind(X)&happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((creative(X)|~quiet(X))<=>(~quiet(X)&funny(X))))&
(![X]:((patient(X)<~>quiet(X))<=>~old(X)))&
(![X]:((happy(X)&~creative(X))<=>(calm(X)|brave(X))))&
(![X]:(~creative(X)=>(brave(X)|~strong(X))))&
(((~creative(john)<~>~quiet(john)))=>((calm(fred)<~>curious(fred))))&
(![X]:((~brave(X)&~quiet(X))<=>(tall(X)|patient(X))))&
((?[X]:(calm(X)))=>((tall(lucy)|~old(lucy))))&
(((~curious(paul)&kind(paul)))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(tall(X)<=>(~creative(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>happy(X))=>(strong(X)|~brave(X))))&
((calm(paul)|old(paul)))&
(?[X]:(kind(X)))&
(?[X]:((~brave(X)|~wise(X))))&
((generous(fred)|~calm(fred)))&
(?[X]:((~brave(X)|~strong(X))))&
((~patient(susan)|~curious(susan)))&
((generous(fred)&kind(fred)))&
(?[X]:((generous(X)<~>kind(X)))) | ~creative(fred) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7695617765698050818276595
% SZS output start Proof for 7695617765698050818276595
3. ! [X0] : ((~humble(X0) | ~tall(X0)) => (wise(X0) & ~creative(X0))) [input p2]
15. ! [X0] : (tall(X0) <=> (~creative(X0) <~> ~humble(X0))) [input p14]
25. creative(fred) [input hypothesis]
27. ! [X0] : ((wise(X0) & ~creative(X0)) | (humble(X0) & tall(X0))) [ennf transformation 3]
61. ! [X0] : ((tall(X0) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0)))) & (((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ~tall(X0))) [nnf transformation 15]
82. ~creative(X0) | tall(X0) [cnf transformation 27]
83. ~creative(X0) | humble(X0) [cnf transformation 27]
118. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 61]
134. creative(fred) [cnf transformation 25]
226. ~creative(X0) | ~tall(X0) [subsumption resolution 118,83]
227. ~creative(X0) [subsumption resolution 226,82]
281. $false [subsumption resolution 134,227]
% SZS output end Proof for 7695617765698050818276595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not happy is not curious or not happy.
If paul is both not strong and not old then someone is both not creative and kind and vice versa.
Everyone who is happy or wise is not happy or rich and vice versa.
Everyone who is old or tall is not happy.
If someone is both not tall and not rich then someone is either patient or not quiet.
If someone is wise then susan is either not kind or old and vice versa.
Everyone who is either not calm or not rich is strong.
Everyone who is not humble or happy is either not curious or generous and vice versa.
If fred is either not strong or not generous then someone is not creative and vice versa.
Everyone who is either not generous or quiet is both not curious and strong.
If mary is wise or not happy then susan is not strong and vice versa.
If lucy is either not humble or not creative then someone is not wise or happy.
If someone is not happy or generous then john is either not funny or brave and vice versa.
If fred is not calm then someone is funny and vice versa.
Everyone who is not quiet is patient.
Everyone who is humble or not kind is not happy.
Mary is funny.
Fred is both not tall and not brave.
Mary is both kind and rich.
Someone is not rich or rich.
Someone is wise or not quiet.
Someone is either humble or not kind.
Lucy is not old or not tall. | Mary is rich. | entailment | (![X]:((~brave(X)|~happy(X))=>(~curious(X)|~happy(X))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((happy(X)|wise(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|tall(X))=>~happy(X)))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(wise(X)))<=>((~kind(susan)<~>old(susan))))&
(![X]:((~calm(X)<~>~rich(X))=>strong(X)))&
(![X]:((~humble(X)|happy(X))<=>(~curious(X)<~>generous(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)<~>quiet(X))=>(~curious(X)&strong(X))))&
(((wise(mary)|~happy(mary)))<=>(~strong(susan)))&
(((~humble(lucy)<~>~creative(lucy)))=>(?[X]:((~wise(X)|happy(X)))))&
((?[X]:((~happy(X)|generous(X))))<=>((~funny(john)<~>brave(john))))&
((~calm(fred))<=>(?[X]:(funny(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(![X]:((humble(X)|~kind(X))=>~happy(X)))&
(funny(mary))&
((~tall(fred)&~brave(fred)))&
((kind(mary)&rich(mary)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((humble(X)<~>~kind(X))))&
((~old(lucy)|~tall(lucy))) | rich(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 885857883848629118283849
% SZS output start Proof for 885857883848629118283849
19. rich(mary) & kind(mary) [input p18]
24. ~rich(mary) [input hypothesis]
132. rich(mary) [cnf transformation 19]
138. ~rich(mary) [cnf transformation 24]
316. $false [subsumption resolution 138,132]
% SZS output end Proof for 885857883848629118283849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not strong is both happy and tall and vice versa.
If lucy is not funny or old then someone is both calm and patient and vice versa.
Everyone who is not patient or tall is either not generous or humble and vice versa.
If fred is either not strong or not happy then someone is not patient.
Everyone who is creative or happy is either not curious or not brave.
If susan is either not old or not quiet then lucy is either funny or not patient and vice versa.
If someone is either generous or not kind then someone is either not old or quiet.
If someone is either patient or not rich then someone is not old or quiet and vice versa.
Everyone who is both not wise and not funny is calm and vice versa.
Everyone who is creative or happy is tall or not quiet.
Everyone who is humble is both not curious and not wise and vice versa.
Everyone who is patient is not curious or not quiet.
If someone is humble or funny then someone is patient and vice versa.
Everyone who is both not creative and not funny is wise or strong and vice versa.
If john is not calm or wise then someone is old or not kind and vice versa.
If someone is quiet or generous then someone is both curious and not tall and vice versa.
Someone is either generous or not rich.
John is either not curious or patient.
Someone is strong or not patient.
Susan is quiet.
Mary is either old or humble.
Susan is either not curious or not calm.
John is either not quiet or not kind. | John is quiet. | neutral | (![X]:((old(X)|~strong(X))<=>(happy(X)&tall(X))))&
(((~funny(lucy)|old(lucy)))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:((~patient(X)|tall(X))<=>(~generous(X)<~>humble(X))))&
(((~strong(fred)<~>~happy(fred)))=>(?[X]:(~patient(X))))&
(![X]:((creative(X)|happy(X))=>(~curious(X)<~>~brave(X))))&
(((~old(susan)<~>~quiet(susan)))<=>((funny(lucy)<~>~patient(lucy))))&
((?[X]:((generous(X)<~>~kind(X))))=>(?[X]:((~old(X)<~>quiet(X)))))&
((?[X]:((patient(X)<~>~rich(X))))<=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:((~wise(X)&~funny(X))<=>calm(X)))&
(![X]:((creative(X)|happy(X))=>(tall(X)|~quiet(X))))&
(![X]:(humble(X)<=>(~curious(X)&~wise(X))))&
(![X]:(patient(X)=>(~curious(X)|~quiet(X))))&
((?[X]:((humble(X)|funny(X))))<=>(?[X]:(patient(X))))&
(![X]:((~creative(X)&~funny(X))<=>(wise(X)|strong(X))))&
(((~calm(john)|wise(john)))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((curious(X)&~tall(X)))))&
(?[X]:((generous(X)<~>~rich(X))))&
((~curious(john)<~>patient(john)))&
(?[X]:((strong(X)|~patient(X))))&
(quiet(susan))&
((old(mary)<~>humble(mary)))&
((~curious(susan)<~>~calm(susan)))&
((~quiet(john)<~>~kind(john))) | quiet(john) | [] | null | 0 |
If alice is not creative or old then someone is calm or not rich and vice versa.
If someone is not funny then someone is either curious or kind and vice versa.
If someone is quiet or rich then someone is both not rich and quiet.
If fred is either kind or creative then someone is either creative or brave and vice versa.
If someone is not wise then someone is calm or not funny and vice versa.
Everyone who is either not happy or not brave is either not generous or happy and vice versa.
If someone is patient then someone is both not tall and wise.
Everyone who is not kind is both calm and strong and vice versa.
If someone is not generous or not kind then someone is humble.
Everyone who is not funny or rich is both not brave and humble.
If alice is both creative and calm then paul is both not patient and old and vice versa.
Everyone who is either not old or not creative is not kind or not curious and vice versa.
If fred is funny or not old then fred is curious.
Everyone who is not calm or patient is not kind and vice versa.
Everyone who is both not rich and not funny is not tall.
If john is either not funny or calm then paul is calm or creative and vice versa.
Susan is not strong or not wise.
Someone is funny or not rich.
Alice is creative.
Someone is not kind or wise.
Someone is both old and rich.
Someone is not patient.
Someone is generous.
Someone is either not quiet or not funny. | Paul is not patient. | entailment | (((~creative(alice)|old(alice)))<=>(?[X]:((calm(X)|~rich(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)<~>kind(X)))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:((~rich(X)&quiet(X)))))&
(((kind(fred)<~>creative(fred)))<=>(?[X]:((creative(X)<~>brave(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:((~happy(X)<~>~brave(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:(~kind(X)<=>(calm(X)&strong(X))))&
((?[X]:((~generous(X)|~kind(X))))=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|rich(X))=>(~brave(X)&humble(X))))&
(((creative(alice)&calm(alice)))<=>((~patient(paul)&old(paul))))&
(![X]:((~old(X)<~>~creative(X))<=>(~kind(X)|~curious(X))))&
(((funny(fred)|~old(fred)))=>(curious(fred)))&
(![X]:((~calm(X)|patient(X))<=>~kind(X)))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(((~funny(john)<~>calm(john)))<=>((calm(paul)|creative(paul))))&
((~strong(susan)|~wise(susan)))&
(?[X]:((funny(X)|~rich(X))))&
(creative(alice))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:((old(X)&rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | ~patient(paul) | [
"p7",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5993328626163569964246727
% SZS output start Proof for 5993328626163569964246727
8. ! [X0] : (~kind(X0) <=> (strong(X0) & calm(X0))) [input p7]
11. (calm(alice) & creative(alice)) <=> (old(paul) & ~patient(paul)) [input p10]
14. ! [X0] : ((patient(X0) | ~calm(X0)) <=> ~kind(X0)) [input p13]
19. creative(alice) [input p18]
25. patient(paul) [input hypothesis]
65. ! [X0] : ((~kind(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | kind(X0))) [nnf transformation 8]
66. ! [X0] : ((~kind(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | kind(X0))) [flattening 65]
67. ((calm(alice) & creative(alice)) | (~old(paul) | patient(paul))) & ((old(paul) & ~patient(paul)) | (~calm(alice) | ~creative(alice))) [nnf transformation 11]
68. ((calm(alice) & creative(alice)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ~calm(alice) | ~creative(alice)) [flattening 67]
71. ! [X0] : (((patient(X0) | ~calm(X0)) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [nnf transformation 14]
72. ! [X0] : ((patient(X0) | ~calm(X0) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [flattening 71]
120. calm(X0) | kind(X0) [cnf transformation 66]
125. ~patient(paul) | ~calm(alice) | ~creative(alice) [cnf transformation 68]
137. ~kind(X0) | calm(X0) [cnf transformation 72]
148. creative(alice) [cnf transformation 19]
156. patient(paul) [cnf transformation 25]
165. 2 <=> creative(alice) [avatar definition]
289. 29 <=> patient(paul) [avatar definition]
297. 31 <=> calm(alice) [avatar definition]
298. ~calm(alice) <- (~31) [avatar component clause 297]
303. ~2 | ~31 | ~29 [avatar split clause 125,289,297,165]
319. calm(X0) [subsumption resolution 137,120]
351. 2 [avatar split clause 148,165]
371. 29 [avatar split clause 156,289]
372. $false <- (~31) [subsumption resolution 298,319]
373. 31 [avatar contradiction clause 372]
376. $false [avatar sat refutation 303,351,371,373]
% SZS output end Proof for 5993328626163569964246727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich is either quiet or brave and vice versa.
Everyone who is both not brave and old is either not strong or patient.
If someone is happy or rich then someone is not wise.
Everyone who is not happy or patient is strong.
Everyone who is not tall or not patient is both not wise and not generous.
If someone is both calm and funny then mary is either brave or not calm and vice versa.
Everyone who is not humble or not rich is both generous and not tall and vice versa.
Everyone who is not wise is either not generous or not calm and vice versa.
If someone is generous or not creative then mary is both not curious and not funny.
If someone is either creative or humble then john is either humble or curious and vice versa.
If someone is both rich and not funny then susan is not rich or not quiet and vice versa.
Everyone who is both tall and not humble is either not wise or funny and vice versa.
Everyone who is both tall and old is curious.
Everyone who is old or not strong is not tall and vice versa.
If lucy is not generous or not quiet then someone is brave.
If someone is either kind or old then someone is not patient.
Someone is not curious or not old.
Mary is kind or not curious.
Mary is either not old or not generous.
Someone is both old and not curious.
Fred is not happy or not tall.
Paul is not creative or not calm.
Mary is either strong or calm. | Paul is not patient. | contradiction | (![X]:((~brave(X)<~>rich(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((~brave(X)&old(X))=>(~strong(X)<~>patient(X))))&
((?[X]:((happy(X)|rich(X))))=>(?[X]:(~wise(X))))&
(![X]:((~happy(X)|patient(X))=>strong(X)))&
(![X]:((~tall(X)|~patient(X))=>(~wise(X)&~generous(X))))&
((?[X]:((calm(X)&funny(X))))<=>((brave(mary)<~>~calm(mary))))&
(![X]:((~humble(X)|~rich(X))<=>(generous(X)&~tall(X))))&
(![X]:(~wise(X)<=>(~generous(X)<~>~calm(X))))&
((?[X]:((generous(X)|~creative(X))))=>((~curious(mary)&~funny(mary))))&
((?[X]:((creative(X)<~>humble(X))))<=>((humble(john)<~>curious(john))))&
((?[X]:((rich(X)&~funny(X))))<=>((~rich(susan)|~quiet(susan))))&
(![X]:((tall(X)&~humble(X))<=>(~wise(X)<~>funny(X))))&
(![X]:((tall(X)&old(X))=>curious(X)))&
(![X]:((old(X)|~strong(X))<=>~tall(X)))&
(((~generous(lucy)|~quiet(lucy)))=>(?[X]:(brave(X))))&
((?[X]:((kind(X)<~>old(X))))=>(?[X]:(~patient(X))))&
(?[X]:((~curious(X)|~old(X))))&
((kind(mary)|~curious(mary)))&
((~old(mary)<~>~generous(mary)))&
(?[X]:((old(X)&~curious(X))))&
((~happy(fred)|~tall(fred)))&
((~creative(paul)|~calm(paul)))&
((strong(mary)<~>calm(mary))) | ~patient(paul) | [
"p4",
"p6",
"p7",
"p8",
"p11",
"p13",
"p18",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2555536926824947788935988
% SZS output start Proof for 2555536926824947788935988
5. ! [X0] : ((~patient(X0) | ~tall(X0)) => (~generous(X0) & ~wise(X0))) [input p4]
7. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> (~tall(X0) & generous(X0))) [input p6]
8. ! [X0] : (~wise(X0) <=> (~generous(X0) <~> ~calm(X0))) [input p7]
9. ? [X0] : (~creative(X0) | generous(X0)) => (~funny(mary) & ~curious(mary)) [input p8]
12. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~wise(X0) <~> funny(X0))) [input p11]
14. ! [X0] : ((~strong(X0) | old(X0)) <=> ~tall(X0)) [input p13]
19. ~old(mary) <~> ~generous(mary) [input p18]
22. ~calm(paul) | ~creative(paul) [input p21]
23. strong(mary) <~> calm(mary) [input p22]
24. ~patient(paul) [input hypothesis]
31. ! [X0] : ((~generous(X0) & ~wise(X0)) | (patient(X0) & tall(X0))) [ennf transformation 5]
32. (~funny(mary) & ~curious(mary)) | ! [X0] : (creative(X0) & ~generous(X0)) [ennf transformation 9]
46. ! [X0] : (((~rich(X0) | ~humble(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (rich(X0) & humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((~rich(X0) | ~humble(X0) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | (rich(X0) & humble(X0)))) [flattening 46]
48. ! [X0] : ((~wise(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | wise(X0))) [nnf transformation 8]
58. ! [X0] : (((~humble(X0) & tall(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (humble(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((~humble(X0) & tall(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | humble(X0) | ~tall(X0))) [flattening 58]
60. ! [X0] : (((~strong(X0) | old(X0)) | tall(X0)) & (~tall(X0) | (strong(X0) & ~old(X0)))) [nnf transformation 14]
61. ! [X0] : ((~strong(X0) | old(X0) | tall(X0)) & (~tall(X0) | (strong(X0) & ~old(X0)))) [flattening 60]
70. (generous(mary) | old(mary)) & (~generous(mary) | ~old(mary)) [nnf transformation 19]
73. (~calm(mary) | ~strong(mary)) & (calm(mary) | strong(mary)) [nnf transformation 23]
88. ~wise(X0) | tall(X0) [cnf transformation 31]
89. ~wise(X0) | patient(X0) [cnf transformation 31]
91. ~generous(X0) | patient(X0) [cnf transformation 31]
100. ~tall(X0) | humble(X0) [cnf transformation 47]
104. calm(X0) | generous(X0) | wise(X0) [cnf transformation 48]
106. ~generous(X0) | ~wise(X0) | calm(X0) [cnf transformation 48]
110. ~funny(mary) | creative(X0) [cnf transformation 32]
126. tall(X0) | funny(X0) | wise(X0) [cnf transformation 59]
128. ~humble(X0) | funny(X0) | wise(X0) [cnf transformation 59]
131. ~tall(X0) | ~old(X0) [cnf transformation 61]
132. ~tall(X0) | strong(X0) [cnf transformation 61]
141. generous(mary) | old(mary) [cnf transformation 70]
145. ~calm(paul) | ~creative(paul) [cnf transformation 22]
147. ~calm(mary) | ~strong(mary) [cnf transformation 73]
148. ~patient(paul) [cnf transformation 24]
168. 4 <=> calm(mary) [avatar definition]
169. ~calm(mary) <- (~4) [avatar component clause 168]
193. 9 <=> ! [X0] : creative(X0) [avatar definition]
194. creative(X0) <- (9) [avatar component clause 193]
196. 10 <=> funny(mary) [avatar definition]
198. ~funny(mary) <- (~10) [avatar component clause 196]
199. 9 | ~10 [avatar split clause 110,196,193]
260. funny(X0) | tall(X0) [subsumption resolution 126,88]
302. 32 <=> old(mary) [avatar definition]
304. old(mary) <- (32) [avatar component clause 302]
306. 33 <=> generous(mary) [avatar definition]
308. generous(mary) <- (33) [avatar component clause 306]
309. 32 | 33 [avatar split clause 141,306,302]
321. 36 <=> creative(paul) [avatar definition]
323. ~creative(paul) <- (~36) [avatar component clause 321]
325. 37 <=> calm(paul) [avatar definition]
327. ~calm(paul) <- (~37) [avatar component clause 325]
328. ~36 | ~37 [avatar split clause 145,325,321]
330. 38 <=> strong(mary) [avatar definition]
332. ~strong(mary) <- (~38) [avatar component clause 330]
333. ~38 | ~4 [avatar split clause 147,168,330]
362. tall(mary) <- (~10) [resolution 260,198]
364. strong(mary) <- (~10) [resolution 362,132]
365. ~old(mary) <- (~10) [resolution 362,131]
368. $false <- (~10, ~38) [subsumption resolution 364,332]
369. 10 | 38 [avatar contradiction clause 368]
370. $false <- (~10, 32) [subsumption resolution 365,304]
371. 10 | ~32 [avatar contradiction clause 370]
372. $false <- (9, ~36) [resolution 194,323]
373. ~9 | 36 [avatar contradiction clause 372]
377. tall(mary) <- (~10) [resolution 198,260]
395. generous(paul) | wise(paul) <- (~37) [resolution 104,327]
399. 41 <=> wise(paul) [avatar definition]
401. wise(paul) <- (41) [avatar component clause 399]
403. 42 <=> generous(paul) [avatar definition]
405. generous(paul) <- (42) [avatar component clause 403]
406. 41 | 42 | 37 [avatar split clause 395,325,403,399]
410. humble(mary) <- (~10) [resolution 377,100]
419. ~wise(mary) | calm(mary) <- (33) [resolution 106,308]
429. ~wise(mary) <- (~4, 33) [subsumption resolution 419,169]
446. patient(paul) <- (41) [resolution 401,89]
448. $false <- (41) [subsumption resolution 446,148]
449. ~41 [avatar contradiction clause 448]
514. funny(mary) | wise(mary) <- (~10) [resolution 410,128]
515. wise(mary) <- (~10) [subsumption resolution 514,198]
516. $false <- (~4, ~10, 33) [subsumption resolution 515,429]
517. 4 | 10 | ~33 [avatar contradiction clause 516]
560. patient(paul) <- (42) [resolution 405,91]
563. $false <- (42) [subsumption resolution 560,148]
564. ~42 [avatar contradiction clause 563]
565. $false [avatar sat refutation 199,309,328,333,369,371,373,406,449,517,564]
% SZS output end Proof for 2555536926824947788935988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not strong then mary is both not humble and not brave.
If someone is either old or wise then alice is not curious and vice versa.
Everyone who is generous is either not tall or old and vice versa.
Everyone who is wise or creative is both funny and not old and vice versa.
If paul is not humble or not tall then mary is not patient.
If paul is not happy or generous then fred is both not quiet and not strong and vice versa.
Everyone who is either not kind or funny is either calm or funny and vice versa.
Everyone who is kind is happy or not brave.
Everyone who is not curious or humble is both not brave and happy and vice versa.
Everyone who is not wise or not brave is creative and vice versa.
Everyone who is either not patient or not strong is both quiet and happy.
Everyone who is either creative or not happy is not generous and vice versa.
If someone is both not quiet and not happy then john is either creative or quiet and vice versa.
If fred is happy then someone is both not calm and not generous.
Everyone who is patient is both not curious and not strong and vice versa.
If someone is humble then susan is both brave and patient and vice versa.
Someone is either patient or not curious.
Lucy is happy.
Someone is not quiet or not rich.
Someone is not strong.
Susan is not generous or not funny.
Lucy is not old or not rich. | Susan is not creative. | neutral | ((?[X]:((~happy(X)<~>~strong(X))))=>((~humble(mary)&~brave(mary))))&
((?[X]:((old(X)<~>wise(X))))<=>(~curious(alice)))&
(![X]:(generous(X)<=>(~tall(X)<~>old(X))))&
(![X]:((wise(X)|creative(X))<=>(funny(X)&~old(X))))&
(((~humble(paul)|~tall(paul)))=>(~patient(mary)))&
(((~happy(paul)|generous(paul)))<=>((~quiet(fred)&~strong(fred))))&
(![X]:((~kind(X)<~>funny(X))<=>(calm(X)<~>funny(X))))&
(![X]:(kind(X)=>(happy(X)|~brave(X))))&
(![X]:((~curious(X)|humble(X))<=>(~brave(X)&happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>creative(X)))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((?[X]:(humble(X)))<=>((brave(susan)&patient(susan))))&
(?[X]:((patient(X)<~>~curious(X))))&
(happy(lucy))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:(~strong(X)))&
((~generous(susan)|~funny(susan)))&
((~old(lucy)|~rich(lucy))) | ~creative(susan) | [] | null | 0 |
If someone is both humble and not generous then someone is not kind or creative.
Everyone who is old is not wise or not brave.
Everyone who is not rich or not funny is both not patient and not brave and vice versa.
If john is not calm then fred is not creative or not humble and vice versa.
Everyone who is either patient or creative is either not brave or not creative and vice versa.
If lucy is kind or not generous then someone is either not wise or humble.
Everyone who is not wise is kind or not strong and vice versa.
If alice is generous then alice is either strong or patient.
Everyone who is humble is both rich and not calm and vice versa.
Everyone who is both funny and happy is both kind and generous.
Everyone who is not kind or not curious is either not tall or not kind.
Everyone who is both strong and not happy is both not tall and wise.
If someone is not creative then mary is both not brave and not curious.
If someone is either not kind or happy then someone is both not generous and wise and vice versa.
Everyone who is both creative and not old is either quiet or strong.
Everyone who is not brave is either strong or not rich.
Lucy is both not strong and curious.
Susan is tall or curious.
Alice is humble or generous.
Susan is either not humble or kind.
Someone is both not funny and not generous.
Lucy is funny or brave.
Susan is not creative. | Lucy is generous. | neutral | ((?[X]:((humble(X)&~generous(X))))=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:(old(X)=>(~wise(X)|~brave(X))))&
(![X]:((~rich(X)|~funny(X))<=>(~patient(X)&~brave(X))))&
((~calm(john))<=>((~creative(fred)|~humble(fred))))&
(![X]:((patient(X)<~>creative(X))<=>(~brave(X)<~>~creative(X))))&
(((kind(lucy)|~generous(lucy)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(~wise(X)<=>(kind(X)|~strong(X))))&
((generous(alice))=>((strong(alice)<~>patient(alice))))&
(![X]:(humble(X)<=>(rich(X)&~calm(X))))&
(![X]:((funny(X)&happy(X))=>(kind(X)&generous(X))))&
(![X]:((~kind(X)|~curious(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((strong(X)&~happy(X))=>(~tall(X)&wise(X))))&
((?[X]:(~creative(X)))=>((~brave(mary)&~curious(mary))))&
((?[X]:((~kind(X)<~>happy(X))))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((creative(X)&~old(X))=>(quiet(X)<~>strong(X))))&
(![X]:(~brave(X)=>(strong(X)<~>~rich(X))))&
((~strong(lucy)&curious(lucy)))&
((tall(susan)|curious(susan)))&
((humble(alice)|generous(alice)))&
((~humble(susan)<~>kind(susan)))&
(?[X]:((~funny(X)&~generous(X))))&
((funny(lucy)|brave(lucy)))&
(~creative(susan)) | generous(lucy) | [] | null | 0 |
Everyone who is both not happy and old is strong.
Everyone who is funny or not kind is either humble or not generous and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is humble is either wise or rich and vice versa.
If someone is calm or creative then alice is not generous or strong and vice versa.
If lucy is funny then alice is both humble and happy and vice versa.
Everyone who is not tall is calm and vice versa.
If alice is both creative and not generous then someone is both funny and kind and vice versa.
Everyone who is not strong or patient is curious or not happy and vice versa.
Everyone who is both not brave and humble is not quiet.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Mary is old or generous.
Someone is both not kind and not patient.
Susan is not quiet or old.
Someone is not brave.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave. | Mary is brave. | contradiction | (![X]:((~happy(X)&old(X))=>strong(X)))&
(![X]:((funny(X)|~kind(X))<=>(humble(X)<~>~generous(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>((~generous(alice)|strong(alice))))&
((funny(lucy))<=>((humble(alice)&happy(alice))))&
(![X]:(~tall(X)<=>calm(X)))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((~strong(X)|patient(X))<=>(curious(X)|~happy(X))))&
(![X]:((~brave(X)&humble(X))=>~quiet(X)))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
((old(mary)|generous(mary)))&
(?[X]:((~kind(X)&~patient(X))))&
((~quiet(susan)|old(susan)))&
(?[X]:(~brave(X)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary))) | brave(mary) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3171002108052700225707030
% SZS output start Proof for 3171002108052700225707030
24. ~brave(mary) & ~generous(mary) [input p23]
25. brave(mary) [input hypothesis]
133. ~brave(mary) [cnf transformation 24]
134. brave(mary) [cnf transformation 25]
280. $false [subsumption resolution 134,133]
% SZS output end Proof for 3171002108052700225707030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both strong and quiet then john is either not wise or kind and vice versa.
Everyone who is calm is patient.
If someone is both not tall and not happy then someone is rich or tall and vice versa.
Everyone who is both not creative and wise is both strong and happy and vice versa.
If someone is not quiet then susan is both not brave and not strong and vice versa.
Everyone who is strong or curious is quiet and vice versa.
If someone is not funny then someone is both not curious and brave and vice versa.
If someone is humble then someone is both not old and tall.
If someone is wise or curious then someone is creative.
Everyone who is either not wise or kind is not kind or not wise.
If someone is wise then someone is either not kind or not happy.
If someone is either tall or strong then someone is either wise or not strong and vice versa.
Everyone who is both not patient and not rich is tall or not strong.
Everyone who is not funny is either not strong or not generous and vice versa.
Everyone who is humble is both not funny and kind and vice versa.
Everyone who is both not creative and creative is not quiet and vice versa.
Someone is not creative or brave.
Someone is quiet.
Someone is patient or not tall.
Paul is both patient and curious.
Susan is funny or wise.
Someone is either curious or wise.
Someone is either kind or wise.
Fred is not tall or not calm. | Susan is strong. | neutral | (((strong(mary)&quiet(mary)))<=>((~wise(john)<~>kind(john))))&
(![X]:(calm(X)=>patient(X)))&
((?[X]:((~tall(X)&~happy(X))))<=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~creative(X)&wise(X))<=>(strong(X)&happy(X))))&
((?[X]:(~quiet(X)))<=>((~brave(susan)&~strong(susan))))&
(![X]:((strong(X)|curious(X))<=>quiet(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:((wise(X)|curious(X))))=>(?[X]:(creative(X))))&
(![X]:((~wise(X)<~>kind(X))=>(~kind(X)|~wise(X))))&
((?[X]:(wise(X)))=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)|~strong(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~generous(X))))&
(![X]:(humble(X)<=>(~funny(X)&kind(X))))&
(![X]:((~creative(X)&creative(X))<=>~quiet(X)))&
(?[X]:((~creative(X)|brave(X))))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)|~tall(X))))&
((patient(paul)&curious(paul)))&
((funny(susan)|wise(susan)))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((kind(X)<~>wise(X))))&
((~tall(fred)|~calm(fred))) | strong(susan) | [] | null | 0 |
Everyone who is generous or not old is both not quiet and not old.
If someone is creative or not wise then susan is quiet or happy.
Everyone who is not creative is both kind and not rich and vice versa.
If someone is kind then someone is generous or humble.
If alice is either not wise or calm then alice is not strong.
If alice is curious or not patient then someone is either calm or kind.
Everyone who is both not kind and quiet is not happy and vice versa.
If john is both not strong and rich then someone is creative and vice versa.
If john is tall or humble then lucy is curious or rich and vice versa.
If fred is not curious or not wise then lucy is not old and vice versa.
Everyone who is either happy or not old is both kind and tall.
If lucy is kind or calm then someone is either brave or not brave and vice versa.
Everyone who is calm is both not calm and kind.
Everyone who is either old or not quiet is not humble and vice versa.
Everyone who is not kind or not calm is generous and vice versa.
Everyone who is either not curious or generous is either not wise or not curious and vice versa.
Someone is funny.
Someone is creative.
Someone is not humble or patient.
Someone is old or curious.
Someone is either not quiet or brave.
Lucy is creative or not calm. | Lucy is not tall. | neutral | (![X]:((generous(X)|~old(X))=>(~quiet(X)&~old(X))))&
((?[X]:((creative(X)|~wise(X))))=>((quiet(susan)|happy(susan))))&
(![X]:(~creative(X)<=>(kind(X)&~rich(X))))&
((?[X]:(kind(X)))=>(?[X]:((generous(X)|humble(X)))))&
(((~wise(alice)<~>calm(alice)))=>(~strong(alice)))&
(((curious(alice)|~patient(alice)))=>(?[X]:((calm(X)<~>kind(X)))))&
(![X]:((~kind(X)&quiet(X))<=>~happy(X)))&
(((~strong(john)&rich(john)))<=>(?[X]:(creative(X))))&
(((tall(john)|humble(john)))<=>((curious(lucy)|rich(lucy))))&
(((~curious(fred)|~wise(fred)))<=>(~old(lucy)))&
(![X]:((happy(X)<~>~old(X))=>(kind(X)&tall(X))))&
(((kind(lucy)|calm(lucy)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:(calm(X)=>(~calm(X)&kind(X))))&
(![X]:((old(X)<~>~quiet(X))<=>~humble(X)))&
(![X]:((~kind(X)|~calm(X))<=>generous(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(~wise(X)<~>~curious(X))))&
(?[X]:(funny(X)))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|patient(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((creative(lucy)|~calm(lucy))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either not generous or not kind is both not creative and wise.
If mary is not brave or funny then someone is not happy.
If paul is not calm or old then someone is wise and vice versa.
Everyone who is funny is not happy and vice versa.
If mary is both not curious and not quiet then someone is both not tall and rich and vice versa.
If someone is not humble then someone is not quiet and vice versa.
Everyone who is not quiet or not funny is either not tall or not kind.
If someone is either curious or not funny then someone is both not creative and not generous.
Everyone who is either not quiet or not wise is either not happy or not quiet.
If someone is not brave then paul is old.
Everyone who is tall or wise is either not calm or strong and vice versa.
Everyone who is strong or not strong is not patient and vice versa.
If alice is rich then someone is either not tall or not kind.
If mary is either old or generous then someone is not tall.
Everyone who is both not old and strong is either not brave or not rich and vice versa.
If someone is not rich or curious then john is either not rich or strong.
Mary is not strong.
Someone is not generous.
Paul is both not generous and calm.
Someone is tall.
Mary is funny.
Someone is both rich and not curious.
Susan is either not humble or not rich. | Mary is funny. | entailment | (![X]:((~generous(X)<~>~kind(X))=>(~creative(X)&wise(X))))&
(((~brave(mary)|funny(mary)))=>(?[X]:(~happy(X))))&
(((~calm(paul)|old(paul)))<=>(?[X]:(wise(X))))&
(![X]:(funny(X)<=>~happy(X)))&
(((~curious(mary)&~quiet(mary)))<=>(?[X]:((~tall(X)&rich(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~tall(X)<~>~kind(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~quiet(X)<~>~wise(X))=>(~happy(X)<~>~quiet(X))))&
((?[X]:(~brave(X)))=>(old(paul)))&
(![X]:((tall(X)|wise(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((strong(X)|~strong(X))<=>~patient(X)))&
((rich(alice))=>(?[X]:((~tall(X)<~>~kind(X)))))&
(((old(mary)<~>generous(mary)))=>(?[X]:(~tall(X))))&
(![X]:((~old(X)&strong(X))<=>(~brave(X)<~>~rich(X))))&
((?[X]:((~rich(X)|curious(X))))=>((~rich(john)<~>strong(john))))&
(~strong(mary))&
(?[X]:(~generous(X)))&
((~generous(paul)&calm(paul)))&
(?[X]:(tall(X)))&
(funny(mary))&
(?[X]:((rich(X)&~curious(X))))&
((~humble(susan)<~>~rich(susan))) | funny(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3636817121761265989453036
% SZS output start Proof for 3636817121761265989453036
21. funny(mary) [input p20]
24. ~funny(mary) [input hypothesis]
132. funny(mary) [cnf transformation 21]
137. ~funny(mary) [cnf transformation 24]
141. 1 <=> funny(mary) [avatar definition]
274. 1 [avatar split clause 132,141]
285. ~1 [avatar split clause 137,141]
286. $false [avatar sat refutation 274,285]
% SZS output end Proof for 3636817121761265989453036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not brave is not calm. If mary is creative or happy then paul is both not patient and not old. Everyone who is kind or brave is rich and vice versa. If alice is both not generous and not funny then someone is not quiet or patient. If someone is both not old and not brave then paul is not strong. Everyone who is both not tall and wise is curious. Everyone who is both not old and kind is either not curious or generous and vice versa. Everyone who is generous is quiet or tall. If susan is wise then alice is both creative and not strong and vice versa. If someone is either not old or not quiet then paul is either not humble or creative. If alice is old then john is not happy. If someone is not rich then someone is both not patient and not calm and vice versa. Everyone who is both not kind and not wise is tall or generous and vice versa. Everyone who is either brave or not humble is not brave or not kind. Everyone who is both quiet and old is not curious or curious. If lucy is funny then someone is happy or calm. Someone is either patient or not kind. Alice is both not calm and curious. Someone is both old and not rich. Someone is either humble or brave. Fred is old. Lucy is wise or quiet. Someone is curious or not humble. Someone is either wise or humble. | Alice is calm. | contradiction | (![X]:((tall(X)<~>~brave(X))=>~calm(X)))&
(((creative(mary)|happy(mary)))=>((~patient(paul)&~old(paul))))&
(![X]:((kind(X)|brave(X))<=>rich(X)))&
(((~generous(alice)&~funny(alice)))=>(?[X]:((~quiet(X)|patient(X)))))&
((?[X]:((~old(X)&~brave(X))))=>(~strong(paul)))&
(![X]:((~tall(X)&wise(X))=>curious(X)))&
(![X]:((~old(X)&kind(X))<=>(~curious(X)<~>generous(X))))&
(![X]:(generous(X)=>(quiet(X)|tall(X))))&
((wise(susan))<=>((creative(alice)&~strong(alice))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~humble(paul)<~>creative(paul))))&
((old(alice))=>(~happy(john)))&
((?[X]:(~rich(X)))<=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:((~kind(X)&~wise(X))<=>(tall(X)|generous(X))))&
(![X]:((brave(X)<~>~humble(X))=>(~brave(X)|~kind(X))))&
(![X]:((quiet(X)&old(X))=>(~curious(X)|curious(X))))&
((funny(lucy))=>(?[X]:((happy(X)|calm(X)))))&
(?[X]:((patient(X)<~>~kind(X))))&
((~calm(alice)&curious(alice)))&
(?[X]:((old(X)&~rich(X))))&
(?[X]:((humble(X)<~>brave(X))))&
(old(fred))&
((wise(lucy)|quiet(lucy)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((wise(X)<~>humble(X)))) | calm(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3879502006338088025919759
% SZS output start Proof for 3879502006338088025919759
18. curious(alice) & ~calm(alice) [input p17]
25. calm(alice) [input hypothesis]
117. ~calm(alice) [cnf transformation 18]
128. calm(alice) [cnf transformation 25]
299. $false [subsumption resolution 128,117]
% SZS output end Proof for 3879502006338088025919759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not strong and generous then john is both patient and not funny and vice versa. If someone is either not quiet or curious then someone is both not strong and creative. If someone is not funny then someone is quiet or generous and vice versa. Everyone who is either quiet or not kind is not quiet or strong. Everyone who is either rich or brave is either quiet or not calm and vice versa. If someone is both generous and patient then fred is either patient or strong and vice versa. If susan is strong or tall then alice is both not wise and not tall. Everyone who is not creative is rich and vice versa. If paul is either calm or rich then someone is either not kind or not curious and vice versa. Everyone who is either kind or strong is not quiet or wise. Everyone who is rich is strong or creative and vice versa. Everyone who is not funny or patient is not rich or rich. If alice is both kind and funny then john is curious. Everyone who is calm is rich and vice versa. If someone is quiet then someone is either not creative or not humble and vice versa. Everyone who is wise is both not old and not creative and vice versa. Someone is not patient. Mary is either tall or not brave. Fred is generous. Someone is not wise. Someone is quiet or humble. Mary is not patient. Fred is either not funny or quiet. | Susan is not strong. | contradiction | (((~strong(paul)&generous(paul)))<=>((patient(john)&~funny(john))))&
((?[X]:((~quiet(X)<~>curious(X))))=>(?[X]:((~strong(X)&creative(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((quiet(X)<~>~kind(X))=>(~quiet(X)|strong(X))))&
(![X]:((rich(X)<~>brave(X))<=>(quiet(X)<~>~calm(X))))&
((?[X]:((generous(X)&patient(X))))<=>((patient(fred)<~>strong(fred))))&
(((strong(susan)|tall(susan)))=>((~wise(alice)&~tall(alice))))&
(![X]:(~creative(X)<=>rich(X)))&
(((calm(paul)<~>rich(paul)))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((kind(X)<~>strong(X))=>(~quiet(X)|wise(X))))&
(![X]:(rich(X)<=>(strong(X)|creative(X))))&
(![X]:((~funny(X)|patient(X))=>(~rich(X)|rich(X))))&
(((kind(alice)&funny(alice)))=>(curious(john)))&
(![X]:(calm(X)<=>rich(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:(wise(X)<=>(~old(X)&~creative(X))))&
(?[X]:(~patient(X)))&
((tall(mary)<~>~brave(mary)))&
(generous(fred))&
(?[X]:(~wise(X)))&
(?[X]:((quiet(X)|humble(X))))&
(~patient(mary))&
((~funny(fred)<~>quiet(fred))) | ~strong(susan) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3467376560547037489492958
% SZS output start Proof for 3467376560547037489492958
8. ! [X0] : (~creative(X0) <=> rich(X0)) [input p7]
11. ! [X0] : (rich(X0) <=> (creative(X0) | strong(X0))) [input p10]
24. ~strong(susan) [input hypothesis]
55. ! [X0] : ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))) [nnf transformation 8]
61. ! [X0] : ((rich(X0) | (~creative(X0) & ~strong(X0))) & ((creative(X0) | strong(X0)) | ~rich(X0))) [nnf transformation 11]
62. ! [X0] : ((rich(X0) | (~creative(X0) & ~strong(X0))) & (creative(X0) | strong(X0) | ~rich(X0))) [flattening 61]
110. rich(X0) | creative(X0) [cnf transformation 55]
111. ~rich(X0) | ~creative(X0) [cnf transformation 55]
122. creative(X0) | strong(X0) | ~rich(X0) [cnf transformation 62]
124. rich(X0) | ~creative(X0) [cnf transformation 62]
146. ~strong(susan) [cnf transformation 24]
245. 22 <=> strong(susan) [avatar definition]
247. ~strong(susan) <- (~22) [avatar component clause 245]
285. rich(X0) [subsumption resolution 124,110]
286. creative(X0) | strong(X0) [subsumption resolution 122,285]
352. ~22 [avatar split clause 146,245]
364. ~creative(X1) [resolution 111,285]
369. strong(X0) [resolution 286,364]
384. $false <- (~22) [resolution 369,247]
385. 22 [avatar contradiction clause 384]
387. $false [avatar sat refutation 352,385]
% SZS output end Proof for 3467376560547037489492958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or not rich then someone is not patient and vice versa. Everyone who is both not generous and tall is both not funny and humble and vice versa. Everyone who is either not old or patient is not generous and vice versa. Everyone who is both not brave and not patient is either not patient or not wise and vice versa. Everyone who is either calm or funny is both not kind and not happy and vice versa. Everyone who is either not funny or happy is generous or rich and vice versa. If paul is patient or not happy then someone is either quiet or not rich. If someone is both not kind and generous then fred is humble or not quiet. Everyone who is either not tall or happy is quiet and vice versa. Everyone who is both not quiet and not generous is both not generous and funny. Everyone who is both wise and tall is either curious or generous. If someone is either generous or funny then someone is both kind and not strong and vice versa. If someone is both not strong and old then paul is both not generous and curious. Everyone who is not quiet is either patient or calm. Everyone who is funny is brave and vice versa. Everyone who is not humble or happy is either not patient or not wise. John is either curious or not kind. John is both wise and not curious. Someone is both happy and tall. Someone is not old. Someone is both not generous and not rich. Someone is curious. Someone is not rich or quiet. Someone is not curious. | John is rich. | neutral | ((?[X]:((old(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~generous(X)&tall(X))<=>(~funny(X)&humble(X))))&
(![X]:((~old(X)<~>patient(X))<=>~generous(X)))&
(![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>~wise(X))))&
(![X]:((calm(X)<~>funny(X))<=>(~kind(X)&~happy(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(generous(X)|rich(X))))&
(((patient(paul)|~happy(paul)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&generous(X))))=>((humble(fred)|~quiet(fred))))&
(![X]:((~tall(X)<~>happy(X))<=>quiet(X)))&
(![X]:((~quiet(X)&~generous(X))=>(~generous(X)&funny(X))))&
(![X]:((wise(X)&tall(X))=>(curious(X)<~>generous(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((~strong(X)&old(X))))=>((~generous(paul)&curious(paul))))&
(![X]:(~quiet(X)=>(patient(X)<~>calm(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~humble(X)|happy(X))=>(~patient(X)<~>~wise(X))))&
((curious(john)<~>~kind(john)))&
((wise(john)&~curious(john)))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:(~curious(X))) | rich(john) | [] | null | 0 |
If fred is generous then paul is both old and patient.
Everyone who is both not happy and wise is brave.
Everyone who is either kind or not strong is either curious or funny and vice versa.
If someone is tall or not strong then john is both not humble and curious.
If someone is either not calm or not quiet then paul is both tall and not kind and vice versa.
Everyone who is both generous and not strong is not patient or not humble and vice versa.
If susan is not brave then paul is patient and vice versa.
If alice is both not humble and quiet then someone is old and vice versa.
Everyone who is old or strong is both not creative and not strong and vice versa.
Everyone who is either funny or not rich is both not curious and generous and vice versa.
If alice is not quiet or not funny then someone is not calm or quiet and vice versa.
If someone is wise then lucy is either brave or quiet.
If someone is both not humble and not tall then someone is either not tall or not quiet.
Everyone who is both not kind and kind is not tall.
If mary is either not curious or old then someone is both not brave and not quiet and vice versa.
If someone is not creative then someone is either not creative or not happy and vice versa.
Susan is not happy or strong.
Someone is not creative.
Susan is either rich or not old.
Someone is either patient or not generous.
Paul is rich.
Paul is curious.
John is patient or brave. | Fred is not happy. | neutral | ((generous(fred))=>((old(paul)&patient(paul))))&
(![X]:((~happy(X)&wise(X))=>brave(X)))&
(![X]:((kind(X)<~>~strong(X))<=>(curious(X)<~>funny(X))))&
((?[X]:((tall(X)|~strong(X))))=>((~humble(john)&curious(john))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((tall(paul)&~kind(paul))))&
(![X]:((generous(X)&~strong(X))<=>(~patient(X)|~humble(X))))&
((~brave(susan))<=>(patient(paul)))&
(((~humble(alice)&quiet(alice)))<=>(?[X]:(old(X))))&
(![X]:((old(X)|strong(X))<=>(~creative(X)&~strong(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(~curious(X)&generous(X))))&
(((~quiet(alice)|~funny(alice)))<=>(?[X]:((~calm(X)|quiet(X)))))&
((?[X]:(wise(X)))=>((brave(lucy)<~>quiet(lucy))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~kind(X)&kind(X))=>~tall(X)))&
(((~curious(mary)<~>old(mary)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((~happy(susan)|strong(susan)))&
(?[X]:(~creative(X)))&
((rich(susan)<~>~old(susan)))&
(?[X]:((patient(X)<~>~generous(X))))&
(rich(paul))&
(curious(paul))&
((patient(john)|brave(john))) | ~happy(fred) | [] | null | 0 |
Everyone who is not tall or humble is either calm or not kind and vice versa.
Everyone who is both generous and humble is not rich or happy and vice versa.
Everyone who is both not tall and calm is either not generous or not quiet.
Everyone who is not funny is either not brave or not rich.
Everyone who is not generous or not humble is either not happy or rich and vice versa.
If alice is either not wise or curious then someone is both not quiet and humble.
Everyone who is either not tall or not patient is kind.
If someone is patient then paul is both tall and not rich and vice versa.
Everyone who is both creative and funny is not humble and vice versa.
If someone is either strong or rich then paul is both not humble and not calm.
If fred is both not brave and not humble then john is either not happy or strong.
Everyone who is not brave is not kind.
Everyone who is either happy or strong is not brave and vice versa.
If susan is either creative or not wise then someone is either not happy or generous and vice versa.
If someone is strong or not rich then someone is tall.
Someone is either generous or wise.
Someone is either kind or funny.
Someone is either tall or kind.
Someone is tall or kind.
Someone is wise. | Susan is not calm. | entailment | (![X]:((~tall(X)|humble(X))<=>(calm(X)<~>~kind(X))))&
(![X]:((generous(X)&humble(X))<=>(~rich(X)|happy(X))))&
(![X]:((~tall(X)&calm(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~brave(X)<~>~rich(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~happy(X)<~>rich(X))))&
(((~wise(alice)<~>curious(alice)))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>kind(X)))&
((?[X]:(patient(X)))<=>((tall(paul)&~rich(paul))))&
(![X]:((creative(X)&funny(X))<=>~humble(X)))&
((?[X]:((strong(X)<~>rich(X))))=>((~humble(paul)&~calm(paul))))&
(((~brave(fred)&~humble(fred)))=>((~happy(john)<~>strong(john))))&
(![X]:(~brave(X)=>~kind(X)))&
(![X]:((happy(X)<~>strong(X))<=>~brave(X)))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(tall(X))))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((kind(X)<~>funny(X))))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:((tall(X)|kind(X))))&
(?[X]:(wise(X))) | ~calm(susan) | [
"p0",
"p1",
"p4",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1042325286874261256282453
% SZS output start Proof for 1042325286874261256282453
1. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p0]
2. ! [X0] : ((humble(X0) & generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p1]
5. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> (~happy(X0) <~> rich(X0))) [input p4]
10. ? [X0] : (strong(X0) <~> rich(X0)) => (~calm(paul) & ~humble(paul)) [input p9]
12. ! [X0] : (~brave(X0) => ~kind(X0)) [input p11]
13. ! [X0] : ((happy(X0) <~> strong(X0)) <=> ~brave(X0)) [input p12]
21. calm(susan) [input hypothesis]
28. (~calm(paul) & ~humble(paul)) | ! [X0] : (strong(X0) <=> rich(X0)) [ennf transformation 10]
31. ! [X0] : (~kind(X0) | brave(X0)) [ennf transformation 12]
33. ! [X0] : (((humble(X0) | ~tall(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (~humble(X0) & tall(X0)))) [nnf transformation 1]
34. ! [X0] : ((humble(X0) | ~tall(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (~humble(X0) & tall(X0)))) [flattening 33]
35. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 2]
36. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ~humble(X0) | ~generous(X0))) [flattening 35]
39. ! [X0] : (((~humble(X0) | ~generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (humble(X0) & generous(X0)))) [nnf transformation 5]
40. ! [X0] : ((~humble(X0) | ~generous(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (humble(X0) & generous(X0)))) [flattening 39]
52. (~calm(paul) & ~humble(paul)) | ! [X0] : ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))) [nnf transformation 28]
54. ! [X0] : ((((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | brave(X0)) & (~brave(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))))) [nnf transformation 13]
78. ~calm(X0) | kind(X0) | ~humble(X0) [cnf transformation 34]
81. ~rich(X0) | happy(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 36]
82. rich(X0) | generous(X0) [cnf transformation 36]
83. ~happy(X0) | generous(X0) [cnf transformation 36]
84. rich(X0) | humble(X0) [cnf transformation 36]
85. ~happy(X0) | humble(X0) [cnf transformation 36]
92. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 40]
93. ~rich(X0) | happy(X0) | humble(X0) [cnf transformation 40]
94. ~humble(X0) | ~generous(X0) | rich(X0) | happy(X0) [cnf transformation 40]
95. ~humble(X0) | ~generous(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 40]
108. ~humble(paul) | rich(X0) | ~strong(X0) [cnf transformation 52]
114. ~kind(X0) | brave(X0) [cnf transformation 31]
115. ~brave(X0) | strong(X0) | ~happy(X0) [cnf transformation 54]
137. calm(susan) [cnf transformation 21]
138. ~generous(X0) | ~happy(X0) | ~rich(X0) [subsumption resolution 95,85]
139. ~happy(X0) | ~rich(X0) [subsumption resolution 138,83]
140. ~generous(X0) | rich(X0) | happy(X0) [subsumption resolution 94,84]
141. happy(X0) | rich(X0) [subsumption resolution 140,82]
142. happy(X0) | humble(X0) [subsumption resolution 93,141]
143. humble(X0) [subsumption resolution 142,85]
144. happy(X0) | generous(X0) [subsumption resolution 92,141]
145. generous(X0) [subsumption resolution 144,83]
188. 10 <=> ! [X0] : (rich(X0) | ~strong(X0)) [avatar definition]
189. ~strong(X0) | rich(X0) <- (10) [avatar component clause 188]
193. rich(X0) | ~strong(X0) [subsumption resolution 108,143]
194. 10 [avatar split clause 193,188]
294. 27 <=> kind(susan) [avatar definition]
296. kind(susan) <- (27) [avatar component clause 294]
299. kind(susan) | ~humble(susan) [resolution 78,137]
301. kind(susan) [subsumption resolution 299,143]
302. 27 [avatar split clause 301,294]
307. brave(susan) <- (27) [resolution 296,114]
456. strong(susan) | ~happy(susan) <- (27) [resolution 307,115]
459. 45 <=> happy(susan) [avatar definition]
460. happy(susan) <- (45) [avatar component clause 459]
461. ~happy(susan) <- (~45) [avatar component clause 459]
463. 46 <=> strong(susan) [avatar definition]
465. strong(susan) <- (46) [avatar component clause 463]
466. ~45 | 46 | ~27 [avatar split clause 456,294,463,459]
472. 48 <=> rich(susan) [avatar definition]
473. rich(susan) <- (48) [avatar component clause 472]
474. ~rich(susan) <- (~48) [avatar component clause 472]
596. rich(susan) <- (~45) [resolution 461,141]
597. $false <- (~45, ~48) [subsumption resolution 596,474]
598. 45 | 48 [avatar contradiction clause 597]
604. ~rich(susan) <- (45) [resolution 460,139]
609. rich(susan) <- (10, 46) [resolution 465,189]
612. 48 | ~10 | ~46 [avatar split clause 609,463,188,472]
613. ~48 | ~45 [avatar split clause 604,459,472]
619. happy(susan) | ~humble(susan) | ~generous(susan) <- (48) [resolution 473,81]
621. ~humble(susan) | ~generous(susan) <- (~45, 48) [subsumption resolution 619,461]
622. ~generous(susan) <- (~45, 48) [subsumption resolution 621,143]
623. $false <- (~45, 48) [subsumption resolution 622,145]
624. 45 | ~48 [avatar contradiction clause 623]
627. $false [avatar sat refutation 194,302,466,598,612,613,624]
% SZS output end Proof for 1042325286874261256282453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is brave is either not wise or not kind and vice versa. Everyone who is either not wise or not curious is either not brave or funny and vice versa. If susan is either not generous or strong then someone is either patient or not funny and vice versa. If someone is not curious or brave then john is either not happy or not generous. If john is not old or generous then paul is patient or old. Everyone who is generous is both strong and not patient. Everyone who is quiet or kind is happy or funny and vice versa. Everyone who is both generous and wise is not humble and vice versa. If someone is both not tall and not old then someone is brave or not generous and vice versa. If susan is kind then someone is both funny and patient and vice versa. Everyone who is not quiet is both creative and funny and vice versa. Everyone who is not kind or not humble is not generous or not curious. If john is not curious then someone is wise or not rich. If someone is kind then someone is both curious and not kind. Everyone who is kind or quiet is both strong and patient and vice versa. Everyone who is both kind and calm is quiet. Someone is either creative or not curious. Paul is both creative and wise. Someone is rich. | Paul is funny. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~brave(X)<~>funny(X))))&
(((~generous(susan)<~>strong(susan)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((~curious(X)|brave(X))))=>((~happy(john)<~>~generous(john))))&
(((~old(john)|generous(john)))=>((patient(paul)|old(paul))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~curious(X))))&
((creative(paul)&wise(paul)))&
(?[X]:(rich(X))) | funny(paul) | [
"p2",
"p5",
"p6",
"p9",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 53303509105337871690110
% SZS output start Proof for 53303509105337871690110
3. (~generous(susan) <~> strong(susan)) <=> ? [X0] : (patient(X0) <~> ~funny(X0)) [input p2]
6. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p5]
7. ! [X0] : ((kind(X0) | quiet(X0)) <=> (funny(X0) | happy(X0))) [input p6]
10. kind(susan) <=> ? [X0] : (patient(X0) & funny(X0)) [input p9]
11. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p14]
18. wise(paul) & creative(paul) [input p17]
20. funny(paul) [input hypothesis]
28. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 6]
37. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [nnf transformation 3]
38. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [rectify 37]
39. ? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) => ((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) [choice axiom]
40. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [skolemisation 38,39]
42. ! [X0] : (((kind(X0) | quiet(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 7]
43. ! [X0] : ((kind(X0) | quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 42]
49. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X0] : (patient(X0) & funny(X0)) | ~kind(susan)) [nnf transformation 10]
50. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X1] : (patient(X1) & funny(X1)) | ~kind(susan)) [rectify 49]
51. ? [X1] : (patient(X1) & funny(X1)) => (patient(sK3) & funny(sK3)) [choice axiom]
52. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & ((patient(sK3) & funny(sK3)) | ~kind(susan)) [skolemisation 50,51]
53. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 11]
54. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 53]
60. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 15]
61. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 60]
85. ~strong(susan) | generous(susan) | ~funny(X0) | ~patient(X0) [cnf transformation 40]
94. ~patient(X0) | ~generous(X0) [cnf transformation 28]
98. ~funny(X0) | quiet(X0) | kind(X0) [cnf transformation 43]
107. kind(susan) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
110. ~creative(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 54]
116. ~kind(X0) | strong(X0) [cnf transformation 61]
118. ~kind(X0) | patient(X0) [cnf transformation 61]
123. creative(paul) [cnf transformation 18]
126. funny(paul) [cnf transformation 20]
131. 2 <=> generous(susan) [avatar definition]
133. generous(susan) <- (2) [avatar component clause 131]
135. 3 <=> strong(susan) [avatar definition]
137. ~strong(susan) <- (~3) [avatar component clause 135]
140. 4 <=> ! [X0] : (~funny(X0) | ~patient(X0)) [avatar definition]
141. ~patient(X0) | ~funny(X0) <- (4) [avatar component clause 140]
142. 4 | 2 | ~3 [avatar split clause 85,135,131,140]
176. 11 <=> patient(paul) [avatar definition]
177. ~patient(paul) <- (~11) [avatar component clause 176]
178. patient(paul) <- (11) [avatar component clause 176]
217. 20 <=> kind(susan) [avatar definition]
219. kind(susan) <- (20) [avatar component clause 217]
220. 4 | 20 [avatar split clause 107,217,140]
279. ~funny(paul) <- (4, 11) [resolution 141,178]
282. $false <- (4, 11) [subsumption resolution 279,126]
283. ~4 | ~11 [avatar contradiction clause 282]
289. strong(susan) <- (20) [resolution 219,116]
290. $false <- (~3, 20) [subsumption resolution 289,137]
291. 3 | ~20 [avatar contradiction clause 290]
304. 31 <=> kind(paul) [avatar definition]
306. kind(paul) <- (31) [avatar component clause 304]
314. patient(paul) <- (31) [resolution 306,118]
318. $false <- (~11, 31) [subsumption resolution 314,177]
319. 11 | ~31 [avatar contradiction clause 318]
340. quiet(paul) | kind(paul) [resolution 98,126]
374. patient(susan) <- (20) [resolution 219,118]
402. ~funny(paul) | ~quiet(paul) [resolution 110,123]
404. ~quiet(paul) [subsumption resolution 402,126]
407. kind(paul) [subsumption resolution 340,404]
408. 31 [avatar split clause 407,304]
510. ~generous(susan) <- (20) [resolution 374,94]
511. $false <- (2, 20) [subsumption resolution 510,133]
512. ~2 | ~20 [avatar contradiction clause 511]
513. $false [avatar sat refutation 142,220,283,291,319,408,512]
% SZS output end Proof for 53303509105337871690110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then fred is either not curious or not happy and vice versa.
If someone is not quiet then someone is both generous and not quiet and vice versa.
Everyone who is not tall or tall is either patient or not happy.
Everyone who is either curious or happy is both brave and not brave and vice versa.
If mary is not creative then mary is either brave or tall and vice versa.
Everyone who is not creative is generous.
If someone is brave or creative then paul is not generous.
If someone is both calm and not brave then mary is both wise and curious.
Everyone who is either calm or curious is either generous or not funny and vice versa.
Everyone who is kind is both not brave and not funny and vice versa.
If susan is both tall and not curious then susan is both not rich and not funny and vice versa.
Everyone who is humble or patient is happy or patient and vice versa.
Everyone who is both not calm and not strong is either rich or not wise.
If john is not tall or not curious then someone is not strong or strong.
Everyone who is both not brave and creative is both not patient and quiet.
Someone is either not rich or humble.
Someone is either not creative or patient.
Mary is funny.
Someone is either old or not quiet.
Someone is generous or not happy.
Someone is generous.
Mary is tall. | Paul is not kind. | entailment | ((?[X]:(~patient(X)))<=>((~curious(fred)<~>~happy(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((?[X]:((brave(X)|creative(X))))=>(~generous(paul)))&
((?[X]:((calm(X)&~brave(X))))=>((wise(mary)&curious(mary))))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)<~>~funny(X))))&
(![X]:(kind(X)<=>(~brave(X)&~funny(X))))&
(((tall(susan)&~curious(susan)))<=>((~rich(susan)&~funny(susan))))&
(![X]:((humble(X)|patient(X))<=>(happy(X)|patient(X))))&
(![X]:((~calm(X)&~strong(X))=>(rich(X)<~>~wise(X))))&
(((~tall(john)|~curious(john)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((~brave(X)&creative(X))=>(~patient(X)&quiet(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(funny(mary))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:(generous(X)))&
(tall(mary)) | ~kind(paul) | [
"p0",
"p3",
"p5",
"p6",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3968567235800517549424530
% SZS output start Proof for 3968567235800517549424530
1. ? [X0] : ~patient(X0) <=> (~curious(fred) <~> ~happy(fred)) [input p0]
4. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~brave(X0) & brave(X0))) [input p3]
6. ! [X0] : (~creative(X0) => generous(X0)) [input p5]
7. ? [X0] : (creative(X0) | brave(X0)) => ~generous(paul) [input p6]
10. ! [X0] : (kind(X0) <=> (~funny(X0) & ~brave(X0))) [input p9]
15. ! [X0] : ((creative(X0) & ~brave(X0)) => (quiet(X0) & ~patient(X0))) [input p14]
17. ? [X0] : (~creative(X0) <~> patient(X0)) [input p16]
23. kind(paul) [input hypothesis]
25. ! [X0] : (kind(X0) => (~funny(X0) & ~brave(X0))) [unused predicate definition removal 10]
27. ! [X0] : (generous(X0) | creative(X0)) [ennf transformation 6]
28. ~generous(paul) | ! [X0] : (~creative(X0) & ~brave(X0)) [ennf transformation 7]
30. ! [X0] : ((~funny(X0) & ~brave(X0)) | ~kind(X0)) [ennf transformation 25]
34. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~creative(X0) | brave(X0))) [ennf transformation 15]
35. ! [X0] : ((quiet(X0) & ~patient(X0)) | ~creative(X0) | brave(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X0] : patient(X0)) [nnf transformation 1]
37. (? [X0] : ~patient(X0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X1] : patient(X1)) [rectify 36]
38. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
39. (~patient(sK0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X1] : patient(X1)) [skolemisation 37,38]
46. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [flattening 46]
60. ? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) [nnf transformation 17]
61. ? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) => ((~patient(sK5) | creative(sK5)) & (patient(sK5) | ~creative(sK5))) [choice axiom]
62. (~patient(sK5) | creative(sK5)) & (patient(sK5) | ~creative(sK5)) [skolemisation 60,61]
70. ~happy(fred) | ~curious(fred) | patient(X1) [cnf transformation 39]
71. happy(fred) | curious(fred) | patient(X1) [cnf transformation 39]
81. brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 47]
82. brave(X0) | curious(X0) | ~happy(X0) [cnf transformation 47]
83. ~brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 47]
84. ~brave(X0) | curious(X0) | ~happy(X0) [cnf transformation 47]
91. creative(X0) | generous(X0) [cnf transformation 27]
93. ~generous(paul) | ~creative(X0) [cnf transformation 28]
104. ~kind(X0) | ~brave(X0) [cnf transformation 30]
118. ~creative(X0) | ~patient(X0) | brave(X0) [cnf transformation 35]
123. ~patient(sK5) | creative(sK5) [cnf transformation 62]
130. kind(paul) [cnf transformation 23]
132. 1 <=> happy(fred) [avatar definition]
133. ~happy(fred) <- (~1) [avatar component clause 132]
134. happy(fred) <- (1) [avatar component clause 132]
136. 2 <=> curious(fred) [avatar definition]
137. curious(fred) <- (2) [avatar component clause 136]
146. 4 <=> ! [X1] : patient(X1) [avatar definition]
147. patient(X1) <- (4) [avatar component clause 146]
148. 4 | 2 | 1 [avatar split clause 71,132,136,146]
149. 4 | ~2 | ~1 [avatar split clause 70,132,136,146]
173. ~happy(X0) | curious(X0) [subsumption resolution 82,84]
174. ~curious(X0) | happy(X0) [subsumption resolution 81,83]
192. 13 <=> ! [X0] : ~creative(X0) [avatar definition]
193. ~creative(X0) <- (13) [avatar component clause 192]
195. 14 <=> generous(paul) [avatar definition]
198. 13 | ~14 [avatar split clause 93,195,192]
248. 25 <=> creative(sK5) [avatar definition]
250. creative(sK5) <- (25) [avatar component clause 248]
252. 26 <=> patient(sK5) [avatar definition]
254. ~patient(sK5) <- (~26) [avatar component clause 252]
255. 25 | ~26 [avatar split clause 123,252,248]
283. ~brave(paul) [resolution 104,130]
291. happy(fred) <- (2) [resolution 174,137]
292. $false <- (~1, 2) [subsumption resolution 291,133]
293. 1 | ~2 [avatar contradiction clause 292]
294. curious(fred) <- (1) [resolution 134,173]
298. 2 | ~1 [avatar split clause 294,132,136]
301. $false <- (4, ~26) [resolution 147,254]
303. ~4 | 26 [avatar contradiction clause 301]
313. ~patient(X0) | brave(X0) | generous(X0) [resolution 118,91]
315. brave(X0) | generous(X0) <- (4) [subsumption resolution 313,147]
323. generous(paul) <- (4) [resolution 315,283]
328. 14 | ~4 [avatar split clause 323,146,195]
330. $false <- (13, 25) [resolution 193,250]
331. ~13 | ~25 [avatar contradiction clause 330]
332. $false [avatar sat refutation 148,149,198,255,293,298,303,328,331]
% SZS output end Proof for 3968567235800517549424530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not rich or brave then someone is not generous or not creative and vice versa. Everyone who is not generous or not kind is humble and vice versa. Everyone who is both creative and not humble is both not curious and brave and vice versa. Everyone who is brave is either patient or not creative and vice versa. Everyone who is not wise is quiet or not creative. If someone is generous or not curious then someone is both brave and not humble and vice versa. If mary is either not kind or happy then fred is not creative and vice versa. Everyone who is both not rich and not quiet is both not generous and tall. If someone is both not creative and not curious then someone is creative or kind and vice versa. If lucy is either not calm or not patient then someone is either not strong or not tall and vice versa. Everyone who is patient is not funny. Everyone who is either not wise or generous is both funny and not rich. If susan is either not brave or generous then someone is generous or not brave and vice versa. If someone is not strong or not calm then someone is tall or calm. If someone is either brave or not generous then fred is both not happy and happy. If fred is tall or funny then someone is calm or generous. Someone is happy. Someone is not tall. Fred is brave. Susan is both not quiet and strong. John is wise. Fred is both tall and curious. Mary is both not generous and not patient. | John is not generous. | entailment | (((~rich(mary)|brave(mary)))<=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:((~generous(X)|~kind(X))<=>humble(X)))&
(![X]:((creative(X)&~humble(X))<=>(~curious(X)&brave(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~creative(X))))&
(![X]:(~wise(X)=>(quiet(X)|~creative(X))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((brave(X)&~humble(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(~creative(fred)))&
(![X]:((~rich(X)&~quiet(X))=>(~generous(X)&tall(X))))&
((?[X]:((~creative(X)&~curious(X))))<=>(?[X]:((creative(X)|kind(X)))))&
(((~calm(lucy)<~>~patient(lucy)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:(patient(X)=>~funny(X)))&
(![X]:((~wise(X)<~>generous(X))=>(funny(X)&~rich(X))))&
(((~brave(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:((brave(X)<~>~generous(X))))=>((~happy(fred)&happy(fred))))&
(((tall(fred)|funny(fred)))=>(?[X]:((calm(X)|generous(X)))))&
(?[X]:(happy(X)))&
(?[X]:(~tall(X)))&
(brave(fred))&
((~quiet(susan)&strong(susan)))&
(wise(john))&
((tall(fred)&curious(fred)))&
((~generous(mary)&~patient(mary))) | ~generous(john) | [
"p1",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1489800627415233341516664
% SZS output start Proof for 1489800627415233341516664
2. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> humble(X0)) [input p1]
6. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X0] : (~humble(X0) & brave(X0)) [input p5]
15. ? [X0] : (brave(X0) <~> ~generous(X0)) => (happy(fred) & ~happy(fred)) [input p14]
24. generous(john) [input hypothesis]
25. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X1] : (~humble(X1) & brave(X1)) [rectify 6]
35. (happy(fred) & ~happy(fred)) | ! [X0] : (brave(X0) <=> ~generous(X0)) [ennf transformation 15]
42. ! [X0] : (((~kind(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [nnf transformation 2]
43. ! [X0] : ((~kind(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [flattening 42]
47. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X1] : (~humble(X1) & brave(X1)) | ! [X0] : (curious(X0) & ~generous(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X2] : (~humble(X2) & brave(X2)) | ! [X3] : (curious(X3) & ~generous(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | generous(X0)) => (~curious(sK1) | generous(sK1)) [choice axiom]
50. ? [X2] : (~humble(X2) & brave(X2)) => (~humble(sK2) & brave(sK2)) [choice axiom]
51. ((~curious(sK1) | generous(sK1)) | ! [X1] : (humble(X1) | ~brave(X1))) & ((~humble(sK2) & brave(sK2)) | ! [X3] : (curious(X3) & ~generous(X3))) [skolemisation 48,50,49]
70. (happy(fred) & ~happy(fred)) | ! [X0] : ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 35]
81. humble(X0) | generous(X0) [cnf transformation 43]
93. brave(sK2) | ~generous(X3) [cnf transformation 51]
95. ~humble(sK2) | ~generous(X3) [cnf transformation 51]
130. ~happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
132. happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
146. generous(john) [cnf transformation 24]
189. 11 <=> humble(sK2) [avatar definition]
191. ~humble(sK2) <- (~11) [avatar component clause 189]
194. 12 <=> ! [X3] : ~generous(X3) [avatar definition]
195. ~generous(X3) <- (12) [avatar component clause 194]
196. 12 | ~11 [avatar split clause 95,189,194]
198. 13 <=> brave(sK2) [avatar definition]
200. brave(sK2) <- (13) [avatar component clause 198]
202. 12 | 13 [avatar split clause 93,198,194]
324. 40 <=> happy(fred) [avatar definition]
329. 41 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
330. ~generous(X0) | ~brave(X0) <- (41) [avatar component clause 329]
331. 41 | 40 [avatar split clause 132,324,329]
333. 41 | ~40 [avatar split clause 130,324,329]
353. generous(sK2) <- (~11) [resolution 81,191]
370. $false <- (12) [resolution 195,146]
374. ~12 [avatar contradiction clause 370]
380. ~brave(sK2) <- (~11, 41) [resolution 330,353]
383. $false <- (~11, 13, 41) [subsumption resolution 380,200]
384. 11 | ~13 | ~41 [avatar contradiction clause 383]
385. $false [avatar sat refutation 196,202,331,333,374,384]
% SZS output end Proof for 1489800627415233341516664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not wise and calm then john is old or patient.
Everyone who is either happy or not tall is not curious.
Everyone who is both creative and not curious is old.
Everyone who is not brave or not generous is not calm and vice versa.
If someone is either generous or strong then someone is not tall and vice versa.
If lucy is both happy and not tall then lucy is humble or not happy and vice versa.
Everyone who is funny or old is either old or not old and vice versa.
Everyone who is not curious or brave is either strong or not strong and vice versa.
If someone is either quiet or not creative then fred is either not funny or wise and vice versa.
If someone is not creative or calm then alice is both not generous and not tall and vice versa.
If fred is either strong or happy then lucy is both patient and quiet.
If lucy is not funny then paul is both happy and brave and vice versa.
Everyone who is both not patient and not humble is not wise and vice versa.
If someone is either not funny or not old then someone is both patient and not strong.
Everyone who is either not wise or not calm is tall.
If lucy is not patient or generous then someone is quiet or not old and vice versa.
Someone is either tall or curious.
Paul is both not tall and funny.
Mary is either not patient or not quiet.
John is either patient or not tall.
Alice is both funny and patient.
Someone is either old or tall.
Someone is creative.
John is calm or rich. | Alice is not creative. | contradiction | (((~wise(paul)&calm(paul)))=>((old(john)|patient(john))))&
(![X]:((happy(X)<~>~tall(X))=>~curious(X)))&
(![X]:((creative(X)&~curious(X))=>old(X)))&
(![X]:((~brave(X)|~generous(X))<=>~calm(X)))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:(~tall(X))))&
(((happy(lucy)&~tall(lucy)))<=>((humble(lucy)|~happy(lucy))))&
(![X]:((funny(X)|old(X))<=>(old(X)<~>~old(X))))&
(![X]:((~curious(X)|brave(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>((~funny(fred)<~>wise(fred))))&
((?[X]:((~creative(X)|calm(X))))<=>((~generous(alice)&~tall(alice))))&
(((strong(fred)<~>happy(fred)))=>((patient(lucy)&quiet(lucy))))&
((~funny(lucy))<=>((happy(paul)&brave(paul))))&
(![X]:((~patient(X)&~humble(X))<=>~wise(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>(?[X]:((patient(X)&~strong(X)))))&
(![X]:((~wise(X)<~>~calm(X))=>tall(X)))&
(((~patient(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)|~old(X)))))&
(?[X]:((tall(X)<~>curious(X))))&
((~tall(paul)&funny(paul)))&
((~patient(mary)<~>~quiet(mary)))&
((patient(john)<~>~tall(john)))&
((funny(alice)&patient(alice)))&
(?[X]:((old(X)<~>tall(X))))&
(?[X]:(creative(X)))&
((calm(john)|rich(john))) | ~creative(alice) | [
"p3",
"p9",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 16849138008138300277921
% SZS output start Proof for 16849138008138300277921
4. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> ~calm(X0)) [input p3]
10. ? [X0] : (calm(X0) | ~creative(X0)) <=> (~tall(alice) & ~generous(alice)) [input p9]
13. ! [X0] : ((~humble(X0) & ~patient(X0)) <=> ~wise(X0)) [input p12]
15. ! [X0] : ((~wise(X0) <~> ~calm(X0)) => tall(X0)) [input p14]
21. patient(alice) & funny(alice) [input p20]
25. ~creative(alice) [input hypothesis]
36. ! [X0] : (tall(X0) | (~wise(X0) <=> ~calm(X0))) [ennf transformation 15]
38. ! [X0] : (((~generous(X0) | ~brave(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) & brave(X0)))) [nnf transformation 4]
39. ! [X0] : ((~generous(X0) | ~brave(X0) | calm(X0)) & (~calm(X0) | (generous(X0) & brave(X0)))) [flattening 38]
55. (? [X0] : (calm(X0) | ~creative(X0)) | (tall(alice) | generous(alice))) & ((~tall(alice) & ~generous(alice)) | ! [X0] : (~calm(X0) & creative(X0))) [nnf transformation 10]
56. (? [X0] : (calm(X0) | ~creative(X0)) | tall(alice) | generous(alice)) & ((~tall(alice) & ~generous(alice)) | ! [X0] : (~calm(X0) & creative(X0))) [flattening 55]
57. (? [X0] : (calm(X0) | ~creative(X0)) | tall(alice) | generous(alice)) & ((~tall(alice) & ~generous(alice)) | ! [X1] : (~calm(X1) & creative(X1))) [rectify 56]
58. ? [X0] : (calm(X0) | ~creative(X0)) => (calm(sK3) | ~creative(sK3)) [choice axiom]
59. ((calm(sK3) | ~creative(sK3)) | tall(alice) | generous(alice)) & ((~tall(alice) & ~generous(alice)) | ! [X1] : (~calm(X1) & creative(X1))) [skolemisation 57,58]
63. ! [X0] : (((~humble(X0) & ~patient(X0)) | wise(X0)) & (~wise(X0) | (humble(X0) | patient(X0)))) [nnf transformation 13]
64. ! [X0] : (((~humble(X0) & ~patient(X0)) | wise(X0)) & (~wise(X0) | humble(X0) | patient(X0))) [flattening 63]
69. ! [X0] : (tall(X0) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) [nnf transformation 36]
90. ~calm(X0) | generous(X0) [cnf transformation 39]
121. ~generous(alice) | creative(X1) [cnf transformation 59]
123. ~tall(alice) | creative(X1) [cnf transformation 59]
134. ~patient(X0) | wise(X0) [cnf transformation 64]
141. ~wise(X0) | tall(X0) | calm(X0) [cnf transformation 69]
155. patient(alice) [cnf transformation 21]
159. ~creative(alice) [cnf transformation 25]
259. 20 <=> generous(alice) [avatar definition]
260. ~generous(alice) <- (~20) [avatar component clause 259]
263. 21 <=> tall(alice) [avatar definition]
264. ~tall(alice) <- (~21) [avatar component clause 263]
280. 25 <=> ! [X1] : creative(X1) [avatar definition]
281. creative(X1) <- (25) [avatar component clause 280]
282. 25 | ~21 [avatar split clause 123,263,280]
284. 25 | ~20 [avatar split clause 121,259,280]
405. wise(alice) [resolution 134,155]
458. tall(alice) | calm(alice) [resolution 141,405]
461. calm(alice) <- (~21) [subsumption resolution 458,264]
502. generous(alice) <- (~21) [resolution 461,90]
504. $false <- (~20, ~21) [subsumption resolution 502,260]
505. 20 | 21 [avatar contradiction clause 504]
512. $false <- (25) [resolution 281,159]
521. ~25 [avatar contradiction clause 512]
522. $false [avatar sat refutation 282,284,505,521]
% SZS output end Proof for 16849138008138300277921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not strong or not generous then john is curious or calm. Everyone who is not humble or strong is both not happy and not patient. If susan is not patient then lucy is both not brave and quiet and vice versa. If someone is either not old or not calm then susan is not generous or not tall and vice versa. If mary is both tall and not strong then someone is calm and vice versa. If someone is not brave then lucy is happy. Everyone who is rich or generous is both strong and calm. If someone is not wise or curious then someone is not curious and vice versa. Everyone who is not kind or patient is both not kind and wise. If someone is both calm and not quiet then someone is calm and vice versa. If mary is curious or strong then lucy is both happy and not strong and vice versa. Everyone who is not wise is not tall or wise. If someone is brave or funny then fred is not happy and vice versa. If someone is not calm or funny then someone is creative. Everyone who is not curious is not patient or not rich. Everyone who is either not funny or not old is not humble or rich. Susan is either brave or generous. Fred is not calm or not curious. Lucy is both not generous and not humble. Someone is patient. Someone is either creative or not quiet. Someone is generous or quiet. Someone is kind. Someone is both happy and not wise. | Susan is not strong. | entailment | (((~strong(paul)<~>~generous(paul)))=>((curious(john)|calm(john))))&
(![X]:((~humble(X)|strong(X))=>(~happy(X)&~patient(X))))&
((~patient(susan))<=>((~brave(lucy)&quiet(lucy))))&
((?[X]:((~old(X)<~>~calm(X))))<=>((~generous(susan)|~tall(susan))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:(calm(X))))&
((?[X]:(~brave(X)))=>(happy(lucy)))&
(![X]:((rich(X)|generous(X))=>(strong(X)&calm(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)|patient(X))=>(~kind(X)&wise(X))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:(calm(X))))&
(((curious(mary)|strong(mary)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:(~wise(X)=>(~tall(X)|wise(X))))&
((?[X]:((brave(X)|funny(X))))<=>(~happy(fred)))&
((?[X]:((~calm(X)|funny(X))))=>(?[X]:(creative(X))))&
(![X]:(~curious(X)=>(~patient(X)|~rich(X))))&
(![X]:((~funny(X)<~>~old(X))=>(~humble(X)|rich(X))))&
((brave(susan)<~>generous(susan)))&
((~calm(fred)|~curious(fred)))&
((~generous(lucy)&~humble(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((happy(X)&~wise(X)))) | ~strong(susan) | [
"p1",
"p2",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 729171610515127883284866
% SZS output start Proof for 729171610515127883284866
2. ! [X0] : ((strong(X0) | ~humble(X0)) => (~patient(X0) & ~happy(X0))) [input p1]
3. ~patient(susan) <=> (quiet(lucy) & ~brave(lucy)) [input p2]
6. ? [X0] : ~brave(X0) => happy(lucy) [input p5]
19. ~humble(lucy) & ~generous(lucy) [input p18]
25. strong(susan) [input hypothesis]
31. ! [X0] : ((~patient(X0) & ~happy(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 2]
32. happy(lucy) | ! [X0] : brave(X0) [ennf transformation 6]
43. (~patient(susan) | (~quiet(lucy) | brave(lucy))) & ((quiet(lucy) & ~brave(lucy)) | patient(susan)) [nnf transformation 3]
44. (~patient(susan) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | patient(susan)) [flattening 43]
89. ~happy(X0) | humble(X0) [cnf transformation 31]
92. ~patient(X0) | ~strong(X0) [cnf transformation 31]
93. ~brave(lucy) | patient(susan) [cnf transformation 44]
105. happy(lucy) | brave(X0) [cnf transformation 32]
138. ~humble(lucy) [cnf transformation 19]
146. strong(susan) [cnf transformation 25]
167. 5 <=> brave(lucy) [avatar definition]
168. ~brave(lucy) <- (~5) [avatar component clause 167]
175. 7 <=> patient(susan) [avatar definition]
176. patient(susan) <- (7) [avatar component clause 175]
180. 7 | ~5 [avatar split clause 93,167,175]
228. 18 <=> ! [X0] : brave(X0) [avatar definition]
229. brave(X0) <- (18) [avatar component clause 228]
231. 19 <=> happy(lucy) [avatar definition]
233. happy(lucy) <- (19) [avatar component clause 231]
234. 18 | 19 [avatar split clause 105,231,228]
355. $false <- (~5, 18) [subsumption resolution 168,229]
356. 5 | ~18 [avatar contradiction clause 355]
360. humble(lucy) <- (19) [resolution 89,233]
361. $false <- (19) [subsumption resolution 360,138]
362. ~19 [avatar contradiction clause 361]
367. ~strong(susan) <- (7) [resolution 92,176]
368. $false <- (7) [subsumption resolution 367,146]
369. ~7 [avatar contradiction clause 368]
370. $false [avatar sat refutation 180,234,356,362,369]
% SZS output end Proof for 729171610515127883284866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not creative then fred is both not strong and brave and vice versa. If lucy is both rich and funny then paul is not humble or not generous. If lucy is both not calm and creative then john is not humble or not wise and vice versa. Everyone who is creative is not tall or not rich. If someone is patient or not creative then someone is not kind and vice versa. Everyone who is either not brave or not funny is not brave and vice versa. Everyone who is not creative is kind or calm. Everyone who is both not tall and not brave is not happy. Everyone who is either not creative or not funny is calm or funny. If someone is either creative or not tall then john is both funny and not rich. Everyone who is either not wise or humble is not generous or wise and vice versa. Everyone who is either not tall or quiet is rich and vice versa. Everyone who is both happy and quiet is both not humble and not generous and vice versa. Everyone who is not calm or not humble is either kind or not generous. Everyone who is funny or not creative is not old and vice versa. Everyone who is either not generous or old is both creative and funny and vice versa. Fred is both quiet and calm. Someone is creative or happy. John is both not creative and calm. Someone is not wise or funny. Someone is either funny or generous. Fred is not strong. Someone is both generous and not calm. Someone is both not strong and not calm. | Fred is not humble. | neutral | ((?[X]:((curious(X)|~creative(X))))<=>((~strong(fred)&brave(fred))))&
(((rich(lucy)&funny(lucy)))=>((~humble(paul)|~generous(paul))))&
(((~calm(lucy)&creative(lucy)))<=>((~humble(john)|~wise(john))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~funny(X))<=>~brave(X)))&
(![X]:(~creative(X)=>(kind(X)|calm(X))))&
(![X]:((~tall(X)&~brave(X))=>~happy(X)))&
(![X]:((~creative(X)<~>~funny(X))=>(calm(X)|funny(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>((funny(john)&~rich(john))))&
(![X]:((~wise(X)<~>humble(X))<=>(~generous(X)|wise(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>rich(X)))&
(![X]:((happy(X)&quiet(X))<=>(~humble(X)&~generous(X))))&
(![X]:((~calm(X)|~humble(X))=>(kind(X)<~>~generous(X))))&
(![X]:((funny(X)|~creative(X))<=>~old(X)))&
(![X]:((~generous(X)<~>old(X))<=>(creative(X)&funny(X))))&
((quiet(fred)&calm(fred)))&
(?[X]:((creative(X)|happy(X))))&
((~creative(john)&calm(john)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((funny(X)<~>generous(X))))&
(~strong(fred))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~strong(X)&~calm(X)))) | ~humble(fred) | [] | null | 0 |
Everyone who is either not rich or brave is curious and vice versa. If someone is calm then paul is either not old or brave and vice versa. If lucy is either not generous or generous then susan is not creative. Everyone who is both not kind and old is both not creative and old and vice versa. Everyone who is both not brave and not calm is both not wise and not old. If someone is funny or not funny then someone is either happy or not strong and vice versa. Everyone who is both happy and not happy is either not happy or not brave and vice versa. If paul is not kind then someone is not calm or not happy and vice versa. Everyone who is not rich or tall is either old or not kind. Everyone who is either not calm or not generous is either curious or not happy and vice versa. Everyone who is either curious or not brave is either brave or tall and vice versa. If someone is not calm or not quiet then mary is either not rich or not tall and vice versa. Everyone who is either not patient or strong is both funny and not tall and vice versa. Everyone who is either strong or not brave is either not rich or kind. If lucy is either wise or curious then john is funny and vice versa. Everyone who is either tall or not rich is both tall and not funny and vice versa. Susan is not curious. Someone is either not strong or not creative. Lucy is not brave. Susan is either not funny or not wise. Someone is either not tall or happy. Someone is both not calm and not happy. Alice is either patient or old. Susan is not calm. | Lucy is not generous. | neutral | (![X]:((~rich(X)<~>brave(X))<=>curious(X)))&
((?[X]:(calm(X)))<=>((~old(paul)<~>brave(paul))))&
(((~generous(lucy)<~>generous(lucy)))=>(~creative(susan)))&
(![X]:((~kind(X)&old(X))<=>(~creative(X)&old(X))))&
(![X]:((~brave(X)&~calm(X))=>(~wise(X)&~old(X))))&
((?[X]:((funny(X)|~funny(X))))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((happy(X)&~happy(X))<=>(~happy(X)<~>~brave(X))))&
((~kind(paul))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~rich(X)|tall(X))=>(old(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(curious(X)<~>~happy(X))))&
(![X]:((curious(X)<~>~brave(X))<=>(brave(X)<~>tall(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~rich(mary)<~>~tall(mary))))&
(![X]:((~patient(X)<~>strong(X))<=>(funny(X)&~tall(X))))&
(![X]:((strong(X)<~>~brave(X))=>(~rich(X)<~>kind(X))))&
(((wise(lucy)<~>curious(lucy)))<=>(funny(john)))&
(![X]:((tall(X)<~>~rich(X))<=>(tall(X)&~funny(X))))&
(~curious(susan))&
(?[X]:((~strong(X)<~>~creative(X))))&
(~brave(lucy))&
((~funny(susan)<~>~wise(susan)))&
(?[X]:((~tall(X)<~>happy(X))))&
(?[X]:((~calm(X)&~happy(X))))&
((patient(alice)<~>old(alice)))&
(~calm(susan)) | ~generous(lucy) | [] | null | 0 |
If alice is both strong and not brave then lucy is kind or strong and vice versa.
If lucy is either rich or not wise then paul is happy.
If john is both kind and quiet then susan is either wise or tall.
Everyone who is both generous and calm is both not quiet and quiet.
If fred is patient then susan is not calm and vice versa.
If mary is not happy then someone is not strong and vice versa.
If someone is both rich and kind then someone is either tall or brave and vice versa.
Everyone who is either strong or not curious is strong.
Everyone who is not brave or old is both not strong and kind and vice versa.
If someone is either calm or rich then alice is strong or not funny.
Everyone who is either not calm or rich is both tall and not curious.
If alice is generous or happy then someone is old or tall.
If someone is both creative and rich then someone is both calm and strong and vice versa.
Everyone who is either not strong or patient is not humble.
Everyone who is generous or old is either wise or not calm and vice versa.
Everyone who is tall or not rich is not curious or quiet.
Someone is not strong.
Mary is not rich or tall.
Alice is quiet or creative.
Fred is both patient and creative.
Mary is both humble and tall.
Someone is not funny.
Alice is both curious and rich.
Paul is both not funny and not curious. | Lucy is not kind. | entailment | (((strong(alice)&~brave(alice)))<=>((kind(lucy)|strong(lucy))))&
(((rich(lucy)<~>~wise(lucy)))=>(happy(paul)))&
(((kind(john)&quiet(john)))=>((wise(susan)<~>tall(susan))))&
(![X]:((generous(X)&calm(X))=>(~quiet(X)&quiet(X))))&
((patient(fred))<=>(~calm(susan)))&
((~happy(mary))<=>(?[X]:(~strong(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:((strong(X)<~>~curious(X))=>strong(X)))&
(![X]:((~brave(X)|old(X))<=>(~strong(X)&kind(X))))&
((?[X]:((calm(X)<~>rich(X))))=>((strong(alice)|~funny(alice))))&
(![X]:((~calm(X)<~>rich(X))=>(tall(X)&~curious(X))))&
(((generous(alice)|happy(alice)))=>(?[X]:((old(X)|tall(X)))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((~strong(X)<~>patient(X))=>~humble(X)))&
(![X]:((generous(X)|old(X))<=>(wise(X)<~>~calm(X))))&
(![X]:((tall(X)|~rich(X))=>(~curious(X)|quiet(X))))&
(?[X]:(~strong(X)))&
((~rich(mary)|tall(mary)))&
((quiet(alice)|creative(alice)))&
((patient(fred)&creative(fred)))&
((humble(mary)&tall(mary)))&
(?[X]:(~funny(X)))&
((curious(alice)&rich(alice)))&
((~funny(paul)&~curious(paul))) | ~kind(lucy) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 9005410956294591246820868
% SZS output start Proof for 9005410956294591246820868
1. (~brave(alice) & strong(alice)) <=> (strong(lucy) | kind(lucy)) [input p0]
9. ! [X0] : ((old(X0) | ~brave(X0)) <=> (kind(X0) & ~strong(X0))) [input p8]
25. kind(lucy) [input hypothesis]
42. ((~brave(alice) & strong(alice)) | (~strong(lucy) & ~kind(lucy))) & ((strong(lucy) | kind(lucy)) | (brave(alice) | ~strong(alice))) [nnf transformation 1]
43. ((~brave(alice) & strong(alice)) | (~strong(lucy) & ~kind(lucy))) & (strong(lucy) | kind(lucy) | brave(alice) | ~strong(alice)) [flattening 42]
57. ! [X0] : (((old(X0) | ~brave(X0)) | (~kind(X0) | strong(X0))) & ((kind(X0) & ~strong(X0)) | (~old(X0) & brave(X0)))) [nnf transformation 9]
58. ! [X0] : ((old(X0) | ~brave(X0) | ~kind(X0) | strong(X0)) & ((kind(X0) & ~strong(X0)) | (~old(X0) & brave(X0)))) [flattening 57]
73. strong(alice) | ~kind(lucy) [cnf transformation 43]
75. ~brave(alice) | ~kind(lucy) [cnf transformation 43]
95. ~strong(X0) | brave(X0) [cnf transformation 58]
130. kind(lucy) [cnf transformation 25]
137. 2 <=> brave(alice) [avatar definition]
139. ~brave(alice) <- (~2) [avatar component clause 137]
142. 3 <=> kind(lucy) [avatar definition]
145. ~3 | ~2 [avatar split clause 75,137,142]
147. 4 <=> strong(alice) [avatar definition]
149. strong(alice) <- (4) [avatar component clause 147]
151. ~3 | 4 [avatar split clause 73,147,142]
306. 3 [avatar split clause 130,142]
307. brave(alice) <- (4) [resolution 95,149]
308. $false <- (~2, 4) [subsumption resolution 307,139]
309. 2 | ~4 [avatar contradiction clause 308]
310. $false [avatar sat refutation 145,151,306,309]
% SZS output end Proof for 9005410956294591246820868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is patient then fred is either not brave or quiet and vice versa.
If susan is not generous then someone is rich and vice versa.
Everyone who is either not tall or rich is both happy and tall.
Everyone who is either wise or tall is not brave.
If susan is either kind or not humble then someone is happy or patient and vice versa.
Everyone who is not creative or rich is either quiet or not curious and vice versa.
Everyone who is both brave and old is tall and vice versa.
Everyone who is either not humble or tall is not wise and vice versa.
Everyone who is generous or brave is either not happy or kind.
Everyone who is either old or patient is either not happy or wise.
If susan is not old then someone is patient.
Everyone who is both not rich and patient is not strong.
Everyone who is not curious or not calm is not quiet.
Everyone who is not wise is strong or not old and vice versa.
If someone is both not old and generous then someone is both happy and funny and vice versa.
Everyone who is either not rich or not wise is either not creative or curious.
Someone is not funny.
Mary is happy or strong.
Lucy is both not creative and not wise.
Someone is calm or not humble.
Mary is funny or not brave.
Someone is both not happy and tall.
John is either strong or generous. | John is generous. | neutral | ((patient(fred))<=>((~brave(fred)<~>quiet(fred))))&
((~generous(susan))<=>(?[X]:(rich(X))))&
(![X]:((~tall(X)<~>rich(X))=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>tall(X))=>~brave(X)))&
(((kind(susan)<~>~humble(susan)))<=>(?[X]:((happy(X)|patient(X)))))&
(![X]:((~creative(X)|rich(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((brave(X)&old(X))<=>tall(X)))&
(![X]:((~humble(X)<~>tall(X))<=>~wise(X)))&
(![X]:((generous(X)|brave(X))=>(~happy(X)<~>kind(X))))&
(![X]:((old(X)<~>patient(X))=>(~happy(X)<~>wise(X))))&
((~old(susan))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&patient(X))=>~strong(X)))&
(![X]:((~curious(X)|~calm(X))=>~quiet(X)))&
(![X]:(~wise(X)<=>(strong(X)|~old(X))))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~rich(X)<~>~wise(X))=>(~creative(X)<~>curious(X))))&
(?[X]:(~funny(X)))&
((happy(mary)|strong(mary)))&
((~creative(lucy)&~wise(lucy)))&
(?[X]:((calm(X)|~humble(X))))&
((funny(mary)|~brave(mary)))&
(?[X]:((~happy(X)&tall(X))))&
((strong(john)<~>generous(john))) | generous(john) | [] | null | 0 |
Everyone who is either old or not happy is kind or not calm and vice versa. Everyone who is either wise or patient is both not patient and not old and vice versa. If susan is either not wise or not funny then someone is either happy or not funny. If someone is either not patient or curious then someone is both wise and happy. Everyone who is generous is either not strong or not quiet and vice versa. Everyone who is not quiet is both curious and not calm. If someone is not patient or not wise then someone is funny and vice versa. If someone is both not old and tall then someone is either not happy or not humble. Everyone who is not humble is either tall or strong. Everyone who is not curious or not kind is not strong or creative and vice versa. Everyone who is either not tall or tall is not old. If john is rich then someone is both not generous and brave and vice versa. If lucy is either happy or not strong then someone is both patient and not humble. If susan is either not kind or rich then someone is both not rich and not wise and vice versa. Everyone who is both quiet and brave is both brave and not humble and vice versa. Everyone who is both not old and not strong is either not humble or kind. Someone is generous or not brave. Someone is either not patient or humble. Someone is either humble or not brave. Someone is not rich. Someone is not humble. Someone is patient. Someone is calm or not curious. Alice is tall. | John is not wise. | contradiction | (![X]:((old(X)<~>~happy(X))<=>(kind(X)|~calm(X))))&
(![X]:((wise(X)<~>patient(X))<=>(~patient(X)&~old(X))))&
(((~wise(susan)<~>~funny(susan)))=>(?[X]:((happy(X)<~>~funny(X)))))&
((?[X]:((~patient(X)<~>curious(X))))=>(?[X]:((wise(X)&happy(X)))))&
(![X]:(generous(X)<=>(~strong(X)<~>~quiet(X))))&
(![X]:(~quiet(X)=>(curious(X)&~calm(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:(~humble(X)=>(tall(X)<~>strong(X))))&
(![X]:((~curious(X)|~kind(X))<=>(~strong(X)|creative(X))))&
(![X]:((~tall(X)<~>tall(X))=>~old(X)))&
((rich(john))<=>(?[X]:((~generous(X)&brave(X)))))&
(((happy(lucy)<~>~strong(lucy)))=>(?[X]:((patient(X)&~humble(X)))))&
(((~kind(susan)<~>rich(susan)))<=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((quiet(X)&brave(X))<=>(brave(X)&~humble(X))))&
(![X]:((~old(X)&~strong(X))=>(~humble(X)<~>kind(X))))&
(?[X]:((generous(X)|~brave(X))))&
(?[X]:((~patient(X)<~>humble(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~humble(X)))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|~curious(X))))&
(tall(alice)) | ~wise(john) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1319325076378617705346309
% SZS output start Proof for 1319325076378617705346309
2. ! [X0] : ((wise(X0) <~> patient(X0)) <=> (~old(X0) & ~patient(X0))) [input p1]
11. ! [X0] : ((~tall(X0) <~> tall(X0)) => ~old(X0)) [input p10]
25. ~wise(john) [input hypothesis]
34. ! [X0] : (~old(X0) | (~tall(X0) <=> tall(X0))) [ennf transformation 11]
40. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [flattening 40]
62. ! [X0] : (~old(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 34]
100. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 41]
103. patient(X0) | wise(X0) | old(X0) | patient(X0) [cnf transformation 41]
130. ~old(X0) | tall(X0) | tall(X0) [cnf transformation 62]
131. ~old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 62]
161. ~wise(john) [cnf transformation 25]
162. ~old(X0) | tall(X0) [duplicate literal removal 130]
163. ~tall(X0) | ~old(X0) [duplicate literal removal 131]
164. ~patient(X0) | wise(X0) [duplicate literal removal 100]
165. patient(X0) | wise(X0) | old(X0) [duplicate literal removal 103]
214. 11 <=> ! [X3] : wise(X3) [avatar definition]
215. wise(X3) <- (11) [avatar component clause 214]
238. ~old(X0) [subsumption resolution 162,163]
514. wise(X1) | old(X1) | wise(X1) [resolution 165,164]
515. wise(X1) | old(X1) [duplicate literal removal 514]
518. wise(X1) [subsumption resolution 515,238]
519. 11 [avatar split clause 518,214]
522. $false <- (11) [resolution 215,161]
525. ~11 [avatar contradiction clause 522]
527. $false [avatar sat refutation 519,525]
% SZS output end Proof for 1319325076378617705346309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave then someone is both not rich and kind. Everyone who is either brave or not humble is both rich and not funny. If susan is both not patient and not old then alice is tall or not curious. If someone is happy or generous then alice is not patient or not tall and vice versa. If lucy is generous then susan is not funny. If fred is either strong or kind then someone is not generous or not old and vice versa. Everyone who is both not brave and not old is either not old or not patient and vice versa. Everyone who is brave or happy is both not patient and generous and vice versa. Everyone who is both funny and humble is not old or wise. Everyone who is both not patient and old is happy or generous. If mary is either not brave or calm then mary is both not wise and funny. Everyone who is either calm or not calm is either creative or not funny. Everyone who is not old is both old and wise and vice versa. Everyone who is not strong or not patient is either funny or brave. Someone is not happy. Someone is both calm and quiet. Someone is both not quiet and tall. Someone is patient. Fred is funny or tall. Someone is creative or not generous. | Susan is funny. | contradiction | ((~brave(lucy))=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~humble(X))=>(rich(X)&~funny(X))))&
(((~patient(susan)&~old(susan)))=>((tall(alice)|~curious(alice))))&
((?[X]:((happy(X)|generous(X))))<=>((~patient(alice)|~tall(alice))))&
((generous(lucy))=>(~funny(susan)))&
(((strong(fred)<~>kind(fred)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)<~>~patient(X))))&
(![X]:((brave(X)|happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((funny(X)&humble(X))=>(~old(X)|wise(X))))&
(![X]:((~patient(X)&old(X))=>(happy(X)|generous(X))))&
(((~brave(mary)<~>calm(mary)))=>((~wise(mary)&funny(mary))))&
(![X]:((calm(X)<~>~calm(X))=>(creative(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(old(X)&wise(X))))&
(![X]:((~strong(X)|~patient(X))=>(funny(X)<~>brave(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:(patient(X)))&
((funny(fred)|tall(fred)))&
(?[X]:((creative(X)|~generous(X)))) | funny(susan) | [
"p1",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3071974080588446596103822
% SZS output start Proof for 3071974080588446596103822
2. ! [X0] : ((brave(X0) <~> ~humble(X0)) => (~funny(X0) & rich(X0))) [input p1]
7. ! [X0] : ((~old(X0) & ~brave(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p6]
8. ! [X0] : ((happy(X0) | brave(X0)) <=> (generous(X0) & ~patient(X0))) [input p7]
9. ! [X0] : ((humble(X0) & funny(X0)) => (wise(X0) | ~old(X0))) [input p8]
13. ! [X0] : (~old(X0) <=> (wise(X0) & old(X0))) [input p12]
21. funny(susan) [input hypothesis]
24. ! [X0] : ((~funny(X0) & rich(X0)) | (brave(X0) <=> ~humble(X0))) [ennf transformation 2]
26. ! [X0] : ((wise(X0) | ~old(X0)) | (~humble(X0) | ~funny(X0))) [ennf transformation 9]
27. ! [X0] : (wise(X0) | ~old(X0) | ~humble(X0) | ~funny(X0)) [flattening 26]
35. ! [X0] : ((~funny(X0) & rich(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 24]
45. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (old(X0) | brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | old(X0) | brave(X0))) [flattening 45]
47. ! [X0] : (((happy(X0) | brave(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | brave(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 47]
51. ! [X0] : ((~old(X0) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | old(X0))) [nnf transformation 13]
52. ! [X0] : ((~old(X0) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | old(X0))) [flattening 51]
69. ~funny(X0) | brave(X0) | humble(X0) [cnf transformation 35]
86. ~old(X0) | ~old(X0) | patient(X0) [cnf transformation 46]
87. ~patient(X0) | ~brave(X0) [cnf transformation 48]
92. ~old(X0) | wise(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 27]
102. old(X0) | old(X0) [cnf transformation 52]
104. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 52]
117. funny(susan) [cnf transformation 21]
118. old(X0) [duplicate literal removal 102]
119. ~wise(X0) | ~old(X0) [duplicate literal removal 104]
125. ~old(X0) | patient(X0) [duplicate literal removal 86]
171. 11 <=> funny(susan) [avatar definition]
172. funny(susan) <- (11) [avatar component clause 171]
176. 12 <=> ! [X0] : old(X0) [avatar definition]
177. old(X0) <- (12) [avatar component clause 176]
226. 12 [avatar split clause 118,176]
246. 11 [avatar split clause 117,171]
252. patient(X0) <- (12) [resolution 125,177]
254. ~brave(X0) <- (12) [resolution 252,87]
269. brave(susan) | humble(susan) <- (11) [resolution 69,172]
271. humble(susan) <- (11, 12) [subsumption resolution 269,254]
284. ~funny(X0) | ~humble(X0) | wise(X0) <- (12) [resolution 92,177]
285. ~humble(susan) | wise(susan) <- (11, 12) [resolution 284,172]
287. wise(susan) <- (11, 12) [subsumption resolution 285,271]
289. ~old(susan) <- (11, 12) [resolution 287,119]
290. $false <- (11, 12) [subsumption resolution 289,177]
291. ~11 | ~12 [avatar contradiction clause 290]
292. $false [avatar sat refutation 226,246,291]
% SZS output end Proof for 3071974080588446596103822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not generous is not quiet and vice versa.
If alice is either not quiet or not brave then someone is not curious.
If alice is calm or funny then susan is both old and not happy and vice versa.
If someone is either not quiet or strong then john is either not rich or curious.
Everyone who is both not rich and creative is both generous and not quiet.
If someone is not quiet then mary is both not rich and calm and vice versa.
If someone is creative or not rich then someone is either tall or brave and vice versa.
If someone is either rich or funny then lucy is either curious or patient and vice versa.
If fred is either humble or not brave then someone is old or not strong and vice versa.
Everyone who is either not wise or calm is not rich.
Everyone who is old is not creative or not funny.
If fred is both old and strong then someone is creative or happy and vice versa.
If someone is not humble then someone is both kind and not tall.
If someone is calm or not tall then alice is both not happy and not generous and vice versa.
If alice is rich or creative then mary is both not creative and not humble.
If paul is either not funny or humble then lucy is both brave and not quiet and vice versa.
Fred is both patient and wise.
Someone is humble.
Someone is old.
Someone is not funny.
Someone is both not curious and not patient.
Someone is quiet or curious.
Someone is not strong.
Someone is both funny and humble. | Fred is not patient. | contradiction | (![X]:((~rich(X)<~>~generous(X))<=>~quiet(X)))&
(((~quiet(alice)<~>~brave(alice)))=>(?[X]:(~curious(X))))&
(((calm(alice)|funny(alice)))<=>((old(susan)&~happy(susan))))&
((?[X]:((~quiet(X)<~>strong(X))))=>((~rich(john)<~>curious(john))))&
(![X]:((~rich(X)&creative(X))=>(generous(X)&~quiet(X))))&
((?[X]:(~quiet(X)))<=>((~rich(mary)&calm(mary))))&
((?[X]:((creative(X)|~rich(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
((?[X]:((rich(X)<~>funny(X))))<=>((curious(lucy)<~>patient(lucy))))&
(((humble(fred)<~>~brave(fred)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~wise(X)<~>calm(X))=>~rich(X)))&
(![X]:(old(X)=>(~creative(X)|~funny(X))))&
(((old(fred)&strong(fred)))<=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)&~tall(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>((~happy(alice)&~generous(alice))))&
(((rich(alice)|creative(alice)))=>((~creative(mary)&~humble(mary))))&
(((~funny(paul)<~>humble(paul)))<=>((brave(lucy)&~quiet(lucy))))&
((patient(fred)&wise(fred)))&
(?[X]:(humble(X)))&
(?[X]:(old(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)&~patient(X))))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)&humble(X)))) | ~patient(fred) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 65804521215135278444020
% SZS output start Proof for 65804521215135278444020
17. wise(fred) & patient(fred) [input p16]
25. ~patient(fred) [input hypothesis]
157. patient(fred) [cnf transformation 17]
168. ~patient(fred) [cnf transformation 25]
442. $false [subsumption resolution 168,157]
% SZS output end Proof for 65804521215135278444020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and curious is both not curious and not brave.
Everyone who is generous or not rich is tall.
If someone is either not rich or not creative then alice is happy and vice versa.
Everyone who is both wise and rich is creative.
If someone is generous then someone is both calm and strong.
If mary is either calm or not strong then alice is both not wise and old and vice versa.
If lucy is either tall or not patient then susan is strong or brave and vice versa.
If someone is not tall then someone is brave or not quiet.
Everyone who is generous is either humble or old.
Everyone who is not rich or not generous is either curious or strong.
If mary is not kind then fred is generous or not wise and vice versa.
Everyone who is either not brave or calm is not calm and vice versa.
If someone is patient or not creative then mary is creative.
Everyone who is not creative is either curious or creative and vice versa.
If someone is humble then susan is either not old or not rich and vice versa.
Everyone who is both not quiet and not generous is happy and vice versa.
Someone is either not generous or quiet.
Lucy is either not patient or curious.
Someone is either not kind or not strong.
Someone is both not old and not brave.
Paul is either rich or kind. | Alice is not humble. | neutral | (![X]:((~strong(X)&curious(X))=>(~curious(X)&~brave(X))))&
(![X]:((generous(X)|~rich(X))=>tall(X)))&
((?[X]:((~rich(X)<~>~creative(X))))<=>(happy(alice)))&
(![X]:((wise(X)&rich(X))=>creative(X)))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)&strong(X)))))&
(((calm(mary)<~>~strong(mary)))<=>((~wise(alice)&old(alice))))&
(((tall(lucy)<~>~patient(lucy)))<=>((strong(susan)|brave(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(generous(X)=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|~generous(X))=>(curious(X)<~>strong(X))))&
((~kind(mary))<=>((generous(fred)|~wise(fred))))&
(![X]:((~brave(X)<~>calm(X))<=>~calm(X)))&
((?[X]:((patient(X)|~creative(X))))=>(creative(mary)))&
(![X]:(~creative(X)<=>(curious(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~old(susan)<~>~rich(susan))))&
(![X]:((~quiet(X)&~generous(X))<=>happy(X)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~patient(lucy)<~>curious(lucy)))&
(?[X]:((~kind(X)<~>~strong(X))))&
(?[X]:((~old(X)&~brave(X))))&
((rich(paul)<~>kind(paul))) | ~humble(alice) | [] | null | 0 |
Everyone who is both happy and kind is either not calm or funny and vice versa.
Everyone who is not old is not generous or quiet and vice versa.
If someone is happy or creative then john is both rich and creative and vice versa.
Everyone who is both not patient and not strong is both not creative and strong.
If paul is either not funny or not creative then lucy is either humble or kind.
If alice is either wise or not funny then mary is either patient or creative.
If fred is either funny or brave then lucy is both not strong and strong.
Everyone who is both creative and rich is either quiet or calm and vice versa.
Everyone who is either brave or not humble is not rich.
Everyone who is both not rich and happy is either old or not quiet and vice versa.
Everyone who is either not generous or not calm is not quiet and vice versa.
Everyone who is either not old or wise is both humble and tall.
Everyone who is not brave or brave is both old and wise.
Everyone who is either not old or not funny is curious and vice versa.
If someone is both not old and not strong then someone is both funny and kind and vice versa.
Everyone who is not rich is not creative or patient and vice versa.
Lucy is generous.
Someone is not calm.
Someone is not brave or brave.
Alice is both not rich and not quiet.
Mary is generous.
Mary is either old or strong. | Lucy is not funny. | contradiction | (![X]:((happy(X)&kind(X))<=>(~calm(X)<~>funny(X))))&
(![X]:(~old(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((happy(X)|creative(X))))<=>((rich(john)&creative(john))))&
(![X]:((~patient(X)&~strong(X))=>(~creative(X)&strong(X))))&
(((~funny(paul)<~>~creative(paul)))=>((humble(lucy)<~>kind(lucy))))&
(((wise(alice)<~>~funny(alice)))=>((patient(mary)<~>creative(mary))))&
(((funny(fred)<~>brave(fred)))=>((~strong(lucy)&strong(lucy))))&
(![X]:((creative(X)&rich(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((brave(X)<~>~humble(X))=>~rich(X)))&
(![X]:((~rich(X)&happy(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>wise(X))=>(humble(X)&tall(X))))&
(![X]:((~brave(X)|brave(X))=>(old(X)&wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>curious(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:(~rich(X)<=>(~creative(X)|patient(X))))&
(generous(lucy))&
(?[X]:(~calm(X)))&
(?[X]:((~brave(X)|brave(X))))&
((~rich(alice)&~quiet(alice)))&
(generous(mary))&
((old(mary)<~>strong(mary))) | ~funny(lucy) | [
"p0",
"p1",
"p2",
"p7",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4350426886869116836382575
% SZS output start Proof for 4350426886869116836382575
1. ! [X0] : ((kind(X0) & happy(X0)) <=> (~calm(X0) <~> funny(X0))) [input p0]
2. ! [X0] : (~old(X0) <=> (quiet(X0) | ~generous(X0))) [input p1]
3. ? [X0] : (creative(X0) | happy(X0)) <=> (creative(john) & rich(john)) [input p2]
8. ! [X0] : ((rich(X0) & creative(X0)) <=> (quiet(X0) <~> calm(X0))) [input p7]
11. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> ~quiet(X0)) [input p10]
13. ! [X0] : ((brave(X0) | ~brave(X0)) => (wise(X0) & old(X0))) [input p12]
16. ! [X0] : (~rich(X0) <=> (patient(X0) | ~creative(X0))) [input p15]
23. ~funny(lucy) [input hypothesis]
33. ! [X0] : ((wise(X0) & old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 13]
34. ! [X0] : (((kind(X0) & happy(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (~kind(X0) | ~happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((kind(X0) & happy(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~kind(X0) | ~happy(X0))) [flattening 34]
36. ! [X0] : ((~old(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | old(X0))) [nnf transformation 2]
37. ! [X0] : ((~old(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | old(X0))) [flattening 36]
38. (? [X0] : (creative(X0) | happy(X0)) | (~creative(john) | ~rich(john))) & ((creative(john) & rich(john)) | ! [X0] : (~creative(X0) & ~happy(X0))) [nnf transformation 3]
39. (? [X0] : (creative(X0) | happy(X0)) | ~creative(john) | ~rich(john)) & ((creative(john) & rich(john)) | ! [X0] : (~creative(X0) & ~happy(X0))) [flattening 38]
40. (? [X0] : (creative(X0) | happy(X0)) | ~creative(john) | ~rich(john)) & ((creative(john) & rich(john)) | ! [X1] : (~creative(X1) & ~happy(X1))) [rectify 39]
41. ? [X0] : (creative(X0) | happy(X0)) => (creative(sK0) | happy(sK0)) [choice axiom]
42. ((creative(sK0) | happy(sK0)) | ~creative(john) | ~rich(john)) & ((creative(john) & rich(john)) | ! [X1] : (~creative(X1) & ~happy(X1))) [skolemisation 40,41]
46. ! [X0] : (((rich(X0) & creative(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~rich(X0) | ~creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((rich(X0) & creative(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~rich(X0) | ~creative(X0))) [flattening 46]
51. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 11]
58. ! [X0] : ((~rich(X0) | (~patient(X0) & creative(X0))) & ((patient(X0) | ~creative(X0)) | rich(X0))) [nnf transformation 16]
59. ! [X0] : ((~rich(X0) | (~patient(X0) & creative(X0))) & (patient(X0) | ~creative(X0) | rich(X0))) [flattening 58]
67. funny(X0) | happy(X0) | calm(X0) [cnf transformation 35]
72. ~old(X0) | generous(X0) [cnf transformation 37]
73. ~quiet(X0) | ~old(X0) [cnf transformation 37]
74. rich(john) | ~happy(X1) [cnf transformation 42]
75. rich(john) | ~creative(X1) [cnf transformation 42]
93. ~rich(X0) | quiet(X0) | calm(X0) | ~creative(X0) [cnf transformation 47]
96. ~calm(X0) | quiet(X0) | creative(X0) [cnf transformation 47]
109. ~generous(X0) | ~calm(X0) | quiet(X0) [cnf transformation 51]
113. old(X0) | brave(X0) [cnf transformation 33]
114. ~brave(X0) | old(X0) [cnf transformation 33]
122. ~rich(X0) | creative(X0) [cnf transformation 59]
132. ~funny(lucy) [cnf transformation 23]
135. 1 <=> rich(john) [avatar definition]
136. rich(john) <- (1) [avatar component clause 135]
139. 2 <=> creative(john) [avatar definition]
140. creative(john) <- (2) [avatar component clause 139]
152. 5 <=> ! [X1] : ~creative(X1) [avatar definition]
153. ~creative(X1) <- (5) [avatar component clause 152]
156. 6 <=> ! [X1] : ~happy(X1) [avatar definition]
157. ~happy(X1) <- (6) [avatar component clause 156]
159. 5 | 1 [avatar split clause 75,135,152]
160. 6 | 1 [avatar split clause 74,135,156]
220. old(X0) [subsumption resolution 113,114]
234. generous(X0) [resolution 72,220]
242. happy(lucy) | calm(lucy) [resolution 67,132]
247. calm(lucy) <- (6) [subsumption resolution 242,157]
265. quiet(lucy) | creative(lucy) <- (6) [resolution 96,247]
316. creative(john) <- (1) [resolution 136,122]
380. ~calm(X0) | quiet(X0) [resolution 109,234]
446. 38 <=> creative(lucy) [avatar definition]
448. creative(lucy) <- (38) [avatar component clause 446]
450. 39 <=> quiet(lucy) [avatar definition]
452. quiet(lucy) <- (39) [avatar component clause 450]
453. 38 | 39 | ~6 [avatar split clause 265,156,450,446]
464. ~old(lucy) <- (39) [resolution 452,73]
465. $false <- (39) [subsumption resolution 464,220]
466. ~39 [avatar contradiction clause 465]
475. quiet(john) | calm(john) | ~creative(john) <- (1) [resolution 93,136]
478. quiet(john) | calm(john) <- (1, 2) [subsumption resolution 475,140]
479. quiet(john) <- (1, 2) [subsumption resolution 478,380]
489. ~old(john) <- (1, 2) [resolution 479,73]
491. $false <- (1, 2) [subsumption resolution 489,220]
492. ~1 | ~2 [avatar contradiction clause 491]
499. 2 | ~1 [avatar split clause 316,135,139]
508. $false <- (5, 38) [resolution 153,448]
511. ~5 | ~38 [avatar contradiction clause 508]
512. $false [avatar sat refutation 159,160,453,466,492,499,511]
% SZS output end Proof for 4350426886869116836382575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is creative or brave then someone is either old or kind and vice versa. Everyone who is tall is both quiet and not rich and vice versa. Everyone who is not calm is not patient and vice versa. If paul is either not quiet or patient then fred is both brave and not kind. If someone is quiet or tall then someone is not brave or humble. Everyone who is tall or happy is not wise. Everyone who is strong or not rich is not quiet or not funny and vice versa. Everyone who is calm or generous is wise or not creative. Everyone who is rich or curious is both not brave and not funny and vice versa. Everyone who is not creative or not kind is either not happy or humble and vice versa. Everyone who is humble or not rich is either old or not funny. Everyone who is not funny or patient is not old and vice versa. If fred is either not quiet or generous then someone is both humble and not funny and vice versa. Everyone who is not funny is both tall and not patient. If paul is happy then someone is either old or patient. Everyone who is generous is wise or not calm. Someone is patient or tall. John is either curious or tall. Someone is not tall or not happy. Someone is not wise or rich. Fred is both happy and not old. Paul is old or rich. | Fred is not calm. | entailment | (((creative(paul)|brave(paul)))<=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(quiet(X)&~rich(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(((~quiet(paul)<~>patient(paul)))=>((brave(fred)&~kind(fred))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((tall(X)|happy(X))=>~wise(X)))&
(![X]:((strong(X)|~rich(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((calm(X)|generous(X))=>(wise(X)|~creative(X))))&
(![X]:((rich(X)|curious(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((humble(X)|~rich(X))=>(old(X)<~>~funny(X))))&
(![X]:((~funny(X)|patient(X))<=>~old(X)))&
(((~quiet(fred)<~>generous(fred)))<=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:(~funny(X)=>(tall(X)&~patient(X))))&
((happy(paul))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(generous(X)=>(wise(X)|~calm(X))))&
(?[X]:((patient(X)|tall(X))))&
((curious(john)<~>tall(john)))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~wise(X)|rich(X))))&
((happy(fred)&~old(fred)))&
((old(paul)|rich(paul))) | ~calm(fred) | [
"p2",
"p8",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4374983663682790163651405
% SZS output start Proof for 4374983663682790163651405
3. ! [X0] : (~calm(X0) <=> ~patient(X0)) [input p2]
9. ! [X0] : ((curious(X0) | rich(X0)) <=> (~funny(X0) & ~brave(X0))) [input p8]
11. ! [X0] : ((~rich(X0) | humble(X0)) => (old(X0) <~> ~funny(X0))) [input p10]
14. ! [X0] : (~funny(X0) => (~patient(X0) & tall(X0))) [input p13]
21. ~old(fred) & happy(fred) [input p20]
23. calm(fred) [input hypothesis]
30. ! [X0] : ((old(X0) <~> ~funny(X0)) | (rich(X0) & ~humble(X0))) [ennf transformation 11]
31. ! [X0] : ((~patient(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
42. ! [X0] : ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))) [nnf transformation 3]
49. ! [X0] : (((curious(X0) | rich(X0)) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 9]
50. ! [X0] : ((curious(X0) | rich(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 49]
53. ! [X0] : (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (rich(X0) & ~humble(X0))) [nnf transformation 30]
80. ~calm(X0) | patient(X0) [cnf transformation 42]
97. ~funny(X0) | ~rich(X0) [cnf transformation 50]
107. ~funny(X0) | old(X0) | rich(X0) [cnf transformation 53]
120. ~patient(X0) | funny(X0) [cnf transformation 31]
130. ~old(fred) [cnf transformation 21]
132. calm(fred) [cnf transformation 23]
197. ~funny(X0) | old(X0) [subsumption resolution 107,97]
284. patient(fred) [resolution 80,132]
310. funny(fred) [resolution 120,284]
345. old(fred) [resolution 310,197]
351. $false [subsumption resolution 345,130]
% SZS output end Proof for 4374983663682790163651405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not funny then lucy is strong or kind and vice versa.
Everyone who is both patient and not creative is either not old or not patient and vice versa.
Everyone who is both not rich and not kind is humble or not old and vice versa.
If alice is both not brave and generous then susan is either old or not rich and vice versa.
If someone is not happy then someone is not kind or not brave and vice versa.
If paul is either strong or not brave then susan is funny or calm and vice versa.
Everyone who is both not rich and patient is brave.
If lucy is not old then john is either humble or funny and vice versa.
If someone is quiet then someone is either not calm or not funny.
If someone is not creative then someone is old or generous and vice versa.
Everyone who is either creative or not creative is either kind or not patient and vice versa.
Everyone who is not tall or not patient is either old or not tall and vice versa.
Everyone who is curious is tall or curious.
If someone is both not kind and curious then someone is either tall or not generous.
Everyone who is either calm or old is calm or wise.
If mary is both old and curious then someone is both not generous and not strong.
Lucy is not happy or humble.
Lucy is both curious and happy.
Someone is humble.
Someone is calm.
John is not old.
Someone is both not rich and curious.
Someone is both funny and humble. | Susan is rich. | contradiction | ((~funny(alice))<=>((strong(lucy)|kind(lucy))))&
(![X]:((patient(X)&~creative(X))<=>(~old(X)<~>~patient(X))))&
(![X]:((~rich(X)&~kind(X))<=>(humble(X)|~old(X))))&
(((~brave(alice)&generous(alice)))<=>((old(susan)<~>~rich(susan))))&
((?[X]:(~happy(X)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(((strong(paul)<~>~brave(paul)))<=>((funny(susan)|calm(susan))))&
(![X]:((~rich(X)&patient(X))=>brave(X)))&
((~old(lucy))<=>((humble(john)<~>funny(john))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((old(X)|generous(X)))))&
(![X]:((creative(X)<~>~creative(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((~tall(X)|~patient(X))<=>(old(X)<~>~tall(X))))&
(![X]:(curious(X)=>(tall(X)|curious(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>old(X))=>(calm(X)|wise(X))))&
(((old(mary)&curious(mary)))=>(?[X]:((~generous(X)&~strong(X)))))&
((~happy(lucy)|humble(lucy)))&
((curious(lucy)&happy(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
(~old(john))&
(?[X]:((~rich(X)&curious(X))))&
(?[X]:((funny(X)&humble(X)))) | rich(susan) | [
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 556842426538354198012731
% SZS output start Proof for 556842426538354198012731
2. ! [X0] : ((~creative(X0) & patient(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p1]
3. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~old(X0) | humble(X0))) [input p2]
12. ! [X0] : ((~patient(X0) | ~tall(X0)) <=> (old(X0) <~> ~tall(X0))) [input p11]
24. rich(susan) [input hypothesis]
40. ! [X0] : (((~creative(X0) & patient(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (creative(X0) | ~patient(X0)))) [nnf transformation 2]
41. ! [X0] : (((~creative(X0) & patient(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | creative(X0) | ~patient(X0))) [flattening 40]
42. ! [X0] : (((~kind(X0) & ~rich(X0)) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 3]
43. ! [X0] : (((~kind(X0) & ~rich(X0)) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | kind(X0) | rich(X0))) [flattening 42]
60. ! [X0] : (((~patient(X0) | ~tall(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (patient(X0) & tall(X0)))) [nnf transformation 12]
61. ! [X0] : ((~patient(X0) | ~tall(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (patient(X0) & tall(X0)))) [flattening 60]
82. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 41]
87. ~rich(X0) | old(X0) [cnf transformation 43]
123. tall(X0) | ~old(X0) | tall(X0) [cnf transformation 61]
125. ~patient(X0) | ~tall(X0) | ~tall(X0) | ~old(X0) [cnf transformation 61]
142. rich(susan) [cnf transformation 24]
143. tall(X0) | ~old(X0) [duplicate literal removal 123]
144. ~patient(X0) | ~tall(X0) | ~old(X0) [duplicate literal removal 125]
150. patient(X0) | ~old(X0) [duplicate literal removal 82]
179. 6 <=> rich(susan) [avatar definition]
180. rich(susan) <- (6) [avatar component clause 179]
263. 23 <=> ! [X1] : ~old(X1) [avatar definition]
264. ~old(X1) <- (23) [avatar component clause 263]
280. ~tall(X0) | ~old(X0) [subsumption resolution 144,150]
281. ~old(X0) [subsumption resolution 143,280]
282. 23 [avatar split clause 281,263]
325. 6 [avatar split clause 142,179]
335. old(susan) <- (6) [resolution 87,180]
336. $false <- (6, 23) [subsumption resolution 335,264]
337. ~6 | ~23 [avatar contradiction clause 336]
338. $false [avatar sat refutation 282,325,337]
% SZS output end Proof for 556842426538354198012731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not brave is tall.
If susan is both not happy and strong then fred is not old.
If someone is not humble or not quiet then someone is both strong and not wise and vice versa.
Everyone who is brave is not happy or patient and vice versa.
If someone is happy or kind then someone is not wise and vice versa.
Everyone who is either curious or calm is not quiet and vice versa.
Everyone who is either not patient or humble is both happy and not generous and vice versa.
Everyone who is not strong is not quiet or not old and vice versa.
Everyone who is humble is either not patient or not quiet.
If someone is not brave then someone is both not curious and creative and vice versa.
If someone is generous then fred is old or not generous and vice versa.
If john is either wise or not strong then someone is both not quiet and brave.
Everyone who is not curious is not old or not generous.
Everyone who is not patient or funny is wise.
Everyone who is funny is not wise and vice versa.
If someone is not quiet then someone is not wise.
Someone is rich.
Someone is not curious or not quiet.
Susan is not old or not tall.
Lucy is not strong.
Susan is creative.
Mary is quiet or not brave. | Mary is not old. | neutral | (![X]:((kind(X)<~>~brave(X))=>tall(X)))&
(((~happy(susan)&strong(susan)))=>(~old(fred)))&
((?[X]:((~humble(X)|~quiet(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(brave(X)<=>(~happy(X)|patient(X))))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:(~wise(X))))&
(![X]:((curious(X)<~>calm(X))<=>~quiet(X)))&
(![X]:((~patient(X)<~>humble(X))<=>(happy(X)&~generous(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~old(X))))&
(![X]:(humble(X)=>(~patient(X)<~>~quiet(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~curious(X)&creative(X)))))&
((?[X]:(generous(X)))<=>((old(fred)|~generous(fred))))&
(((wise(john)<~>~strong(john)))=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:(~curious(X)=>(~old(X)|~generous(X))))&
(![X]:((~patient(X)|funny(X))=>wise(X)))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(~wise(X))))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)|~quiet(X))))&
((~old(susan)|~tall(susan)))&
(~strong(lucy))&
(creative(susan))&
((quiet(mary)|~brave(mary))) | ~old(mary) | [] | null | 0 |
If someone is not old or not wise then lucy is both brave and quiet and vice versa.
If john is both quiet and brave then someone is either not old or happy.
Everyone who is both not creative and kind is not quiet or not humble.
Everyone who is both kind and not wise is either not kind or tall.
Everyone who is either not wise or not patient is either wise or not quiet and vice versa.
If someone is both not tall and brave then mary is kind or brave and vice versa.
If lucy is not funny then john is both creative and not quiet and vice versa.
If paul is both not humble and happy then paul is both creative and not patient and vice versa.
If fred is both wise and not rich then paul is both not generous and wise and vice versa.
Everyone who is both quiet and not old is both not old and humble and vice versa.
Everyone who is both not generous and not patient is not quiet.
Everyone who is either curious or old is either humble or not quiet and vice versa.
Everyone who is not happy or not quiet is both rich and old.
If someone is either calm or rich then someone is both wise and not creative and vice versa.
If someone is curious then john is quiet and vice versa.
Everyone who is both not quiet and not kind is generous and vice versa.
Mary is both not strong and brave.
Someone is either not brave or not creative.
Someone is not quiet.
Susan is happy.
Paul is wise or brave.
Someone is kind or patient. | Lucy is not quiet. | entailment | ((?[X]:((~old(X)|~wise(X))))<=>((brave(lucy)&quiet(lucy))))&
(((quiet(john)&brave(john)))=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~creative(X)&kind(X))=>(~quiet(X)|~humble(X))))&
(![X]:((kind(X)&~wise(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(wise(X)<~>~quiet(X))))&
((?[X]:((~tall(X)&brave(X))))<=>((kind(mary)|brave(mary))))&
((~funny(lucy))<=>((creative(john)&~quiet(john))))&
(((~humble(paul)&happy(paul)))<=>((creative(paul)&~patient(paul))))&
(((wise(fred)&~rich(fred)))<=>((~generous(paul)&wise(paul))))&
(![X]:((quiet(X)&~old(X))<=>(~old(X)&humble(X))))&
(![X]:((~generous(X)&~patient(X))=>~quiet(X)))&
(![X]:((curious(X)<~>old(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~happy(X)|~quiet(X))=>(rich(X)&old(X))))&
((?[X]:((calm(X)<~>rich(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
((?[X]:(curious(X)))<=>(quiet(john)))&
(![X]:((~quiet(X)&~kind(X))<=>generous(X)))&
((~strong(mary)&brave(mary)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:(~quiet(X)))&
(happy(susan))&
((wise(paul)|brave(paul)))&
(?[X]:((kind(X)|patient(X)))) | ~quiet(lucy) | [
"p4",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4438764639656215804782878
% SZS output start Proof for 4438764639656215804782878
5. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> (wise(X0) <~> ~quiet(X0))) [input p4]
11. ! [X0] : ((~patient(X0) & ~generous(X0)) => ~quiet(X0)) [input p10]
16. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> generous(X0)) [input p15]
23. quiet(lucy) [input hypothesis]
32. ! [X0] : (~quiet(X0) | (patient(X0) | generous(X0))) [ennf transformation 11]
33. ! [X0] : (~quiet(X0) | patient(X0) | generous(X0)) [flattening 32]
44. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 5]
68. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 16]
69. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | kind(X0) | quiet(X0))) [flattening 68]
87. ~quiet(X0) | wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 44]
90. quiet(X0) | ~wise(X0) | ~wise(X0) | patient(X0) [cnf transformation 44]
91. ~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 44]
94. patient(X0) | wise(X0) | wise(X0) | quiet(X0) [cnf transformation 44]
115. ~quiet(X0) | patient(X0) | generous(X0) [cnf transformation 33]
137. ~generous(X0) | ~quiet(X0) [cnf transformation 69]
146. quiet(lucy) [cnf transformation 23]
147. ~quiet(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 87]
148. quiet(X0) | ~wise(X0) | patient(X0) [duplicate literal removal 90]
149. ~patient(X0) | ~wise(X0) | ~quiet(X0) [duplicate literal removal 91]
150. patient(X0) | wise(X0) | quiet(X0) [duplicate literal removal 94]
157. 2 <=> quiet(lucy) [avatar definition]
158. quiet(lucy) <- (2) [avatar component clause 157]
197. patient(X0) | quiet(X0) [subsumption resolution 148,150]
198. ~patient(X0) | ~quiet(X0) [subsumption resolution 147,149]
274. generous(X0) | patient(X0) [subsumption resolution 115,197]
345. 2 [avatar split clause 146,157]
357. patient(X1) | ~quiet(X1) [resolution 274,137]
358. patient(X1) [subsumption resolution 357,197]
359. ~quiet(X0) [resolution 358,198]
412. $false <- (2) [resolution 359,158]
414. ~2 [avatar contradiction clause 412]
415. $false [avatar sat refutation 345,414]
% SZS output end Proof for 4438764639656215804782878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is old and vice versa. If someone is tall then someone is generous or calm and vice versa. Everyone who is brave is not patient or not wise. Everyone who is either generous or old is both rich and creative. Everyone who is kind is either kind or rich and vice versa. Everyone who is strong is either not kind or not quiet. Everyone who is both quiet and wise is both humble and not kind. Everyone who is not creative or not brave is both generous and curious and vice versa. Everyone who is either old or brave is wise or not creative and vice versa. If john is not brave then someone is not brave or not curious and vice versa. If someone is curious or not calm then someone is both happy and not old. Everyone who is not funny or old is either funny or not quiet. If someone is not tall then alice is either brave or not humble. If someone is not old then someone is either calm or kind and vice versa. If someone is both creative and funny then mary is brave or not rich. Everyone who is generous is not funny or tall and vice versa. Mary is not wise or not curious. Fred is both not happy and not patient. Paul is wise. Someone is strong. Mary is both not strong and humble. Someone is brave. Mary is not old or patient. | John is not generous. | contradiction | ((?[X]:(~rich(X)))<=>(?[X]:(old(X))))&
((?[X]:(tall(X)))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:(brave(X)=>(~patient(X)|~wise(X))))&
(![X]:((generous(X)<~>old(X))=>(rich(X)&creative(X))))&
(![X]:(kind(X)<=>(kind(X)<~>rich(X))))&
(![X]:(strong(X)=>(~kind(X)<~>~quiet(X))))&
(![X]:((quiet(X)&wise(X))=>(humble(X)&~kind(X))))&
(![X]:((~creative(X)|~brave(X))<=>(generous(X)&curious(X))))&
(![X]:((old(X)<~>brave(X))<=>(wise(X)|~creative(X))))&
((~brave(john))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:((curious(X)|~calm(X))))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((~funny(X)|old(X))=>(funny(X)<~>~quiet(X))))&
((?[X]:(~tall(X)))=>((brave(alice)<~>~humble(alice))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)<~>kind(X)))))&
((?[X]:((creative(X)&funny(X))))=>((brave(mary)|~rich(mary))))&
(![X]:(generous(X)<=>(~funny(X)|tall(X))))&
((~wise(mary)|~curious(mary)))&
((~happy(fred)&~patient(fred)))&
(wise(paul))&
(?[X]:(strong(X)))&
((~strong(mary)&humble(mary)))&
(?[X]:(brave(X)))&
((~old(mary)|patient(mary))) | ~generous(john) | [
"p0",
"p3",
"p4",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6440524585713312164697168
% SZS output start Proof for 6440524585713312164697168
1. ? [X0] : ~rich(X0) <=> ? [X0] : old(X0) [input p0]
4. ! [X0] : ((generous(X0) <~> old(X0)) => (creative(X0) & rich(X0))) [input p3]
5. ! [X0] : (kind(X0) <=> (kind(X0) <~> rich(X0))) [input p4]
8. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & generous(X0))) [input p7]
9. ! [X0] : ((old(X0) <~> brave(X0)) <=> (~creative(X0) | wise(X0))) [input p8]
10. ~brave(john) <=> ? [X0] : (~curious(X0) | ~brave(X0)) [input p9]
24. ~generous(john) [input hypothesis]
25. ? [X0] : ~rich(X0) <=> ? [X1] : old(X1) [rectify 1]
31. ! [X0] : ((creative(X0) & rich(X0)) | (generous(X0) <=> old(X0))) [ennf transformation 4]
40. (? [X0] : ~rich(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : rich(X0)) [nnf transformation 25]
41. (? [X0] : ~rich(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : rich(X3)) [rectify 40]
42. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
43. ? [X2] : old(X2) => old(sK1) [choice axiom]
44. (~rich(sK0) | ! [X1] : ~old(X1)) & (old(sK1) | ! [X3] : rich(X3)) [skolemisation 41,43,42]
50. ! [X0] : ((creative(X0) & rich(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) [nnf transformation 31]
51. ! [X0] : ((kind(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 5]
53. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 8]
54. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (brave(X0) & creative(X0)))) [flattening 53]
55. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [flattening 55]
57. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & (? [X0] : (~curious(X0) | ~brave(X0)) | brave(john)) [nnf transformation 10]
58. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & (? [X1] : (~curious(X1) | ~brave(X1)) | brave(john)) [rectify 57]
59. ? [X1] : (~curious(X1) | ~brave(X1)) => (~curious(sK4) | ~brave(sK4)) [choice axiom]
60. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & ((~curious(sK4) | ~brave(sK4)) | brave(john)) [skolemisation 58,59]
77. old(sK1) | rich(X3) [cnf transformation 44]
84. ~old(X0) | generous(X0) | rich(X0) [cnf transformation 50]
88. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 51]
90. kind(X0) | kind(X0) | ~rich(X0) [cnf transformation 51]
96. brave(X0) | generous(X0) [cnf transformation 54]
99. ~curious(X0) | ~creative(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 54]
105. ~brave(X0) | ~old(X0) | creative(X0) [cnf transformation 56]
107. ~brave(john) | brave(X0) [cnf transformation 60]
108. ~brave(john) | curious(X0) [cnf transformation 60]
136. ~generous(john) [cnf transformation 24]
138. ~rich(X0) | ~kind(X0) [duplicate literal removal 88]
139. ~rich(X0) | kind(X0) [duplicate literal removal 90]
149. 3 <=> ! [X3] : rich(X3) [avatar definition]
150. rich(X3) <- (3) [avatar component clause 149]
152. 4 <=> old(sK1) [avatar definition]
154. old(sK1) <- (4) [avatar component clause 152]
155. 3 | 4 [avatar split clause 77,152,149]
180. ~rich(X0) [subsumption resolution 138,139]
182. 11 <=> ! [X0] : curious(X0) [avatar definition]
183. curious(X0) <- (11) [avatar component clause 182]
185. 12 <=> brave(john) [avatar definition]
187. ~brave(john) <- (~12) [avatar component clause 185]
188. 11 | ~12 [avatar split clause 108,185,182]
190. 13 <=> ! [X0] : brave(X0) [avatar definition]
191. brave(X0) <- (13) [avatar component clause 190]
192. 13 | ~12 [avatar split clause 107,185,190]
280. $false <- (3) [subsumption resolution 150,180]
281. ~3 [avatar contradiction clause 280]
291. generous(john) <- (~12) [resolution 96,187]
293. $false <- (~12) [subsumption resolution 291,136]
294. 12 [avatar contradiction clause 293]
319. generous(sK1) | rich(sK1) <- (4) [resolution 84,154]
321. generous(sK1) <- (4) [subsumption resolution 319,180]
356. ~old(X0) | creative(X0) <- (13) [resolution 105,191]
368. creative(sK1) <- (4, 13) [resolution 356,154]
385. ~creative(X2) | ~brave(X2) | ~generous(X2) <- (11) [resolution 99,183]
386. ~creative(X2) | ~generous(X2) <- (11, 13) [subsumption resolution 385,191]
394. ~generous(sK1) <- (4, 11, 13) [resolution 386,368]
396. $false <- (4, 11, 13) [subsumption resolution 394,321]
397. ~4 | ~11 | ~13 [avatar contradiction clause 396]
400. $false [avatar sat refutation 155,188,192,281,294,397]
% SZS output end Proof for 6440524585713312164697168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both tall and not old then alice is either not humble or not wise.
Everyone who is either not patient or old is either not curious or calm.
If alice is either wise or not tall then paul is not old or quiet.
Everyone who is both wise and rich is not funny and vice versa.
Everyone who is either funny or not generous is not curious.
Everyone who is either strong or not humble is both not old and patient.
Everyone who is rich is strong or rich.
Everyone who is tall or brave is not patient or kind and vice versa.
Everyone who is both old and not generous is both not old and not calm and vice versa.
Everyone who is both not patient and not rich is both not happy and happy.
If someone is both rich and not old then alice is both happy and not curious.
Everyone who is not rich is both not happy and not humble and vice versa.
If mary is either wise or not brave then mary is both wise and funny.
Everyone who is not funny or tall is both rich and not rich.
Everyone who is both strong and not tall is strong.
If john is both not wise and not rich then someone is not happy and vice versa.
Mary is brave.
Someone is not strong.
Someone is either not creative or humble.
Paul is either not kind or not tall.
Fred is patient or not rich.
Fred is not wise or humble.
Lucy is not wise or not quiet. | Paul is not tall. | entailment | (((tall(paul)&~old(paul)))=>((~humble(alice)<~>~wise(alice))))&
(![X]:((~patient(X)<~>old(X))=>(~curious(X)<~>calm(X))))&
(((wise(alice)<~>~tall(alice)))=>((~old(paul)|quiet(paul))))&
(![X]:((wise(X)&rich(X))<=>~funny(X)))&
(![X]:((funny(X)<~>~generous(X))=>~curious(X)))&
(![X]:((strong(X)<~>~humble(X))=>(~old(X)&patient(X))))&
(![X]:(rich(X)=>(strong(X)|rich(X))))&
(![X]:((tall(X)|brave(X))<=>(~patient(X)|kind(X))))&
(![X]:((old(X)&~generous(X))<=>(~old(X)&~calm(X))))&
(![X]:((~patient(X)&~rich(X))=>(~happy(X)&happy(X))))&
((?[X]:((rich(X)&~old(X))))=>((happy(alice)&~curious(alice))))&
(![X]:(~rich(X)<=>(~happy(X)&~humble(X))))&
(((wise(mary)<~>~brave(mary)))=>((wise(mary)&funny(mary))))&
(![X]:((~funny(X)|tall(X))=>(rich(X)&~rich(X))))&
(![X]:((strong(X)&~tall(X))=>strong(X)))&
(((~wise(john)&~rich(john)))<=>(?[X]:(~happy(X))))&
(brave(mary))&
(?[X]:(~strong(X)))&
(?[X]:((~creative(X)<~>humble(X))))&
((~kind(paul)<~>~tall(paul)))&
((patient(fred)|~rich(fred)))&
((~wise(fred)|humble(fred)))&
((~wise(lucy)|~quiet(lucy))) | ~tall(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7456789784454729125791306
% SZS output start Proof for 7456789784454729125791306
14. ! [X0] : ((tall(X0) | ~funny(X0)) => (~rich(X0) & rich(X0))) [input p13]
24. tall(paul) [input hypothesis]
38. ! [X0] : ((~rich(X0) & rich(X0)) | (~tall(X0) & funny(X0))) [ennf transformation 14]
104. rich(X0) | ~tall(X0) [cnf transformation 38]
106. ~rich(X0) | ~tall(X0) [cnf transformation 38]
120. tall(paul) [cnf transformation 24]
182. ~tall(X0) [subsumption resolution 104,106]
232. $false [subsumption resolution 120,182]
% SZS output end Proof for 7456789784454729125791306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not patient is either not brave or not wise. If someone is not humble then mary is either funny or not brave and vice versa. If someone is old then someone is not calm and vice versa. Everyone who is patient or not happy is not brave and vice versa. Everyone who is both humble and not wise is both wise and humble and vice versa. Everyone who is quiet or creative is both funny and humble. If susan is not humble or old then someone is not quiet and vice versa. If someone is both not humble and generous then susan is generous and vice versa. If someone is rich or not old then someone is either not humble or not funny. If someone is either funny or not patient then someone is either wise or funny and vice versa. Everyone who is both rich and not kind is not calm and vice versa. Everyone who is either not wise or not curious is either brave or not wise and vice versa. If someone is not happy or not rich then lucy is old and vice versa. Everyone who is both brave and not quiet is tall or calm and vice versa. Everyone who is either funny or quiet is either not calm or not generous. John is either calm or strong. Someone is either not tall or not quiet. Someone is not strong or not brave. Someone is rich. John is both generous and not creative. John is both not curious and old. | Susan is not brave. | neutral | (![X]:((strong(X)|~patient(X))=>(~brave(X)<~>~wise(X))))&
((?[X]:(~humble(X)))<=>((funny(mary)<~>~brave(mary))))&
((?[X]:(old(X)))<=>(?[X]:(~calm(X))))&
(![X]:((patient(X)|~happy(X))<=>~brave(X)))&
(![X]:((humble(X)&~wise(X))<=>(wise(X)&humble(X))))&
(![X]:((quiet(X)|creative(X))=>(funny(X)&humble(X))))&
(((~humble(susan)|old(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~humble(X)&generous(X))))<=>(generous(susan)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~humble(X)<~>~funny(X)))))&
((?[X]:((funny(X)<~>~patient(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:((rich(X)&~kind(X))<=>~calm(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>(brave(X)<~>~wise(X))))&
((?[X]:((~happy(X)|~rich(X))))<=>(old(lucy)))&
(![X]:((brave(X)&~quiet(X))<=>(tall(X)|calm(X))))&
(![X]:((funny(X)<~>quiet(X))=>(~calm(X)<~>~generous(X))))&
((calm(john)<~>strong(john)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:(rich(X)))&
((generous(john)&~creative(john)))&
((~curious(john)&old(john))) | ~brave(susan) | [] | null | 0 |
If susan is both not generous and not curious then someone is rich and vice versa. If paul is not old then susan is both curious and old and vice versa. Everyone who is not patient is both not old and funny and vice versa. Everyone who is not funny is either tall or brave and vice versa. Everyone who is either not curious or rich is not patient and vice versa. Everyone who is not wise is not quiet or not generous. Everyone who is either brave or not patient is not kind or not wise and vice versa. If someone is both curious and humble then alice is either creative or old and vice versa. Everyone who is not rich is not old. Everyone who is both not strong and rich is either not generous or old. If alice is either old or not wise then john is both strong and brave. If someone is not creative or generous then mary is not quiet and vice versa. Everyone who is strong or brave is both not rich and tall. Someone is kind or not funny. Mary is either not rich or generous. Lucy is humble. Paul is not brave or brave. Fred is both not creative and humble. John is either not humble or not old. | John is generous. | neutral | (((~generous(susan)&~curious(susan)))<=>(?[X]:(rich(X))))&
((~old(paul))<=>((curious(susan)&old(susan))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:(~funny(X)<=>(tall(X)<~>brave(X))))&
(![X]:((~curious(X)<~>rich(X))<=>~patient(X)))&
(![X]:(~wise(X)=>(~quiet(X)|~generous(X))))&
(![X]:((brave(X)<~>~patient(X))<=>(~kind(X)|~wise(X))))&
((?[X]:((curious(X)&humble(X))))<=>((creative(alice)<~>old(alice))))&
(![X]:(~rich(X)=>~old(X)))&
(![X]:((~strong(X)&rich(X))=>(~generous(X)<~>old(X))))&
(((old(alice)<~>~wise(alice)))=>((strong(john)&brave(john))))&
((?[X]:((~creative(X)|generous(X))))<=>(~quiet(mary)))&
(![X]:((strong(X)|brave(X))=>(~rich(X)&tall(X))))&
(?[X]:((kind(X)|~funny(X))))&
((~rich(mary)<~>generous(mary)))&
(humble(lucy))&
((~brave(paul)|brave(paul)))&
((~creative(fred)&humble(fred)))&
((~humble(john)<~>~old(john))) | generous(john) | [] | null | 0 |
Everyone who is not happy is generous.
Everyone who is not quiet or funny is creative.
If paul is happy then someone is either wise or not funny.
If someone is not wise or old then someone is wise.
If someone is either not creative or rich then mary is both not patient and not happy.
Everyone who is creative is not strong.
If lucy is not wise then someone is both happy and not wise.
Everyone who is either not brave or old is both wise and strong and vice versa.
Everyone who is either not brave or not humble is both not strong and not calm and vice versa.
Everyone who is not quiet is either strong or old.
Everyone who is either old or not humble is not creative or not tall.
Everyone who is not brave is either creative or not strong and vice versa.
Everyone who is generous is both not funny and funny.
Everyone who is not tall is kind or strong.
If fred is not calm then mary is not patient or happy.
If someone is both not happy and not old then fred is not brave and vice versa.
Someone is not creative or kind.
Mary is either not humble or not brave.
Someone is either not strong or happy.
Someone is creative or not brave.
Someone is either not curious or not rich.
Someone is both not wise and happy.
Susan is either not tall or humble. | Susan is happy. | entailment | (![X]:(~happy(X)=>generous(X)))&
(![X]:((~quiet(X)|funny(X))=>creative(X)))&
((happy(paul))=>(?[X]:((wise(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:(wise(X))))&
((?[X]:((~creative(X)<~>rich(X))))=>((~patient(mary)&~happy(mary))))&
(![X]:(creative(X)=>~strong(X)))&
((~wise(lucy))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~brave(X)<~>old(X))<=>(wise(X)&strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>old(X))))&
(![X]:((old(X)<~>~humble(X))=>(~creative(X)|~tall(X))))&
(![X]:(~brave(X)<=>(creative(X)<~>~strong(X))))&
(![X]:(generous(X)=>(~funny(X)&funny(X))))&
(![X]:(~tall(X)=>(kind(X)|strong(X))))&
((~calm(fred))=>((~patient(mary)|happy(mary))))&
((?[X]:((~happy(X)&~old(X))))<=>(~brave(fred)))&
(?[X]:((~creative(X)|kind(X))))&
((~humble(mary)<~>~brave(mary)))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((~curious(X)<~>~rich(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~tall(susan)<~>humble(susan))) | happy(susan) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5330150451480570845782050
% SZS output start Proof for 5330150451480570845782050
1. ! [X0] : (~happy(X0) => generous(X0)) [input p0]
13. ! [X0] : (generous(X0) => (funny(X0) & ~funny(X0))) [input p12]
24. ~happy(susan) [input hypothesis]
32. ! [X0] : (generous(X0) | happy(X0)) [ennf transformation 1]
41. ! [X0] : ((funny(X0) & ~funny(X0)) | ~generous(X0)) [ennf transformation 13]
73. generous(X0) | happy(X0) [cnf transformation 32]
102. ~funny(X0) | ~generous(X0) [cnf transformation 41]
103. funny(X0) | ~generous(X0) [cnf transformation 41]
118. ~happy(susan) [cnf transformation 24]
173. ~generous(X0) [subsumption resolution 102,103]
241. happy(X0) [resolution 73,173]
244. $false [resolution 241,118]
% SZS output end Proof for 5330150451480570845782050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not old is not tall or rich. Everyone who is not happy or creative is patient or not rich. If john is both kind and not rich then someone is not wise. If paul is either not tall or tall then fred is either not old or not rich and vice versa. Everyone who is both calm and not patient is either patient or generous. Everyone who is either not rich or not quiet is either generous or not quiet and vice versa. If lucy is not tall or not humble then someone is humble. If someone is both not brave and not quiet then alice is not calm or not quiet. Everyone who is either not kind or not happy is not creative or not curious. If someone is not generous then someone is both not humble and not creative and vice versa. Everyone who is both humble and not strong is brave. Everyone who is both not strong and creative is both curious and not strong and vice versa. If paul is both not kind and not patient then someone is both quiet and not kind and vice versa. Everyone who is happy is not generous and vice versa. If mary is not strong then someone is tall. If someone is calm or kind then john is not happy and vice versa. Someone is wise. Someone is either calm or not rich. Someone is not wise or strong. Lucy is curious or patient. Fred is old. Paul is quiet. Fred is not creative. | Alice is not quiet. | neutral | (![X]:((strong(X)&~old(X))=>(~tall(X)|rich(X))))&
(![X]:((~happy(X)|creative(X))=>(patient(X)|~rich(X))))&
(((kind(john)&~rich(john)))=>(?[X]:(~wise(X))))&
(((~tall(paul)<~>tall(paul)))<=>((~old(fred)<~>~rich(fred))))&
(![X]:((calm(X)&~patient(X))=>(patient(X)<~>generous(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(generous(X)<~>~quiet(X))))&
(((~tall(lucy)|~humble(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((~brave(X)&~quiet(X))))=>((~calm(alice)|~quiet(alice))))&
(![X]:((~kind(X)<~>~happy(X))=>(~creative(X)|~curious(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:((humble(X)&~strong(X))=>brave(X)))&
(![X]:((~strong(X)&creative(X))<=>(curious(X)&~strong(X))))&
(((~kind(paul)&~patient(paul)))<=>(?[X]:((quiet(X)&~kind(X)))))&
(![X]:(happy(X)<=>~generous(X)))&
((~strong(mary))=>(?[X]:(tall(X))))&
((?[X]:((calm(X)|kind(X))))<=>(~happy(john)))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)<~>~rich(X))))&
(?[X]:((~wise(X)|strong(X))))&
((curious(lucy)|patient(lucy)))&
(old(fred))&
(quiet(paul))&
(~creative(fred)) | ~quiet(alice) | [] | null | 0 |
If someone is kind then someone is tall or kind and vice versa.
Everyone who is both curious and not rich is both not tall and happy and vice versa.
If someone is either funny or tall then someone is either quiet or not tall and vice versa.
Everyone who is not strong or rich is either wise or not patient and vice versa.
If someone is not kind then susan is both not generous and not creative.
If paul is either not brave or quiet then paul is calm and vice versa.
Everyone who is old or not creative is both not old and not strong.
Everyone who is creative is patient or kind and vice versa.
Everyone who is either patient or not curious is not calm.
Everyone who is both creative and old is not happy or not curious and vice versa.
If someone is not brave or patient then someone is either not brave or creative.
Everyone who is not funny or rich is either strong or not generous and vice versa.
If someone is either not tall or not generous then someone is either calm or not quiet.
If fred is both not tall and brave then someone is generous.
Everyone who is either wise or not wise is kind or not rich.
Everyone who is patient is either not humble or rich.
Someone is both not quiet and wise.
Someone is either happy or generous.
Someone is strong.
Someone is curious.
John is not funny or curious.
Someone is not old or not curious.
Someone is either funny or patient. | John is old. | contradiction | ((?[X]:(kind(X)))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:((curious(X)&~rich(X))<=>(~tall(X)&happy(X))))&
((?[X]:((funny(X)<~>tall(X))))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~strong(X)|rich(X))<=>(wise(X)<~>~patient(X))))&
((?[X]:(~kind(X)))=>((~generous(susan)&~creative(susan))))&
(((~brave(paul)<~>quiet(paul)))<=>(calm(paul)))&
(![X]:((old(X)|~creative(X))=>(~old(X)&~strong(X))))&
(![X]:(creative(X)<=>(patient(X)|kind(X))))&
(![X]:((patient(X)<~>~curious(X))=>~calm(X)))&
(![X]:((creative(X)&old(X))<=>(~happy(X)|~curious(X))))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:((~funny(X)|rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((~tall(X)<~>~generous(X))))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(((~tall(fred)&brave(fred)))=>(?[X]:(generous(X))))&
(![X]:((wise(X)<~>~wise(X))=>(kind(X)|~rich(X))))&
(![X]:(patient(X)=>(~humble(X)<~>rich(X))))&
(?[X]:((~quiet(X)&wise(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:(strong(X)))&
(?[X]:(curious(X)))&
((~funny(john)|curious(john)))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((funny(X)<~>patient(X)))) | old(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2143649014913850220595458
% SZS output start Proof for 2143649014913850220595458
7. ! [X0] : ((~creative(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p6]
24. old(john) [input hypothesis]
30. ! [X0] : ((~strong(X0) & ~old(X0)) | (creative(X0) & ~old(X0))) [ennf transformation 7]
114. ~old(X0) | ~old(X0) [cnf transformation 30]
157. old(john) [cnf transformation 24]
160. ~old(X0) [duplicate literal removal 114]
310. $false [subsumption resolution 157,160]
% SZS output end Proof for 2143649014913850220595458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not patient is either humble or not tall.
If someone is both creative and wise then someone is generous or quiet and vice versa.
If someone is both not calm and calm then someone is either humble or generous and vice versa.
If someone is not curious or not happy then susan is either not wise or not strong and vice versa.
Everyone who is funny is both not calm and generous and vice versa.
If alice is kind or not quiet then someone is brave.
Everyone who is either happy or strong is not tall and vice versa.
Everyone who is both calm and generous is both happy and not wise and vice versa.
Everyone who is not humble is curious or rich and vice versa.
If someone is either humble or not calm then paul is either generous or not kind and vice versa.
If alice is either not quiet or not patient then someone is both not strong and old and vice versa.
Everyone who is not kind or not calm is both creative and wise and vice versa.
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.
Someone is either kind or not happy.
Fred is not old or calm.
Fred is either brave or old.
Fred is not strong or creative.
Someone is either rich or humble.
Someone is tall or rich. | Alice is creative. | neutral | (![X]:((brave(X)<~>~patient(X))=>(humble(X)<~>~tall(X))))&
((?[X]:((creative(X)&wise(X))))<=>(?[X]:((generous(X)|quiet(X)))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((humble(X)<~>generous(X)))))&
((?[X]:((~curious(X)|~happy(X))))<=>((~wise(susan)<~>~strong(susan))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
(((kind(alice)|~quiet(alice)))=>(?[X]:(brave(X))))&
(![X]:((happy(X)<~>strong(X))<=>~tall(X)))&
(![X]:((calm(X)&generous(X))<=>(happy(X)&~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)|rich(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~quiet(alice)<~>~patient(alice)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~kind(X)|~calm(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]:((kind(X)<~>~happy(X))))&
((~old(fred)|calm(fred)))&
((brave(fred)<~>old(fred)))&
((~strong(fred)|creative(fred)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((tall(X)|rich(X)))) | creative(alice) | [] | null | 0 |
If someone is both not strong and not kind then mary is either calm or patient and vice versa.
Everyone who is either not quiet or generous is either not rich or calm.
If susan is funny or not rich then someone is not wise or generous.
Everyone who is not calm or funny is not tall and vice versa.
Everyone who is either not strong or old is either strong or brave and vice versa.
If paul is either not old or not patient then someone is calm.
Everyone who is creative or not brave is curious.
Everyone who is humble is both not strong and curious and vice versa.
Everyone who is either not strong or not creative is both calm and humble and vice versa.
If susan is humble or not old then paul is not brave.
Everyone who is quiet is either strong or not humble and vice versa.
Everyone who is happy or not brave is either not curious or not wise and vice versa.
Everyone who is both not quiet and not brave is not generous or not wise and vice versa.
If mary is either not tall or not wise then fred is not kind or brave and vice versa.
Everyone who is quiet is old or not brave.
Everyone who is not happy or brave is humble and vice versa.
Someone is humble or generous.
Paul is either creative or not wise.
Someone is rich.
Someone is funny or not generous.
Someone is calm.
John is either not old or not strong.
Someone is either kind or happy.
John is both kind and generous. | John is happy. | contradiction | ((?[X]:((~strong(X)&~kind(X))))<=>((calm(mary)<~>patient(mary))))&
(![X]:((~quiet(X)<~>generous(X))=>(~rich(X)<~>calm(X))))&
(((funny(susan)|~rich(susan)))=>(?[X]:((~wise(X)|generous(X)))))&
(![X]:((~calm(X)|funny(X))<=>~tall(X)))&
(![X]:((~strong(X)<~>old(X))<=>(strong(X)<~>brave(X))))&
(((~old(paul)<~>~patient(paul)))=>(?[X]:(calm(X))))&
(![X]:((creative(X)|~brave(X))=>curious(X)))&
(![X]:(humble(X)<=>(~strong(X)&curious(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>(calm(X)&humble(X))))&
(((humble(susan)|~old(susan)))=>(~brave(paul)))&
(![X]:(quiet(X)<=>(strong(X)<~>~humble(X))))&
(![X]:((happy(X)|~brave(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(~generous(X)|~wise(X))))&
(((~tall(mary)<~>~wise(mary)))<=>((~kind(fred)|brave(fred))))&
(![X]:(quiet(X)=>(old(X)|~brave(X))))&
(![X]:((~happy(X)|brave(X))<=>humble(X)))&
(?[X]:((humble(X)|generous(X))))&
((creative(paul)<~>~wise(paul)))&
(?[X]:(rich(X)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>~strong(john)))&
(?[X]:((kind(X)<~>happy(X))))&
((kind(john)&generous(john))) | happy(john) | [
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4446543503579799682760259
% SZS output start Proof for 4446543503579799682760259
5. ! [X0] : ((~strong(X0) <~> old(X0)) <=> (strong(X0) <~> brave(X0))) [input p4]
7. ! [X0] : ((~brave(X0) | creative(X0)) => curious(X0)) [input p6]
8. ! [X0] : (humble(X0) <=> (curious(X0) & ~strong(X0))) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> (humble(X0) & calm(X0))) [input p8]
12. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~curious(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (~wise(X0) | ~generous(X0))) [input p12]
16. ! [X0] : ((brave(X0) | ~happy(X0)) <=> humble(X0)) [input p15]
22. ~old(john) <~> ~strong(john) [input p21]
25. happy(john) [input hypothesis]
29. ! [X0] : (curious(X0) | (brave(X0) & ~creative(X0))) [ennf transformation 7]
42. ! [X0] : ((((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0))))) [nnf transformation 5]
46. ! [X0] : ((humble(X0) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | ~humble(X0))) [nnf transformation 8]
47. ! [X0] : ((humble(X0) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | ~humble(X0))) [flattening 46]
48. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | (~humble(X0) | ~calm(X0))) & ((humble(X0) & calm(X0)) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 9]
49. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ~humble(X0) | ~calm(X0)) & ((humble(X0) & calm(X0)) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [flattening 48]
51. ! [X0] : (((~brave(X0) | happy(X0)) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0)))) & (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | (brave(X0) & ~happy(X0)))) [nnf transformation 12]
52. ! [X0] : ((~brave(X0) | happy(X0) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0)))) & (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | (brave(X0) & ~happy(X0)))) [flattening 51]
53. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & ((~wise(X0) | ~generous(X0)) | (brave(X0) | quiet(X0)))) [nnf transformation 13]
54. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & (~wise(X0) | ~generous(X0) | brave(X0) | quiet(X0))) [flattening 53]
57. ! [X0] : (((brave(X0) | ~happy(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 16]
58. ! [X0] : ((brave(X0) | ~happy(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & happy(X0)))) [flattening 57]
68. (strong(john) | old(john)) & (~strong(john) | ~old(john)) [nnf transformation 22]
87. brave(X0) | strong(X0) | old(X0) | strong(X0) [cnf transformation 42]
90. ~brave(X0) | ~strong(X0) | ~strong(X0) | ~old(X0) [cnf transformation 42]
91. old(X0) | ~strong(X0) | brave(X0) | ~strong(X0) [cnf transformation 42]
94. ~old(X0) | strong(X0) | strong(X0) | ~brave(X0) [cnf transformation 42]
97. ~creative(X0) | curious(X0) [cnf transformation 29]
98. curious(X0) | brave(X0) [cnf transformation 29]
99. ~humble(X0) | ~strong(X0) [cnf transformation 47]
101. ~curious(X0) | humble(X0) | strong(X0) [cnf transformation 47]
105. humble(X0) | ~strong(X0) | creative(X0) [cnf transformation 49]
114. ~happy(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 52]
124. ~brave(X0) | wise(X0) [cnf transformation 54]
133. ~brave(X0) | humble(X0) [cnf transformation 58]
134. ~happy(X0) | brave(X0) | ~humble(X0) [cnf transformation 58]
141. ~strong(john) | ~old(john) [cnf transformation 68]
142. strong(john) | old(john) [cnf transformation 68]
147. happy(john) [cnf transformation 25]
148. brave(X0) | strong(X0) | old(X0) [duplicate literal removal 87]
149. ~brave(X0) | ~strong(X0) | ~old(X0) [duplicate literal removal 90]
150. ~strong(X0) | old(X0) | brave(X0) [duplicate literal removal 91]
151. ~brave(X0) | strong(X0) | ~old(X0) [duplicate literal removal 94]
195. ~brave(X0) | ~old(X0) [subsumption resolution 149,151]
196. brave(X0) | old(X0) [subsumption resolution 148,150]
212. ~strong(X0) | creative(X0) [subsumption resolution 105,99]
283. 26 <=> old(john) [avatar definition]
284. ~old(john) <- (~26) [avatar component clause 283]
285. old(john) <- (26) [avatar component clause 283]
287. 27 <=> strong(john) [avatar definition]
288. ~strong(john) <- (~27) [avatar component clause 287]
289. strong(john) <- (27) [avatar component clause 287]
290. 26 | 27 [avatar split clause 142,287,283]
291. ~26 | ~27 [avatar split clause 141,287,283]
312. old(X2) | wise(X2) [resolution 196,124]
333. humble(X0) | strong(X0) | brave(X0) [resolution 101,98]
336. humble(X0) | strong(X0) [subsumption resolution 333,133]
343. ~curious(john) | ~wise(john) [resolution 114,147]
346. 32 <=> wise(john) [avatar definition]
350. 33 <=> curious(john) [avatar definition]
353. ~32 | ~33 [avatar split clause 343,350,346]
360. brave(john) | ~humble(john) [resolution 134,147]
371. wise(john) <- (~26) [resolution 284,312]
373. creative(john) <- (27) [resolution 289,212]
378. curious(john) <- (27) [resolution 373,97]
381. 32 | 26 [avatar split clause 371,283,346]
383. 34 <=> humble(john) [avatar definition]
385. ~humble(john) <- (~34) [avatar component clause 383]
387. 35 <=> brave(john) [avatar definition]
389. brave(john) <- (35) [avatar component clause 387]
390. ~34 | 35 [avatar split clause 360,387,383]
391. 33 | ~27 [avatar split clause 378,287,350]
502. strong(john) <- (~34) [resolution 336,385]
505. $false <- (~27, ~34) [subsumption resolution 502,288]
506. 27 | 34 [avatar contradiction clause 505]
512. ~old(john) <- (35) [resolution 389,195]
519. $false <- (26, 35) [subsumption resolution 512,285]
520. ~26 | ~35 [avatar contradiction clause 519]
523. $false [avatar sat refutation 290,291,353,381,390,391,506,520]
% SZS output end Proof for 4446543503579799682760259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not wise is either not generous or not curious and vice versa.
If lucy is both tall and wise then lucy is both not patient and generous.
Everyone who is strong or not curious is curious or not creative and vice versa.
Everyone who is either creative or not old is either strong or humble and vice versa.
If lucy is humble then someone is either not kind or creative and vice versa.
Everyone who is either not strong or curious is either not curious or wise and vice versa.
If susan is not funny or creative then paul is calm and vice versa.
If someone is not brave or not kind then alice is not quiet and vice versa.
If alice is either patient or brave then someone is both patient and quiet.
Everyone who is not quiet is either creative or patient.
Everyone who is not generous is both funny and strong and vice versa.
Everyone who is curious or strong is either not brave or not tall and vice versa.
If alice is not kind then someone is creative or brave.
If someone is not rich or happy then mary is not happy or not calm.
If susan is not wise then mary is both not calm and brave.
Everyone who is curious or funny is either quiet or happy.
John is curious or not brave.
Someone is not tall or not quiet.
Lucy is both not old and patient.
Fred is either wise or not generous.
Lucy is not brave or funny.
Someone is curious or not calm.
Someone is not humble or curious.
Someone is curious or not quiet. | Fred is not funny. | entailment | (![X]:((brave(X)<~>~wise(X))<=>(~generous(X)<~>~curious(X))))&
(((tall(lucy)&wise(lucy)))=>((~patient(lucy)&generous(lucy))))&
(![X]:((strong(X)|~curious(X))<=>(curious(X)|~creative(X))))&
(![X]:((creative(X)<~>~old(X))<=>(strong(X)<~>humble(X))))&
((humble(lucy))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:((~strong(X)<~>curious(X))<=>(~curious(X)<~>wise(X))))&
(((~funny(susan)|creative(susan)))<=>(calm(paul)))&
((?[X]:((~brave(X)|~kind(X))))<=>(~quiet(alice)))&
(((patient(alice)<~>brave(alice)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:(~quiet(X)=>(creative(X)<~>patient(X))))&
(![X]:(~generous(X)<=>(funny(X)&strong(X))))&
(![X]:((curious(X)|strong(X))<=>(~brave(X)<~>~tall(X))))&
((~kind(alice))=>(?[X]:((creative(X)|brave(X)))))&
((?[X]:((~rich(X)|happy(X))))=>((~happy(mary)|~calm(mary))))&
((~wise(susan))=>((~calm(mary)&brave(mary))))&
(![X]:((curious(X)|funny(X))=>(quiet(X)<~>happy(X))))&
((curious(john)|~brave(john)))&
(?[X]:((~tall(X)|~quiet(X))))&
((~old(lucy)&patient(lucy)))&
((wise(fred)<~>~generous(fred)))&
((~brave(lucy)|funny(lucy)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:((curious(X)|~quiet(X)))) | ~funny(fred) | [
"p2",
"p5",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7440531209055910414507996
% SZS output start Proof for 7440531209055910414507996
3. ! [X0] : ((~curious(X0) | strong(X0)) <=> (~creative(X0) | curious(X0))) [input p2]
6. ! [X0] : ((~strong(X0) <~> curious(X0)) <=> (~curious(X0) <~> wise(X0))) [input p5]
11. ! [X0] : (~generous(X0) <=> (strong(X0) & funny(X0))) [input p10]
20. wise(fred) <~> ~generous(fred) [input p19]
25. funny(fred) [input hypothesis]
37. ! [X0] : (((~curious(X0) | strong(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (curious(X0) & ~strong(X0)))) [nnf transformation 3]
38. ! [X0] : ((~curious(X0) | strong(X0) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | (curious(X0) & ~strong(X0)))) [flattening 37]
44. ! [X0] : ((((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0))))) [nnf transformation 6]
55. ! [X0] : ((~generous(X0) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | generous(X0))) [nnf transformation 11]
56. ! [X0] : ((~generous(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | generous(X0))) [flattening 55]
64. (generous(fred) | ~wise(fred)) & (~generous(fred) | wise(fred)) [nnf transformation 20]
83. ~curious(X0) | strong(X0) | ~curious(X0) [cnf transformation 38]
98. wise(X0) | ~curious(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 44]
99. ~wise(X0) | curious(X0) | curious(X0) | strong(X0) [cnf transformation 44]
101. curious(X0) | ~strong(X0) | wise(X0) | curious(X0) [cnf transformation 44]
118. strong(X0) | generous(X0) [cnf transformation 56]
119. ~funny(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 56]
138. ~generous(fred) | wise(fred) [cnf transformation 64]
139. generous(fred) | ~wise(fred) [cnf transformation 64]
144. funny(fred) [cnf transformation 25]
145. wise(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 98]
146. ~wise(X0) | curious(X0) | strong(X0) [duplicate literal removal 99]
147. curious(X0) | ~strong(X0) | wise(X0) [duplicate literal removal 101]
150. ~curious(X0) | strong(X0) [duplicate literal removal 83]
191. ~wise(X0) | strong(X0) [subsumption resolution 146,150]
192. ~strong(X0) | wise(X0) [subsumption resolution 145,147]
306. 34 <=> wise(fred) [avatar definition]
307. wise(fred) <- (34) [avatar component clause 306]
308. ~wise(fred) <- (~34) [avatar component clause 306]
310. 35 <=> generous(fred) [avatar definition]
311. ~generous(fred) <- (~35) [avatar component clause 310]
312. generous(fred) <- (35) [avatar component clause 310]
313. ~34 | 35 [avatar split clause 139,310,306]
314. 34 | ~35 [avatar split clause 138,310,306]
353. generous(X0) | wise(X0) [resolution 192,118]
355. wise(fred) <- (~35) [resolution 353,311]
356. $false <- (~34, ~35) [subsumption resolution 355,308]
357. 34 | 35 [avatar contradiction clause 356]
358. strong(fred) <- (34) [resolution 307,191]
393. ~strong(fred) | ~generous(fred) [resolution 119,144]
395. ~generous(fred) <- (34) [subsumption resolution 393,358]
396. $false <- (34, 35) [subsumption resolution 395,312]
397. ~34 | ~35 [avatar contradiction clause 396]
398. $false [avatar sat refutation 313,314,357,397]
% SZS output end Proof for 7440531209055910414507996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either creative or patient.
If someone is both kind and humble then someone is not brave or rich.
If alice is tall or rich then fred is either rich or not calm.
Everyone who is old or tall is both tall and not strong and vice versa.
Everyone who is not tall is either curious or happy and vice versa.
Everyone who is both not curious and tall is kind or rich and vice versa.
If someone is quiet then lucy is calm or not calm.
If someone is both not quiet and not curious then susan is rich or not generous and vice versa.
Everyone who is wise or not strong is humble.
If fred is both tall and brave then someone is not quiet.
If someone is both not strong and strong then john is happy.
If susan is both not creative and patient then lucy is not creative or not strong and vice versa.
Everyone who is both happy and wise is kind and vice versa.
If someone is not happy then someone is either not generous or creative and vice versa.
If mary is brave or not funny then someone is kind.
If alice is either not happy or not tall then paul is either not patient or quiet and vice versa.
Someone is not brave or not tall.
Someone is both not brave and humble.
John is either wise or not funny.
Fred is curious.
Someone is not humble.
Paul is creative.
Someone is either not old or not funny.
Susan is either old or not strong. | Mary is not brave. | entailment | (![X]:(funny(X)=>(creative(X)<~>patient(X))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(((tall(alice)|rich(alice)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&~strong(X))))&
(![X]:(~tall(X)<=>(curious(X)<~>happy(X))))&
(![X]:((~curious(X)&tall(X))<=>(kind(X)|rich(X))))&
((?[X]:(quiet(X)))=>((calm(lucy)|~calm(lucy))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((rich(susan)|~generous(susan))))&
(![X]:((wise(X)|~strong(X))=>humble(X)))&
(((tall(fred)&brave(fred)))=>(?[X]:(~quiet(X))))&
((?[X]:((~strong(X)&strong(X))))=>(happy(john)))&
(((~creative(susan)&patient(susan)))<=>((~creative(lucy)|~strong(lucy))))&
(![X]:((happy(X)&wise(X))<=>kind(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((~generous(X)<~>creative(X)))))&
(((brave(mary)|~funny(mary)))=>(?[X]:(kind(X))))&
(((~happy(alice)<~>~tall(alice)))<=>((~patient(paul)<~>quiet(paul))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~brave(X)&humble(X))))&
((wise(john)<~>~funny(john)))&
(curious(fred))&
(?[X]:(~humble(X)))&
(creative(paul))&
(?[X]:((~old(X)<~>~funny(X))))&
((old(susan)<~>~strong(susan))) | ~brave(mary) | [
"p4",
"p5",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3260004071429916751996858
% SZS output start Proof for 3260004071429916751996858
5. ! [X0] : (~tall(X0) <=> (curious(X0) <~> happy(X0))) [input p4]
6. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (rich(X0) | kind(X0))) [input p5]
13. ! [X0] : ((wise(X0) & happy(X0)) <=> kind(X0)) [input p12]
15. (~funny(mary) | brave(mary)) => ? [X0] : kind(X0) [input p14]
25. brave(mary) [input hypothesis]
37. ? [X0] : kind(X0) | (funny(mary) & ~brave(mary)) [ennf transformation 15]
45. ! [X0] : ((~tall(X0) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | tall(X0))) [nnf transformation 5]
46. ! [X0] : (((tall(X0) & ~curious(X0)) | (~rich(X0) & ~kind(X0))) & ((rich(X0) | kind(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 6]
47. ! [X0] : (((tall(X0) & ~curious(X0)) | (~rich(X0) & ~kind(X0))) & (rich(X0) | kind(X0) | ~tall(X0) | curious(X0))) [flattening 46]
57. ! [X0] : (((wise(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | (~wise(X0) | ~happy(X0)))) [nnf transformation 13]
58. ! [X0] : (((wise(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | ~wise(X0) | ~happy(X0))) [flattening 57]
64. ? [X0] : kind(X0) => kind(sK5) [choice axiom]
65. kind(sK5) | (funny(mary) & ~brave(mary)) [skolemisation 37,64]
93. ~happy(X0) | curious(X0) | ~tall(X0) [cnf transformation 45]
95. ~curious(X0) | ~kind(X0) [cnf transformation 47]
97. ~kind(X0) | tall(X0) [cnf transformation 47]
115. ~kind(X0) | happy(X0) [cnf transformation 58]
121. kind(sK5) | ~brave(mary) [cnf transformation 65]
143. brave(mary) [cnf transformation 25]
264. 27 <=> kind(sK5) [avatar definition]
266. kind(sK5) <- (27) [avatar component clause 264]
269. 28 <=> brave(mary) [avatar definition]
272. ~28 | 27 [avatar split clause 121,264,269]
324. 28 [avatar split clause 143,269]
328. tall(sK5) <- (27) [resolution 97,266]
332. happy(sK5) <- (27) [resolution 115,266]
376. curious(sK5) | ~tall(sK5) <- (27) [resolution 93,332]
379. curious(sK5) <- (27) [subsumption resolution 376,328]
440. ~kind(sK5) <- (27) [resolution 379,95]
441. $false <- (27) [subsumption resolution 440,266]
442. ~27 [avatar contradiction clause 441]
443. $false [avatar sat refutation 272,324,442]
% SZS output end Proof for 3260004071429916751996858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not humble is not curious and vice versa.
If someone is both not old and not funny then someone is either not funny or wise and vice versa.
Everyone who is either not patient or not strong is happy or funny.
Everyone who is both not kind and tall is both happy and tall and vice versa.
If someone is both not happy and happy then someone is quiet and vice versa.
Everyone who is generous or old is not happy or not brave and vice versa.
If someone is not rich then someone is either patient or funny and vice versa.
If lucy is both not humble and not generous then someone is not wise or patient and vice versa.
If lucy is both not funny and kind then alice is patient or rich.
Everyone who is either not generous or not patient is both strong and happy and vice versa.
Everyone who is brave is either not kind or not tall and vice versa.
If someone is either not humble or not rich then someone is not funny and vice versa.
If susan is not quiet or happy then someone is both strong and not calm.
Everyone who is humble or strong is either curious or not rich.
Everyone who is not happy is not curious or old.
Everyone who is both rich and wise is either not tall or not humble and vice versa.
Someone is either wise or creative.
Someone is not wise or rich.
John is wise.
Someone is curious.
Someone is either brave or patient.
Susan is both funny and not creative.
Lucy is strong or not rich. | Alice is wise. | neutral | (![X]:((~creative(X)|~humble(X))<=>~curious(X)))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(![X]:((~patient(X)<~>~strong(X))=>(happy(X)|funny(X))))&
(![X]:((~kind(X)&tall(X))<=>(happy(X)&tall(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|old(X))<=>(~happy(X)|~brave(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:((~wise(X)|patient(X)))))&
(((~funny(lucy)&kind(lucy)))=>((patient(alice)|rich(alice))))&
(![X]:((~generous(X)<~>~patient(X))<=>(strong(X)&happy(X))))&
(![X]:(brave(X)<=>(~kind(X)<~>~tall(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:(~funny(X))))&
(((~quiet(susan)|happy(susan)))=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~curious(X)|old(X))))&
(![X]:((rich(X)&wise(X))<=>(~tall(X)<~>~humble(X))))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((~wise(X)|rich(X))))&
(wise(john))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((funny(susan)&~creative(susan)))&
((strong(lucy)|~rich(lucy))) | wise(alice) | [] | null | 0 |
Everyone who is both not strong and patient is humble.
If someone is not old then someone is not curious or happy and vice versa.
Everyone who is either not quiet or patient is brave or quiet.
Everyone who is both patient and wise is not old.
If someone is not happy or not generous then someone is kind or not humble and vice versa.
If someone is either not kind or quiet then paul is either humble or not wise.
If someone is either not creative or wise then paul is not wise or funny.
Everyone who is either not patient or quiet is both patient and not quiet and vice versa.
Everyone who is happy or humble is both generous and not calm.
If paul is either not old or brave then susan is either patient or not generous.
Everyone who is curious or not funny is not patient or generous and vice versa.
If susan is both funny and not generous then alice is either calm or not generous.
If someone is humble or not old then paul is both patient and curious and vice versa.
Everyone who is not funny is wise.
Everyone who is both not happy and tall is patient or not brave.
Someone is both not humble and not funny.
Someone is not happy or not wise.
Someone is quiet.
Someone is either not kind or old.
Susan is not funny.
Someone is rich or old.
Fred is not humble.
Fred is either not strong or not curious. | Alice is old. | entailment | (![X]:((~strong(X)&patient(X))=>humble(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)|happy(X)))))&
(![X]:((~quiet(X)<~>patient(X))=>(brave(X)|quiet(X))))&
(![X]:((patient(X)&wise(X))=>~old(X)))&
((?[X]:((~happy(X)|~generous(X))))<=>(?[X]:((kind(X)|~humble(X)))))&
((?[X]:((~kind(X)<~>quiet(X))))=>((humble(paul)<~>~wise(paul))))&
((?[X]:((~creative(X)<~>wise(X))))=>((~wise(paul)|funny(paul))))&
(![X]:((~patient(X)<~>quiet(X))<=>(patient(X)&~quiet(X))))&
(![X]:((happy(X)|humble(X))=>(generous(X)&~calm(X))))&
(((~old(paul)<~>brave(paul)))=>((patient(susan)<~>~generous(susan))))&
(![X]:((curious(X)|~funny(X))<=>(~patient(X)|generous(X))))&
(((funny(susan)&~generous(susan)))=>((calm(alice)<~>~generous(alice))))&
((?[X]:((humble(X)|~old(X))))<=>((patient(paul)&curious(paul))))&
(![X]:(~funny(X)=>wise(X)))&
(![X]:((~happy(X)&tall(X))=>(patient(X)|~brave(X))))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~funny(susan))&
(?[X]:((rich(X)|old(X))))&
(~humble(fred))&
((~strong(fred)<~>~curious(fred))) | old(alice) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8141130772207769765761479
% SZS output start Proof for 8141130772207769765761479
8. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (~quiet(X0) & patient(X0))) [input p7]
13. ? [X0] : (~old(X0) | humble(X0)) <=> (curious(paul) & patient(paul)) [input p12]
24. ~old(alice) [input hypothesis]
56. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (quiet(X0) | ~patient(X0))) & ((~quiet(X0) & patient(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 8]
57. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | quiet(X0) | ~patient(X0)) & ((~quiet(X0) & patient(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 56]
62. (? [X0] : (~old(X0) | humble(X0)) | (~curious(paul) | ~patient(paul))) & ((curious(paul) & patient(paul)) | ! [X0] : (old(X0) & ~humble(X0))) [nnf transformation 13]
63. (? [X0] : (~old(X0) | humble(X0)) | ~curious(paul) | ~patient(paul)) & ((curious(paul) & patient(paul)) | ! [X0] : (old(X0) & ~humble(X0))) [flattening 62]
64. (? [X0] : (~old(X0) | humble(X0)) | ~curious(paul) | ~patient(paul)) & ((curious(paul) & patient(paul)) | ! [X1] : (old(X1) & ~humble(X1))) [rectify 63]
65. ? [X0] : (~old(X0) | humble(X0)) => (~old(sK4) | humble(sK4)) [choice axiom]
66. ((~old(sK4) | humble(sK4)) | ~curious(paul) | ~patient(paul)) & ((curious(paul) & patient(paul)) | ! [X1] : (old(X1) & ~humble(X1))) [skolemisation 64,65]
97. ~quiet(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 57]
98. quiet(X0) | ~patient(X0) | quiet(X0) | ~patient(X0) [cnf transformation 57]
115. patient(paul) | old(X1) [cnf transformation 66]
130. ~old(alice) [cnf transformation 24]
132. ~quiet(X0) | ~patient(X0) [duplicate literal removal 97]
133. quiet(X0) | ~patient(X0) [duplicate literal removal 98]
148. 4 <=> ! [X3] : old(X3) [avatar definition]
149. old(X3) <- (4) [avatar component clause 148]
221. ~patient(X0) [subsumption resolution 132,133]
263. old(X1) [subsumption resolution 115,221]
264. 4 [avatar split clause 263,148]
299. $false <- (4) [resolution 149,130]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 264,300]
% SZS output end Proof for 8141130772207769765761479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not brave is either not happy or wise.
If someone is not brave then lucy is tall.
Everyone who is either not happy or not brave is either not rich or not tall and vice versa.
Everyone who is patient is both not kind and humble and vice versa.
Everyone who is tall or not rich is strong.
If someone is not patient then someone is either creative or not generous.
Everyone who is not generous is not wise.
Everyone who is both not rich and tall is not generous.
Everyone who is either not funny or rich is patient.
Everyone who is both kind and not generous is either not calm or rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is creative is either rich or not quiet and vice versa.
If someone is kind or not happy then someone is both not generous and not humble and vice versa.
Everyone who is either generous or strong is both not wise and not brave and vice versa.
Everyone who is both curious and not wise is not generous and vice versa.
Everyone who is both generous and not brave is both not wise and not humble and vice versa.
John is either not happy or not curious.
Alice is wise.
Someone is both not calm and generous.
Someone is both not brave and not curious.
Alice is both happy and not rich.
Someone is either not patient or not curious.
Someone is either quiet or not creative. | Lucy is not wise. | contradiction | (![X]:((humble(X)&~brave(X))=>(~happy(X)<~>wise(X))))&
((?[X]:(~brave(X)))=>(tall(lucy)))&
(![X]:((~happy(X)<~>~brave(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(![X]:((generous(X)&~brave(X))<=>(~wise(X)&~humble(X))))&
((~happy(john)<~>~curious(john)))&
(wise(alice))&
(?[X]:((~calm(X)&generous(X))))&
(?[X]:((~brave(X)&~curious(X))))&
((happy(alice)&~rich(alice)))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:((quiet(X)<~>~creative(X)))) | ~wise(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4489409461214739420940442
% SZS output start Proof for 4489409461214739420940442
1. ! [X0] : ((~brave(X0) & humble(X0)) => (~happy(X0) <~> wise(X0))) [input p0]
2. ? [X0] : ~brave(X0) => tall(lucy) [input p1]
4. ! [X0] : (patient(X0) <=> (humble(X0) & ~kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | tall(X0)) => strong(X0)) [input p4]
7. ! [X0] : (~generous(X0) => ~wise(X0)) [input p6]
11. ! [X0] : (~generous(X0) <=> patient(X0)) [input p10]
13. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X0] : (~humble(X0) & ~generous(X0)) [input p12]
14. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p13]
16. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~humble(X0) & ~wise(X0))) [input p15]
20. ? [X0] : (~curious(X0) & ~brave(X0)) [input p19]
24. ~wise(lucy) [input hypothesis]
26. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X1] : (~humble(X1) & ~generous(X1)) [rectify 13]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (brave(X0) | ~humble(X0))) [ennf transformation 1]
28. ! [X0] : ((~happy(X0) <~> wise(X0)) | brave(X0) | ~humble(X0)) [flattening 27]
29. tall(lucy) | ! [X0] : brave(X0) [ennf transformation 2]
30. ! [X0] : (strong(X0) | (rich(X0) & ~tall(X0))) [ennf transformation 5]
32. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 7]
36. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | brave(X0) | ~humble(X0)) [nnf transformation 28]
38. ! [X0] : ((patient(X0) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [nnf transformation 4]
39. ! [X0] : ((patient(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [flattening 38]
47. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 11]
49. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X1] : (~humble(X1) & ~generous(X1)) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 26]
50. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X2] : (~humble(X2) & ~generous(X2)) | ! [X3] : (happy(X3) & ~kind(X3))) [rectify 49]
51. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK1) | kind(sK1)) [choice axiom]
52. ? [X2] : (~humble(X2) & ~generous(X2)) => (~humble(sK2) & ~generous(sK2)) [choice axiom]
53. ((~happy(sK1) | kind(sK1)) | ! [X1] : (humble(X1) | generous(X1))) & ((~humble(sK2) & ~generous(sK2)) | ! [X3] : (happy(X3) & ~kind(X3))) [skolemisation 50,52,51]
54. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 14]
55. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 54]
58. ! [X0] : (((~brave(X0) & generous(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 16]
59. ! [X0] : (((~brave(X0) & generous(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | brave(X0) | ~generous(X0))) [flattening 58]
63. ? [X0] : (~curious(X0) & ~brave(X0)) => (~curious(sK4) & ~brave(sK4)) [choice axiom]
64. ~curious(sK4) & ~brave(sK4) [skolemisation 20,63]
71. ~happy(X0) | wise(X0) | brave(X0) | ~humble(X0) [cnf transformation 36]
73. tall(lucy) | brave(X0) [cnf transformation 29]
83. ~patient(X0) | humble(X0) [cnf transformation 39]
84. ~humble(X0) | patient(X0) | kind(X0) [cnf transformation 39]
85. ~tall(X0) | strong(X0) [cnf transformation 30]
89. ~wise(X0) | generous(X0) [cnf transformation 32]
99. generous(X0) | patient(X0) [cnf transformation 47]
100. ~generous(X0) | ~patient(X0) [cnf transformation 47]
105. ~generous(sK2) | ~kind(X3) [cnf transformation 53]
106. ~generous(sK2) | happy(X3) [cnf transformation 53]
107. ~humble(sK2) | ~kind(X3) [cnf transformation 53]
108. ~humble(sK2) | happy(X3) [cnf transformation 53]
113. ~strong(X0) | generous(X0) | ~brave(X0) [cnf transformation 55]
115. ~generous(X0) | ~strong(X0) | brave(X0) | wise(X0) [cnf transformation 55]
119. ~wise(X0) | brave(X0) | ~generous(X0) [cnf transformation 59]
121. generous(X0) | humble(X0) | wise(X0) [cnf transformation 59]
122. ~brave(X0) | humble(X0) | wise(X0) [cnf transformation 59]
128. ~brave(sK4) [cnf transformation 64]
136. ~wise(lucy) [cnf transformation 24]
138. 1 <=> ! [X0] : brave(X0) [avatar definition]
139. brave(X0) <- (1) [avatar component clause 138]
141. 2 <=> tall(lucy) [avatar definition]
143. tall(lucy) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 73,141,138]
159. 6 <=> ! [X1] : (humble(X1) | generous(X1)) [avatar definition]
160. generous(X1) | humble(X1) <- (6) [avatar component clause 159]
171. 9 <=> ! [X3] : happy(X3) [avatar definition]
172. happy(X3) <- (9) [avatar component clause 171]
174. 10 <=> humble(sK2) [avatar definition]
177. 9 | ~10 [avatar split clause 108,174,171]
179. 11 <=> ! [X3] : ~kind(X3) [avatar definition]
180. ~kind(X3) <- (11) [avatar component clause 179]
181. 11 | ~10 [avatar split clause 107,174,179]
183. 12 <=> generous(sK2) [avatar definition]
185. ~generous(sK2) <- (~12) [avatar component clause 183]
186. 9 | ~12 [avatar split clause 106,183,171]
187. 11 | ~12 [avatar split clause 105,183,179]
190. generous(X0) | humble(X0) [subsumption resolution 121,89]
191. 6 [avatar split clause 190,159]
192. ~wise(X0) | brave(X0) [subsumption resolution 119,89]
224. strong(lucy) <- (2) [resolution 85,143]
227. patient(sK2) <- (~12) [resolution 99,185]
232. humble(sK2) <- (~12) [resolution 227,83]
235. 10 | 12 [avatar split clause 232,183,174]
374. generous(lucy) | ~brave(lucy) <- (2) [resolution 113,224]
377. 36 <=> brave(lucy) [avatar definition]
379. ~brave(lucy) <- (~36) [avatar component clause 377]
381. 37 <=> generous(lucy) [avatar definition]
383. generous(lucy) <- (37) [avatar component clause 381]
384. ~36 | 37 | ~2 [avatar split clause 374,141,381,377]
471. wise(X0) | brave(X0) | ~humble(X0) <- (9) [resolution 71,172]
472. ~humble(X0) | brave(X0) <- (9) [subsumption resolution 471,192]
525. ~strong(X1) | brave(X1) | wise(X1) | humble(X1) <- (6) [resolution 115,160]
534. ~strong(X1) | wise(X1) | humble(X1) <- (6) [subsumption resolution 525,122]
626. 59 <=> humble(lucy) [avatar definition]
628. humble(lucy) <- (59) [avatar component clause 626]
637. 61 <=> patient(lucy) [avatar definition]
638. ~patient(lucy) <- (~61) [avatar component clause 637]
689. wise(lucy) | humble(lucy) <- (2, 6) [resolution 534,224]
710. brave(lucy) <- (9, 59) [resolution 628,472]
712. $false <- (9, ~36, 59) [subsumption resolution 710,379]
713. ~9 | 36 | ~59 [avatar contradiction clause 712]
714. humble(lucy) <- (2, 6) [subsumption resolution 689,136]
715. 59 | ~2 | ~6 [avatar split clause 714,159,141,626]
725. $false <- (1) [resolution 139,128]
728. ~1 [avatar contradiction clause 725]
751. ~patient(lucy) <- (37) [resolution 383,100]
754. ~61 | ~37 [avatar split clause 751,381,637]
758. patient(lucy) | kind(lucy) <- (59) [resolution 628,84]
759. kind(lucy) <- (59, ~61) [subsumption resolution 758,638]
760. $false <- (11, 59, ~61) [subsumption resolution 759,180]
761. ~11 | ~59 | 61 [avatar contradiction clause 760]
762. $false [avatar sat refutation 144,177,181,186,187,191,235,384,713,715,728,754,761]
% SZS output end Proof for 4489409461214739420940442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not rich is not rich or tall.
Everyone who is rich or patient is quiet.
Everyone who is not wise or quiet is not old.
Everyone who is not strong or curious is calm.
If susan is both not patient and calm then paul is both not rich and kind.
Everyone who is either not quiet or not generous is quiet.
Everyone who is both kind and not calm is not kind or not humble.
If alice is either not brave or not rich then someone is not kind.
Everyone who is either not creative or calm is not curious or not strong and vice versa.
If mary is wise or rich then someone is humble.
Everyone who is not humble is not rich or rich.
Everyone who is not generous is calm or patient.
If someone is not strong then someone is both kind and old and vice versa.
Everyone who is either tall or not wise is both not quiet and not tall.
Everyone who is either patient or humble is not brave and vice versa.
If paul is kind or not tall then john is either not tall or not old and vice versa.
Paul is either kind or tall.
Someone is either not humble or kind.
John is not strong.
John is not quiet.
Someone is both tall and funny.
Someone is not wise.
Someone is either strong or funny.
Someone is both quiet and not curious. | Paul is not tall. | neutral | (![X]:((~creative(X)|~rich(X))=>(~rich(X)|tall(X))))&
(![X]:((rich(X)|patient(X))=>quiet(X)))&
(![X]:((~wise(X)|quiet(X))=>~old(X)))&
(![X]:((~strong(X)|curious(X))=>calm(X)))&
(((~patient(susan)&calm(susan)))=>((~rich(paul)&kind(paul))))&
(![X]:((~quiet(X)<~>~generous(X))=>quiet(X)))&
(![X]:((kind(X)&~calm(X))=>(~kind(X)|~humble(X))))&
(((~brave(alice)<~>~rich(alice)))=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~curious(X)|~strong(X))))&
(((wise(mary)|rich(mary)))=>(?[X]:(humble(X))))&
(![X]:(~humble(X)=>(~rich(X)|rich(X))))&
(![X]:(~generous(X)=>(calm(X)|patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((tall(X)<~>~wise(X))=>(~quiet(X)&~tall(X))))&
(![X]:((patient(X)<~>humble(X))<=>~brave(X)))&
(((kind(paul)|~tall(paul)))<=>((~tall(john)<~>~old(john))))&
((kind(paul)<~>tall(paul)))&
(?[X]:((~humble(X)<~>kind(X))))&
(~strong(john))&
(~quiet(john))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~wise(X)))&
(?[X]:((strong(X)<~>funny(X))))&
(?[X]:((quiet(X)&~curious(X)))) | ~tall(paul) | [] | null | 0 |
If someone is old then lucy is either calm or humble and vice versa.
Everyone who is either not curious or quiet is old and vice versa.
Everyone who is not curious or kind is not wise or not creative and vice versa.
Everyone who is not patient is not wise and vice versa.
Everyone who is either not tall or strong is tall or not patient and vice versa.
Everyone who is happy is both not humble and humble and vice versa.
Everyone who is strong is patient or not happy.
If mary is kind then alice is generous and vice versa.
If john is kind or not calm then someone is either generous or curious and vice versa.
If lucy is strong then susan is not funny or kind.
If lucy is not generous or old then someone is not old or old and vice versa.
If alice is either not old or rich then alice is either not humble or not patient and vice versa.
If someone is wise or not tall then someone is tall.
Everyone who is both wise and not patient is not patient and vice versa.
Everyone who is both brave and funny is not strong or not funny and vice versa.
Everyone who is generous is old or brave.
Someone is brave or wise.
Someone is either patient or humble.
Someone is not humble or generous.
Susan is either not strong or not tall.
Susan is not humble.
John is not strong or not quiet.
Someone is either wise or rich. | John is not quiet. | entailment | ((?[X]:(old(X)))<=>((calm(lucy)<~>humble(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>old(X)))&
(![X]:((~curious(X)|kind(X))<=>(~wise(X)|~creative(X))))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(tall(X)|~patient(X))))&
(![X]:(happy(X)<=>(~humble(X)&humble(X))))&
(![X]:(strong(X)=>(patient(X)|~happy(X))))&
((kind(mary))<=>(generous(alice)))&
(((kind(john)|~calm(john)))<=>(?[X]:((generous(X)<~>curious(X)))))&
((strong(lucy))=>((~funny(susan)|kind(susan))))&
(((~generous(lucy)|old(lucy)))<=>(?[X]:((~old(X)|old(X)))))&
(((~old(alice)<~>rich(alice)))<=>((~humble(alice)<~>~patient(alice))))&
((?[X]:((wise(X)|~tall(X))))=>(?[X]:(tall(X))))&
(![X]:((wise(X)&~patient(X))<=>~patient(X)))&
(![X]:((brave(X)&funny(X))<=>(~strong(X)|~funny(X))))&
(![X]:(generous(X)=>(old(X)|brave(X))))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~humble(X)|generous(X))))&
((~strong(susan)<~>~tall(susan)))&
(~humble(susan))&
((~strong(john)|~quiet(john)))&
(?[X]:((wise(X)<~>rich(X)))) | ~quiet(john) | [
"p3",
"p4",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6833627503722099774801775
% SZS output start Proof for 6833627503722099774801775
4. ! [X0] : (~patient(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~patient(X0) | tall(X0))) [input p4]
14. ! [X0] : ((~patient(X0) & wise(X0)) <=> ~patient(X0)) [input p13]
22. ~quiet(john) | ~strong(john) [input p21]
24. quiet(john) [input hypothesis]
43. ! [X0] : ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))) [nnf transformation 4]
44. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (patient(X0) & ~tall(X0))) & ((~patient(X0) | tall(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (patient(X0) & ~tall(X0))) & (~patient(X0) | tall(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 44]
61. ! [X0] : (((~patient(X0) & wise(X0)) | patient(X0)) & (~patient(X0) | (patient(X0) | ~wise(X0)))) [nnf transformation 14]
62. ! [X0] : (((~patient(X0) & wise(X0)) | patient(X0)) & (~patient(X0) | patient(X0) | ~wise(X0))) [flattening 61]
88. ~wise(X0) | patient(X0) [cnf transformation 43]
90. ~patient(X0) | tall(X0) | strong(X0) | tall(X0) [cnf transformation 45]
92. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 45]
122. wise(X0) | patient(X0) [cnf transformation 62]
137. ~quiet(john) | ~strong(john) [cnf transformation 22]
140. quiet(john) [cnf transformation 24]
143. ~patient(X0) | tall(X0) | strong(X0) [duplicate literal removal 90]
144. ~tall(X0) | strong(X0) [duplicate literal removal 92]
164. ~patient(X0) | strong(X0) [subsumption resolution 143,144]
265. patient(X0) [subsumption resolution 122,88]
289. 30 <=> strong(john) [avatar definition]
291. ~strong(john) <- (~30) [avatar component clause 289]
293. 31 <=> quiet(john) [avatar definition]
296. ~30 | ~31 [avatar split clause 137,293,289]
307. 31 [avatar split clause 140,293]
314. strong(X0) [resolution 164,265]
316. $false <- (~30) [resolution 314,291]
317. 30 [avatar contradiction clause 316]
319. $false [avatar sat refutation 296,307,317]
% SZS output end Proof for 6833627503722099774801775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then john is either not tall or not brave and vice versa.
Everyone who is either not strong or rich is both not funny and not creative and vice versa.
If someone is not patient or not tall then someone is not wise and vice versa.
If mary is either humble or brave then alice is not strong or not tall and vice versa.
If alice is either not strong or generous then someone is both not old and rich.
Everyone who is both not generous and not creative is humble and vice versa.
Everyone who is brave or not strong is both old and not patient and vice versa.
If someone is both not old and tall then someone is both not tall and not brave.
Everyone who is rich is not wise and vice versa.
Everyone who is strong is both not tall and not strong and vice versa.
Everyone who is old or quiet is either humble or creative and vice versa.
If susan is either not curious or not creative then susan is both patient and wise.
Everyone who is not quiet is both not old and not brave.
If john is tall or not patient then someone is rich or tall.
Everyone who is not calm or not strong is old or tall.
Everyone who is both calm and not strong is tall or brave and vice versa.
Alice is brave or not strong.
Someone is not rich.
Mary is either tall or curious.
Mary is either patient or creative.
Someone is humble.
Someone is happy or brave. | Susan is not curious. | neutral | ((?[X]:(humble(X)))<=>((~tall(john)<~>~brave(john))))&
(![X]:((~strong(X)<~>rich(X))<=>(~funny(X)&~creative(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~wise(X))))&
(((humble(mary)<~>brave(mary)))<=>((~strong(alice)|~tall(alice))))&
(((~strong(alice)<~>generous(alice)))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((~generous(X)&~creative(X))<=>humble(X)))&
(![X]:((brave(X)|~strong(X))<=>(old(X)&~patient(X))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:(rich(X)<=>~wise(X)))&
(![X]:(strong(X)<=>(~tall(X)&~strong(X))))&
(![X]:((old(X)|quiet(X))<=>(humble(X)<~>creative(X))))&
(((~curious(susan)<~>~creative(susan)))=>((patient(susan)&wise(susan))))&
(![X]:(~quiet(X)=>(~old(X)&~brave(X))))&
(((tall(john)|~patient(john)))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~calm(X)|~strong(X))=>(old(X)|tall(X))))&
(![X]:((calm(X)&~strong(X))<=>(tall(X)|brave(X))))&
((brave(alice)|~strong(alice)))&
(?[X]:(~rich(X)))&
((tall(mary)<~>curious(mary)))&
((patient(mary)<~>creative(mary)))&
(?[X]:(humble(X)))&
(?[X]:((happy(X)|brave(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is either humble or not happy is both not brave and not creative and vice versa. If mary is either funny or wise then fred is kind. Everyone who is either brave or not strong is both rich and old and vice versa. If someone is not kind or curious then someone is both curious and not brave. Everyone who is either patient or happy is either not tall or old and vice versa. If paul is not kind then alice is creative. Everyone who is patient or brave is either not rich or not tall and vice versa. If someone is patient or not humble then alice is both not strong and not wise and vice versa. Everyone who is both not wise and wise is rich or not patient. Everyone who is either not rich or wise is curious or not humble. Everyone who is brave is both rich and humble and vice versa. Everyone who is either brave or not strong is patient or strong. Everyone who is both not creative and patient is either not wise or kind and vice versa. Everyone who is either curious or not strong is both not generous and not rich. If paul is both not quiet and rich then fred is happy or not strong. If paul is not patient then fred is either not rich or not tall and vice versa. Lucy is both not happy and not calm. Someone is both creative and not wise. Someone is both wise and not quiet. Mary is either patient or rich. John is quiet. Someone is patient or not kind. Someone is both kind and not tall. | Mary is not strong. | contradiction | (![X]:((humble(X)<~>~happy(X))<=>(~brave(X)&~creative(X))))&
(((funny(mary)<~>wise(mary)))=>(kind(fred)))&
(![X]:((brave(X)<~>~strong(X))<=>(rich(X)&old(X))))&
((?[X]:((~kind(X)|curious(X))))=>(?[X]:((curious(X)&~brave(X)))))&
(![X]:((patient(X)<~>happy(X))<=>(~tall(X)<~>old(X))))&
((~kind(paul))=>(creative(alice)))&
(![X]:((patient(X)|brave(X))<=>(~rich(X)<~>~tall(X))))&
((?[X]:((patient(X)|~humble(X))))<=>((~strong(alice)&~wise(alice))))&
(![X]:((~wise(X)&wise(X))=>(rich(X)|~patient(X))))&
(![X]:((~rich(X)<~>wise(X))=>(curious(X)|~humble(X))))&
(![X]:(brave(X)<=>(rich(X)&humble(X))))&
(![X]:((brave(X)<~>~strong(X))=>(patient(X)|strong(X))))&
(![X]:((~creative(X)&patient(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~generous(X)&~rich(X))))&
(((~quiet(paul)&rich(paul)))=>((happy(fred)|~strong(fred))))&
((~patient(paul))<=>((~rich(fred)<~>~tall(fred))))&
((~happy(lucy)&~calm(lucy)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((wise(X)&~quiet(X))))&
((patient(mary)<~>rich(mary)))&
(quiet(john))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:((kind(X)&~tall(X)))) | ~strong(mary) | [
"p0",
"p2",
"p4",
"p6",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7709920233608190023483937
% SZS output start Proof for 7709920233608190023483937
1. ! [X0] : ((humble(X0) <~> ~happy(X0)) <=> (~creative(X0) & ~brave(X0))) [input p0]
3. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (old(X0) & rich(X0))) [input p2]
5. ! [X0] : ((patient(X0) <~> happy(X0)) <=> (~tall(X0) <~> old(X0))) [input p4]
7. ! [X0] : ((brave(X0) | patient(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p6]
11. ! [X0] : (brave(X0) <=> (humble(X0) & rich(X0))) [input p10]
12. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (strong(X0) | patient(X0))) [input p11]
20. patient(mary) <~> rich(mary) [input p19]
24. ~strong(mary) [input hypothesis]
35. ! [X0] : ((strong(X0) | patient(X0)) | (brave(X0) <=> ~strong(X0))) [ennf transformation 12]
36. ! [X0] : (strong(X0) | patient(X0) | (brave(X0) <=> ~strong(X0))) [flattening 35]
40. ! [X0] : ((((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | (creative(X0) | brave(X0))) & ((~creative(X0) & ~brave(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))))) [nnf transformation 1]
41. ! [X0] : ((((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | creative(X0) | brave(X0)) & ((~creative(X0) & ~brave(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))))) [flattening 40]
43. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 3]
44. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 43]
48. ! [X0] : ((((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) & (((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0))))) [nnf transformation 5]
49. ! [X0] : (((brave(X0) | patient(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~brave(X0) & ~patient(X0)))) [nnf transformation 7]
50. ! [X0] : ((brave(X0) | patient(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~brave(X0) & ~patient(X0)))) [flattening 49]
57. ! [X0] : ((brave(X0) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ~brave(X0))) [nnf transformation 11]
58. ! [X0] : ((brave(X0) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ~brave(X0))) [flattening 57]
59. ! [X0] : (strong(X0) | patient(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) [nnf transformation 36]
68. (~rich(mary) | ~patient(mary)) & (rich(mary) | patient(mary)) [nnf transformation 20]
73. ~brave(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 41]
82. rich(X0) | brave(X0) | strong(X0) [cnf transformation 44]
86. ~old(X0) | ~brave(X0) | strong(X0) | ~rich(X0) [cnf transformation 44]
95. tall(X0) | patient(X0) | old(X0) | happy(X0) [cnf transformation 48]
101. ~tall(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 50]
114. ~brave(X0) | rich(X0) [cnf transformation 58]
115. ~brave(X0) | humble(X0) [cnf transformation 58]
118. strong(X0) | patient(X0) | brave(X0) | strong(X0) [cnf transformation 59]
138. ~rich(mary) | ~patient(mary) [cnf transformation 68]
143. ~strong(mary) [cnf transformation 24]
144. patient(X0) | strong(X0) | brave(X0) [duplicate literal removal 118]
247. 23 <=> patient(mary) [avatar definition]
249. ~patient(mary) <- (~23) [avatar component clause 247]
251. 24 <=> rich(mary) [avatar definition]
252. rich(mary) <- (24) [avatar component clause 251]
253. ~rich(mary) <- (~24) [avatar component clause 251]
254. ~23 | ~24 [avatar split clause 138,251,247]
284. brave(mary) | strong(mary) <- (~24) [resolution 82,253]
286. brave(mary) <- (~24) [subsumption resolution 284,143]
325. rich(mary) <- (~24) [resolution 286,114]
327. 34 <=> happy(mary) [avatar definition]
328. ~happy(mary) <- (~34) [avatar component clause 327]
331. 35 <=> humble(mary) [avatar definition]
337. $false <- (~24) [subsumption resolution 325,253]
338. 24 [avatar contradiction clause 337]
351. 37 <=> brave(mary) [avatar definition]
353. brave(mary) <- (37) [avatar component clause 351]
420. strong(mary) | brave(mary) <- (~23) [resolution 144,249]
422. brave(mary) <- (~23) [subsumption resolution 420,143]
423. 37 | 23 [avatar split clause 422,247,351]
433. ~happy(mary) | ~humble(mary) <- (37) [resolution 353,73]
434. humble(mary) <- (37) [resolution 353,115]
440. 35 | ~37 [avatar split clause 434,351,331]
441. ~35 | ~34 | ~37 [avatar split clause 433,351,327,331]
482. patient(X2) | old(X2) | happy(X2) | ~rich(X2) | ~brave(X2) [resolution 95,101]
496. ~brave(X2) | old(X2) | happy(X2) | patient(X2) [subsumption resolution 482,114]
735. old(mary) | happy(mary) | patient(mary) <- (37) [resolution 496,353]
736. old(mary) | patient(mary) <- (~34, 37) [subsumption resolution 735,328]
737. old(mary) <- (~23, ~34, 37) [subsumption resolution 736,249]
813. ~brave(mary) | strong(mary) | ~rich(mary) <- (~23, ~34, 37) [resolution 737,86]
815. strong(mary) | ~rich(mary) <- (~23, ~34, 37) [subsumption resolution 813,353]
816. ~rich(mary) <- (~23, ~34, 37) [subsumption resolution 815,143]
817. $false <- (~23, 24, ~34, 37) [subsumption resolution 816,252]
818. 23 | ~24 | 34 | ~37 [avatar contradiction clause 817]
819. $false [avatar sat refutation 254,338,423,440,441,818]
% SZS output end Proof for 7709920233608190023483937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not tall then lucy is both happy and not kind.
Everyone who is patient is not kind or wise and vice versa.
Everyone who is not brave is curious or kind.
Everyone who is both humble and not humble is both not quiet and not creative.
Everyone who is either not calm or brave is quiet and vice versa.
Everyone who is funny or not brave is both not happy and not calm.
Everyone who is not old or not tall is not creative.
Everyone who is not wise is both not tall and not brave.
Everyone who is rich is either old or wise and vice versa.
Everyone who is both not funny and patient is not rich.
Everyone who is not wise or not creative is not tall or calm.
If someone is not happy then someone is either not creative or calm and vice versa.
If mary is either strong or calm then mary is strong.
Everyone who is not creative or wise is not quiet or not creative and vice versa.
If someone is quiet then paul is happy or not quiet.
Everyone who is either not creative or not quiet is either calm or old.
Someone is not kind.
Someone is not creative.
Susan is either not wise or not funny.
John is wise.
Someone is patient.
Alice is not old or funny.
Someone is both old and funny.
Someone is not rich or not generous. | Lucy is not funny. | entailment | ((?[X]:(~tall(X)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(patient(X)<=>(~kind(X)|wise(X))))&
(![X]:(~brave(X)=>(curious(X)|kind(X))))&
(![X]:((humble(X)&~humble(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~calm(X)<~>brave(X))<=>quiet(X)))&
(![X]:((funny(X)|~brave(X))=>(~happy(X)&~calm(X))))&
(![X]:((~old(X)|~tall(X))=>~creative(X)))&
(![X]:(~wise(X)=>(~tall(X)&~brave(X))))&
(![X]:(rich(X)<=>(old(X)<~>wise(X))))&
(![X]:((~funny(X)&patient(X))=>~rich(X)))&
(![X]:((~wise(X)|~creative(X))=>(~tall(X)|calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((strong(mary)<~>calm(mary)))=>(strong(mary)))&
(![X]:((~creative(X)|wise(X))<=>(~quiet(X)|~creative(X))))&
((?[X]:(quiet(X)))=>((happy(paul)|~quiet(paul))))&
(![X]:((~creative(X)<~>~quiet(X))=>(calm(X)<~>old(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~creative(X)))&
((~wise(susan)<~>~funny(susan)))&
(wise(john))&
(?[X]:(patient(X)))&
((~old(alice)|funny(alice)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~rich(X)|~generous(X)))) | ~funny(lucy) | [
"p0",
"p4",
"p5",
"p7",
"p10",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4312202552145636809987586
% SZS output start Proof for 4312202552145636809987586
1. ? [X0] : ~tall(X0) => (~kind(lucy) & happy(lucy)) [input p0]
5. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> quiet(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | funny(X0)) => (~calm(X0) & ~happy(X0))) [input p5]
8. ! [X0] : (~wise(X0) => (~brave(X0) & ~tall(X0))) [input p7]
11. ! [X0] : ((~creative(X0) | ~wise(X0)) => (calm(X0) | ~tall(X0))) [input p10]
12. ? [X0] : ~happy(X0) <=> ? [X0] : (~creative(X0) <~> calm(X0)) [input p11]
14. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (~creative(X0) | ~quiet(X0))) [input p13]
23. ? [X0] : (funny(X0) & old(X0)) [input p22]
25. funny(lucy) [input hypothesis]
26. ? [X0] : ~happy(X0) <=> ? [X1] : (~creative(X1) <~> calm(X1)) [rectify 12]
30. (~kind(lucy) & happy(lucy)) | ! [X0] : tall(X0) [ennf transformation 1]
33. ! [X0] : ((~calm(X0) & ~happy(X0)) | (brave(X0) & ~funny(X0))) [ennf transformation 6]
35. ! [X0] : ((~brave(X0) & ~tall(X0)) | wise(X0)) [ennf transformation 8]
39. ! [X0] : ((calm(X0) | ~tall(X0)) | (creative(X0) & wise(X0))) [ennf transformation 11]
40. ! [X0] : (calm(X0) | ~tall(X0) | (creative(X0) & wise(X0))) [flattening 39]
47. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | ~quiet(X0)) & (quiet(X0) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 5]
49. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X1] : ((~calm(X1) | creative(X1)) & (calm(X1) | ~creative(X1))) | ! [X0] : happy(X0)) [nnf transformation 26]
50. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) | ! [X3] : happy(X3)) [rectify 49]
51. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
52. ? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) => ((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) [choice axiom]
53. (~happy(sK0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) | ! [X3] : happy(X3)) [skolemisation 50,52,51]
55. ! [X0] : (((wise(X0) | ~creative(X0)) | (creative(X0) & quiet(X0))) & ((~creative(X0) | ~quiet(X0)) | (~wise(X0) & creative(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~creative(X0) | (creative(X0) & quiet(X0))) & (~creative(X0) | ~quiet(X0) | (~wise(X0) & creative(X0)))) [flattening 55]
65. ? [X0] : (funny(X0) & old(X0)) => (funny(sK5) & old(sK5)) [choice axiom]
66. funny(sK5) & old(sK5) [skolemisation 23,65]
67. happy(lucy) | tall(X0) [cnf transformation 30]
74. calm(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
75. ~calm(X0) | quiet(X0) | ~brave(X0) [cnf transformation 47]
76. ~calm(X0) | brave(X0) | ~quiet(X0) [cnf transformation 47]
78. ~funny(X0) | ~happy(X0) [cnf transformation 33]
81. ~calm(X0) | brave(X0) [cnf transformation 33]
84. ~tall(X0) | wise(X0) [cnf transformation 35]
90. ~tall(X0) | calm(X0) | creative(X0) [cnf transformation 40]
91. calm(sK1) | ~creative(sK1) | happy(X3) [cnf transformation 53]
92. ~calm(sK1) | creative(sK1) | happy(X3) [cnf transformation 53]
98. ~creative(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 56]
114. funny(sK5) [cnf transformation 66]
115. funny(lucy) [cnf transformation 25]
118. 1 <=> ! [X0] : tall(X0) [avatar definition]
119. tall(X0) <- (1) [avatar component clause 118]
126. 3 <=> happy(lucy) [avatar definition]
129. 1 | 3 [avatar split clause 67,126,118]
139. 6 <=> ! [X1] : (calm(X1) | creative(X1)) [avatar definition]
140. calm(X1) | creative(X1) <- (6) [avatar component clause 139]
143. 7 <=> ! [X3] : happy(X3) [avatar definition]
144. happy(X3) <- (7) [avatar component clause 143]
146. 8 <=> creative(sK1) [avatar definition]
148. creative(sK1) <- (8) [avatar component clause 146]
150. 9 <=> calm(sK1) [avatar definition]
151. calm(sK1) <- (9) [avatar component clause 150]
152. ~calm(sK1) <- (~9) [avatar component clause 150]
153. 7 | 8 | ~9 [avatar split clause 92,150,146,143]
154. 7 | ~8 | 9 [avatar split clause 91,150,146,143]
199. ~happy(sK5) [resolution 78,114]
200. ~happy(lucy) [resolution 78,115]
203. ~3 [avatar split clause 200,126]
206. wise(X0) <- (1) [resolution 84,119]
213. brave(X0) | quiet(X0) | brave(X0) [resolution 74,81]
218. quiet(X0) | brave(X0) [duplicate literal removal 213]
256. calm(X0) | creative(X0) <- (1) [resolution 90,119]
257. 6 | ~1 [avatar split clause 256,118,139]
263. creative(sK1) <- (6, ~9) [resolution 140,152]
269. 8 | ~6 | 9 [avatar split clause 263,150,139,146]
273. $false <- (7) [resolution 144,199]
274. ~7 [avatar contradiction clause 273]
279. brave(sK1) | ~quiet(sK1) <- (9) [resolution 151,76]
280. quiet(sK1) | ~brave(sK1) <- (9) [resolution 151,75]
282. brave(sK1) <- (9) [subsumption resolution 279,218]
283. quiet(sK1) <- (9) [subsumption resolution 280,282]
284. ~quiet(sK1) | ~wise(sK1) <- (8) [resolution 98,148]
285. ~wise(sK1) <- (8, 9) [subsumption resolution 284,283]
286. $false <- (1, 8, 9) [subsumption resolution 285,206]
287. ~1 | ~8 | ~9 [avatar contradiction clause 286]
288. $false [avatar sat refutation 129,153,154,203,257,269,274,287]
% SZS output end Proof for 4312202552145636809987586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not brave or not strong then someone is either not wise or old and vice versa.
If susan is funny then someone is both not humble and not funny and vice versa.
Everyone who is funny is both not kind and not calm.
Everyone who is both creative and rich is patient or quiet.
Everyone who is both creative and curious is not kind or not funny.
Everyone who is either curious or kind is brave or tall.
If fred is not curious or rich then someone is not tall or not creative and vice versa.
If fred is humble then alice is either not wise or not rich and vice versa.
Everyone who is both strong and creative is either not tall or rich.
If paul is both wise and not humble then someone is both not patient and old and vice versa.
If someone is either not calm or curious then lucy is either not rich or not generous and vice versa.
Everyone who is both old and calm is not kind or not wise and vice versa.
Everyone who is not old is either not old or quiet and vice versa.
If someone is calm or creative then someone is tall or kind and vice versa.
If paul is tall then susan is brave.
If someone is wise or not happy then lucy is kind and vice versa.
Someone is tall.
Someone is not wise.
John is both rich and not funny.
Someone is not strong.
Paul is not old.
Someone is not rich or not curious.
Lucy is not generous or tall.
Someone is both curious and not generous. | Paul is not wise. | contradiction | (((~brave(john)<~>~strong(john)))<=>(?[X]:((~wise(X)<~>old(X)))))&
((funny(susan))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:(funny(X)=>(~kind(X)&~calm(X))))&
(![X]:((creative(X)&rich(X))=>(patient(X)|quiet(X))))&
(![X]:((creative(X)&curious(X))=>(~kind(X)|~funny(X))))&
(![X]:((curious(X)<~>kind(X))=>(brave(X)|tall(X))))&
(((~curious(fred)|rich(fred)))<=>(?[X]:((~tall(X)|~creative(X)))))&
((humble(fred))<=>((~wise(alice)<~>~rich(alice))))&
(![X]:((strong(X)&creative(X))=>(~tall(X)<~>rich(X))))&
(((wise(paul)&~humble(paul)))<=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((~calm(X)<~>curious(X))))<=>((~rich(lucy)<~>~generous(lucy))))&
(![X]:((old(X)&calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:(~old(X)<=>(~old(X)<~>quiet(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((tall(X)|kind(X)))))&
((tall(paul))=>(brave(susan)))&
((?[X]:((wise(X)|~happy(X))))<=>(kind(lucy)))&
(?[X]:(tall(X)))&
(?[X]:(~wise(X)))&
((rich(john)&~funny(john)))&
(?[X]:(~strong(X)))&
(~old(paul))&
(?[X]:((~rich(X)|~curious(X))))&
((~generous(lucy)|tall(lucy)))&
(?[X]:((curious(X)&~generous(X)))) | ~wise(paul) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8290106663069992590841122
% SZS output start Proof for 8290106663069992590841122
12. ! [X0] : ((calm(X0) & old(X0)) <=> (~wise(X0) | ~kind(X0))) [input p11]
21. ~old(paul) [input p20]
25. ~wise(paul) [input hypothesis]
62. ! [X0] : (((calm(X0) & old(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (~calm(X0) | ~old(X0)))) [nnf transformation 12]
63. ! [X0] : (((calm(X0) & old(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | ~calm(X0) | ~old(X0))) [flattening 62]
125. old(X0) | wise(X0) [cnf transformation 63]
145. ~old(paul) [cnf transformation 21]
150. ~wise(paul) [cnf transformation 25]
166. 4 <=> ! [X0] : (old(X0) | wise(X0)) [avatar definition]
167. old(X0) | wise(X0) <- (4) [avatar component clause 166]
252. 22 <=> wise(paul) [avatar definition]
253. ~wise(paul) <- (~22) [avatar component clause 252]
296. 4 [avatar split clause 125,166]
374. ~22 [avatar split clause 150,252]
384. wise(paul) <- (4) [resolution 167,145]
386. $false <- (4, ~22) [subsumption resolution 384,253]
387. ~4 | 22 [avatar contradiction clause 386]
390. $false [avatar sat refutation 296,374,387]
% SZS output end Proof for 8290106663069992590841122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not rich and not tall then someone is both not rich and not creative.
If someone is not humble or patient then john is either not rich or old and vice versa.
Everyone who is not brave is both not happy and rich and vice versa.
Everyone who is either not generous or old is either creative or not humble.
Everyone who is both tall and rich is patient or not patient and vice versa.
If paul is either humble or not wise then john is quiet.
Everyone who is not happy is both not funny and not happy.
Everyone who is either not wise or kind is not wise or not calm and vice versa.
Everyone who is either not humble or wise is generous or not kind.
Everyone who is both not calm and funny is not rich or not creative.
If mary is either quiet or not happy then mary is either patient or not patient.
Everyone who is not brave or generous is either not calm or not old and vice versa.
If someone is both not funny and not curious then someone is either generous or not humble and vice versa.
If someone is both kind and not strong then susan is both not kind and old.
Everyone who is both kind and not patient is either not quiet or not wise and vice versa.
Everyone who is not wise or kind is either humble or funny.
Someone is both wise and happy.
Paul is both not calm and not patient.
Paul is old or not strong.
Mary is both not kind and funny.
Paul is either creative or not brave.
Lucy is patient or not quiet.
Alice is not old or funny. | Lucy is not calm. | neutral | (((~rich(susan)&~tall(susan)))=>(?[X]:((~rich(X)&~creative(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~rich(john)<~>old(john))))&
(![X]:(~brave(X)<=>(~happy(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))=>(creative(X)<~>~humble(X))))&
(![X]:((tall(X)&rich(X))<=>(patient(X)|~patient(X))))&
(((humble(paul)<~>~wise(paul)))=>(quiet(john)))&
(![X]:(~happy(X)=>(~funny(X)&~happy(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~humble(X)<~>wise(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)&funny(X))=>(~rich(X)|~creative(X))))&
(((quiet(mary)<~>~happy(mary)))=>((patient(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
((?[X]:((kind(X)&~strong(X))))=>((~kind(susan)&old(susan))))&
(![X]:((kind(X)&~patient(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)|kind(X))=>(humble(X)<~>funny(X))))&
(?[X]:((wise(X)&happy(X))))&
((~calm(paul)&~patient(paul)))&
((old(paul)|~strong(paul)))&
((~kind(mary)&funny(mary)))&
((creative(paul)<~>~brave(paul)))&
((patient(lucy)|~quiet(lucy)))&
((~old(alice)|funny(alice))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not curious is not calm or not patient. Everyone who is both rich and patient is either not wise or not quiet and vice versa. Everyone who is either tall or not curious is both not generous and not quiet and vice versa. If someone is either happy or generous then fred is brave and vice versa. If lucy is both rich and not funny then alice is not patient and vice versa. Everyone who is generous is not quiet or not brave. If someone is not strong then paul is not quiet or not rich. If john is old or funny then paul is old. Everyone who is tall is both curious and not patient and vice versa. Everyone who is not calm is both not old and strong. Everyone who is tall is both kind and not curious. If someone is both wise and not brave then john is either not tall or not wise and vice versa. If someone is both calm and tall then someone is not happy. If someone is not happy or kind then susan is old or calm. If john is not patient or funny then someone is either not patient or humble and vice versa. Everyone who is not curious or curious is both not tall and not curious. Someone is kind. Lucy is not generous. John is not strong or not humble. Someone is calm. Fred is either curious or patient. Paul is either old or calm. Lucy is either not tall or not strong. | John is not old. | entailment | (![X]:(~curious(X)=>(~calm(X)|~patient(X))))&
(![X]:((rich(X)&patient(X))<=>(~wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((happy(X)<~>generous(X))))<=>(brave(fred)))&
(((rich(lucy)&~funny(lucy)))<=>(~patient(alice)))&
(![X]:(generous(X)=>(~quiet(X)|~brave(X))))&
((?[X]:(~strong(X)))=>((~quiet(paul)|~rich(paul))))&
(((old(john)|funny(john)))=>(old(paul)))&
(![X]:(tall(X)<=>(curious(X)&~patient(X))))&
(![X]:(~calm(X)=>(~old(X)&strong(X))))&
(![X]:(tall(X)=>(kind(X)&~curious(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((~tall(john)<~>~wise(john))))&
((?[X]:((calm(X)&tall(X))))=>(?[X]:(~happy(X))))&
((?[X]:((~happy(X)|kind(X))))=>((old(susan)|calm(susan))))&
(((~patient(john)|funny(john)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((~curious(X)|curious(X))=>(~tall(X)&~curious(X))))&
(?[X]:(kind(X)))&
(~generous(lucy))&
((~strong(john)|~humble(john)))&
(?[X]:(calm(X)))&
((curious(fred)<~>patient(fred)))&
((old(paul)<~>calm(paul)))&
((~tall(lucy)<~>~strong(lucy))) | ~old(john) | [
"p7",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 668533444443856659997070
% SZS output start Proof for 668533444443856659997070
8. (funny(john) | old(john)) => old(paul) [input p7]
10. ! [X0] : (~calm(X0) => (strong(X0) & ~old(X0))) [input p9]
22. old(paul) <~> calm(paul) [input p21]
24. old(john) [input hypothesis]
32. old(paul) | (~funny(john) & ~old(john)) [ennf transformation 8]
33. ! [X0] : ((strong(X0) & ~old(X0)) | calm(X0)) [ennf transformation 10]
68. (~calm(paul) | ~old(paul)) & (calm(paul) | old(paul)) [nnf transformation 22]
92. old(paul) | ~old(john) [cnf transformation 32]
97. ~old(X0) | calm(X0) [cnf transformation 33]
127. ~calm(paul) | ~old(paul) [cnf transformation 68]
130. old(john) [cnf transformation 24]
186. 13 <=> old(paul) [avatar definition]
191. 14 <=> old(john) [avatar definition]
194. ~14 | 13 [avatar split clause 92,186,191]
265. ~old(paul) [subsumption resolution 127,97]
266. ~13 [avatar split clause 265,186]
269. 14 [avatar split clause 130,191]
270. $false [avatar sat refutation 194,266,269]
% SZS output end Proof for 668533444443856659997070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not humble then someone is not brave or curious and vice versa.
If someone is creative then susan is either strong or calm and vice versa.
If someone is both not calm and rich then someone is not strong.
If alice is either rich or not humble then susan is not strong or not generous and vice versa.
If mary is both generous and kind then mary is happy or not calm.
If fred is creative then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Paul is both humble and not curious.
Fred is either not rich or humble.
Someone is both wise and not rich.
Fred is either patient or quiet. | John is not strong. | neutral | (((patient(lucy)|~humble(lucy)))<=>(?[X]:((~brave(X)|curious(X)))))&
((?[X]:(creative(X)))<=>((strong(susan)<~>calm(susan))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:(~strong(X))))&
(((rich(alice)<~>~humble(alice)))<=>((~strong(susan)|~generous(susan))))&
(((generous(mary)&kind(mary)))=>((happy(mary)|~calm(mary))))&
((creative(fred))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
((humble(paul)&~curious(paul)))&
((~rich(fred)<~>humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
((patient(fred)<~>quiet(fred))) | ~strong(john) | [] | null | 0 |
If mary is not tall then fred is kind or not rich and vice versa. Everyone who is both not humble and old is tall. Everyone who is not generous or not humble is both not brave and wise and vice versa. Everyone who is not humble or not funny is not strong or not happy and vice versa. Everyone who is either kind or humble is either not strong or not humble. Everyone who is quiet is both not curious and strong. Everyone who is both not old and happy is curious or not tall. Everyone who is not kind or old is not happy or not tall. Everyone who is not patient is funny and vice versa. Everyone who is either quiet or not generous is both not patient and not curious. Everyone who is either not brave or not quiet is generous or not creative and vice versa. If alice is both creative and wise then someone is creative or not curious and vice versa. If someone is both not happy and not rich then fred is both not wise and not brave and vice versa. If alice is not quiet then fred is not brave or curious. Everyone who is not funny or happy is not rich and vice versa. If alice is both happy and not calm then fred is both not rich and not patient and vice versa. Paul is either strong or not curious. Someone is not happy or strong. Someone is either not wise or not tall. Someone is not patient. John is either curious or not happy. Alice is not kind or creative. Someone is both old and funny. Someone is both not rich and happy. | Fred is not generous. | neutral | ((~tall(mary))<=>((kind(fred)|~rich(fred))))&
(![X]:((~humble(X)&old(X))=>tall(X)))&
(![X]:((~generous(X)|~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((~humble(X)|~funny(X))<=>(~strong(X)|~happy(X))))&
(![X]:((kind(X)<~>humble(X))=>(~strong(X)<~>~humble(X))))&
(![X]:(quiet(X)=>(~curious(X)&strong(X))))&
(![X]:((~old(X)&happy(X))=>(curious(X)|~tall(X))))&
(![X]:((~kind(X)|old(X))=>(~happy(X)|~tall(X))))&
(![X]:(~patient(X)<=>funny(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~patient(X)&~curious(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(generous(X)|~creative(X))))&
(((creative(alice)&wise(alice)))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((~happy(X)&~rich(X))))<=>((~wise(fred)&~brave(fred))))&
((~quiet(alice))=>((~brave(fred)|curious(fred))))&
(![X]:((~funny(X)|happy(X))<=>~rich(X)))&
(((happy(alice)&~calm(alice)))<=>((~rich(fred)&~patient(fred))))&
((strong(paul)<~>~curious(paul)))&
(?[X]:((~happy(X)|strong(X))))&
(?[X]:((~wise(X)<~>~tall(X))))&
(?[X]:(~patient(X)))&
((curious(john)<~>~happy(john)))&
((~kind(alice)|creative(alice)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~rich(X)&happy(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is not happy or not rich is either quiet or happy and vice versa.
Everyone who is strong or not wise is either calm or rich and vice versa.
Everyone who is humble is happy and vice versa.
Everyone who is not patient is either not tall or funny and vice versa.
If someone is patient or happy then fred is not strong.
Everyone who is both tall and not generous is calm.
If someone is not wise or creative then someone is patient and vice versa.
Everyone who is not strong or not generous is both kind and not rich and vice versa.
Everyone who is either not patient or not happy is not strong or patient and vice versa.
Everyone who is funny is not quiet or not kind.
Everyone who is either not strong or not generous is humble.
Everyone who is either not curious or curious is not happy and vice versa.
Everyone who is both brave and not tall is patient or wise and vice versa.
Everyone who is both not happy and curious is both curious and not tall and vice versa.
Everyone who is either strong or generous is not calm.
If paul is funny or humble then fred is either rich or kind.
Someone is not curious.
John is not old or rich.
Someone is both not old and kind.
Someone is either not wise or quiet.
Someone is either not rich or brave.
Someone is calm.
John is either not old or rich. | John is not funny. | entailment | (![X]:((~happy(X)|~rich(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((strong(X)|~wise(X))<=>(calm(X)<~>rich(X))))&
(![X]:(humble(X)<=>happy(X)))&
(![X]:(~patient(X)<=>(~tall(X)<~>funny(X))))&
((?[X]:((patient(X)|happy(X))))=>(~strong(fred)))&
(![X]:((tall(X)&~generous(X))=>calm(X)))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~strong(X)|~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(![X]:(funny(X)=>(~quiet(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>humble(X)))&
(![X]:((~curious(X)<~>curious(X))<=>~happy(X)))&
(![X]:((brave(X)&~tall(X))<=>(patient(X)|wise(X))))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)&~tall(X))))&
(![X]:((strong(X)<~>generous(X))=>~calm(X)))&
(((funny(paul)|humble(paul)))=>((rich(fred)<~>kind(fred))))&
(?[X]:(~curious(X)))&
((~old(john)|rich(john)))&
(?[X]:((~old(X)&kind(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>rich(john))) | ~funny(john) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7894490970211164133662033
% SZS output start Proof for 7894490970211164133662033
1. ! [X0] : ((~rich(X0) | ~happy(X0)) <=> (quiet(X0) <~> happy(X0))) [input p0]
4. ! [X0] : (~patient(X0) <=> (~tall(X0) <~> funny(X0))) [input p3]
5. ? [X0] : (happy(X0) | patient(X0)) => ~strong(fred) [input p4]
7. ? [X0] : (creative(X0) | ~wise(X0)) <=> ? [X0] : patient(X0) [input p6]
8. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (~rich(X0) & kind(X0))) [input p7]
9. ! [X0] : ((~patient(X0) <~> ~happy(X0)) <=> (patient(X0) | ~strong(X0))) [input p8]
10. ! [X0] : (funny(X0) => (~kind(X0) | ~quiet(X0))) [input p9]
12. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> ~happy(X0)) [input p11]
13. ! [X0] : ((~tall(X0) & brave(X0)) <=> (wise(X0) | patient(X0))) [input p12]
24. funny(john) [input hypothesis]
25. ? [X0] : (creative(X0) | ~wise(X0)) <=> ? [X1] : patient(X1) [rectify 7]
26. ~strong(fred) | ! [X0] : (~happy(X0) & ~patient(X0)) [ennf transformation 5]
29. ! [X0] : ((~kind(X0) | ~quiet(X0)) | ~funny(X0)) [ennf transformation 10]
30. ! [X0] : (~kind(X0) | ~quiet(X0) | ~funny(X0)) [flattening 29]
34. ! [X0] : (((~rich(X0) | ~happy(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (rich(X0) & happy(X0)))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | ~happy(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (rich(X0) & happy(X0)))) [flattening 34]
39. ! [X0] : ((~patient(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | patient(X0))) [nnf transformation 4]
40. (? [X0] : (creative(X0) | ~wise(X0)) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : (~creative(X0) & wise(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) | ~wise(X0)) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : (~creative(X3) & wise(X3))) [rectify 40]
42. ? [X0] : (creative(X0) | ~wise(X0)) => (creative(sK0) | ~wise(sK0)) [choice axiom]
43. ? [X2] : patient(X2) => patient(sK1) [choice axiom]
44. ((creative(sK0) | ~wise(sK0)) | ! [X1] : ~patient(X1)) & (patient(sK1) | ! [X3] : (~creative(X3) & wise(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((~generous(X0) | ~strong(X0)) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | (generous(X0) & strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((~generous(X0) | ~strong(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | (generous(X0) & strong(X0)))) [flattening 45]
47. ! [X0] : ((((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0))))) [nnf transformation 9]
48. ! [X0] : ((((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0))))) [flattening 47]
50. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | happy(X0)) & (~happy(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 12]
51. ! [X0] : (((~tall(X0) & brave(X0)) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | (tall(X0) | ~brave(X0)))) [nnf transformation 13]
52. ! [X0] : (((~tall(X0) & brave(X0)) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | tall(X0) | ~brave(X0))) [flattening 51]
71. quiet(X0) | happy(X0) | rich(X0) [cnf transformation 35]
85. ~funny(X0) | tall(X0) | patient(X0) [cnf transformation 39]
86. ~patient(X0) | funny(X0) | tall(X0) [cnf transformation 39]
88. ~strong(fred) | ~patient(X0) [cnf transformation 26]
91. patient(sK1) | wise(X3) [cnf transformation 44]
94. kind(X0) | strong(X0) [cnf transformation 46]
96. ~rich(X0) | strong(X0) [cnf transformation 46]
103. patient(X0) | happy(X0) | strong(X0) [cnf transformation 48]
105. ~kind(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 30]
108. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 50]
109. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 50]
115. ~tall(X0) | ~patient(X0) [cnf transformation 52]
116. ~tall(X0) | ~wise(X0) [cnf transformation 52]
138. funny(john) [cnf transformation 24]
139. ~happy(X0) | curious(X0) [duplicate literal removal 108]
140. ~curious(X0) | ~happy(X0) [duplicate literal removal 109]
146. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
147. ~happy(X0) <- (1) [avatar component clause 146]
149. 2 <=> strong(fred) [avatar definition]
151. ~strong(fred) <- (~2) [avatar component clause 149]
154. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
155. ~patient(X0) <- (3) [avatar component clause 154]
156. 3 | ~2 [avatar split clause 88,149,154]
170. 7 <=> patient(sK1) [avatar definition]
172. patient(sK1) <- (7) [avatar component clause 170]
175. 8 <=> ! [X3] : wise(X3) [avatar definition]
176. wise(X3) <- (8) [avatar component clause 175]
177. 8 | 7 [avatar split clause 91,170,175]
179. ~happy(X0) [subsumption resolution 139,140]
180. 1 [avatar split clause 179,146]
249. tall(john) | patient(john) [resolution 85,138]
251. 19 <=> patient(john) [avatar definition]
253. patient(john) <- (19) [avatar component clause 251]
255. 20 <=> tall(john) [avatar definition]
257. tall(john) <- (20) [avatar component clause 255]
258. 19 | 20 [avatar split clause 249,255,251]
283. happy(X0) | strong(X0) | funny(X0) | tall(X0) [resolution 103,86]
286. funny(X0) | strong(X0) | tall(X0) <- (1) [subsumption resolution 283,147]
293. ~funny(X1) | ~quiet(X1) | strong(X1) [resolution 105,94]
416. ~quiet(X0) | strong(X0) | strong(X0) | tall(X0) <- (1) [resolution 293,286]
417. ~quiet(X0) | strong(X0) | tall(X0) <- (1) [duplicate literal removal 416]
530. strong(X0) | tall(X0) | happy(X0) | rich(X0) <- (1) [resolution 417,71]
536. strong(X0) | tall(X0) | rich(X0) <- (1) [subsumption resolution 530,147]
537. tall(X0) | strong(X0) <- (1) [subsumption resolution 536,96]
585. ~patient(X3) | strong(X3) <- (1) [resolution 537,115]
688. strong(X0) | happy(X0) | strong(X0) <- (1) [resolution 585,103]
691. strong(X0) | happy(X0) <- (1) [duplicate literal removal 688]
692. strong(X0) <- (1) [subsumption resolution 691,147]
693. $false <- (1, ~2) [resolution 692,151]
698. ~1 | 2 [avatar contradiction clause 693]
700. $false <- (3, 19) [resolution 155,253]
701. $false <- (3, 7) [resolution 155,172]
702. ~3 | ~7 [avatar contradiction clause 701]
703. ~3 | ~19 [avatar contradiction clause 700]
711. ~wise(john) <- (20) [resolution 257,116]
713. $false <- (8, 20) [subsumption resolution 711,176]
714. ~8 | ~20 [avatar contradiction clause 713]
715. $false [avatar sat refutation 156,177,180,258,698,702,703,714]
% SZS output end Proof for 7894490970211164133662033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not happy or not patient and vice versa. If someone is tall or brave then someone is both tall and not tall and vice versa. Everyone who is either not generous or kind is both curious and not funny. If paul is creative or humble then someone is either not calm or brave and vice versa. Everyone who is not creative or kind is either not strong or curious and vice versa. If susan is strong then lucy is both not wise and happy and vice versa. Everyone who is both strong and not humble is either generous or not wise. If someone is both not wise and funny then paul is curious. Everyone who is not curious or not brave is calm or rich and vice versa. If susan is both not generous and tall then susan is not quiet or calm. Everyone who is not kind is both not happy and creative. If someone is calm then lucy is patient and vice versa. Everyone who is both wise and curious is curious or not generous. If someone is both humble and not curious then paul is calm or not funny. Everyone who is calm is either strong or not funny and vice versa. Everyone who is either curious or not happy is both humble and not curious. Mary is not brave or not patient. Susan is both quiet and creative. Someone is either rich or not curious. Lucy is both not humble and not brave. Someone is old. Lucy is not humble. Paul is calm. | Paul is strong. | contradiction | (![X]:(~strong(X)<=>(~happy(X)|~patient(X))))&
((?[X]:((tall(X)|brave(X))))<=>(?[X]:((tall(X)&~tall(X)))))&
(![X]:((~generous(X)<~>kind(X))=>(curious(X)&~funny(X))))&
(((creative(paul)|humble(paul)))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((~creative(X)|kind(X))<=>(~strong(X)<~>curious(X))))&
((strong(susan))<=>((~wise(lucy)&happy(lucy))))&
(![X]:((strong(X)&~humble(X))=>(generous(X)<~>~wise(X))))&
((?[X]:((~wise(X)&funny(X))))=>(curious(paul)))&
(![X]:((~curious(X)|~brave(X))<=>(calm(X)|rich(X))))&
(((~generous(susan)&tall(susan)))=>((~quiet(susan)|calm(susan))))&
(![X]:(~kind(X)=>(~happy(X)&creative(X))))&
((?[X]:(calm(X)))<=>(patient(lucy)))&
(![X]:((wise(X)&curious(X))=>(curious(X)|~generous(X))))&
((?[X]:((humble(X)&~curious(X))))=>((calm(paul)|~funny(paul))))&
(![X]:(calm(X)<=>(strong(X)<~>~funny(X))))&
(![X]:((curious(X)<~>~happy(X))=>(humble(X)&~curious(X))))&
((~brave(mary)|~patient(mary)))&
((quiet(susan)&creative(susan)))&
(?[X]:((rich(X)<~>~curious(X))))&
((~humble(lucy)&~brave(lucy)))&
(?[X]:(old(X)))&
(~humble(lucy))&
(calm(paul)) | strong(paul) | [
"p0",
"p4",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4111585566805998224346439
% SZS output start Proof for 4111585566805998224346439
1. ! [X0] : (~strong(X0) <=> (~patient(X0) | ~happy(X0))) [input p0]
5. ! [X0] : ((kind(X0) | ~creative(X0)) <=> (~strong(X0) <~> curious(X0))) [input p4]
11. ! [X0] : (~kind(X0) => (creative(X0) & ~happy(X0))) [input p10]
16. ! [X0] : ((curious(X0) <~> ~happy(X0)) => (~curious(X0) & humble(X0))) [input p15]
24. strong(paul) [input hypothesis]
33. ! [X0] : ((creative(X0) & ~happy(X0)) | kind(X0)) [ennf transformation 11]
38. ! [X0] : ((~curious(X0) & humble(X0)) | (curious(X0) <=> ~happy(X0))) [ennf transformation 16]
39. ! [X0] : ((~strong(X0) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | strong(X0))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | strong(X0))) [flattening 39]
52. ! [X0] : (((kind(X0) | ~creative(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (~kind(X0) & creative(X0)))) [nnf transformation 5]
53. ! [X0] : ((kind(X0) | ~creative(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (~kind(X0) & creative(X0)))) [flattening 52]
64. ! [X0] : ((~curious(X0) & humble(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0)))) [nnf transformation 38]
69. ~strong(X0) | happy(X0) [cnf transformation 40]
87. ~kind(X0) | ~strong(X0) | curious(X0) [cnf transformation 53]
103. ~happy(X0) | kind(X0) [cnf transformation 33]
115. ~curious(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 64]
126. strong(paul) [cnf transformation 24]
127. ~curious(X0) | ~happy(X0) [duplicate literal removal 115]
189. 14 <=> curious(paul) [avatar definition]
191. curious(paul) <- (14) [avatar component clause 189]
256. happy(paul) [resolution 69,126]
258. kind(paul) [resolution 103,256]
280. ~strong(paul) | curious(paul) [resolution 87,258]
281. curious(paul) [subsumption resolution 280,126]
282. 14 [avatar split clause 281,189]
283. ~happy(paul) <- (14) [resolution 191,127]
284. $false <- (14) [subsumption resolution 283,256]
285. ~14 [avatar contradiction clause 284]
286. $false [avatar sat refutation 282,285]
% SZS output end Proof for 4111585566805998224346439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not strong is not creative or not funny.
Everyone who is not wise or not humble is wise.
Everyone who is not patient or brave is either not humble or kind and vice versa.
If someone is either not kind or not brave then someone is not rich or not kind.
If someone is not rich then someone is curious or not creative and vice versa.
Everyone who is curious is not rich.
If someone is curious then someone is tall or not funny and vice versa.
If fred is both not generous and not brave then john is either not curious or humble and vice versa.
Everyone who is either old or strong is funny.
If alice is funny then someone is not calm or not old.
If someone is both not generous and not old then someone is both happy and generous.
Everyone who is rich or brave is not rich.
Everyone who is either kind or not creative is both not generous and rich and vice versa.
If someone is both not tall and humble then someone is generous and vice versa.
If someone is not curious then john is both generous and old and vice versa.
If mary is both creative and not wise then lucy is not happy.
Someone is generous or not creative.
Susan is calm or creative.
Someone is both brave and not curious.
Mary is either not humble or curious.
Fred is not quiet or not creative.
Someone is not humble. | John is not quiet. | neutral | (![X]:((kind(X)|~strong(X))=>(~creative(X)|~funny(X))))&
(![X]:((~wise(X)|~humble(X))=>wise(X)))&
(![X]:((~patient(X)|brave(X))<=>(~humble(X)<~>kind(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(curious(X)=>~rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((tall(X)|~funny(X)))))&
(((~generous(fred)&~brave(fred)))<=>((~curious(john)<~>humble(john))))&
(![X]:((old(X)<~>strong(X))=>funny(X)))&
((funny(alice))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((rich(X)|brave(X))=>~rich(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(~generous(X)&rich(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:(~curious(X)))<=>((generous(john)&old(john))))&
(((creative(mary)&~wise(mary)))=>(~happy(lucy)))&
(?[X]:((generous(X)|~creative(X))))&
((calm(susan)|creative(susan)))&
(?[X]:((brave(X)&~curious(X))))&
((~humble(mary)<~>curious(mary)))&
((~quiet(fred)|~creative(fred)))&
(?[X]:(~humble(X))) | ~quiet(john) | [] | null | 0 |
Everyone who is not kind is not funny.
If paul is not quiet then alice is not old.
Everyone who is not tall or not old is funny or not rich and vice versa.
If someone is not kind then susan is not brave.
Everyone who is either not strong or not curious is both funny and not humble.
If lucy is both not curious and not creative then mary is either not curious or not wise and vice versa.
If someone is old then susan is both wise and not kind.
Everyone who is either not quiet or not humble is not happy.
If mary is not creative then susan is wise or not rich.
If fred is not calm or rich then someone is calm or not humble.
If someone is not tall or generous then someone is happy.
If susan is either not creative or not kind then mary is both humble and happy.
Everyone who is either funny or kind is both old and kind and vice versa.
Everyone who is wise or not kind is funny and vice versa.
Everyone who is not calm is curious or brave and vice versa.
Everyone who is both generous and patient is either not calm or rich and vice versa.
Someone is either happy or not rich.
Alice is not wise or tall.
Someone is either not patient or strong.
Someone is both not humble and not generous.
Someone is not patient or not old.
Someone is either funny or happy.
Someone is either not kind or not quiet. | Susan is not rich. | neutral | (![X]:(~kind(X)=>~funny(X)))&
((~quiet(paul))=>(~old(alice)))&
(![X]:((~tall(X)|~old(X))<=>(funny(X)|~rich(X))))&
((?[X]:(~kind(X)))=>(~brave(susan)))&
(![X]:((~strong(X)<~>~curious(X))=>(funny(X)&~humble(X))))&
(((~curious(lucy)&~creative(lucy)))<=>((~curious(mary)<~>~wise(mary))))&
((?[X]:(old(X)))=>((wise(susan)&~kind(susan))))&
(![X]:((~quiet(X)<~>~humble(X))=>~happy(X)))&
((~creative(mary))=>((wise(susan)|~rich(susan))))&
(((~calm(fred)|rich(fred)))=>(?[X]:((calm(X)|~humble(X)))))&
((?[X]:((~tall(X)|generous(X))))=>(?[X]:(happy(X))))&
(((~creative(susan)<~>~kind(susan)))=>((humble(mary)&happy(mary))))&
(![X]:((funny(X)<~>kind(X))<=>(old(X)&kind(X))))&
(![X]:((wise(X)|~kind(X))<=>funny(X)))&
(![X]:(~calm(X)<=>(curious(X)|brave(X))))&
(![X]:((generous(X)&patient(X))<=>(~calm(X)<~>rich(X))))&
(?[X]:((happy(X)<~>~rich(X))))&
((~wise(alice)|tall(alice)))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:((~patient(X)|~old(X))))&
(?[X]:((funny(X)<~>happy(X))))&
(?[X]:((~kind(X)<~>~quiet(X)))) | ~rich(susan) | [] | null | 0 |
Everyone who is kind is either calm or not wise. Everyone who is either not quiet or kind is not happy. Everyone who is not quiet is not curious or not brave. If john is either rich or not creative then john is both patient and happy. If someone is either generous or patient then lucy is either not kind or not humble and vice versa. If lucy is strong or not happy then alice is both curious and not brave. If someone is not old or not humble then lucy is not humble or patient. Everyone who is both not funny and generous is wise or tall and vice versa. If john is calm or strong then susan is both not calm and not humble. Everyone who is both not calm and not humble is not old and vice versa. If someone is either not funny or generous then someone is both curious and not humble and vice versa. Everyone who is humble or not creative is old and vice versa. Everyone who is not calm or not funny is either not wise or humble. If susan is not generous or not patient then someone is both happy and quiet and vice versa. Everyone who is not funny or generous is either strong or not strong. Everyone who is both not curious and generous is both not rich and not happy. Someone is either funny or patient. Someone is funny or not strong. Someone is tall. Someone is both not funny and not strong. Lucy is both not humble and not calm. Lucy is happy or quiet. Mary is either generous or wise. Susan is either calm or creative. | Mary is not wise. | entailment | (![X]:(kind(X)=>(calm(X)<~>~wise(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~happy(X)))&
(![X]:(~quiet(X)=>(~curious(X)|~brave(X))))&
(((rich(john)<~>~creative(john)))=>((patient(john)&happy(john))))&
((?[X]:((generous(X)<~>patient(X))))<=>((~kind(lucy)<~>~humble(lucy))))&
(((strong(lucy)|~happy(lucy)))=>((curious(alice)&~brave(alice))))&
((?[X]:((~old(X)|~humble(X))))=>((~humble(lucy)|patient(lucy))))&
(![X]:((~funny(X)&generous(X))<=>(wise(X)|tall(X))))&
(((calm(john)|strong(john)))=>((~calm(susan)&~humble(susan))))&
(![X]:((~calm(X)&~humble(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>generous(X))))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((humble(X)|~creative(X))<=>old(X)))&
(![X]:((~calm(X)|~funny(X))=>(~wise(X)<~>humble(X))))&
(((~generous(susan)|~patient(susan)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|generous(X))=>(strong(X)<~>~strong(X))))&
(![X]:((~curious(X)&generous(X))=>(~rich(X)&~happy(X))))&
(?[X]:((funny(X)<~>patient(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)&~strong(X))))&
((~humble(lucy)&~calm(lucy)))&
((happy(lucy)|quiet(lucy)))&
((generous(mary)<~>wise(mary)))&
((calm(susan)<~>creative(susan))) | ~wise(mary) | [
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 335746825003924392231484
% SZS output start Proof for 335746825003924392231484
8. ! [X0] : ((generous(X0) & ~funny(X0)) <=> (tall(X0) | wise(X0))) [input p7]
23. generous(mary) <~> wise(mary) [input p22]
25. wise(mary) [input hypothesis]
47. ! [X0] : (((generous(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0))) & ((tall(X0) | wise(X0)) | (~generous(X0) | funny(X0)))) [nnf transformation 8]
48. ! [X0] : (((generous(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0))) & (tall(X0) | wise(X0) | ~generous(X0) | funny(X0))) [flattening 47]
74. (~wise(mary) | ~generous(mary)) & (wise(mary) | generous(mary)) [nnf transformation 23]
99. generous(X0) | ~wise(X0) [cnf transformation 48]
142. ~wise(mary) | ~generous(mary) [cnf transformation 74]
145. wise(mary) [cnf transformation 25]
323. ~wise(mary) [subsumption resolution 142,99]
331. $false [subsumption resolution 145,323]
% SZS output end Proof for 335746825003924392231484
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and quiet is humble or not humble. Everyone who is funny or not generous is not kind and vice versa. If paul is old or happy then someone is either strong or brave and vice versa. If paul is either old or rich then someone is curious or humble and vice versa. If mary is happy then someone is either tall or not quiet. If paul is happy then someone is both not calm and funny and vice versa. Everyone who is kind is not creative or generous. Everyone who is not patient is wise or quiet and vice versa. Everyone who is not brave is either not quiet or quiet. Everyone who is both not strong and calm is tall and vice versa. If john is either rich or not calm then susan is either not curious or not generous. If paul is either not happy or not calm then someone is not patient or not strong and vice versa. If susan is both calm and wise then lucy is either strong or not calm and vice versa. Everyone who is either not creative or old is either curious or not happy. Everyone who is not brave is either tall or not humble and vice versa. If fred is either generous or funny then alice is patient or brave and vice versa. Someone is tall or not rich. Lucy is happy. Someone is humble. Susan is both tall and not humble. John is either not happy or not strong. Alice is either not quiet or happy. Someone is both strong and not happy. | Mary is creative. | neutral | (![X]:((strong(X)&quiet(X))=>(humble(X)|~humble(X))))&
(![X]:((funny(X)|~generous(X))<=>~kind(X)))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:((~strong(X)&calm(X))<=>tall(X)))&
(((rich(john)<~>~calm(john)))=>((~curious(susan)<~>~generous(susan))))&
(((~happy(paul)<~>~calm(paul)))<=>(?[X]:((~patient(X)|~strong(X)))))&
(((calm(susan)&wise(susan)))<=>((strong(lucy)<~>~calm(lucy))))&
(![X]:((~creative(X)<~>old(X))=>(curious(X)<~>~happy(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~humble(X))))&
(((generous(fred)<~>funny(fred)))<=>((patient(alice)|brave(alice))))&
(?[X]:((tall(X)|~rich(X))))&
(happy(lucy))&
(?[X]:(humble(X)))&
((tall(susan)&~humble(susan)))&
((~happy(john)<~>~strong(john)))&
((~quiet(alice)<~>happy(alice)))&
(?[X]:((strong(X)&~happy(X)))) | creative(mary) | [] | null | 0 |
If someone is either creative or old then someone is either not calm or not brave.
Everyone who is both not creative and creative is both wise and not tall and vice versa.
Everyone who is quiet is either happy or not tall.
If someone is both generous and brave then someone is either tall or generous and vice versa.
Everyone who is either tall or not curious is both not tall and patient.
Everyone who is patient is both not rich and curious and vice versa.
Everyone who is not quiet or not kind is either not rich or tall.
If someone is not patient then someone is both funny and not funny.
If lucy is both not old and not quiet then alice is funny or kind.
If john is both not strong and old then susan is either humble or rich.
Everyone who is not kind or kind is both strong and patient and vice versa.
Everyone who is both not brave and patient is either not calm or not patient.
If someone is either old or kind then someone is creative or not generous and vice versa.
Everyone who is either rich or not brave is both quiet and brave and vice versa.
If someone is both not curious and tall then mary is both not old and old and vice versa.
Everyone who is both not calm and not quiet is tall or wise and vice versa.
Someone is not wise.
Someone is either not quiet or not strong.
Someone is not calm or creative.
Mary is both not rich and not happy.
Someone is either not kind or not brave. | Mary is calm. | entailment | ((?[X]:((creative(X)<~>old(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~creative(X)&creative(X))<=>(wise(X)&~tall(X))))&
(![X]:(quiet(X)=>(happy(X)<~>~tall(X))))&
((?[X]:((generous(X)&brave(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((tall(X)<~>~curious(X))=>(~tall(X)&patient(X))))&
(![X]:(patient(X)<=>(~rich(X)&curious(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~rich(X)<~>tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((funny(X)&~funny(X)))))&
(((~old(lucy)&~quiet(lucy)))=>((funny(alice)|kind(alice))))&
(((~strong(john)&old(john)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~kind(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((~brave(X)&patient(X))=>(~calm(X)<~>~patient(X))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~curious(X)&tall(X))))<=>((~old(mary)&old(mary))))&
(![X]:((~calm(X)&~quiet(X))<=>(tall(X)|wise(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~calm(X)|creative(X))))&
((~rich(mary)&~happy(mary)))&
(?[X]:((~kind(X)<~>~brave(X)))) | calm(mary) | [
"p1",
"p4",
"p5",
"p10",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2250758340380558411159237
% SZS output start Proof for 2250758340380558411159237
2. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (~tall(X0) & wise(X0))) [input p1]
5. ! [X0] : ((tall(X0) <~> ~curious(X0)) => (patient(X0) & ~tall(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (curious(X0) & ~rich(X0))) [input p5]
11. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (patient(X0) & strong(X0))) [input p10]
14. ! [X0] : ((rich(X0) <~> ~brave(X0)) <=> (brave(X0) & quiet(X0))) [input p13]
15. ? [X0] : (tall(X0) & ~curious(X0)) <=> (old(mary) & ~old(mary)) [input p14]
16. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> (wise(X0) | tall(X0))) [input p15]
20. ~happy(mary) & ~rich(mary) [input p19]
22. ~calm(mary) [input hypothesis]
29. ! [X0] : ((patient(X0) & ~tall(X0)) | (tall(X0) <=> ~curious(X0))) [ennf transformation 5]
42. ! [X0] : (((creative(X0) & ~creative(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 2]
43. ! [X0] : (((creative(X0) & ~creative(X0)) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | ~creative(X0) | creative(X0))) [flattening 42]
50. ! [X0] : ((patient(X0) & ~tall(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) [nnf transformation 29]
51. ! [X0] : ((patient(X0) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [nnf transformation 6]
52. ! [X0] : ((patient(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [flattening 51]
58. ! [X0] : (((kind(X0) | ~kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 11]
59. ! [X0] : ((kind(X0) | ~kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [flattening 58]
66. ! [X0] : ((((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0))))) [nnf transformation 14]
67. ! [X0] : ((((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0))))) [flattening 66]
68. (? [X0] : (tall(X0) & ~curious(X0)) | (~old(mary) | old(mary))) & ((old(mary) & ~old(mary)) | ! [X0] : (~tall(X0) | curious(X0))) [nnf transformation 15]
69. (? [X0] : (tall(X0) & ~curious(X0)) | ~old(mary) | old(mary)) & ((old(mary) & ~old(mary)) | ! [X0] : (~tall(X0) | curious(X0))) [flattening 68]
70. (? [X0] : (tall(X0) & ~curious(X0)) | ~old(mary) | old(mary)) & ((old(mary) & ~old(mary)) | ! [X1] : (~tall(X1) | curious(X1))) [rectify 69]
71. ? [X0] : (tall(X0) & ~curious(X0)) => (tall(sK6) & ~curious(sK6)) [choice axiom]
72. ((tall(sK6) & ~curious(sK6)) | ~old(mary) | old(mary)) & ((old(mary) & ~old(mary)) | ! [X1] : (~tall(X1) | curious(X1))) [skolemisation 70,71]
73. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | (quiet(X0) | calm(X0)))) [nnf transformation 16]
74. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | quiet(X0) | calm(X0))) [flattening 73]
91. ~creative(X0) | tall(X0) | ~wise(X0) [cnf transformation 43]
92. ~wise(X0) | tall(X0) | creative(X0) [cnf transformation 43]
101. ~tall(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 50]
105. ~rich(X0) | ~patient(X0) [cnf transformation 52]
119. patient(X0) | kind(X0) [cnf transformation 59]
120. ~kind(X0) | patient(X0) [cnf transformation 59]
133. brave(X0) | rich(X0) | brave(X0) [cnf transformation 67]
134. ~brave(X0) | rich(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 67]
136. ~old(mary) | ~tall(X1) | curious(X1) [cnf transformation 72]
137. old(mary) | ~tall(X1) | curious(X1) [cnf transformation 72]
140. wise(X0) | tall(X0) | quiet(X0) | calm(X0) [cnf transformation 74]
149. ~rich(mary) [cnf transformation 20]
153. ~calm(mary) [cnf transformation 22]
154. rich(X0) | brave(X0) [duplicate literal removal 133]
155. ~quiet(X0) | rich(X0) | ~brave(X0) [duplicate literal removal 134]
157. ~curious(X0) | ~tall(X0) [duplicate literal removal 101]
176. ~wise(X0) | tall(X0) [subsumption resolution 91,92]
209. 12 <=> ! [X1] : patient(X1) [avatar definition]
210. patient(X1) <- (12) [avatar component clause 209]
252. patient(X0) [subsumption resolution 119,120]
253. 12 [avatar split clause 252,209]
289. old(mary) | ~tall(X1) [subsumption resolution 137,157]
291. 30 <=> ! [X1] : ~tall(X1) [avatar definition]
292. ~tall(X1) <- (30) [avatar component clause 291]
294. 31 <=> old(mary) [avatar definition]
297. 30 | 31 [avatar split clause 289,294,291]
298. ~old(mary) | ~tall(X1) [subsumption resolution 136,157]
299. 30 | ~31 [avatar split clause 298,294,291]
300. quiet(X0) | tall(X0) | calm(X0) [subsumption resolution 140,176]
326. brave(X0) | ~patient(X0) [resolution 154,105]
327. brave(X0) <- (12) [subsumption resolution 326,210]
347. tall(X0) | calm(X0) | rich(X0) | ~brave(X0) [resolution 300,155]
352. calm(X0) | rich(X0) | ~brave(X0) <- (30) [subsumption resolution 347,292]
353. rich(X0) | calm(X0) <- (12, 30) [subsumption resolution 352,327]
354. calm(mary) <- (12, 30) [resolution 353,149]
359. $false <- (12, 30) [subsumption resolution 354,153]
360. ~12 | ~30 [avatar contradiction clause 359]
364. $false [avatar sat refutation 253,297,299,360]
% SZS output end Proof for 2250758340380558411159237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or strong is not creative and vice versa.
Everyone who is either calm or not humble is patient or not humble and vice versa.
If someone is not quiet or strong then someone is either happy or humble and vice versa.
Everyone who is either not calm or old is either creative or kind and vice versa.
If susan is rich or not wise then alice is both strong and not wise and vice versa.
Everyone who is not humble or not brave is not patient and vice versa.
If mary is either old or not happy then someone is happy.
Everyone who is both not brave and not rich is both brave and not generous and vice versa.
If someone is not curious then susan is both not brave and not tall.
If john is not generous then someone is both strong and not quiet and vice versa.
If someone is both rich and not generous then someone is both not tall and not generous and vice versa.
Everyone who is both wise and not rich is either strong or curious and vice versa.
If someone is either curious or wise then someone is either not humble or generous and vice versa.
If someone is not strong or not patient then someone is both not humble and not brave.
Everyone who is either not rich or not humble is both generous and brave.
Fred is either not quiet or not old.
Mary is both not funny and strong.
Susan is not creative or kind.
Paul is happy.
Lucy is either happy or not curious.
Paul is brave. | Paul is calm. | entailment | (![X]:((~old(X)<~>strong(X))<=>~creative(X)))&
(![X]:((calm(X)<~>~humble(X))<=>(patient(X)|~humble(X))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((happy(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>old(X))<=>(creative(X)<~>kind(X))))&
(((rich(susan)|~wise(susan)))<=>((strong(alice)&~wise(alice))))&
(![X]:((~humble(X)|~brave(X))<=>~patient(X)))&
(((old(mary)<~>~happy(mary)))=>(?[X]:(happy(X))))&
(![X]:((~brave(X)&~rich(X))<=>(brave(X)&~generous(X))))&
((?[X]:(~curious(X)))=>((~brave(susan)&~tall(susan))))&
((~generous(john))<=>(?[X]:((strong(X)&~quiet(X)))))&
((?[X]:((rich(X)&~generous(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((wise(X)&~rich(X))<=>(strong(X)<~>curious(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:((~strong(X)|~patient(X))))=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((~rich(X)<~>~humble(X))=>(generous(X)&brave(X))))&
((~quiet(fred)<~>~old(fred)))&
((~funny(mary)&strong(mary)))&
((~creative(susan)|kind(susan)))&
(happy(paul))&
((happy(lucy)<~>~curious(lucy)))&
(brave(paul)) | calm(paul) | [
"p1",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8727532552865429875404631
% SZS output start Proof for 8727532552865429875404631
2. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (~humble(X0) | patient(X0))) [input p1]
6. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> ~patient(X0)) [input p5]
8. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (~generous(X0) & brave(X0))) [input p7]
14. ? [X0] : (~patient(X0) | ~strong(X0)) => ? [X0] : (~brave(X0) & ~humble(X0)) [input p13]
15. ! [X0] : ((~rich(X0) <~> ~humble(X0)) => (brave(X0) & generous(X0))) [input p14]
22. ~calm(paul) [input hypothesis]
26. ? [X0] : (~patient(X0) | ~strong(X0)) => ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 14]
30. ? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : (patient(X0) & strong(X0)) [ennf transformation 26]
31. ! [X0] : ((brave(X0) & generous(X0)) | (~rich(X0) <=> ~humble(X0))) [ennf transformation 15]
33. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 2]
34. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 33]
43. ! [X0] : (((~brave(X0) | ~humble(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) & humble(X0)))) [nnf transformation 6]
44. ! [X0] : ((~brave(X0) | ~humble(X0) | patient(X0)) & (~patient(X0) | (brave(X0) & humble(X0)))) [flattening 43]
48. ! [X0] : (((~rich(X0) & ~brave(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 8]
49. ! [X0] : (((~rich(X0) & ~brave(X0)) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | rich(X0) | brave(X0))) [flattening 48]
66. ? [X0] : (~brave(X0) & ~humble(X0)) | ! [X1] : (patient(X1) & strong(X1)) [rectify 30]
67. ? [X0] : (~brave(X0) & ~humble(X0)) => (~brave(sK8) & ~humble(sK8)) [choice axiom]
68. (~brave(sK8) & ~humble(sK8)) | ! [X1] : (patient(X1) & strong(X1)) [skolemisation 66,67]
69. ! [X0] : ((brave(X0) & generous(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) [nnf transformation 31]
78. ~patient(X0) | calm(X0) | ~humble(X0) [cnf transformation 34]
101. ~patient(X0) | humble(X0) [cnf transformation 44]
106. brave(X0) | rich(X0) | brave(X0) [cnf transformation 49]
134. ~humble(sK8) | patient(X1) [cnf transformation 68]
136. ~brave(sK8) | patient(X1) [cnf transformation 68]
140. brave(X0) | ~rich(X0) | humble(X0) [cnf transformation 69]
149. ~calm(paul) [cnf transformation 22]
150. brave(X0) | rich(X0) [duplicate literal removal 106]
318. 37 <=> ! [X1] : patient(X1) [avatar definition]
319. patient(X1) <- (37) [avatar component clause 318]
321. 38 <=> brave(sK8) [avatar definition]
323. ~brave(sK8) <- (~38) [avatar component clause 321]
324. 37 | ~38 [avatar split clause 136,321,318]
330. 40 <=> humble(sK8) [avatar definition]
332. ~humble(sK8) <- (~40) [avatar component clause 330]
333. 37 | ~40 [avatar split clause 134,330,318]
335. brave(X0) | humble(X0) [subsumption resolution 140,150]
377. humble(sK8) <- (~38) [resolution 335,323]
379. $false <- (~38, ~40) [subsumption resolution 377,332]
380. 38 | 40 [avatar contradiction clause 379]
383. humble(X1) <- (37) [resolution 319,101]
427. calm(X0) | ~humble(X0) <- (37) [resolution 78,319]
428. calm(X0) <- (37) [subsumption resolution 427,383]
434. $false <- (37) [resolution 428,149]
437. ~37 [avatar contradiction clause 434]
438. $false [avatar sat refutation 324,333,380,437]
% SZS output end Proof for 8727532552865429875404631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both not generous and not rich.
If lucy is both curious and not calm then lucy is strong.
Everyone who is both curious and rich is both not brave and funny.
If fred is generous or strong then fred is creative or quiet and vice versa.
Everyone who is both humble and old is rich.
Everyone who is either rich or funny is not brave and vice versa.
If someone is kind then someone is both not funny and strong and vice versa.
Everyone who is both calm and brave is brave or not brave.
If paul is either not quiet or tall then someone is both calm and not creative.
If someone is both wise and generous then someone is both tall and patient.
Everyone who is brave is not calm or not strong and vice versa.
If fred is both not generous and rich then alice is either not curious or not generous and vice versa.
If susan is not funny or not wise then someone is old or not humble and vice versa.
Everyone who is both not strong and rich is either not calm or not kind.
Everyone who is not old or not strong is generous and vice versa.
If alice is not kind then lucy is either not creative or strong.
Fred is either quiet or not brave.
Someone is either generous or not rich.
Someone is both not brave and kind.
Paul is rich or not tall.
Someone is not tall.
Someone is both not curious and creative.
Lucy is both not humble and rich.
Lucy is either not brave or not tall. | Fred is brave. | neutral | (![X]:(~strong(X)=>(~generous(X)&~rich(X))))&
(((curious(lucy)&~calm(lucy)))=>(strong(lucy)))&
(![X]:((curious(X)&rich(X))=>(~brave(X)&funny(X))))&
(((generous(fred)|strong(fred)))<=>((creative(fred)|quiet(fred))))&
(![X]:((humble(X)&old(X))=>rich(X)))&
(![X]:((rich(X)<~>funny(X))<=>~brave(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:((calm(X)&brave(X))=>(brave(X)|~brave(X))))&
(((~quiet(paul)<~>tall(paul)))=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:(brave(X)<=>(~calm(X)|~strong(X))))&
(((~generous(fred)&rich(fred)))<=>((~curious(alice)<~>~generous(alice))))&
(((~funny(susan)|~wise(susan)))<=>(?[X]:((old(X)|~humble(X)))))&
(![X]:((~strong(X)&rich(X))=>(~calm(X)<~>~kind(X))))&
(![X]:((~old(X)|~strong(X))<=>generous(X)))&
((~kind(alice))=>((~creative(lucy)<~>strong(lucy))))&
((quiet(fred)<~>~brave(fred)))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~brave(X)&kind(X))))&
((rich(paul)|~tall(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((~curious(X)&creative(X))))&
((~humble(lucy)&rich(lucy)))&
((~brave(lucy)<~>~tall(lucy))) | brave(fred) | [] | null | 0 |
If someone is patient then john is both generous and wise and vice versa. Everyone who is either not old or happy is tall. Everyone who is either not curious or not rich is both not brave and not humble. Everyone who is either not generous or not humble is wise or brave. Everyone who is both calm and old is either not wise or generous. Everyone who is both tall and wise is both not brave and not creative. Everyone who is strong or curious is not brave. If someone is not old or creative then lucy is either not creative or wise. Everyone who is not happy or not brave is not creative and vice versa. Everyone who is either not brave or not generous is not rich or old. Everyone who is wise is strong and vice versa. Everyone who is not tall is not patient. Everyone who is not calm or curious is not tall or not calm and vice versa. Everyone who is not tall or wise is either not patient or tall. Everyone who is either not quiet or not patient is tall. If susan is either not funny or not calm then someone is old or generous. Paul is not kind or humble. Paul is both tall and not generous. John is both strong and not humble. Someone is creative. Someone is both not old and quiet. Mary is not old. Fred is funny. | Fred is generous. | neutral | ((?[X]:(patient(X)))<=>((generous(john)&wise(john))))&
(![X]:((~old(X)<~>happy(X))=>tall(X)))&
(![X]:((~curious(X)<~>~rich(X))=>(~brave(X)&~humble(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(wise(X)|brave(X))))&
(![X]:((calm(X)&old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((tall(X)&wise(X))=>(~brave(X)&~creative(X))))&
(![X]:((strong(X)|curious(X))=>~brave(X)))&
((?[X]:((~old(X)|creative(X))))=>((~creative(lucy)<~>wise(lucy))))&
(![X]:((~happy(X)|~brave(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>~generous(X))=>(~rich(X)|old(X))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:(~tall(X)=>~patient(X)))&
(![X]:((~calm(X)|curious(X))<=>(~tall(X)|~calm(X))))&
(![X]:((~tall(X)|wise(X))=>(~patient(X)<~>tall(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>tall(X)))&
(((~funny(susan)<~>~calm(susan)))=>(?[X]:((old(X)|generous(X)))))&
((~kind(paul)|humble(paul)))&
((tall(paul)&~generous(paul)))&
((strong(john)&~humble(john)))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)&quiet(X))))&
(~old(mary))&
(funny(fred)) | generous(fred) | [] | null | 0 |
Everyone who is generous or not calm is not tall.
If fred is not humble or not tall then alice is both not patient and not humble and vice versa.
If someone is not funny or not patient then mary is brave and vice versa.
Everyone who is old is both not old and curious and vice versa.
Everyone who is happy is either brave or strong and vice versa.
If someone is not creative then susan is not rich or patient and vice versa.
Everyone who is either humble or brave is either strong or not rich.
If paul is not patient or brave then someone is kind.
If paul is both quiet and not curious then alice is both calm and old.
Everyone who is not tall or calm is both not strong and not calm and vice versa.
Everyone who is both not old and not kind is either calm or not generous.
Everyone who is generous or wise is not old or not generous.
Everyone who is either rich or old is not funny.
If someone is either calm or happy then someone is either not funny or not curious and vice versa.
Everyone who is either old or creative is both not creative and not patient.
Mary is strong or generous.
Someone is either generous or happy.
Fred is both not kind and not calm.
Susan is both not creative and patient.
Mary is creative or not patient.
Someone is either not humble or generous.
Someone is either humble or quiet. | Susan is brave. | neutral | (![X]:((generous(X)|~calm(X))=>~tall(X)))&
(((~humble(fred)|~tall(fred)))<=>((~patient(alice)&~humble(alice))))&
((?[X]:((~funny(X)|~patient(X))))<=>(brave(mary)))&
(![X]:(old(X)<=>(~old(X)&curious(X))))&
(![X]:(happy(X)<=>(brave(X)<~>strong(X))))&
((?[X]:(~creative(X)))<=>((~rich(susan)|patient(susan))))&
(![X]:((humble(X)<~>brave(X))=>(strong(X)<~>~rich(X))))&
(((~patient(paul)|brave(paul)))=>(?[X]:(kind(X))))&
(((quiet(paul)&~curious(paul)))=>((calm(alice)&old(alice))))&
(![X]:((~tall(X)|calm(X))<=>(~strong(X)&~calm(X))))&
(![X]:((~old(X)&~kind(X))=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)|wise(X))=>(~old(X)|~generous(X))))&
(![X]:((rich(X)<~>old(X))=>~funny(X)))&
((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((old(X)<~>creative(X))=>(~creative(X)&~patient(X))))&
((strong(mary)|generous(mary)))&
(?[X]:((generous(X)<~>happy(X))))&
((~kind(fred)&~calm(fred)))&
((~creative(susan)&patient(susan)))&
((creative(mary)|~patient(mary)))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((humble(X)<~>quiet(X)))) | brave(susan) | [] | null | 0 |
Everyone who is both not calm and patient is not patient and vice versa. Everyone who is either wise or not kind is either not wise or kind and vice versa. Everyone who is not happy is brave and vice versa. If someone is not tall or quiet then susan is quiet and vice versa. Everyone who is either not generous or creative is either rich or not quiet and vice versa. If fred is either tall or brave then someone is calm or wise. If someone is creative then lucy is both rich and not calm and vice versa. Everyone who is not humble is not rich and vice versa. If someone is either rich or not strong then alice is either not quiet or not brave and vice versa. Everyone who is kind is not kind or not calm. If someone is either not rich or not patient then someone is not generous or rich and vice versa. If susan is either not creative or not calm then john is either not wise or not patient. If fred is curious or not brave then john is both old and not patient. If someone is both not tall and not calm then someone is not strong and vice versa. Everyone who is both tall and curious is quiet and vice versa. Everyone who is both not wise and quiet is generous or creative. Susan is patient. Someone is not quiet. Someone is not rich. Mary is both funny and generous. Alice is calm. Someone is both funny and not quiet. | Fred is not patient. | contradiction | (![X]:((~calm(X)&patient(X))<=>~patient(X)))&
(![X]:((wise(X)<~>~kind(X))<=>(~wise(X)<~>kind(X))))&
(![X]:(~happy(X)<=>brave(X)))&
((?[X]:((~tall(X)|quiet(X))))<=>(quiet(susan)))&
(![X]:((~generous(X)<~>creative(X))<=>(rich(X)<~>~quiet(X))))&
(((tall(fred)<~>brave(fred)))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:(creative(X)))<=>((rich(lucy)&~calm(lucy))))&
(![X]:(~humble(X)<=>~rich(X)))&
((?[X]:((rich(X)<~>~strong(X))))<=>((~quiet(alice)<~>~brave(alice))))&
(![X]:(kind(X)=>(~kind(X)|~calm(X))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~generous(X)|rich(X)))))&
(((~creative(susan)<~>~calm(susan)))=>((~wise(john)<~>~patient(john))))&
(((curious(fred)|~brave(fred)))=>((old(john)&~patient(john))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)&curious(X))<=>quiet(X)))&
(![X]:((~wise(X)&quiet(X))=>(generous(X)|creative(X))))&
(patient(susan))&
(?[X]:(~quiet(X)))&
(?[X]:(~rich(X)))&
((funny(mary)&generous(mary)))&
(calm(alice))&
(?[X]:((funny(X)&~quiet(X)))) | ~patient(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 6559642895250078686932433
% SZS output start Proof for 6559642895250078686932433
1. ! [X0] : ((patient(X0) & ~calm(X0)) <=> ~patient(X0)) [input p0]
23. ~patient(fred) [input hypothesis]
36. ! [X0] : (((patient(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~patient(X0) | calm(X0)))) [nnf transformation 1]
37. ! [X0] : (((patient(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~patient(X0) | calm(X0))) [flattening 36]
77. patient(X0) | patient(X0) [cnf transformation 37]
136. ~patient(fred) [cnf transformation 23]
147. patient(X0) [duplicate literal removal 77]
236. $false [subsumption resolution 136,147]
% SZS output end Proof for 6559642895250078686932433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not patient then paul is rich and vice versa. Everyone who is either wise or not strong is not rich or calm. Everyone who is humble is both happy and brave. Everyone who is not calm is not quiet or not funny. If someone is either quiet or generous then alice is not brave or not rich. If john is not humble then mary is either not humble or humble. If someone is both rich and quiet then someone is either wise or not happy and vice versa. Everyone who is not creative or not patient is both humble and not brave and vice versa. If mary is not kind then mary is either not wise or not generous and vice versa. Everyone who is either not creative or strong is either not creative or not brave and vice versa. Everyone who is not happy is both curious and tall. Everyone who is not rich is old or kind and vice versa. If someone is not old or humble then mary is either brave or not brave and vice versa. Everyone who is calm or not brave is both not calm and rich. Everyone who is rich is either generous or not rich. Everyone who is rich is either creative or generous. Someone is either patient or not kind. Fred is either not kind or kind. Someone is either generous or quiet. Someone is either not strong or happy. Lucy is wise. Someone is not strong or tall. | Alice is not humble. | neutral | ((?[X]:((~quiet(X)&~patient(X))))<=>(rich(paul)))&
(![X]:((wise(X)<~>~strong(X))=>(~rich(X)|calm(X))))&
(![X]:(humble(X)=>(happy(X)&brave(X))))&
(![X]:(~calm(X)=>(~quiet(X)|~funny(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>((~brave(alice)|~rich(alice))))&
((~humble(john))=>((~humble(mary)<~>humble(mary))))&
((?[X]:((rich(X)&quiet(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(humble(X)&~brave(X))))&
((~kind(mary))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>strong(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~happy(X)=>(curious(X)&tall(X))))&
(![X]:(~rich(X)<=>(old(X)|kind(X))))&
((?[X]:((~old(X)|humble(X))))<=>((brave(mary)<~>~brave(mary))))&
(![X]:((calm(X)|~brave(X))=>(~calm(X)&rich(X))))&
(![X]:(rich(X)=>(generous(X)<~>~rich(X))))&
(![X]:(rich(X)=>(creative(X)<~>generous(X))))&
(?[X]:((patient(X)<~>~kind(X))))&
((~kind(fred)<~>kind(fred)))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(wise(lucy))&
(?[X]:((~strong(X)|tall(X)))) | ~humble(alice) | [] | null | 0 |
Everyone who is either not wise or not brave is old and vice versa.
Everyone who is both not humble and not funny is either old or quiet.
If john is either not generous or not quiet then someone is either wise or patient.
Everyone who is generous is either old or generous and vice versa.
If someone is both old and not patient then someone is either patient or not quiet and vice versa.
If someone is patient then paul is old or kind and vice versa.
Everyone who is both patient and not calm is not wise or calm.
Everyone who is both not kind and not brave is not old or not kind and vice versa.
Everyone who is quiet or not strong is strong or funny.
Everyone who is not generous or humble is generous.
Everyone who is both not generous and humble is either happy or not wise and vice versa.
Everyone who is not rich or curious is both not quiet and not wise and vice versa.
If alice is quiet then someone is quiet.
Lucy is not tall or calm.
Someone is not kind or not strong.
John is not curious.
Alice is funny or creative. | Lucy is not wise. | entailment | (![X]:((~wise(X)<~>~brave(X))<=>old(X)))&
(![X]:((~humble(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~generous(john)<~>~quiet(john)))=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(generous(X)<=>(old(X)<~>generous(X))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(patient(X)))<=>((old(paul)|kind(paul))))&
(![X]:((patient(X)&~calm(X))=>(~wise(X)|calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)|~strong(X))=>(strong(X)|funny(X))))&
(![X]:((~generous(X)|humble(X))=>generous(X)))&
(![X]:((~generous(X)&humble(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~rich(X)|curious(X))<=>(~quiet(X)&~wise(X))))&
((quiet(alice))=>(?[X]:(quiet(X))))&
((~tall(lucy)|calm(lucy)))&
(?[X]:((~kind(X)|~strong(X))))&
(~curious(john))&
((funny(alice)|creative(alice))) | ~wise(lucy) | [
"p0",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2699818340970659004502837
% SZS output start Proof for 2699818340970659004502837
1. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> old(X0)) [input p0]
4. ! [X0] : (generous(X0) <=> (old(X0) <~> generous(X0))) [input p3]
8. ! [X0] : ((~brave(X0) & ~kind(X0)) <=> (~kind(X0) | ~old(X0))) [input p7]
18. wise(lucy) [input hypothesis]
29. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ~old(X0)) & (old(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 1]
33. ! [X0] : ((generous(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) & (((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~generous(X0))) [nnf transformation 4]
44. ! [X0] : (((~brave(X0) & ~kind(X0)) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | (brave(X0) | kind(X0)))) [nnf transformation 8]
45. ! [X0] : (((~brave(X0) & ~kind(X0)) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | brave(X0) | kind(X0))) [flattening 44]
53. ~wise(X0) | old(X0) | brave(X0) [cnf transformation 29]
61. ~generous(X0) | ~old(X0) | ~generous(X0) [cnf transformation 33]
62. generous(X0) | generous(X0) | ~old(X0) [cnf transformation 33]
76. ~brave(X0) | old(X0) [cnf transformation 45]
93. wise(lucy) [cnf transformation 18]
95. ~generous(X0) | ~old(X0) [duplicate literal removal 61]
96. ~old(X0) | generous(X0) [duplicate literal removal 62]
117. ~old(X0) [subsumption resolution 95,96]
148. ~brave(X0) [subsumption resolution 76,117]
177. old(lucy) | brave(lucy) [resolution 53,93]
179. brave(lucy) [subsumption resolution 177,117]
180. $false [subsumption resolution 179,148]
% SZS output end Proof for 2699818340970659004502837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not curious is both not creative and not generous. Everyone who is rich or not funny is not calm or creative. Everyone who is patient is both curious and happy. Everyone who is not old or not wise is either not happy or tall. Everyone who is patient is both calm and strong. If someone is either not happy or creative then someone is humble or not brave. Everyone who is not calm or not curious is both curious and kind and vice versa. If someone is kind or brave then mary is both calm and not patient. If susan is both tall and patient then lucy is either quiet or strong. If lucy is both not kind and strong then someone is both not brave and wise and vice versa. If someone is both not calm and wise then lucy is curious. If susan is not calm then someone is either not calm or not patient. Everyone who is creative or not calm is both not happy and happy. Everyone who is not brave or not old is wise or strong and vice versa. If someone is not tall or kind then someone is not calm or strong and vice versa. Mary is not generous or calm. Lucy is either calm or quiet. Someone is generous. Mary is not wise or tall. Someone is both not generous and strong. | Mary is quiet. | neutral | (![X]:((humble(X)|~curious(X))=>(~creative(X)&~generous(X))))&
(![X]:((rich(X)|~funny(X))=>(~calm(X)|creative(X))))&
(![X]:(patient(X)=>(curious(X)&happy(X))))&
(![X]:((~old(X)|~wise(X))=>(~happy(X)<~>tall(X))))&
(![X]:(patient(X)=>(calm(X)&strong(X))))&
((?[X]:((~happy(X)<~>creative(X))))=>(?[X]:((humble(X)|~brave(X)))))&
(![X]:((~calm(X)|~curious(X))<=>(curious(X)&kind(X))))&
((?[X]:((kind(X)|brave(X))))=>((calm(mary)&~patient(mary))))&
(((tall(susan)&patient(susan)))=>((quiet(lucy)<~>strong(lucy))))&
(((~kind(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&wise(X)))))&
((?[X]:((~calm(X)&wise(X))))=>(curious(lucy)))&
((~calm(susan))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((creative(X)|~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|~old(X))<=>(wise(X)|strong(X))))&
((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((~calm(X)|strong(X)))))&
((~generous(mary)|calm(mary)))&
((calm(lucy)<~>quiet(lucy)))&
(?[X]:(generous(X)))&
((~wise(mary)|tall(mary)))&
(?[X]:((~generous(X)&strong(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is not strong or not generous is both old and not tall and vice versa.
Everyone who is both tall and not creative is both not funny and quiet and vice versa.
Everyone who is rich or not strong is both not funny and not patient and vice versa.
Everyone who is curious is either not quiet or not rich.
If someone is both not wise and brave then alice is either tall or not wise and vice versa.
Everyone who is creative or not funny is not old or funny.
Everyone who is creative or not creative is not generous or not old and vice versa.
Everyone who is not generous is patient or not rich and vice versa.
If lucy is both not patient and creative then someone is calm.
Everyone who is not humble is either not creative or not tall.
If paul is either calm or not strong then someone is not quiet and vice versa.
If fred is not rich or not curious then alice is happy.
If someone is rich then paul is not humble and vice versa.
If mary is either curious or not strong then lucy is either not happy or not calm and vice versa.
Everyone who is creative is both quiet and humble and vice versa.
If mary is both not kind and creative then someone is not kind or happy and vice versa.
Mary is not brave.
John is not creative.
Paul is both not kind and not brave.
Alice is either funny or curious.
Someone is wise.
Alice is either wise or not calm.
Someone is both not generous and not tall. | Fred is happy. | neutral | (![X]:((~strong(X)|~generous(X))<=>(old(X)&~tall(X))))&
(![X]:((tall(X)&~creative(X))<=>(~funny(X)&quiet(X))))&
(![X]:((rich(X)|~strong(X))<=>(~funny(X)&~patient(X))))&
(![X]:(curious(X)=>(~quiet(X)<~>~rich(X))))&
((?[X]:((~wise(X)&brave(X))))<=>((tall(alice)<~>~wise(alice))))&
(![X]:((creative(X)|~funny(X))=>(~old(X)|funny(X))))&
(![X]:((creative(X)|~creative(X))<=>(~generous(X)|~old(X))))&
(![X]:(~generous(X)<=>(patient(X)|~rich(X))))&
(((~patient(lucy)&creative(lucy)))=>(?[X]:(calm(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~tall(X))))&
(((calm(paul)<~>~strong(paul)))<=>(?[X]:(~quiet(X))))&
(((~rich(fred)|~curious(fred)))=>(happy(alice)))&
((?[X]:(rich(X)))<=>(~humble(paul)))&
(((curious(mary)<~>~strong(mary)))<=>((~happy(lucy)<~>~calm(lucy))))&
(![X]:(creative(X)<=>(quiet(X)&humble(X))))&
(((~kind(mary)&creative(mary)))<=>(?[X]:((~kind(X)|happy(X)))))&
(~brave(mary))&
(~creative(john))&
((~kind(paul)&~brave(paul)))&
((funny(alice)<~>curious(alice)))&
(?[X]:(wise(X)))&
((wise(alice)<~>~calm(alice)))&
(?[X]:((~generous(X)&~tall(X)))) | happy(fred) | [] | null | 0 |
If fred is not generous or happy then someone is either not patient or not humble and vice versa. If john is kind or not strong then someone is both old and tall and vice versa. If mary is not rich then lucy is funny and vice versa. If someone is either not generous or not brave then mary is either not funny or not patient. Everyone who is both not curious and not brave is patient and vice versa. Everyone who is either calm or brave is humble and vice versa. Everyone who is either not old or strong is creative. Everyone who is not kind is either happy or calm. Everyone who is not tall is either not kind or tall and vice versa. Everyone who is not happy is both old and not tall. Everyone who is either not old or not happy is both patient and curious and vice versa. Everyone who is either not happy or not quiet is either not curious or not generous. Everyone who is tall is either calm or not funny. If someone is either not happy or not rich then someone is not kind and vice versa. Everyone who is either wise or patient is either humble or calm. If someone is not creative or not calm then someone is both not calm and rich and vice versa. Mary is not creative or generous. Someone is not creative. Mary is both strong and quiet. Fred is not strong. Someone is either calm or tall. | John is happy. | entailment | (((~generous(fred)|happy(fred)))<=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((kind(john)|~strong(john)))<=>(?[X]:((old(X)&tall(X)))))&
((~rich(mary))<=>(funny(lucy)))&
((?[X]:((~generous(X)<~>~brave(X))))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~curious(X)&~brave(X))<=>patient(X)))&
(![X]:((calm(X)<~>brave(X))<=>humble(X)))&
(![X]:((~old(X)<~>strong(X))=>creative(X)))&
(![X]:(~kind(X)=>(happy(X)<~>calm(X))))&
(![X]:(~tall(X)<=>(~kind(X)<~>tall(X))))&
(![X]:(~happy(X)=>(old(X)&~tall(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(~curious(X)<~>~generous(X))))&
(![X]:(tall(X)=>(calm(X)<~>~funny(X))))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)<~>patient(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>(?[X]:((~calm(X)&rich(X)))))&
((~creative(mary)|generous(mary)))&
(?[X]:(~creative(X)))&
((strong(mary)&quiet(mary)))&
(~strong(fred))&
(?[X]:((calm(X)<~>tall(X)))) | happy(john) | [
"p4",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8883783042266366947104173
% SZS output start Proof for 8883783042266366947104173
5. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> patient(X0)) [input p4]
10. ! [X0] : (~happy(X0) => (~tall(X0) & old(X0))) [input p9]
11. ! [X0] : ((~old(X0) <~> ~happy(X0)) <=> (curious(X0) & patient(X0))) [input p10]
22. ~happy(john) [input hypothesis]
28. ! [X0] : ((~tall(X0) & old(X0)) | happy(X0)) [ennf transformation 10]
44. ! [X0] : (((~brave(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (brave(X0) | curious(X0)))) [nnf transformation 5]
45. ! [X0] : (((~brave(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | brave(X0) | curious(X0))) [flattening 44]
50. ! [X0] : ((((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))))) [nnf transformation 11]
51. ! [X0] : ((((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))))) [flattening 50]
88. ~curious(X0) | ~patient(X0) [cnf transformation 45]
102. old(X0) | happy(X0) [cnf transformation 28]
105. patient(X0) | ~old(X0) | happy(X0) [cnf transformation 51]
107. curious(X0) | ~old(X0) | happy(X0) [cnf transformation 51]
136. ~happy(john) [cnf transformation 22]
220. curious(X0) | happy(X0) [subsumption resolution 107,102]
222. patient(X0) | happy(X0) [subsumption resolution 105,102]
287. happy(X0) | ~patient(X0) [resolution 220,88]
288. happy(X0) [subsumption resolution 287,222]
289. $false [resolution 288,136]
% SZS output end Proof for 8883783042266366947104173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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