premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either brave or patient is either old or happy.
If lucy is not kind then someone is either curious or generous.
Everyone who is brave is both not rich and tall and vice versa.
Everyone who is either calm or not rich is rich or not calm and vice versa.
Everyone who is funny is curious and vice versa.
Everyone who is not curious or not rich is either humble or not humble and vice versa.
Everyone who is both old and wise is both old and rich and vice versa.
Everyone who is tall is not calm or not tall and vice versa.
If lucy is either wise or calm then someone is not rich or calm and vice versa.
If someone is either not happy or not wise then someone is both creative and not creative and vice versa.
Everyone who is not funny or creative is either brave or not patient.
Everyone who is not old or not humble is either strong or patient and vice versa.
If fred is not calm or tall then susan is patient or not strong.
If someone is either not generous or old then fred is either not tall or not patient.
Everyone who is both not rich and patient is curious.
If someone is both brave and creative then someone is both wise and tall.
Someone is curious or not brave.
John is not strong or wise.
Someone is both not quiet and creative.
John is either strong or funny.
Someone is either brave or not kind.
Fred is creative.
Someone is both not wise and generous.
Alice is not generous or not humble. | Fred is patient. | entailment | (![X]:((brave(X)<~>patient(X))=>(old(X)<~>happy(X))))&
((~kind(lucy))=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:(brave(X)<=>(~rich(X)&tall(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(rich(X)|~calm(X))))&
(![X]:(funny(X)<=>curious(X)))&
(![X]:((~curious(X)|~rich(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((old(X)&wise(X))<=>(old(X)&rich(X))))&
(![X]:(tall(X)<=>(~calm(X)|~tall(X))))&
(((wise(lucy)<~>calm(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((~funny(X)|creative(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~old(X)|~humble(X))<=>(strong(X)<~>patient(X))))&
(((~calm(fred)|tall(fred)))=>((patient(susan)|~strong(susan))))&
((?[X]:((~generous(X)<~>old(X))))=>((~tall(fred)<~>~patient(fred))))&
(![X]:((~rich(X)&patient(X))=>curious(X)))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((wise(X)&tall(X)))))&
(?[X]:((curious(X)|~brave(X))))&
((~strong(john)|wise(john)))&
(?[X]:((~quiet(X)&creative(X))))&
((strong(john)<~>funny(john)))&
(?[X]:((brave(X)<~>~kind(X))))&
(creative(fred))&
(?[X]:((~wise(X)&generous(X))))&
((~generous(alice)|~humble(alice))) | patient(fred) | [
"p2",
"p3",
"p7",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6726606820183336864668616
% SZS output start Proof for 6726606820183336864668616
3. ! [X0] : (brave(X0) <=> (tall(X0) & ~rich(X0))) [input p2]
4. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (~calm(X0) | rich(X0))) [input p3]
8. ! [X0] : (tall(X0) <=> (~tall(X0) | ~calm(X0))) [input p7]
11. ! [X0] : ((creative(X0) | ~funny(X0)) => (brave(X0) <~> ~patient(X0))) [input p10]
22. creative(fred) [input p21]
25. ~patient(fred) [input hypothesis]
31. ! [X0] : ((brave(X0) <~> ~patient(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 11]
42. ! [X0] : ((brave(X0) | (~tall(X0) | rich(X0))) & ((tall(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 3]
43. ! [X0] : ((brave(X0) | ~tall(X0) | rich(X0)) & ((tall(X0) & ~rich(X0)) | ~brave(X0))) [flattening 42]
44. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (calm(X0) & ~rich(X0))) & ((~calm(X0) | rich(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 4]
45. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (calm(X0) & ~rich(X0))) & (~calm(X0) | rich(X0) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [flattening 44]
51. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | ~tall(X0))) [nnf transformation 8]
52. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 51]
62. ! [X0] : (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~creative(X0) & funny(X0))) [nnf transformation 31]
87. ~tall(X0) | brave(X0) | rich(X0) [cnf transformation 43]
91. ~rich(X0) | calm(X0) | calm(X0) [cnf transformation 45]
106. ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 52]
108. tall(X0) | tall(X0) [cnf transformation 52]
124. ~creative(X0) | ~brave(X0) | patient(X0) [cnf transformation 62]
147. creative(fred) [cnf transformation 22]
151. ~patient(fred) [cnf transformation 25]
152. ~tall(X0) | ~calm(X0) [duplicate literal removal 106]
153. tall(X0) [duplicate literal removal 108]
159. ~rich(X0) | calm(X0) [duplicate literal removal 91]
175. ~calm(X0) [subsumption resolution 152,153]
216. 12 <=> patient(fred) [avatar definition]
218. ~patient(fred) <- (~12) [avatar component clause 216]
276. ~12 [avatar split clause 151,216]
288. rich(X0) | brave(X0) [resolution 87,153]
314. ~brave(fred) | patient(fred) [resolution 124,147]
317. brave(X2) | calm(X2) [resolution 288,159]
319. brave(X2) [subsumption resolution 317,175]
338. patient(fred) [subsumption resolution 314,319]
339. $false <- (~12) [subsumption resolution 338,218]
340. 12 [avatar contradiction clause 339]
342. $false [avatar sat refutation 276,340]
% SZS output end Proof for 6726606820183336864668616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not happy then lucy is both not rich and old and vice versa. Everyone who is rich or not kind is both not happy and not creative and vice versa. If someone is curious or generous then susan is either patient or old. Everyone who is humble or not old is not humble or happy. If paul is not rich then paul is either not patient or not kind. Everyone who is calm or not happy is humble or wise. If someone is strong or wise then someone is either not calm or calm and vice versa. Everyone who is not old or rich is patient. Everyone who is either patient or not patient is both not brave and not wise and vice versa. Everyone who is kind or not creative is both happy and not calm. If lucy is both not quiet and wise then someone is not wise. If lucy is either not calm or not humble then paul is both generous and not wise. Everyone who is both not happy and not old is either humble or creative and vice versa. Fred is not humble or old. Someone is not patient or funny. Someone is both not old and funny. Fred is either funny or rich. Fred is either generous or not humble. | Paul is old. | entailment | ((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(((~calm(lucy)<~>~humble(lucy)))=>((generous(paul)&~wise(paul))))&
(![X]:((~happy(X)&~old(X))<=>(humble(X)<~>creative(X))))&
((~humble(fred)|old(fred)))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((~old(X)&funny(X))))&
((funny(fred)<~>rich(fred)))&
((generous(fred)<~>~humble(fred))) | old(paul) | [
"p1",
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5704666756289987988940164
% SZS output start Proof for 5704666756289987988940164
2. ! [X0] : ((~kind(X0) | rich(X0)) <=> (~creative(X0) & ~happy(X0))) [input p1]
5. ~rich(paul) => (~patient(paul) <~> ~kind(paul)) [input p4]
8. ! [X0] : ((rich(X0) | ~old(X0)) => patient(X0)) [input p7]
10. ! [X0] : ((~creative(X0) | kind(X0)) => (~calm(X0) & happy(X0))) [input p9]
19. ~old(paul) [input hypothesis]
26. (~patient(paul) <~> ~kind(paul)) | rich(paul) [ennf transformation 5]
29. ! [X0] : (patient(X0) | (~rich(X0) & old(X0))) [ennf transformation 8]
30. ! [X0] : ((~calm(X0) & happy(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 10]
37. ! [X0] : (((~kind(X0) | rich(X0)) | (creative(X0) | happy(X0))) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~kind(X0) | rich(X0) | creative(X0) | happy(X0)) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [flattening 37]
40. ((kind(paul) | patient(paul)) & (~kind(paul) | ~patient(paul))) | rich(paul) [nnf transformation 26]
63. ~rich(X0) | ~happy(X0) [cnf transformation 38]
64. ~happy(X0) | kind(X0) [cnf transformation 38]
65. ~creative(X0) | ~rich(X0) [cnf transformation 38]
66. ~creative(X0) | kind(X0) [cnf transformation 38]
72. ~kind(paul) | ~patient(paul) | rich(paul) [cnf transformation 40]
82. patient(X0) | old(X0) [cnf transformation 29]
91. creative(X0) | happy(X0) [cnf transformation 30]
112. ~old(paul) [cnf transformation 19]
162. 10 <=> rich(paul) [avatar definition]
164. rich(paul) <- (10) [avatar component clause 162]
166. 11 <=> patient(paul) [avatar definition]
167. ~patient(paul) <- (~11) [avatar component clause 166]
170. 12 <=> kind(paul) [avatar definition]
171. ~kind(paul) <- (~12) [avatar component clause 170]
174. 10 | ~11 | ~12 [avatar split clause 72,170,166,162]
247. happy(X0) | kind(X0) [resolution 91,66]
248. happy(X1) | ~rich(X1) [resolution 91,65]
249. kind(X0) [subsumption resolution 247,64]
250. ~rich(X1) [subsumption resolution 248,63]
254. $false <- (10) [resolution 250,164]
255. ~10 [avatar contradiction clause 254]
256. $false <- (~12) [subsumption resolution 171,249]
257. 12 [avatar contradiction clause 256]
258. old(paul) <- (~11) [resolution 167,82]
259. $false <- (~11) [subsumption resolution 258,112]
260. 11 [avatar contradiction clause 259]
261. $false [avatar sat refutation 174,255,257,260]
% SZS output end Proof for 5704666756289987988940164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then fred is not patient or not happy.
Everyone who is not wise is either not generous or quiet.
If mary is both kind and generous then someone is either creative or wise.
If someone is not calm or strong then someone is either not tall or rich and vice versa.
If someone is either not patient or brave then someone is either humble or not old.
Everyone who is not happy is both not wise and quiet and vice versa.
If alice is both generous and not humble then fred is both humble and not happy and vice versa.
If someone is creative or happy then someone is strong and vice versa.
If someone is both not generous and humble then susan is either not wise or not curious and vice versa.
If someone is not patient then mary is not calm.
If mary is calm or humble then fred is both wise and not old and vice versa.
If paul is not generous then someone is both curious and happy.
Everyone who is not generous is either happy or not humble.
Everyone who is either not creative or old is either not creative or patient.
If someone is either happy or not calm then someone is either kind or funny.
Everyone who is either not creative or generous is not tall.
Susan is not strong.
Someone is both patient and not generous.
Someone is either quiet or not old.
Someone is humble or not rich.
Someone is either not calm or wise.
Mary is happy or not generous.
Someone is rich.
Someone is not kind. | Mary is not happy. | contradiction | ((rich(john))=>((~patient(fred)|~happy(fred))))&
(![X]:(~wise(X)=>(~generous(X)<~>quiet(X))))&
(((kind(mary)&generous(mary)))=>(?[X]:((creative(X)<~>wise(X)))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((~tall(X)<~>rich(X)))))&
((?[X]:((~patient(X)<~>brave(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
(![X]:(~happy(X)<=>(~wise(X)&quiet(X))))&
(((generous(alice)&~humble(alice)))<=>((humble(fred)&~happy(fred))))&
((?[X]:((creative(X)|happy(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((~wise(susan)<~>~curious(susan))))&
((?[X]:(~patient(X)))=>(~calm(mary)))&
(((calm(mary)|humble(mary)))<=>((wise(fred)&~old(fred))))&
((~generous(paul))=>(?[X]:((curious(X)&happy(X)))))&
(![X]:(~generous(X)=>(happy(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>old(X))=>(~creative(X)<~>patient(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((~creative(X)<~>generous(X))=>~tall(X)))&
(~strong(susan))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((~calm(X)<~>wise(X))))&
((happy(mary)|~generous(mary)))&
(?[X]:(rich(X)))&
(?[X]:(~kind(X))) | ~happy(mary) | [
"p1",
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9212355564484518342381983
% SZS output start Proof for 9212355564484518342381983
2. ! [X0] : (~wise(X0) => (~generous(X0) <~> quiet(X0))) [input p1]
6. ! [X0] : (~happy(X0) <=> (quiet(X0) & ~wise(X0))) [input p5]
22. ~generous(mary) | happy(mary) [input p21]
25. ~happy(mary) [input hypothesis]
32. ! [X0] : ((~generous(X0) <~> quiet(X0)) | wise(X0)) [ennf transformation 2]
42. ! [X0] : (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | wise(X0)) [nnf transformation 32]
55. ! [X0] : ((~happy(X0) | (~quiet(X0) | wise(X0))) & ((quiet(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 6]
56. ! [X0] : ((~happy(X0) | ~quiet(X0) | wise(X0)) & ((quiet(X0) & ~wise(X0)) | happy(X0))) [flattening 55]
95. ~quiet(X0) | generous(X0) | wise(X0) [cnf transformation 42]
108. ~wise(X0) | happy(X0) [cnf transformation 56]
109. quiet(X0) | happy(X0) [cnf transformation 56]
152. ~generous(mary) | happy(mary) [cnf transformation 22]
155. ~happy(mary) [cnf transformation 25]
176. 5 <=> generous(mary) [avatar definition]
178. ~generous(mary) <- (~5) [avatar component clause 176]
390. 51 <=> happy(mary) [avatar definition]
391. ~happy(mary) <- (~51) [avatar component clause 390]
393. 51 | ~5 [avatar split clause 152,176,390]
394. ~51 [avatar split clause 155,390]
408. generous(X0) | wise(X0) | happy(X0) [resolution 95,109]
409. generous(X0) | happy(X0) [subsumption resolution 408,108]
420. happy(mary) <- (~5) [resolution 409,178]
424. $false <- (~5, ~51) [subsumption resolution 420,391]
425. 5 | 51 [avatar contradiction clause 424]
426. $false [avatar sat refutation 393,394,425]
% SZS output end Proof for 9212355564484518342381983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If susan is brave then paul is either kind or not creative and vice versa.
Everyone who is not kind or not rich is both not wise and not humble and vice versa.
Everyone who is both not quiet and rich is either not creative or wise and vice versa.
If someone is wise or happy then fred is not strong or humble and vice versa.
If john is either not happy or humble then lucy is either not quiet or not wise.
Everyone who is either patient or not happy is both not humble and not patient.
If john is both not calm and rich then someone is both humble and not strong.
Everyone who is tall or not patient is both not wise and not brave and vice versa.
Everyone who is not creative is either not creative or not generous.
If mary is funny then someone is either wise or not generous and vice versa.
If mary is either curious or tall then someone is not happy.
Everyone who is not old or rich is both not creative and not kind and vice versa.
Everyone who is either not quiet or not tall is not tall or not kind.
If someone is not funny or patient then lucy is either rich or tall.
If someone is not creative then someone is not strong or not wise and vice versa.
Someone is rich.
John is funny or old.
Alice is not brave.
Someone is patient or wise.
Someone is patient.
Lucy is either not funny or not humble.
John is both strong and tall. | Paul is not humble. | entailment | ((brave(susan))<=>((kind(paul)<~>~creative(paul))))&
(![X]:((~kind(X)|~rich(X))<=>(~wise(X)&~humble(X))))&
(![X]:((~quiet(X)&rich(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:((wise(X)|happy(X))))<=>((~strong(fred)|humble(fred))))&
(((~happy(john)<~>humble(john)))=>((~quiet(lucy)<~>~wise(lucy))))&
(![X]:((patient(X)<~>~happy(X))=>(~humble(X)&~patient(X))))&
(((~calm(john)&rich(john)))=>(?[X]:((humble(X)&~strong(X)))))&
(![X]:((tall(X)|~patient(X))<=>(~wise(X)&~brave(X))))&
(![X]:(~creative(X)=>(~creative(X)<~>~generous(X))))&
((funny(mary))<=>(?[X]:((wise(X)<~>~generous(X)))))&
(((curious(mary)<~>tall(mary)))=>(?[X]:(~happy(X))))&
(![X]:((~old(X)|rich(X))<=>(~creative(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(~tall(X)|~kind(X))))&
((?[X]:((~funny(X)|patient(X))))=>((rich(lucy)<~>tall(lucy))))&
((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)|~wise(X)))))&
(?[X]:(rich(X)))&
((funny(john)|old(john)))&
(~brave(alice))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(patient(X)))&
((~funny(lucy)<~>~humble(lucy)))&
((strong(john)&tall(john))) | ~humble(paul) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1835030428384580657246218
% SZS output start Proof for 1835030428384580657246218
2. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> (~humble(X0) & ~wise(X0))) [input p1]
12. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) & ~creative(X0))) [input p11]
23. humble(paul) [input hypothesis]
34. ! [X0] : (((~rich(X0) | ~kind(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (rich(X0) & kind(X0)))) [nnf transformation 2]
35. ! [X0] : ((~rich(X0) | ~kind(X0) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | (rich(X0) & kind(X0)))) [flattening 34]
55. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) | creative(X0))) & ((~kind(X0) & ~creative(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 12]
56. ! [X0] : ((rich(X0) | ~old(X0) | kind(X0) | creative(X0)) & ((~kind(X0) & ~creative(X0)) | (~rich(X0) & old(X0)))) [flattening 55]
77. ~humble(X0) | kind(X0) [cnf transformation 35]
78. ~humble(X0) | rich(X0) [cnf transformation 35]
114. ~rich(X0) | ~kind(X0) [cnf transformation 56]
134. humble(paul) [cnf transformation 23]
143. 2 <=> kind(paul) [avatar definition]
302. kind(paul) [resolution 77,134]
304. rich(paul) [resolution 78,134]
318. ~kind(paul) [resolution 114,304]
326. ~2 [avatar split clause 318,143]
327. 2 [avatar split clause 302,143]
328. $false [avatar sat refutation 326,327]
% SZS output end Proof for 1835030428384580657246218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not kind is either not wise or wise and vice versa.
Everyone who is not wise or not brave is kind and vice versa.
If someone is both quiet and not wise then john is either tall or not rich and vice versa.
If someone is not calm or curious then lucy is either calm or not curious.
Everyone who is old is not kind and vice versa.
Everyone who is not brave or not rich is either not brave or not rich.
If someone is strong then fred is both not patient and funny and vice versa.
If paul is either not creative or not happy then alice is not wise and vice versa.
Everyone who is funny is not quiet and vice versa.
Everyone who is not strong or not quiet is not wise.
Everyone who is generous or not happy is both not brave and creative.
Everyone who is generous or not rich is strong and vice versa.
Everyone who is not strong or creative is either funny or quiet and vice versa.
Everyone who is not generous is both not generous and not old.
If fred is both humble and not old then fred is humble and vice versa.
If susan is creative then alice is either not kind or not quiet and vice versa.
Someone is not wise or generous.
Someone is either not curious or not generous.
Someone is not rich.
Someone is wise or tall.
Lucy is both not happy and not wise.
Someone is not generous.
Someone is either not brave or not quiet. | Paul is not rich. | contradiction | (![X]:((funny(X)<~>~kind(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((~wise(X)|~brave(X))<=>kind(X)))&
((?[X]:((quiet(X)&~wise(X))))<=>((tall(john)<~>~rich(john))))&
((?[X]:((~calm(X)|curious(X))))=>((calm(lucy)<~>~curious(lucy))))&
(![X]:(old(X)<=>~kind(X)))&
(![X]:((~brave(X)|~rich(X))=>(~brave(X)<~>~rich(X))))&
((?[X]:(strong(X)))<=>((~patient(fred)&funny(fred))))&
(((~creative(paul)<~>~happy(paul)))<=>(~wise(alice)))&
(![X]:(funny(X)<=>~quiet(X)))&
(![X]:((~strong(X)|~quiet(X))=>~wise(X)))&
(![X]:((generous(X)|~happy(X))=>(~brave(X)&creative(X))))&
(![X]:((generous(X)|~rich(X))<=>strong(X)))&
(![X]:((~strong(X)|creative(X))<=>(funny(X)<~>quiet(X))))&
(![X]:(~generous(X)=>(~generous(X)&~old(X))))&
(((humble(fred)&~old(fred)))<=>(humble(fred)))&
((creative(susan))<=>((~kind(alice)<~>~quiet(alice))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)|tall(X))))&
((~happy(lucy)&~wise(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((~brave(X)<~>~quiet(X)))) | ~rich(paul) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 286012319674897343422664
% SZS output start Proof for 286012319674897343422664
1. ! [X0] : ((funny(X0) <~> ~kind(X0)) <=> (~wise(X0) <~> wise(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> kind(X0)) [input p1]
5. ! [X0] : (old(X0) <=> ~kind(X0)) [input p4]
6. ! [X0] : ((~rich(X0) | ~brave(X0)) => (~brave(X0) <~> ~rich(X0))) [input p5]
8. (~creative(paul) <~> ~happy(paul)) <=> ~wise(alice) [input p7]
9. ! [X0] : (funny(X0) <=> ~quiet(X0)) [input p8]
10. ! [X0] : ((~quiet(X0) | ~strong(X0)) => ~wise(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | generous(X0)) => (creative(X0) & ~brave(X0))) [input p10]
12. ! [X0] : ((~rich(X0) | generous(X0)) <=> strong(X0)) [input p11]
13. ! [X0] : ((creative(X0) | ~strong(X0)) <=> (funny(X0) <~> quiet(X0))) [input p12]
14. ! [X0] : (~generous(X0) => (~old(X0) & ~generous(X0))) [input p13]
24. ~rich(paul) [input hypothesis]
26. ! [X0] : ((~brave(X0) <~> ~rich(X0)) | (rich(X0) & brave(X0))) [ennf transformation 6]
27. ! [X0] : (~wise(X0) | (quiet(X0) & strong(X0))) [ennf transformation 10]
28. ! [X0] : ((creative(X0) & ~brave(X0)) | (happy(X0) & ~generous(X0))) [ennf transformation 11]
29. ! [X0] : ((~old(X0) & ~generous(X0)) | generous(X0)) [ennf transformation 14]
30. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [nnf transformation 1]
31. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~kind(X0)) & (kind(X0) | (brave(X0) & wise(X0)))) [nnf transformation 2]
32. ! [X0] : ((~brave(X0) | ~wise(X0) | ~kind(X0)) & (kind(X0) | (brave(X0) & wise(X0)))) [flattening 31]
38. ! [X0] : ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))) [nnf transformation 5]
39. ! [X0] : (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (rich(X0) & brave(X0))) [nnf transformation 26]
45. (((happy(paul) | creative(paul)) & (~happy(paul) | ~creative(paul))) | wise(alice)) & (~wise(alice) | ((~creative(paul) | happy(paul)) & (~happy(paul) | creative(paul)))) [nnf transformation 8]
46. ! [X0] : ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))) [nnf transformation 9]
47. ! [X0] : (((~rich(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~generous(X0)))) [nnf transformation 12]
48. ! [X0] : ((~rich(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~generous(X0)))) [flattening 47]
49. ! [X0] : (((creative(X0) | ~strong(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (~creative(X0) & strong(X0)))) [nnf transformation 13]
50. ! [X0] : ((creative(X0) | ~strong(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (~creative(X0) & strong(X0)))) [flattening 49]
72. ~kind(X0) | funny(X0) | wise(X0) | wise(X0) [cnf transformation 30]
73. ~kind(X0) | funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 30]
77. brave(X0) | kind(X0) [cnf transformation 32]
90. old(X0) | kind(X0) [cnf transformation 38]
94. rich(X0) | brave(X0) | rich(X0) [cnf transformation 39]
100. ~happy(paul) | ~creative(paul) | wise(alice) [cnf transformation 45]
102. ~quiet(X0) | ~funny(X0) [cnf transformation 46]
103. quiet(X0) | funny(X0) [cnf transformation 46]
105. ~wise(X0) | quiet(X0) [cnf transformation 27]
106. ~generous(X0) | ~brave(X0) [cnf transformation 28]
107. ~brave(X0) | happy(X0) [cnf transformation 28]
111. strong(X0) | rich(X0) [cnf transformation 48]
117. creative(X0) | ~strong(X0) | quiet(X0) | ~funny(X0) [cnf transformation 50]
118. creative(X0) | ~strong(X0) | funny(X0) | ~quiet(X0) [cnf transformation 50]
120. ~old(X0) | generous(X0) [cnf transformation 29]
138. ~rich(paul) [cnf transformation 24]
140. rich(X0) | brave(X0) [duplicate literal removal 94]
141. ~kind(X0) | funny(X0) | wise(X0) [duplicate literal removal 72]
142. ~wise(X0) | funny(X0) | ~kind(X0) [duplicate literal removal 73]
146. ~kind(X0) | funny(X0) [subsumption resolution 141,142]
209. 14 <=> wise(alice) [avatar definition]
211. wise(alice) <- (14) [avatar component clause 209]
213. 15 <=> creative(paul) [avatar definition]
214. ~creative(paul) <- (~15) [avatar component clause 213]
217. 16 <=> happy(paul) [avatar definition]
221. 14 | ~15 | ~16 [avatar split clause 100,217,213,209]
224. ~strong(X0) | creative(X0) | ~quiet(X0) [subsumption resolution 118,102]
225. ~strong(X0) | creative(X0) | ~funny(X0) [subsumption resolution 117,102]
236. 19 <=> quiet(alice) [avatar definition]
237. ~quiet(alice) <- (~19) [avatar component clause 236]
238. quiet(alice) <- (19) [avatar component clause 236]
240. 20 <=> kind(alice) [avatar definition]
241. kind(alice) <- (20) [avatar component clause 240]
242. ~kind(alice) <- (~20) [avatar component clause 240]
301. quiet(alice) <- (14) [resolution 105,211]
304. $false <- (14, ~19) [subsumption resolution 301,237]
305. ~14 | 19 [avatar contradiction clause 304]
311. ~funny(alice) <- (19) [resolution 238,102]
319. generous(X0) | kind(X0) [resolution 120,90]
321. brave(paul) [resolution 140,138]
326. happy(paul) [resolution 321,107]
329. funny(alice) <- (20) [resolution 146,241]
332. $false <- (19, 20) [subsumption resolution 329,311]
333. ~19 | ~20 [avatar contradiction clause 332]
429. ~quiet(X0) | creative(X0) | rich(X0) [resolution 224,111]
447. ~funny(X0) | creative(X0) | rich(X0) [resolution 225,111]
469. kind(X2) | ~brave(X2) [resolution 319,106]
470. kind(X2) [subsumption resolution 469,77]
482. creative(X1) | rich(X1) | funny(X1) [resolution 429,103]
486. creative(X1) | rich(X1) [subsumption resolution 482,447]
505. $false <- (~20) [resolution 470,242]
508. 20 [avatar contradiction clause 505]
509. 16 [avatar split clause 326,217]
524. rich(paul) <- (~15) [resolution 486,214]
525. $false <- (~15) [subsumption resolution 524,138]
526. 15 [avatar contradiction clause 525]
527. $false [avatar sat refutation 221,305,333,508,509,526]
% SZS output end Proof for 286012319674897343422664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not quiet is either quiet or calm. Everyone who is not creative or funny is not curious or kind. If paul is happy then someone is not creative or not happy and vice versa. If john is either strong or not wise then susan is both not calm and curious. If paul is either not strong or not curious then someone is both patient and creative and vice versa. If john is both old and not old then mary is both not old and funny and vice versa. If fred is both kind and not patient then john is both wise and generous. Everyone who is either humble or funny is both not rich and not quiet and vice versa. If john is creative then john is not old or kind and vice versa. If someone is creative then alice is not quiet and vice versa. Everyone who is either not rich or quiet is not creative or funny. Everyone who is not funny is not quiet or not generous and vice versa. Everyone who is either not calm or not quiet is patient and vice versa. Everyone who is rich is either not strong or not tall and vice versa. Everyone who is both happy and curious is either not tall or not happy and vice versa. Everyone who is not tall or not humble is old or not funny. Alice is wise or happy. Paul is either not wise or not humble. Lucy is either not strong or not curious. Someone is not kind or not quiet. Lucy is old. Someone is strong. Fred is both kind and not brave. Paul is not patient. | Lucy is not happy. | neutral | (![X]:((~happy(X)&~quiet(X))=>(quiet(X)<~>calm(X))))&
(![X]:((~creative(X)|funny(X))=>(~curious(X)|kind(X))))&
((happy(paul))<=>(?[X]:((~creative(X)|~happy(X)))))&
(((strong(john)<~>~wise(john)))=>((~calm(susan)&curious(susan))))&
(((~strong(paul)<~>~curious(paul)))<=>(?[X]:((patient(X)&creative(X)))))&
(((old(john)&~old(john)))<=>((~old(mary)&funny(mary))))&
(((kind(fred)&~patient(fred)))=>((wise(john)&generous(john))))&
(![X]:((humble(X)<~>funny(X))<=>(~rich(X)&~quiet(X))))&
((creative(john))<=>((~old(john)|kind(john))))&
((?[X]:(creative(X)))<=>(~quiet(alice)))&
(![X]:((~rich(X)<~>quiet(X))=>(~creative(X)|funny(X))))&
(![X]:(~funny(X)<=>(~quiet(X)|~generous(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>patient(X)))&
(![X]:(rich(X)<=>(~strong(X)<~>~tall(X))))&
(![X]:((happy(X)&curious(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~tall(X)|~humble(X))=>(old(X)|~funny(X))))&
((wise(alice)|happy(alice)))&
((~wise(paul)<~>~humble(paul)))&
((~strong(lucy)<~>~curious(lucy)))&
(?[X]:((~kind(X)|~quiet(X))))&
(old(lucy))&
(?[X]:(strong(X)))&
((kind(fred)&~brave(fred)))&
(~patient(paul)) | ~happy(lucy) | [] | null | 0 |
Everyone who is old or patient is either kind or not quiet. Everyone who is creative or not generous is both generous and not calm and vice versa. If susan is not wise then someone is both old and rich. If lucy is either creative or wise then someone is both not curious and humble. Everyone who is brave or not tall is both tall and quiet. Everyone who is both wise and not quiet is either not patient or not generous. If someone is not happy or not patient then someone is not humble. If fred is either not curious or tall then someone is curious. If fred is curious or strong then mary is either not happy or brave. If mary is quiet then someone is rich or not brave. If someone is not quiet then someone is either not creative or curious and vice versa. Everyone who is both not happy and funny is generous or not old and vice versa. Everyone who is not calm or not brave is either old or tall and vice versa. Everyone who is either old or not calm is either not humble or funny and vice versa. If someone is both not calm and not humble then john is curious or not calm. If someone is both kind and humble then fred is old. Lucy is both not strong and old. John is not happy. Someone is old. Someone is either not quiet or tall. Fred is not creative. Paul is not happy. | Lucy is not funny. | contradiction | (![X]:((old(X)|patient(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((creative(X)|~generous(X))<=>(generous(X)&~calm(X))))&
((~wise(susan))=>(?[X]:((old(X)&rich(X)))))&
(((creative(lucy)<~>wise(lucy)))=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((brave(X)|~tall(X))=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&~quiet(X))=>(~patient(X)<~>~generous(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~humble(X))))&
(((~curious(fred)<~>tall(fred)))=>(?[X]:(curious(X))))&
(((curious(fred)|strong(fred)))=>((~happy(mary)<~>brave(mary))))&
((quiet(mary))=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((~happy(X)&funny(X))<=>(generous(X)|~old(X))))&
(![X]:((~calm(X)|~brave(X))<=>(old(X)<~>tall(X))))&
(![X]:((old(X)<~>~calm(X))<=>(~humble(X)<~>funny(X))))&
((?[X]:((~calm(X)&~humble(X))))=>((curious(john)|~calm(john))))&
((?[X]:((kind(X)&humble(X))))=>(old(fred)))&
((~strong(lucy)&old(lucy)))&
(~happy(john))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(~creative(fred))&
(~happy(paul)) | ~funny(lucy) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1695793935261867378265007
% SZS output start Proof for 1695793935261867378265007
2. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~calm(X0) & generous(X0))) [input p1]
12. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~old(X0) | generous(X0))) [input p11]
23. ~funny(lucy) [input hypothesis]
43. ! [X0] : (((~generous(X0) | creative(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 2]
44. ! [X0] : ((~generous(X0) | creative(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [flattening 43]
63. ! [X0] : (((funny(X0) & ~happy(X0)) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | (~funny(X0) | happy(X0)))) [nnf transformation 12]
64. ! [X0] : (((funny(X0) & ~happy(X0)) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~funny(X0) | happy(X0))) [flattening 63]
78. generous(X0) | generous(X0) [cnf transformation 44]
106. funny(X0) | ~generous(X0) [cnf transformation 64]
131. ~funny(lucy) [cnf transformation 23]
133. generous(X0) [duplicate literal removal 78]
222. funny(X0) [subsumption resolution 106,133]
241. $false [subsumption resolution 131,222]
% SZS output end Proof for 1695793935261867378265007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise is not creative and vice versa. Everyone who is both not generous and calm is either not wise or not funny. Everyone who is both not quiet and patient is both wise and not funny. Everyone who is not strong is not curious or patient and vice versa. If paul is both not quiet and not patient then someone is both not wise and wise and vice versa. Everyone who is both not brave and brave is both kind and quiet and vice versa. Everyone who is generous is both not calm and not patient and vice versa. Everyone who is either not brave or strong is patient or not wise and vice versa. Everyone who is strong is both strong and not creative. If lucy is not happy then john is old and vice versa. Everyone who is both old and curious is not patient. Everyone who is both not happy and generous is both happy and not generous. Everyone who is both not quiet and brave is either not curious or happy. If someone is both creative and not patient then someone is both tall and strong. Everyone who is both not wise and curious is either not wise or not quiet. If lucy is both not creative and not rich then alice is both creative and not old and vice versa. Fred is humble. Alice is both rich and humble. Someone is not humble. Someone is not brave or funny. Someone is kind or old. Someone is creative or brave. Alice is calm. John is not patient. | Paul is not generous. | neutral | (![X]:((calm(X)<~>~wise(X))<=>~creative(X)))&
(![X]:((~generous(X)&calm(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~quiet(X)&patient(X))=>(wise(X)&~funny(X))))&
(![X]:(~strong(X)<=>(~curious(X)|patient(X))))&
(((~quiet(paul)&~patient(paul)))<=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((~brave(X)&brave(X))<=>(kind(X)&quiet(X))))&
(![X]:(generous(X)<=>(~calm(X)&~patient(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(patient(X)|~wise(X))))&
(![X]:(strong(X)=>(strong(X)&~creative(X))))&
((~happy(lucy))<=>(old(john)))&
(![X]:((old(X)&curious(X))=>~patient(X)))&
(![X]:((~happy(X)&generous(X))=>(happy(X)&~generous(X))))&
(![X]:((~quiet(X)&brave(X))=>(~curious(X)<~>happy(X))))&
((?[X]:((creative(X)&~patient(X))))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(((~creative(lucy)&~rich(lucy)))<=>((creative(alice)&~old(alice))))&
(humble(fred))&
((rich(alice)&humble(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((creative(X)|brave(X))))&
(calm(alice))&
(~patient(john)) | ~generous(paul) | [] | null | 0 |
Everyone who is rich or not curious is either not wise or quiet and vice versa.
Everyone who is either not generous or brave is both not curious and wise and vice versa.
Everyone who is both wise and not generous is humble or wise.
Everyone who is either curious or not rich is either quiet or happy and vice versa.
If john is both not humble and not tall then someone is kind.
Everyone who is both calm and not funny is happy or not generous and vice versa.
Everyone who is both not old and creative is both kind and not funny.
Everyone who is not generous or creative is calm or not creative.
If someone is either not humble or not rich then someone is happy or funny and vice versa.
If someone is quiet then someone is both not quiet and kind.
Everyone who is humble or creative is both not quiet and not tall and vice versa.
If someone is not old or happy then paul is rich.
Everyone who is both not rich and humble is either strong or calm.
If someone is either happy or curious then alice is kind or creative.
Everyone who is both tall and not calm is happy.
Everyone who is both not brave and funny is generous or patient.
Susan is patient.
Someone is both brave and not funny.
Alice is quiet or tall.
Alice is kind.
Someone is both not funny and brave.
Someone is either happy or not tall.
Someone is either patient or not quiet.
Someone is wise or patient. | Susan is wise. | neutral | (![X]:((rich(X)|~curious(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((~generous(X)<~>brave(X))<=>(~curious(X)&wise(X))))&
(![X]:((wise(X)&~generous(X))=>(humble(X)|wise(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(quiet(X)<~>happy(X))))&
(((~humble(john)&~tall(john)))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&~funny(X))<=>(happy(X)|~generous(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)&~funny(X))))&
(![X]:((~generous(X)|creative(X))=>(calm(X)|~creative(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)|creative(X))<=>(~quiet(X)&~tall(X))))&
((?[X]:((~old(X)|happy(X))))=>(rich(paul)))&
(![X]:((~rich(X)&humble(X))=>(strong(X)<~>calm(X))))&
((?[X]:((happy(X)<~>curious(X))))=>((kind(alice)|creative(alice))))&
(![X]:((tall(X)&~calm(X))=>happy(X)))&
(![X]:((~brave(X)&funny(X))=>(generous(X)|patient(X))))&
(patient(susan))&
(?[X]:((brave(X)&~funny(X))))&
((quiet(alice)|tall(alice)))&
(kind(alice))&
(?[X]:((~funny(X)&brave(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((wise(X)|patient(X)))) | wise(susan) | [] | null | 0 |
If alice is both rich and not quiet then fred is either not wise or funny and vice versa. Everyone who is both not quiet and humble is not creative and vice versa. Everyone who is either not curious or not creative is not strong or happy. Everyone who is either not funny or old is old or not funny. Everyone who is generous is not quiet or creative and vice versa. If someone is not rich then lucy is either not old or not patient and vice versa. Everyone who is both creative and not funny is both not quiet and brave. Everyone who is not rich or patient is not brave. If susan is brave then alice is both quiet and not wise and vice versa. If alice is both strong and not quiet then someone is curious or not happy and vice versa. If lucy is not curious then someone is quiet and vice versa. If paul is either kind or not rich then mary is not happy or calm. If paul is both creative and not old then alice is not curious or not kind and vice versa. Everyone who is both not kind and rich is either not brave or not quiet. Everyone who is not funny is not rich or creative. If mary is not strong or not happy then someone is both not rich and rich and vice versa. Paul is not tall. Mary is either not curious or wise. Susan is either not curious or not kind. Someone is either not strong or kind. John is kind or not kind. Someone is not quiet or brave. | Paul is kind. | neutral | (((rich(alice)&~quiet(alice)))<=>((~wise(fred)<~>funny(fred))))&
(![X]:((~quiet(X)&humble(X))<=>~creative(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~strong(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(old(X)|~funny(X))))&
(![X]:(generous(X)<=>(~quiet(X)|creative(X))))&
((?[X]:(~rich(X)))<=>((~old(lucy)<~>~patient(lucy))))&
(![X]:((creative(X)&~funny(X))=>(~quiet(X)&brave(X))))&
(![X]:((~rich(X)|patient(X))=>~brave(X)))&
((brave(susan))<=>((quiet(alice)&~wise(alice))))&
(((strong(alice)&~quiet(alice)))<=>(?[X]:((curious(X)|~happy(X)))))&
((~curious(lucy))<=>(?[X]:(quiet(X))))&
(((kind(paul)<~>~rich(paul)))=>((~happy(mary)|calm(mary))))&
(((creative(paul)&~old(paul)))<=>((~curious(alice)|~kind(alice))))&
(![X]:((~kind(X)&rich(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~rich(X)|creative(X))))&
(((~strong(mary)|~happy(mary)))<=>(?[X]:((~rich(X)&rich(X)))))&
(~tall(paul))&
((~curious(mary)<~>wise(mary)))&
((~curious(susan)<~>~kind(susan)))&
(?[X]:((~strong(X)<~>kind(X))))&
((kind(john)|~kind(john)))&
(?[X]:((~quiet(X)|brave(X)))) | kind(paul) | [] | null | 0 |
Everyone who is not curious or not patient is either not generous or not creative.
Everyone who is happy is not strong or not funny.
Everyone who is not quiet or wise is both brave and old.
If lucy is rich or tall then paul is not humble and vice versa.
Everyone who is creative is not patient.
Everyone who is strong is rich or not kind and vice versa.
Everyone who is both not patient and generous is not brave or curious and vice versa.
Everyone who is generous or funny is both not old and funny.
If someone is either funny or brave then susan is curious or funny.
If someone is funny then paul is both not brave and not rich and vice versa.
Everyone who is either humble or curious is both not wise and patient and vice versa.
If paul is both old and curious then someone is either creative or funny.
Everyone who is generous is both not tall and not creative.
If susan is either creative or not quiet then lucy is not tall or strong.
Everyone who is either not happy or generous is either wise or not brave and vice versa.
Everyone who is both calm and not curious is either old or not kind.
Someone is either curious or not patient.
Someone is humble.
Fred is not happy.
Susan is not generous or happy.
Someone is either not quiet or patient.
Someone is both funny and not strong.
Fred is wise.
Someone is not humble or kind. | Paul is happy. | entailment | (![X]:((~curious(X)|~patient(X))=>(~generous(X)<~>~creative(X))))&
(![X]:(happy(X)=>(~strong(X)|~funny(X))))&
(![X]:((~quiet(X)|wise(X))=>(brave(X)&old(X))))&
(((rich(lucy)|tall(lucy)))<=>(~humble(paul)))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(strong(X)<=>(rich(X)|~kind(X))))&
(![X]:((~patient(X)&generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)&funny(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((curious(susan)|funny(susan))))&
((?[X]:(funny(X)))<=>((~brave(paul)&~rich(paul))))&
(![X]:((humble(X)<~>curious(X))<=>(~wise(X)&patient(X))))&
(((old(paul)&curious(paul)))=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:(generous(X)=>(~tall(X)&~creative(X))))&
(((creative(susan)<~>~quiet(susan)))=>((~tall(lucy)|strong(lucy))))&
(![X]:((~happy(X)<~>generous(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((calm(X)&~curious(X))=>(old(X)<~>~kind(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:(humble(X)))&
(~happy(fred))&
((~generous(susan)|happy(susan)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((funny(X)&~strong(X))))&
(wise(fred))&
(?[X]:((~humble(X)|kind(X)))) | happy(paul) | [
"p2",
"p6",
"p9",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2281343663188639452597238
% SZS output start Proof for 2281343663188639452597238
3. ! [X0] : ((wise(X0) | ~quiet(X0)) => (old(X0) & brave(X0))) [input p2]
7. ! [X0] : ((generous(X0) & ~patient(X0)) <=> (curious(X0) | ~brave(X0))) [input p6]
10. ? [X0] : funny(X0) <=> (~rich(paul) & ~brave(paul)) [input p9]
15. ! [X0] : ((~happy(X0) <~> generous(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p14]
22. ? [X0] : (~strong(X0) & funny(X0)) [input p21]
25. ~happy(paul) [input hypothesis]
30. ! [X0] : ((old(X0) & brave(X0)) | (~wise(X0) & quiet(X0))) [ennf transformation 3]
45. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (~generous(X0) | patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | ~generous(X0) | patient(X0))) [flattening 45]
48. (? [X0] : funny(X0) | (rich(paul) | brave(paul))) & ((~rich(paul) & ~brave(paul)) | ! [X0] : ~funny(X0)) [nnf transformation 10]
49. (? [X0] : funny(X0) | rich(paul) | brave(paul)) & ((~rich(paul) & ~brave(paul)) | ! [X0] : ~funny(X0)) [flattening 48]
50. (? [X0] : funny(X0) | rich(paul) | brave(paul)) & ((~rich(paul) & ~brave(paul)) | ! [X1] : ~funny(X1)) [rectify 49]
51. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
52. (funny(sK0) | rich(paul) | brave(paul)) & ((~rich(paul) & ~brave(paul)) | ! [X1] : ~funny(X1)) [skolemisation 50,51]
59. ! [X0] : ((((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))))) [nnf transformation 15]
68. ? [X0] : (~strong(X0) & funny(X0)) => (~strong(sK5) & funny(sK5)) [choice axiom]
69. ~strong(sK5) & funny(sK5) [skolemisation 22,68]
78. ~wise(X0) | brave(X0) [cnf transformation 30]
91. brave(X0) | generous(X0) [cnf transformation 46]
99. ~brave(paul) | ~funny(X1) [cnf transformation 52]
121. ~generous(X0) | happy(X0) | wise(X0) | brave(X0) [cnf transformation 59]
129. funny(sK5) [cnf transformation 69]
133. ~happy(paul) [cnf transformation 25]
166. 8 <=> brave(paul) [avatar definition]
167. ~brave(paul) <- (~8) [avatar component clause 166]
179. 11 <=> ! [X1] : ~funny(X1) [avatar definition]
180. ~funny(X1) <- (11) [avatar component clause 179]
182. 11 | ~8 [avatar split clause 99,166,179]
217. happy(X0) | wise(X0) | brave(X0) [subsumption resolution 121,91]
218. brave(X0) | happy(X0) [subsumption resolution 217,78]
272. happy(paul) <- (~8) [resolution 218,167]
273. $false <- (~8) [subsumption resolution 272,133]
274. 8 [avatar contradiction clause 273]
277. $false <- (11) [resolution 180,129]
278. ~11 [avatar contradiction clause 277]
281. $false [avatar sat refutation 182,274,278]
% SZS output end Proof for 2281343663188639452597238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is calm or old then someone is both humble and not kind.
If someone is both not strong and not kind then someone is either not happy or patient and vice versa.
Everyone who is both quiet and generous is either not curious or rich and vice versa.
If lucy is both not generous and old then someone is either tall or patient and vice versa.
Everyone who is either not generous or not kind is strong or not kind and vice versa.
Everyone who is either calm or not creative is strong or not quiet and vice versa.
Everyone who is not brave is wise.
If someone is rich then john is not curious or not patient.
If mary is tall or not patient then mary is not rich.
Everyone who is either not old or not brave is calm or not generous.
Everyone who is old is happy.
Everyone who is either not wise or not brave is brave or not happy and vice versa.
Everyone who is strong or old is not generous or wise and vice versa.
Everyone who is humble or not happy is not rich or old and vice versa.
Everyone who is not strong or not humble is not calm or curious and vice versa.
If someone is both not old and happy then lucy is wise.
Alice is either humble or calm.
Mary is both not curious and kind.
Fred is patient.
Someone is not brave.
Someone is not old.
Someone is both wise and patient.
Someone is either not calm or not funny.
Fred is both not quiet and patient. | Mary is strong. | entailment | (((calm(john)|old(john)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((quiet(X)&generous(X))<=>(~curious(X)<~>rich(X))))&
(((~generous(lucy)&old(lucy)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(strong(X)|~kind(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)|~quiet(X))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:(rich(X)))=>((~curious(john)|~patient(john))))&
(((tall(mary)|~patient(mary)))=>(~rich(mary)))&
(![X]:((~old(X)<~>~brave(X))=>(calm(X)|~generous(X))))&
(![X]:(old(X)=>happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)|~happy(X))))&
(![X]:((strong(X)|old(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|~happy(X))<=>(~rich(X)|old(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~old(X)&happy(X))))=>(wise(lucy)))&
((humble(alice)<~>calm(alice)))&
((~curious(mary)&kind(mary)))&
(patient(fred))&
(?[X]:(~brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~calm(X)<~>~funny(X))))&
((~quiet(fred)&patient(fred))) | strong(mary) | [
"p4",
"p6",
"p9",
"p10",
"p11",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3708746162015901817822777
% SZS output start Proof for 3708746162015901817822777
5. ! [X0] : ((~generous(X0) <~> ~kind(X0)) <=> (~kind(X0) | strong(X0))) [input p4]
7. ! [X0] : (~brave(X0) => wise(X0)) [input p6]
10. ! [X0] : ((~old(X0) <~> ~brave(X0)) => (~generous(X0) | calm(X0))) [input p9]
11. ! [X0] : (old(X0) => happy(X0)) [input p10]
12. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (~happy(X0) | brave(X0))) [input p11]
13. ! [X0] : ((old(X0) | strong(X0)) <=> (wise(X0) | ~generous(X0))) [input p12]
15. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (curious(X0) | ~calm(X0))) [input p14]
18. kind(mary) & ~curious(mary) [input p17]
25. ~strong(mary) [input hypothesis]
28. ! [X0] : (wise(X0) | brave(X0)) [ennf transformation 7]
32. ! [X0] : ((~generous(X0) | calm(X0)) | (~old(X0) <=> ~brave(X0))) [ennf transformation 10]
33. ! [X0] : (~generous(X0) | calm(X0) | (~old(X0) <=> ~brave(X0))) [flattening 32]
34. ! [X0] : (happy(X0) | ~old(X0)) [ennf transformation 11]
50. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [nnf transformation 5]
51. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [flattening 50]
54. ! [X0] : (~generous(X0) | calm(X0) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [nnf transformation 33]
55. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 12]
56. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [flattening 55]
57. ! [X0] : (((old(X0) | strong(X0)) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 13]
58. ! [X0] : ((old(X0) | strong(X0) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | (~old(X0) & ~strong(X0)))) [flattening 57]
61. ! [X0] : (((~humble(X0) | ~strong(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((~humble(X0) | ~strong(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | (humble(X0) & strong(X0)))) [flattening 61]
95. ~kind(X0) | strong(X0) | ~kind(X0) | generous(X0) [cnf transformation 51]
100. kind(X0) | generous(X0) | kind(X0) [cnf transformation 51]
107. wise(X0) | brave(X0) [cnf transformation 28]
111. ~brave(X0) | calm(X0) | ~generous(X0) | old(X0) [cnf transformation 54]
113. ~old(X0) | happy(X0) [cnf transformation 34]
115. ~happy(X0) | brave(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
116. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 56]
121. ~generous(X0) | wise(X0) | ~old(X0) [cnf transformation 58]
123. ~wise(X0) | strong(X0) | old(X0) [cnf transformation 58]
128. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 62]
135. ~curious(mary) [cnf transformation 18]
146. ~strong(mary) [cnf transformation 25]
147. ~happy(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 115]
148. ~wise(X0) | ~brave(X0) [duplicate literal removal 116]
149. ~kind(X0) | strong(X0) | generous(X0) [duplicate literal removal 95]
150. generous(X0) | kind(X0) [duplicate literal removal 100]
230. generous(X0) | strong(X0) [subsumption resolution 149,150]
257. ~wise(X0) | ~happy(X0) [subsumption resolution 147,148]
326. ~old(X0) | wise(X0) | strong(X0) [resolution 121,230]
330. 32 <=> old(mary) [avatar definition]
331. old(mary) <- (32) [avatar component clause 330]
334. 33 <=> wise(mary) [avatar definition]
336. wise(mary) <- (33) [avatar component clause 334]
339. brave(X0) | old(X0) | strong(X0) [resolution 123,107]
386. 39 <=> calm(mary) [avatar definition]
388. calm(mary) <- (39) [avatar component clause 386]
391. 40 <=> happy(mary) [avatar definition]
393. happy(mary) <- (40) [avatar component clause 391]
469. old(X0) | strong(X0) | calm(X0) | ~generous(X0) | old(X0) [resolution 339,111]
470. old(X0) | strong(X0) | calm(X0) | ~generous(X0) [duplicate literal removal 469]
480. strong(X0) | old(X0) | calm(X0) [subsumption resolution 470,230]
585. old(mary) | calm(mary) [resolution 480,146]
608. curious(mary) | strong(mary) <- (39) [resolution 388,128]
612. strong(mary) <- (39) [subsumption resolution 608,135]
613. $false <- (39) [subsumption resolution 612,146]
614. ~39 [avatar contradiction clause 613]
615. 39 | 32 [avatar split clause 585,330,386]
627. wise(mary) | strong(mary) <- (32) [resolution 331,326]
629. happy(mary) <- (32) [resolution 331,113]
632. 40 | ~32 [avatar split clause 629,330,391]
635. ~happy(mary) <- (33) [resolution 336,257]
637. $false <- (33, 40) [subsumption resolution 635,393]
638. ~33 | ~40 [avatar contradiction clause 637]
641. wise(mary) <- (32) [subsumption resolution 627,146]
642. 33 | ~32 [avatar split clause 641,330,334]
643. $false [avatar sat refutation 614,615,632,638,642]
% SZS output end Proof for 3708746162015901817822777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both patient and quiet then someone is both calm and tall.
Everyone who is curious or not strong is strong or not generous and vice versa.
If someone is both not wise and not patient then susan is not strong or not curious.
If someone is either kind or strong then someone is both not creative and not patient.
If john is either wise or generous then someone is not wise or not calm and vice versa.
Everyone who is not wise or creative is both not happy and not rich.
Everyone who is either generous or not curious is not calm.
If fred is either not rich or old then paul is either not calm or not kind.
Everyone who is humble is curious or tall and vice versa.
Everyone who is strong is not curious and vice versa.
If john is both not funny and funny then someone is generous.
Everyone who is not wise or funny is not brave or humble and vice versa.
Everyone who is both curious and not patient is either not funny or not rich.
Everyone who is both creative and kind is not patient and vice versa.
If fred is not humble then someone is either not kind or not rich and vice versa.
Someone is wise.
Paul is patient or not wise.
Mary is wise or not quiet.
Susan is both brave and wise. | Fred is quiet. | neutral | (((patient(susan)&quiet(susan)))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:((curious(X)|~strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~wise(X)&~patient(X))))=>((~strong(susan)|~curious(susan))))&
((?[X]:((kind(X)<~>strong(X))))=>(?[X]:((~creative(X)&~patient(X)))))&
(((wise(john)<~>generous(john)))<=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~rich(X))))&
(![X]:((generous(X)<~>~curious(X))=>~calm(X)))&
(((~rich(fred)<~>old(fred)))=>((~calm(paul)<~>~kind(paul))))&
(![X]:(humble(X)<=>(curious(X)|tall(X))))&
(![X]:(strong(X)<=>~curious(X)))&
(((~funny(john)&funny(john)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~patient(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)&kind(X))<=>~patient(X)))&
((~humble(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(?[X]:(wise(X)))&
((patient(paul)|~wise(paul)))&
((wise(mary)|~quiet(mary)))&
((brave(susan)&wise(susan))) | quiet(fred) | [] | null | 0 |
Everyone who is not wise or kind is both tall and wise.
If mary is either not rich or not quiet then someone is not creative or tall and vice versa.
If someone is not generous then susan is both kind and humble.
If lucy is strong or not patient then susan is not rich and vice versa.
If mary is both brave and not calm then someone is both rich and not rich.
Everyone who is not creative or strong is both not generous and rich.
Everyone who is not rich is old or not creative.
If someone is both not happy and wise then someone is not happy.
Everyone who is not tall or not rich is not curious or not strong and vice versa.
If susan is curious or not wise then fred is not old or not wise and vice versa.
Everyone who is not quiet is generous and vice versa.
If someone is not calm or not humble then fred is either not old or wise.
Everyone who is either not creative or calm is either tall or not patient.
Everyone who is both brave and funny is either not humble or not generous and vice versa.
If someone is not kind then lucy is not old.
John is either not quiet or not strong.
Paul is both not happy and not kind.
Someone is either not humble or not brave.
Someone is not creative.
Paul is both not calm and rich.
Lucy is either not strong or funny.
Someone is either brave or not curious.
Someone is both generous and not calm. | Susan is not strong. | entailment | (![X]:((~wise(X)|kind(X))=>(tall(X)&wise(X))))&
(((~rich(mary)<~>~quiet(mary)))<=>(?[X]:((~creative(X)|tall(X)))))&
((?[X]:(~generous(X)))=>((kind(susan)&humble(susan))))&
(((strong(lucy)|~patient(lucy)))<=>(~rich(susan)))&
(((brave(mary)&~calm(mary)))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((~creative(X)|strong(X))=>(~generous(X)&rich(X))))&
(![X]:(~rich(X)=>(old(X)|~creative(X))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~curious(X)|~strong(X))))&
(((curious(susan)|~wise(susan)))<=>((~old(fred)|~wise(fred))))&
(![X]:(~quiet(X)<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))=>((~old(fred)<~>wise(fred))))&
(![X]:((~creative(X)<~>calm(X))=>(tall(X)<~>~patient(X))))&
(![X]:((brave(X)&funny(X))<=>(~humble(X)<~>~generous(X))))&
((?[X]:(~kind(X)))=>(~old(lucy)))&
((~quiet(john)<~>~strong(john)))&
((~happy(paul)&~kind(paul)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:(~creative(X)))&
((~calm(paul)&rich(paul)))&
((~strong(lucy)<~>funny(lucy)))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:((generous(X)&~calm(X)))) | ~strong(susan) | [
"p0",
"p2",
"p5",
"p8",
"p9",
"p11",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4847565152061988190581677
% SZS output start Proof for 4847565152061988190581677
1. ! [X0] : ((kind(X0) | ~wise(X0)) => (wise(X0) & tall(X0))) [input p0]
3. ? [X0] : ~generous(X0) => (humble(susan) & kind(susan)) [input p2]
6. ! [X0] : ((strong(X0) | ~creative(X0)) => (rich(X0) & ~generous(X0))) [input p5]
9. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> (~strong(X0) | ~curious(X0))) [input p8]
10. (~wise(susan) | curious(susan)) <=> (~wise(fred) | ~old(fred)) [input p9]
12. ? [X0] : (~humble(X0) | ~calm(X0)) => (~old(fred) <~> wise(fred)) [input p11]
19. ? [X0] : ~creative(X0) [input p18]
20. rich(paul) & ~calm(paul) [input p19]
24. strong(susan) [input hypothesis]
26. ! [X0] : ((wise(X0) & tall(X0)) | (~kind(X0) & wise(X0))) [ennf transformation 1]
27. (humble(susan) & kind(susan)) | ! [X0] : generous(X0) [ennf transformation 3]
30. ! [X0] : ((rich(X0) & ~generous(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 6]
34. (~old(fred) <~> wise(fred)) | ! [X0] : (humble(X0) & calm(X0)) [ennf transformation 12]
48. ! [X0] : (((~rich(X0) | ~tall(X0)) | (strong(X0) & curious(X0))) & ((~strong(X0) | ~curious(X0)) | (rich(X0) & tall(X0)))) [nnf transformation 9]
49. ! [X0] : ((~rich(X0) | ~tall(X0) | (strong(X0) & curious(X0))) & (~strong(X0) | ~curious(X0) | (rich(X0) & tall(X0)))) [flattening 48]
50. ((~wise(susan) | curious(susan)) | (wise(fred) & old(fred))) & ((~wise(fred) | ~old(fred)) | (wise(susan) & ~curious(susan))) [nnf transformation 10]
51. (~wise(susan) | curious(susan) | (wise(fred) & old(fred))) & (~wise(fred) | ~old(fred) | (wise(susan) & ~curious(susan))) [flattening 50]
53. ((~wise(fred) | old(fred)) & (wise(fred) | ~old(fred))) | ! [X0] : (humble(X0) & calm(X0)) [nnf transformation 34]
61. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
62. ~creative(sK4) [skolemisation 19,61]
70. ~kind(X0) | tall(X0) [cnf transformation 26]
71. wise(X0) | wise(X0) [cnf transformation 26]
79. kind(susan) | generous(X0) [cnf transformation 27]
86. ~generous(X0) | creative(X0) [cnf transformation 30]
89. ~strong(X0) | rich(X0) [cnf transformation 30]
94. ~rich(X0) | ~tall(X0) | curious(X0) [cnf transformation 49]
96. ~wise(fred) | ~old(fred) | ~curious(susan) [cnf transformation 51]
104. ~wise(fred) | old(fred) | calm(X0) [cnf transformation 53]
123. ~creative(sK4) [cnf transformation 62]
124. ~calm(paul) [cnf transformation 20]
132. strong(susan) [cnf transformation 24]
133. wise(X0) [duplicate literal removal 71]
147. 4 <=> ! [X0] : creative(X0) [avatar definition]
148. creative(X0) <- (4) [avatar component clause 147]
163. 7 <=> ! [X0] : generous(X0) [avatar definition]
164. generous(X0) <- (7) [avatar component clause 163]
171. 9 <=> kind(susan) [avatar definition]
173. kind(susan) <- (9) [avatar component clause 171]
174. 7 | 9 [avatar split clause 79,171,163]
176. 10 <=> rich(susan) [avatar definition]
178. rich(susan) <- (10) [avatar component clause 176]
216. 18 <=> old(fred) [avatar definition]
220. 19 <=> curious(susan) [avatar definition]
224. ~old(fred) | ~curious(susan) [subsumption resolution 96,133]
225. ~19 | ~18 [avatar split clause 224,216,220]
231. old(fred) | calm(X0) [subsumption resolution 104,133]
233. 21 <=> ! [X0] : calm(X0) [avatar definition]
234. calm(X0) <- (21) [avatar component clause 233]
235. 21 | 18 [avatar split clause 231,216,233]
281. creative(X0) <- (7) [resolution 86,164]
282. 4 | ~7 [avatar split clause 281,163,147]
283. $false <- (4) [resolution 148,123]
286. ~4 [avatar contradiction clause 283]
288. tall(susan) <- (9) [resolution 173,70]
292. rich(susan) [resolution 89,132]
295. 10 [avatar split clause 292,176]
302. ~tall(susan) | curious(susan) <- (10) [resolution 94,178]
316. curious(susan) <- (9, 10) [subsumption resolution 302,288]
351. 19 | ~9 | ~10 [avatar split clause 316,176,171,220]
354. $false <- (21) [resolution 234,124]
357. ~21 [avatar contradiction clause 354]
358. $false [avatar sat refutation 174,225,235,282,286,295,351,357]
% SZS output end Proof for 4847565152061988190581677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or tall is both wise and not generous and vice versa.
If lucy is not happy then john is either not happy or not patient.
If someone is both humble and not calm then someone is humble or patient.
Everyone who is happy is either not curious or brave and vice versa.
If fred is both not old and generous then paul is both not funny and rich.
Everyone who is not kind is tall and vice versa.
If susan is rich then mary is either creative or not kind.
Everyone who is not funny or not tall is brave and vice versa.
Everyone who is both not humble and quiet is both not generous and patient and vice versa.
Everyone who is not creative or quiet is not kind and vice versa.
Everyone who is either not old or humble is not quiet or not calm and vice versa.
Everyone who is both not patient and calm is both not funny and not kind and vice versa.
If susan is both not funny and generous then alice is either strong or brave.
Everyone who is either not wise or not quiet is both not curious and rich and vice versa.
Everyone who is rich or brave is either patient or kind.
If paul is not brave then paul is either brave or old and vice versa.
Susan is both not calm and not curious.
Someone is calm.
Someone is either tall or happy.
Susan is either not rich or curious.
John is generous.
Someone is either calm or creative.
Someone is either strong or not curious. | Fred is creative. | neutral | (![X]:((~strong(X)<~>tall(X))<=>(wise(X)&~generous(X))))&
((~happy(lucy))=>((~happy(john)<~>~patient(john))))&
((?[X]:((humble(X)&~calm(X))))=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(happy(X)<=>(~curious(X)<~>brave(X))))&
(((~old(fred)&generous(fred)))=>((~funny(paul)&rich(paul))))&
(![X]:(~kind(X)<=>tall(X)))&
((rich(susan))=>((creative(mary)<~>~kind(mary))))&
(![X]:((~funny(X)|~tall(X))<=>brave(X)))&
(![X]:((~humble(X)&quiet(X))<=>(~generous(X)&patient(X))))&
(![X]:((~creative(X)|quiet(X))<=>~kind(X)))&
(![X]:((~old(X)<~>humble(X))<=>(~quiet(X)|~calm(X))))&
(![X]:((~patient(X)&calm(X))<=>(~funny(X)&~kind(X))))&
(((~funny(susan)&generous(susan)))=>((strong(alice)<~>brave(alice))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(~curious(X)&rich(X))))&
(![X]:((rich(X)|brave(X))=>(patient(X)<~>kind(X))))&
((~brave(paul))<=>((brave(paul)<~>old(paul))))&
((~calm(susan)&~curious(susan)))&
(?[X]:(calm(X)))&
(?[X]:((tall(X)<~>happy(X))))&
((~rich(susan)<~>curious(susan)))&
(generous(john))&
(?[X]:((calm(X)<~>creative(X))))&
(?[X]:((strong(X)<~>~curious(X)))) | creative(fred) | [] | null | 0 |
Everyone who is calm or not rich is either quiet or not curious.
Everyone who is not kind is both not wise and not curious and vice versa.
Everyone who is either old or not happy is both not wise and kind.
Everyone who is happy is curious or not curious.
Everyone who is strong or not generous is both patient and not happy.
Everyone who is both not wise and generous is either patient or not kind and vice versa.
Everyone who is either kind or not kind is either not funny or not tall and vice versa.
If someone is strong or not curious then john is not kind.
Everyone who is either not patient or not rich is brave and vice versa.
Everyone who is not strong is not old or funny.
Everyone who is both not creative and not funny is quiet or not rich and vice versa.
If alice is not quiet then someone is both humble and kind.
If someone is either tall or rich then lucy is both not strong and patient.
Everyone who is either curious or not happy is both funny and old and vice versa.
If someone is either not tall or curious then someone is not humble.
Everyone who is not humble is both not generous and not rich and vice versa.
Paul is strong or not happy. | Alice is not funny. | neutral | (![X]:((calm(X)|~rich(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~curious(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)&kind(X))))&
(![X]:(happy(X)=>(curious(X)|~curious(X))))&
(![X]:((strong(X)|~generous(X))=>(patient(X)&~happy(X))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~generous(X)&~rich(X))))&
((strong(paul)|~happy(paul))) | ~funny(alice) | [] | null | 0 |
If someone is either not quiet or patient then alice is either tall or not calm and vice versa.
Everyone who is not tall or tall is funny.
Everyone who is both funny and not wise is happy and vice versa.
If alice is both not creative and not happy then fred is not rich.
Everyone who is not quiet or not rich is not humble or not wise.
Everyone who is either calm or tall is creative and vice versa.
Everyone who is either tall or not quiet is wise or kind.
Everyone who is either creative or patient is not old and vice versa.
If someone is either tall or happy then mary is either not kind or happy.
If john is curious then someone is not curious or rich and vice versa.
If someone is both generous and kind then someone is both not brave and kind.
Everyone who is creative is both strong and not happy.
Everyone who is either not happy or not wise is not brave and vice versa.
If someone is not tall or not wise then someone is not quiet.
Everyone who is quiet is both funny and not funny and vice versa.
Everyone who is either not creative or not patient is either not happy or not patient.
Fred is not kind or strong.
Paul is not generous or not tall.
Paul is either curious or calm.
Fred is not quiet or not old.
Susan is both not calm and not strong.
Someone is tall or not old. | Susan is not brave. | entailment | ((?[X]:((~quiet(X)<~>patient(X))))<=>((tall(alice)<~>~calm(alice))))&
(![X]:((~tall(X)|tall(X))=>funny(X)))&
(![X]:((funny(X)&~wise(X))<=>happy(X)))&
(((~creative(alice)&~happy(alice)))=>(~rich(fred)))&
(![X]:((~quiet(X)|~rich(X))=>(~humble(X)|~wise(X))))&
(![X]:((calm(X)<~>tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>~quiet(X))=>(wise(X)|kind(X))))&
(![X]:((creative(X)<~>patient(X))<=>~old(X)))&
((?[X]:((tall(X)<~>happy(X))))=>((~kind(mary)<~>happy(mary))))&
((curious(john))<=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:((generous(X)&kind(X))))=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:(creative(X)=>(strong(X)&~happy(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>~brave(X)))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)&~funny(X))))&
(![X]:((~creative(X)<~>~patient(X))=>(~happy(X)<~>~patient(X))))&
((~kind(fred)|strong(fred)))&
((~generous(paul)|~tall(paul)))&
((curious(paul)<~>calm(paul)))&
((~quiet(fred)|~old(fred)))&
((~calm(susan)&~strong(susan)))&
(?[X]:((tall(X)|~old(X)))) | ~brave(susan) | [
"p1",
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5346276072079866484621694
% SZS output start Proof for 5346276072079866484621694
2. ! [X0] : ((tall(X0) | ~tall(X0)) => funny(X0)) [input p1]
3. ! [X0] : ((~wise(X0) & funny(X0)) <=> happy(X0)) [input p2]
13. ! [X0] : ((~happy(X0) <~> ~wise(X0)) <=> ~brave(X0)) [input p12]
23. brave(susan) [input hypothesis]
30. ! [X0] : ((~happy(X0) <~> ~wise(X0)) => ~brave(X0)) [unused predicate definition removal 13]
31. ! [X0] : (funny(X0) | (~tall(X0) & tall(X0))) [ennf transformation 2]
39. ! [X0] : (~brave(X0) | (~happy(X0) <=> ~wise(X0))) [ennf transformation 30]
46. ! [X0] : (((~wise(X0) & funny(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) | ~funny(X0)))) [nnf transformation 3]
47. ! [X0] : (((~wise(X0) & funny(X0)) | ~happy(X0)) & (happy(X0) | wise(X0) | ~funny(X0))) [flattening 46]
56. ! [X0] : (~brave(X0) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) [nnf transformation 39]
74. funny(X0) | tall(X0) [cnf transformation 31]
75. funny(X0) | ~tall(X0) [cnf transformation 31]
76. happy(X0) | wise(X0) | ~funny(X0) [cnf transformation 47]
78. ~wise(X0) | ~happy(X0) [cnf transformation 47]
97. ~brave(X0) | ~wise(X0) | happy(X0) [cnf transformation 56]
98. ~brave(X0) | ~happy(X0) | wise(X0) [cnf transformation 56]
115. brave(susan) [cnf transformation 23]
148. funny(X0) [subsumption resolution 74,75]
149. happy(X0) | wise(X0) [subsumption resolution 76,148]
202. ~brave(X0) | ~happy(X0) [subsumption resolution 98,78]
203. ~brave(X0) | happy(X0) [subsumption resolution 97,149]
204. ~brave(X0) [subsumption resolution 203,202]
248. $false [subsumption resolution 115,204]
% SZS output end Proof for 5346276072079866484621694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and funny is rich.
If alice is either quiet or not old then mary is generous.
Everyone who is humble is either tall or not brave.
If mary is both kind and patient then john is brave or not wise.
If someone is wise then mary is both rich and old.
If someone is curious or not tall then lucy is either tall or not rich and vice versa.
If susan is not wise then someone is both not rich and curious.
If someone is not tall then lucy is both not strong and not curious.
Everyone who is either funny or not quiet is either quiet or not creative.
Everyone who is both brave and calm is both happy and not generous and vice versa.
If someone is either not brave or not curious then john is either not curious or quiet and vice versa.
If susan is either generous or quiet then someone is tall.
Everyone who is quiet or not brave is both not old and calm.
If someone is either not generous or humble then lucy is strong.
If someone is either calm or not tall then john is either not rich or not brave.
If someone is either strong or not creative then susan is both not kind and happy and vice versa.
Someone is old.
Fred is rich.
Someone is tall.
Fred is not wise.
Someone is kind or not calm.
Someone is both not old and generous.
Someone is wise.
Someone is kind. | Mary is not brave. | contradiction | (![X]:((~kind(X)&funny(X))=>rich(X)))&
(((quiet(alice)<~>~old(alice)))=>(generous(mary)))&
(![X]:(humble(X)=>(tall(X)<~>~brave(X))))&
(((kind(mary)&patient(mary)))=>((brave(john)|~wise(john))))&
((?[X]:(wise(X)))=>((rich(mary)&old(mary))))&
((?[X]:((curious(X)|~tall(X))))<=>((tall(lucy)<~>~rich(lucy))))&
((~wise(susan))=>(?[X]:((~rich(X)&curious(X)))))&
((?[X]:(~tall(X)))=>((~strong(lucy)&~curious(lucy))))&
(![X]:((funny(X)<~>~quiet(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((brave(X)&calm(X))<=>(happy(X)&~generous(X))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((~curious(john)<~>quiet(john))))&
(((generous(susan)<~>quiet(susan)))=>(?[X]:(tall(X))))&
(![X]:((quiet(X)|~brave(X))=>(~old(X)&calm(X))))&
((?[X]:((~generous(X)<~>humble(X))))=>(strong(lucy)))&
((?[X]:((calm(X)<~>~tall(X))))=>((~rich(john)<~>~brave(john))))&
((?[X]:((strong(X)<~>~creative(X))))<=>((~kind(susan)&happy(susan))))&
(?[X]:(old(X)))&
(rich(fred))&
(?[X]:(tall(X)))&
(~wise(fred))&
(?[X]:((kind(X)|~calm(X))))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:(wise(X)))&
(?[X]:(kind(X))) | ~brave(mary) | [
"p4",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1758250919091918536995176
% SZS output start Proof for 1758250919091918536995176
5. ? [X0] : wise(X0) => (old(mary) & rich(mary)) [input p4]
13. ! [X0] : ((~brave(X0) | quiet(X0)) => (calm(X0) & ~old(X0))) [input p12]
23. ? [X0] : wise(X0) [input p22]
25. ~brave(mary) [input hypothesis]
31. (old(mary) & rich(mary)) | ! [X0] : ~wise(X0) [ennf transformation 5]
36. ! [X0] : ((calm(X0) & ~old(X0)) | (brave(X0) & ~quiet(X0))) [ennf transformation 13]
72. ? [X0] : wise(X0) => wise(sK9) [choice axiom]
73. wise(sK9) [skolemisation 23,72]
82. old(mary) | ~wise(X0) [cnf transformation 31]
112. ~old(X0) | brave(X0) [cnf transformation 36]
134. wise(sK9) [cnf transformation 73]
136. ~brave(mary) [cnf transformation 25]
154. 4 <=> ! [X0] : ~wise(X0) [avatar definition]
155. ~wise(X0) <- (4) [avatar component clause 154]
157. 5 <=> old(mary) [avatar definition]
159. old(mary) <- (5) [avatar component clause 157]
160. 4 | 5 [avatar split clause 82,157,154]
329. $false <- (4) [resolution 155,134]
330. ~4 [avatar contradiction clause 329]
334. brave(mary) <- (5) [resolution 112,159]
335. $false <- (5) [subsumption resolution 334,136]
336. ~5 [avatar contradiction clause 335]
337. $false [avatar sat refutation 160,330,336]
% SZS output end Proof for 1758250919091918536995176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not generous is tall and vice versa.
If john is both not brave and not quiet then susan is either old or not kind.
Everyone who is not tall is both not strong and creative.
If someone is happy or not brave then someone is strong or not wise and vice versa.
If someone is wise or not happy then someone is both brave and not happy.
If mary is either kind or not strong then mary is not funny or old.
If fred is both not generous and creative then someone is either not wise or not kind.
Everyone who is not patient or not creative is both not humble and humble and vice versa.
Everyone who is either kind or humble is both not funny and generous.
Everyone who is both creative and not old is either not wise or not patient.
If someone is not tall then alice is both not wise and not happy.
Everyone who is not curious is either not generous or not happy.
Everyone who is not humble is either not creative or strong.
Everyone who is both not brave and strong is either not quiet or not wise and vice versa.
If fred is humble then alice is calm or not tall and vice versa.
If someone is both not curious and old then someone is both not calm and humble.
Lucy is either not humble or not creative.
Someone is both funny and happy.
Alice is creative.
Someone is both not old and not brave.
Someone is either not humble or not kind.
Someone is either wise or not curious.
Someone is funny or rich. | Lucy is curious. | entailment | (![X]:((~happy(X)&~generous(X))<=>tall(X)))&
(((~brave(john)&~quiet(john)))=>((old(susan)<~>~kind(susan))))&
(![X]:(~tall(X)=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((kind(mary)<~>~strong(mary)))=>((~funny(mary)|old(mary))))&
(((~generous(fred)&creative(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(~funny(X)&generous(X))))&
(![X]:((creative(X)&~old(X))=>(~wise(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>((~wise(alice)&~happy(alice))))&
(![X]:(~curious(X)=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~brave(X)&strong(X))<=>(~quiet(X)<~>~wise(X))))&
((humble(fred))<=>((calm(alice)|~tall(alice))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((~calm(X)&humble(X)))))&
((~humble(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&happy(X))))&
(creative(alice))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((funny(X)|rich(X)))) | curious(lucy) | [
"p0",
"p2",
"p7",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8483142045448726391747193
% SZS output start Proof for 8483142045448726391747193
1. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> tall(X0)) [input p0]
3. ! [X0] : (~tall(X0) => (creative(X0) & ~strong(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (humble(X0) & ~humble(X0))) [input p7]
12. ! [X0] : (~curious(X0) => (~generous(X0) <~> ~happy(X0))) [input p11]
13. ! [X0] : (~humble(X0) => (~creative(X0) <~> strong(X0))) [input p12]
17. ~humble(lucy) <~> ~creative(lucy) [input p16]
24. ~curious(lucy) [input hypothesis]
31. ! [X0] : ((creative(X0) & ~strong(X0)) | tall(X0)) [ennf transformation 3]
41. ! [X0] : ((~generous(X0) <~> ~happy(X0)) | curious(X0)) [ennf transformation 12]
42. ! [X0] : ((~creative(X0) <~> strong(X0)) | humble(X0)) [ennf transformation 13]
44. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) | happy(X0)))) [nnf transformation 1]
45. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | generous(X0) | happy(X0))) [flattening 44]
59. ! [X0] : (((~creative(X0) | ~patient(X0)) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
60. ! [X0] : ((~creative(X0) | ~patient(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | (creative(X0) & patient(X0)))) [flattening 59]
63. ! [X0] : (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | curious(X0)) [nnf transformation 41]
64. ! [X0] : (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | humble(X0)) [nnf transformation 42]
72. (creative(lucy) | humble(lucy)) & (~creative(lucy) | ~humble(lucy)) [nnf transformation 17]
84. ~tall(X0) | ~happy(X0) [cnf transformation 45]
85. ~tall(X0) | ~generous(X0) [cnf transformation 45]
88. ~strong(X0) | tall(X0) [cnf transformation 31]
103. ~humble(X0) | creative(X0) [cnf transformation 60]
105. humble(X0) | creative(X0) [cnf transformation 60]
116. curious(X0) | generous(X0) | happy(X0) [cnf transformation 63]
117. strong(X0) | ~creative(X0) | humble(X0) [cnf transformation 64]
130. ~creative(lucy) | ~humble(lucy) [cnf transformation 72]
141. ~curious(lucy) [cnf transformation 24]
246. creative(X0) [subsumption resolution 103,105]
263. humble(X0) | strong(X0) [subsumption resolution 117,246]
292. ~humble(lucy) [subsumption resolution 130,246]
324. strong(lucy) [resolution 263,292]
328. tall(lucy) [resolution 324,88]
368. generous(lucy) | happy(lucy) [resolution 116,141]
371. 42 <=> happy(lucy) [avatar definition]
373. happy(lucy) <- (42) [avatar component clause 371]
375. 43 <=> generous(lucy) [avatar definition]
378. 42 | 43 [avatar split clause 368,375,371]
471. ~generous(lucy) [resolution 328,85]
472. ~happy(lucy) [resolution 328,84]
473. ~43 [avatar split clause 471,375]
474. $false <- (42) [subsumption resolution 472,373]
475. ~42 [avatar contradiction clause 474]
476. $false [avatar sat refutation 378,473,475]
% SZS output end Proof for 8483142045448726391747193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then paul is rich or not quiet and vice versa.
If someone is generous then fred is either not happy or not patient and vice versa.
Everyone who is not creative or not humble is funny and vice versa.
Everyone who is either curious or kind is brave and vice versa.
Everyone who is wise or curious is humble or not calm.
If lucy is quiet or brave then someone is funny.
If someone is both not funny and not curious then alice is funny and vice versa.
Everyone who is not wise or quiet is both curious and not humble and vice versa.
If john is both calm and not tall then paul is both calm and happy.
If mary is both not strong and old then fred is both funny and not brave and vice versa.
If someone is patient or not humble then paul is happy or wise.
Everyone who is either humble or funny is not kind or not strong.
If susan is not kind then susan is both generous and not old and vice versa.
Everyone who is funny or tall is patient and vice versa.
Everyone who is either happy or humble is either not brave or not calm.
Everyone who is generous or not calm is both funny and strong and vice versa.
Paul is wise.
Someone is not humble.
Someone is humble.
Someone is generous.
Mary is not generous.
Lucy is both creative and not patient.
Alice is patient or not calm.
Someone is rich. | Lucy is not calm. | contradiction | ((?[X]:(~creative(X)))<=>((rich(paul)|~quiet(paul))))&
((?[X]:(generous(X)))<=>((~happy(fred)<~>~patient(fred))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((generous(X)|~calm(X))<=>(funny(X)&strong(X))))&
(wise(paul))&
(?[X]:(~humble(X)))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(~generous(mary))&
((creative(lucy)&~patient(lucy)))&
((patient(alice)|~calm(alice)))&
(?[X]:(rich(X))) | ~calm(lucy) | [
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7227142420218073326749764
% SZS output start Proof for 7227142420218073326749764
14. ! [X0] : ((tall(X0) | funny(X0)) <=> patient(X0)) [input p13]
16. ! [X0] : ((~calm(X0) | generous(X0)) <=> (strong(X0) & funny(X0))) [input p15]
22. ~patient(lucy) & creative(lucy) [input p21]
25. ~calm(lucy) [input hypothesis]
61. ! [X0] : (((tall(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~funny(X0)))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~funny(X0)))) [flattening 61]
64. ! [X0] : (((~calm(X0) | generous(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (calm(X0) & ~generous(X0)))) [nnf transformation 16]
65. ! [X0] : ((~calm(X0) | generous(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | (calm(X0) & ~generous(X0)))) [flattening 64]
113. ~funny(X0) | patient(X0) [cnf transformation 62]
121. calm(X0) | funny(X0) [cnf transformation 65]
131. ~patient(lucy) [cnf transformation 22]
134. ~calm(lucy) [cnf transformation 25]
302. funny(lucy) [resolution 121,134]
362. patient(lucy) [resolution 302,113]
364. $false [subsumption resolution 362,131]
% SZS output end Proof for 7227142420218073326749764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and wise is creative or curious and vice versa.
Everyone who is either not quiet or patient is rich and vice versa.
If john is both not kind and not curious then mary is both calm and not brave.
If paul is either not creative or not humble then alice is curious or not curious and vice versa.
Everyone who is both not humble and tall is both not patient and not funny.
If someone is both not generous and not kind then john is not creative or not rich.
Everyone who is both patient and not happy is both tall and kind and vice versa.
Everyone who is either creative or not old is either quiet or not brave and vice versa.
Everyone who is brave or humble is kind and vice versa.
Everyone who is either funny or not rich is not old.
If mary is not calm or not curious then alice is not rich and vice versa.
If someone is either not old or rich then someone is not happy or not kind and vice versa.
Everyone who is both not brave and not rich is creative.
If paul is both not curious and not funny then someone is not old or not tall.
Everyone who is kind or not humble is either funny or not quiet and vice versa.
If someone is both patient and strong then lucy is both curious and creative.
Someone is not brave or not curious.
Someone is kind or creative.
Someone is either curious or not strong.
Someone is both not quiet and not strong.
Someone is not creative or curious.
Susan is both not tall and quiet.
Someone is both not humble and not generous.
Paul is quiet or not curious. | Susan is not kind. | contradiction | (![X]:((~quiet(X)&wise(X))<=>(creative(X)|curious(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>rich(X)))&
(((~kind(john)&~curious(john)))=>((calm(mary)&~brave(mary))))&
(((~creative(paul)<~>~humble(paul)))<=>((curious(alice)|~curious(alice))))&
(![X]:((~humble(X)&tall(X))=>(~patient(X)&~funny(X))))&
((?[X]:((~generous(X)&~kind(X))))=>((~creative(john)|~rich(john))))&
(![X]:((patient(X)&~happy(X))<=>(tall(X)&kind(X))))&
(![X]:((creative(X)<~>~old(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((brave(X)|humble(X))<=>kind(X)))&
(![X]:((funny(X)<~>~rich(X))=>~old(X)))&
(((~calm(mary)|~curious(mary)))<=>(~rich(alice)))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((~brave(X)&~rich(X))=>creative(X)))&
(((~curious(paul)&~funny(paul)))=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((kind(X)|~humble(X))<=>(funny(X)<~>~quiet(X))))&
((?[X]:((patient(X)&strong(X))))=>((curious(lucy)&creative(lucy))))&
(?[X]:((~brave(X)|~curious(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((~creative(X)|curious(X))))&
((~tall(susan)&quiet(susan)))&
(?[X]:((~humble(X)&~generous(X))))&
((quiet(paul)|~curious(paul))) | ~kind(susan) | [
"p0",
"p7",
"p8",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5882269846338851118387257
% SZS output start Proof for 5882269846338851118387257
1. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (curious(X0) | creative(X0))) [input p0]
8. ! [X0] : ((creative(X0) <~> ~old(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p7]
9. ! [X0] : ((humble(X0) | brave(X0)) <=> kind(X0)) [input p8]
10. ! [X0] : ((funny(X0) <~> ~rich(X0)) => ~old(X0)) [input p9]
13. ! [X0] : ((~rich(X0) & ~brave(X0)) => creative(X0)) [input p12]
15. ! [X0] : ((~humble(X0) | kind(X0)) <=> (funny(X0) <~> ~quiet(X0))) [input p14]
22. quiet(susan) & ~tall(susan) [input p21]
25. ~kind(susan) [input hypothesis]
33. ! [X0] : (~old(X0) | (funny(X0) <=> ~rich(X0))) [ennf transformation 10]
34. ! [X0] : (creative(X0) | (rich(X0) | brave(X0))) [ennf transformation 13]
35. ! [X0] : (creative(X0) | rich(X0) | brave(X0)) [flattening 34]
39. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~curious(X0) & ~creative(X0))) & ((curious(X0) | creative(X0)) | (~wise(X0) | quiet(X0)))) [nnf transformation 1]
40. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~curious(X0) & ~creative(X0))) & (curious(X0) | creative(X0) | ~wise(X0) | quiet(X0))) [flattening 39]
46. ! [X0] : ((((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0))))) [nnf transformation 8]
47. ! [X0] : (((humble(X0) | brave(X0)) | ~kind(X0)) & (kind(X0) | (~humble(X0) & ~brave(X0)))) [nnf transformation 9]
48. ! [X0] : ((humble(X0) | brave(X0) | ~kind(X0)) & (kind(X0) | (~humble(X0) & ~brave(X0)))) [flattening 47]
49. ! [X0] : (~old(X0) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0)))) [nnf transformation 33]
59. ! [X0] : (((~humble(X0) | kind(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (humble(X0) & ~kind(X0)))) [nnf transformation 15]
60. ! [X0] : ((~humble(X0) | kind(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (humble(X0) & ~kind(X0)))) [flattening 59]
75. ~creative(X0) | ~quiet(X0) [cnf transformation 40]
101. brave(X0) | ~quiet(X0) | creative(X0) | old(X0) [cnf transformation 46]
105. old(X0) | ~creative(X0) | quiet(X0) | brave(X0) [cnf transformation 46]
106. ~brave(X0) | kind(X0) [cnf transformation 48]
107. ~humble(X0) | kind(X0) [cnf transformation 48]
109. ~old(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 49]
120. brave(X0) | rich(X0) | creative(X0) [cnf transformation 35]
123. ~quiet(X0) | funny(X0) | humble(X0) [cnf transformation 60]
138. quiet(susan) [cnf transformation 22]
142. ~kind(susan) [cnf transformation 25]
189. ~creative(X0) | old(X0) | brave(X0) [subsumption resolution 105,75]
191. ~quiet(X0) | brave(X0) | old(X0) [subsumption resolution 101,189]
395. funny(susan) | humble(susan) [resolution 123,138]
397. 47 <=> humble(susan) [avatar definition]
399. humble(susan) <- (47) [avatar component clause 397]
401. 48 <=> funny(susan) [avatar definition]
403. funny(susan) <- (48) [avatar component clause 401]
404. 47 | 48 [avatar split clause 395,401,397]
405. kind(susan) <- (47) [resolution 399,107]
406. $false <- (47) [subsumption resolution 405,142]
407. ~47 [avatar contradiction clause 406]
422. brave(susan) | old(susan) [resolution 191,138]
424. 51 <=> old(susan) [avatar definition]
426. old(susan) <- (51) [avatar component clause 424]
428. 52 <=> brave(susan) [avatar definition]
429. ~brave(susan) <- (~52) [avatar component clause 428]
430. brave(susan) <- (52) [avatar component clause 428]
431. 51 | 52 [avatar split clause 422,428,424]
434. ~rich(susan) | ~funny(susan) <- (51) [resolution 426,109]
437. ~rich(susan) <- (48, 51) [subsumption resolution 434,403]
439. rich(susan) | creative(susan) <- (~52) [resolution 429,120]
440. creative(susan) <- (48, 51, ~52) [subsumption resolution 439,437]
454. ~quiet(susan) <- (48, 51, ~52) [resolution 440,75]
455. $false <- (48, 51, ~52) [subsumption resolution 454,138]
456. ~48 | ~51 | 52 [avatar contradiction clause 455]
458. kind(susan) <- (52) [resolution 430,106]
459. $false <- (52) [subsumption resolution 458,142]
460. ~52 [avatar contradiction clause 459]
461. $false [avatar sat refutation 404,407,431,456,460]
% SZS output end Proof for 5882269846338851118387257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or humble is patient or wise.
If alice is tall or not patient then someone is both quiet and patient and vice versa.
Everyone who is not calm is both not patient and curious and vice versa.
If lucy is both not wise and wise then someone is wise or not quiet and vice versa.
Everyone who is both not humble and not tall is both calm and not funny and vice versa.
Everyone who is either curious or not quiet is either not old or calm and vice versa.
If someone is not strong or not creative then someone is humble and vice versa.
If fred is both calm and old then someone is not old or not humble.
Everyone who is either not humble or patient is not wise.
Everyone who is either not rich or not tall is tall or calm and vice versa.
Everyone who is both not happy and not wise is not calm and vice versa.
If someone is not patient then susan is both rich and not tall and vice versa.
Everyone who is tall is either not rich or quiet.
If someone is either wise or curious then someone is not funny or not curious.
Everyone who is not brave or not curious is not kind and vice versa.
If someone is curious then someone is either not creative or tall.
Someone is curious or tall.
Someone is not wise.
Someone is brave or not kind.
Someone is either not funny or curious.
Alice is not strong. | Alice is not happy. | contradiction | (![X]:((~rich(X)|humble(X))=>(patient(X)|wise(X))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:(~calm(X)<=>(~patient(X)&curious(X))))&
(((~wise(lucy)&wise(lucy)))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&~funny(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(?[X]:(humble(X))))&
(((calm(fred)&old(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>patient(X))=>~wise(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>~calm(X)))&
((?[X]:(~patient(X)))<=>((rich(susan)&~tall(susan))))&
(![X]:(tall(X)=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~brave(X)|~curious(X))<=>~kind(X)))&
((?[X]:(curious(X)))=>(?[X]:((~creative(X)<~>tall(X)))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(~strong(alice)) | ~happy(alice) | [
"p0",
"p2",
"p3",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6245380625222426392797285
% SZS output start Proof for 6245380625222426392797285
1. ! [X0] : ((humble(X0) | ~rich(X0)) => (wise(X0) | patient(X0))) [input p0]
3. ! [X0] : (~calm(X0) <=> (curious(X0) & ~patient(X0))) [input p2]
4. (wise(lucy) & ~wise(lucy)) <=> ? [X0] : (~quiet(X0) | wise(X0)) [input p3]
10. ! [X0] : ((~rich(X0) <~> ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & ~happy(X0)) <=> ~calm(X0)) [input p10]
22. ~happy(alice) [input hypothesis]
27. ! [X0] : ((wise(X0) | patient(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 1]
28. ! [X0] : (wise(X0) | patient(X0) | (~humble(X0) & rich(X0))) [flattening 27]
42. ! [X0] : ((~calm(X0) | (~curious(X0) | patient(X0))) & ((curious(X0) & ~patient(X0)) | calm(X0))) [nnf transformation 3]
43. ! [X0] : ((~calm(X0) | ~curious(X0) | patient(X0)) & ((curious(X0) & ~patient(X0)) | calm(X0))) [flattening 42]
44. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | (~wise(lucy) | wise(lucy))) [nnf transformation 4]
45. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | ~wise(lucy) | wise(lucy)) [flattening 44]
46. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X1] : (~quiet(X1) | wise(X1)) | ~wise(lucy) | wise(lucy)) [rectify 45]
47. ? [X1] : (~quiet(X1) | wise(X1)) => (~quiet(sK1) | wise(sK1)) [choice axiom]
48. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & ((~quiet(sK1) | wise(sK1)) | ~wise(lucy) | wise(lucy)) [skolemisation 46,47]
60. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [nnf transformation 10]
61. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [flattening 60]
62. ! [X0] : (((~wise(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) | happy(X0)))) [nnf transformation 11]
63. ! [X0] : (((~wise(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | wise(X0) | happy(X0))) [flattening 62]
87. wise(X0) | patient(X0) | rich(X0) [cnf transformation 28]
94. ~patient(X0) | calm(X0) [cnf transformation 43]
98. ~wise(lucy) | ~wise(X0) [cnf transformation 48]
100. wise(lucy) | ~wise(X0) [cnf transformation 48]
121. calm(X0) | tall(X0) | ~rich(X0) | tall(X0) [cnf transformation 61]
122. ~tall(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 61]
126. ~calm(X0) | wise(X0) | happy(X0) [cnf transformation 63]
128. ~wise(X0) | calm(X0) [cnf transformation 63]
145. ~happy(alice) [cnf transformation 22]
146. calm(X0) | tall(X0) | ~rich(X0) [duplicate literal removal 121]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 122]
176. 7 <=> wise(lucy) [avatar definition]
181. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
182. ~wise(X0) <- (8) [avatar component clause 181]
183. 8 | 7 [avatar split clause 100,176,181]
185. 8 | ~7 [avatar split clause 98,176,181]
231. ~rich(X0) | calm(X0) [subsumption resolution 146,147]
314. patient(X0) | rich(X0) | calm(X0) [resolution 87,128]
325. patient(X0) | calm(X0) [subsumption resolution 314,231]
326. calm(X0) [subsumption resolution 325,94]
370. wise(X1) | happy(X1) [resolution 126,326]
376. happy(X1) <- (8) [subsumption resolution 370,182]
377. $false <- (8) [resolution 376,145]
379. ~8 [avatar contradiction clause 377]
380. $false [avatar sat refutation 183,185,379]
% SZS output end Proof for 6245380625222426392797285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not brave.
If mary is both not rich and not strong then susan is wise and vice versa.
Everyone who is either wise or not patient is not tall or not creative and vice versa.
If someone is not generous then lucy is curious and vice versa.
Everyone who is not happy is not strong.
Everyone who is humble or not tall is quiet.
If john is both not curious and not quiet then someone is both not brave and old and vice versa.
If lucy is happy or rich then susan is both not calm and kind.
Everyone who is either not curious or not wise is either brave or not happy and vice versa.
Everyone who is both rich and brave is not rich.
If fred is rich then someone is either funny or not strong.
Everyone who is either not funny or old is both old and not kind.
If john is wise or curious then lucy is both not brave and brave and vice versa.
If susan is either not tall or not funny then someone is old or not kind and vice versa.
Everyone who is brave is both generous and not wise and vice versa.
Everyone who is either not curious or rich is not calm or not wise.
Someone is generous or not quiet.
Mary is either patient or not brave.
Someone is either not rich or happy.
Someone is generous or not rich.
Alice is wise.
Mary is either funny or not quiet.
Someone is both strong and not brave.
Someone is both not strong and not happy. | Alice is not brave. | entailment | (![X]:(humble(X)=>~brave(X)))&
(((~rich(mary)&~strong(mary)))<=>(wise(susan)))&
(![X]:((wise(X)<~>~patient(X))<=>(~tall(X)|~creative(X))))&
((?[X]:(~generous(X)))<=>(curious(lucy)))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:((humble(X)|~tall(X))=>quiet(X)))&
(((~curious(john)&~quiet(john)))<=>(?[X]:((~brave(X)&old(X)))))&
(((happy(lucy)|rich(lucy)))=>((~calm(susan)&kind(susan))))&
(![X]:((~curious(X)<~>~wise(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((rich(X)&brave(X))=>~rich(X)))&
((rich(fred))=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((~funny(X)<~>old(X))=>(old(X)&~kind(X))))&
(((wise(john)|curious(john)))<=>((~brave(lucy)&brave(lucy))))&
(((~tall(susan)<~>~funny(susan)))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:(brave(X)<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)<~>rich(X))=>(~calm(X)|~wise(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((patient(mary)<~>~brave(mary)))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((generous(X)|~rich(X))))&
(wise(alice))&
((funny(mary)<~>~quiet(mary)))&
(?[X]:((strong(X)&~brave(X))))&
(?[X]:((~strong(X)&~happy(X)))) | ~brave(alice) | [
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3732649229513889692368191
% SZS output start Proof for 3732649229513889692368191
15. ! [X0] : (brave(X0) <=> (~wise(X0) & generous(X0))) [input p14]
21. wise(alice) [input p20]
25. brave(alice) [input hypothesis]
61. ! [X0] : ((brave(X0) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ~brave(X0))) [nnf transformation 15]
62. ! [X0] : ((brave(X0) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ~brave(X0))) [flattening 61]
122. ~wise(X0) | ~brave(X0) [cnf transformation 62]
130. wise(alice) [cnf transformation 21]
137. brave(alice) [cnf transformation 25]
312. ~brave(alice) [resolution 122,130]
313. $false [subsumption resolution 312,137]
% SZS output end Proof for 3732649229513889692368191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not curious is both funny and not quiet and vice versa.
If someone is either calm or not humble then someone is either kind or funny and vice versa.
If paul is not humble or not quiet then someone is both curious and generous.
Everyone who is not quiet is either not funny or humble.
If john is old then someone is funny.
Everyone who is both not old and old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Someone is not calm.
Lucy is kind.
Fred is not tall.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall.
Fred is either wise or strong. | Lucy is not strong. | contradiction | (![X]:((~happy(X)|~curious(X))<=>(funny(X)&~quiet(X))))&
((?[X]:((calm(X)<~>~humble(X))))<=>(?[X]:((kind(X)<~>funny(X)))))&
(((~humble(paul)|~quiet(paul)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:(~quiet(X)=>(~funny(X)<~>humble(X))))&
((old(john))=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
(~tall(fred))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X))))&
((wise(fred)<~>strong(fred))) | ~strong(lucy) | [
"p0",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 112549201279730892878705
% SZS output start Proof for 112549201279730892878705
1. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (~quiet(X0) & funny(X0))) [input p0]
13. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~kind(X0) & rich(X0))) [input p12]
16. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p15]
18. kind(lucy) [input p17]
24. ~strong(lucy) [input hypothesis]
37. ! [X0] : (((~curious(X0) | ~happy(X0)) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 1]
38. ! [X0] : ((~curious(X0) | ~happy(X0) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | (curious(X0) & happy(X0)))) [flattening 37]
64. ! [X0] : (((happy(X0) & ~generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 13]
65. ! [X0] : (((happy(X0) & ~generous(X0)) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ~happy(X0) | generous(X0))) [flattening 64]
69. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 16]
70. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 69]
76. funny(X0) | happy(X0) [cnf transformation 38]
118. ~kind(X0) | ~happy(X0) | generous(X0) [cnf transformation 65]
129. ~generous(X0) | strong(X0) [cnf transformation 70]
130. ~funny(X0) | strong(X0) [cnf transformation 70]
135. kind(lucy) [cnf transformation 18]
141. ~strong(lucy) [cnf transformation 24]
350. ~happy(lucy) | generous(lucy) [resolution 118,135]
355. 33 <=> generous(lucy) [avatar definition]
357. generous(lucy) <- (33) [avatar component clause 355]
359. 34 <=> happy(lucy) [avatar definition]
362. 33 | ~34 [avatar split clause 350,359,355]
396. 39 <=> funny(lucy) [avatar definition]
397. ~funny(lucy) <- (~39) [avatar component clause 396]
398. funny(lucy) <- (39) [avatar component clause 396]
417. strong(lucy) <- (39) [resolution 398,130]
419. $false <- (39) [subsumption resolution 417,141]
420. ~39 [avatar contradiction clause 419]
425. happy(lucy) <- (~39) [resolution 397,76]
431. 34 | 39 [avatar split clause 425,396,359]
435. strong(lucy) <- (33) [resolution 357,129]
436. $false <- (33) [subsumption resolution 435,141]
437. ~33 [avatar contradiction clause 436]
438. $false [avatar sat refutation 362,420,431,437]
% SZS output end Proof for 112549201279730892878705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is not kind or not funny and vice versa. If someone is either not funny or strong then someone is either rich or quiet and vice versa. If alice is both quiet and not funny then someone is either not tall or brave. Everyone who is either not generous or strong is both patient and generous and vice versa. Everyone who is both wise and happy is not calm and vice versa. If someone is either not generous or creative then someone is either not generous or tall. If someone is quiet then mary is both strong and not patient and vice versa. If someone is both strong and rich then john is both not creative and not calm and vice versa. Everyone who is both quiet and tall is happy or patient and vice versa. Everyone who is patient or not tall is quiet. If someone is kind or not rich then someone is not patient and vice versa. Everyone who is wise or not happy is not kind or not calm and vice versa. If john is both brave and not patient then alice is both funny and curious and vice versa. Everyone who is not brave or old is kind or funny. Everyone who is both not kind and not happy is both curious and not curious and vice versa. If john is not strong then someone is both old and tall. Someone is not generous. Paul is not creative. Someone is either brave or calm. Mary is either funny or not strong. Fred is calm. Susan is rich or not generous. Someone is both not patient and kind. | John is not creative. | neutral | (![X]:(~calm(X)<=>(~kind(X)|~funny(X))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(((quiet(alice)&~funny(alice)))=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:((~generous(X)<~>strong(X))<=>(patient(X)&generous(X))))&
(![X]:((wise(X)&happy(X))<=>~calm(X)))&
((?[X]:((~generous(X)<~>creative(X))))=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:(quiet(X)))<=>((strong(mary)&~patient(mary))))&
((?[X]:((strong(X)&rich(X))))<=>((~creative(john)&~calm(john))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)|patient(X))))&
(![X]:((patient(X)|~tall(X))=>quiet(X)))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((wise(X)|~happy(X))<=>(~kind(X)|~calm(X))))&
(((brave(john)&~patient(john)))<=>((funny(alice)&curious(alice))))&
(![X]:((~brave(X)|old(X))=>(kind(X)|funny(X))))&
(![X]:((~kind(X)&~happy(X))<=>(curious(X)&~curious(X))))&
((~strong(john))=>(?[X]:((old(X)&tall(X)))))&
(?[X]:(~generous(X)))&
(~creative(paul))&
(?[X]:((brave(X)<~>calm(X))))&
((funny(mary)<~>~strong(mary)))&
(calm(fred))&
((rich(susan)|~generous(susan)))&
(?[X]:((~patient(X)&kind(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is both not calm and not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
If someone is brave then someone is not funny or patient.
If lucy is not creative or humble then lucy is not quiet.
If alice is not generous then alice is either happy or not creative and vice versa.
Lucy is either not strong or curious.
John is both old and generous.
Susan is not brave or not generous.
Someone is either not patient or patient.
Susan is quiet or generous.
Someone is not strong or not generous.
Susan is quiet or happy. | Alice is not creative. | neutral | (![X]:((~calm(X)&~happy(X))<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)|patient(X)))))&
(((~creative(lucy)|humble(lucy)))=>(~quiet(lucy)))&
((~generous(alice))<=>((happy(alice)<~>~creative(alice))))&
((~strong(lucy)<~>curious(lucy)))&
((old(john)&generous(john)))&
((~brave(susan)|~generous(susan)))&
(?[X]:((~patient(X)<~>patient(X))))&
((quiet(susan)|generous(susan)))&
(?[X]:((~strong(X)|~generous(X))))&
((quiet(susan)|happy(susan))) | ~creative(alice) | [] | null | 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
Alice is both not tall and creative.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Paul is brave. | contradiction | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((~tall(alice)&creative(alice)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | brave(paul) | [
"p0",
"p4",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7816841809406352948978479
% SZS output start Proof for 7816841809406352948978479
1. ! [X0] : ((~patient(X0) | patient(X0)) => (tall(X0) | calm(X0))) [input p0]
5. (old(paul) | strong(paul)) <=> ~tall(paul) [input p4]
9. ! [X0] : ((~humble(X0) | ~old(X0)) <=> funny(X0)) [input p8]
10. ? [X0] : (funny(X0) <~> ~humble(X0)) <=> ? [X0] : (brave(X0) <~> ~calm(X0)) [input p9]
11. ! [X0] : ((~old(X0) | funny(X0)) <=> (~strong(X0) & wise(X0))) [input p10]
12. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> tall(X0))) [input p11]
23. brave(paul) [input hypothesis]
25. ? [X0] : (funny(X0) <~> ~humble(X0)) <=> ? [X1] : (brave(X1) <~> ~calm(X1)) [rectify 10]
30. ! [X0] : ((tall(X0) | calm(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 1]
31. ! [X0] : (tall(X0) | calm(X0) | (patient(X0) & ~patient(X0))) [flattening 30]
45. ((old(paul) | strong(paul)) | tall(paul)) & (~tall(paul) | (~old(paul) & ~strong(paul))) [nnf transformation 5]
46. (old(paul) | strong(paul) | tall(paul)) & (~tall(paul) | (~old(paul) & ~strong(paul))) [flattening 45]
56. ! [X0] : (((~humble(X0) | ~old(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [nnf transformation 9]
57. ! [X0] : ((~humble(X0) | ~old(X0) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [flattening 56]
58. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (? [X1] : ((calm(X1) | ~brave(X1)) & (~calm(X1) | brave(X1))) | ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0)))) [nnf transformation 25]
59. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (? [X2] : ((calm(X2) | ~brave(X2)) & (~calm(X2) | brave(X2))) | ! [X3] : ((funny(X3) | humble(X3)) & (~humble(X3) | ~funny(X3)))) [rectify 58]
60. ? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) => ((humble(sK4) | ~funny(sK4)) & (~humble(sK4) | funny(sK4))) [choice axiom]
61. ? [X2] : ((calm(X2) | ~brave(X2)) & (~calm(X2) | brave(X2))) => ((calm(sK5) | ~brave(sK5)) & (~calm(sK5) | brave(sK5))) [choice axiom]
62. (((humble(sK4) | ~funny(sK4)) & (~humble(sK4) | funny(sK4))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (((calm(sK5) | ~brave(sK5)) & (~calm(sK5) | brave(sK5))) | ! [X3] : ((funny(X3) | humble(X3)) & (~humble(X3) | ~funny(X3)))) [skolemisation 59,61,60]
63. ! [X0] : (((~old(X0) | funny(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 11]
64. ! [X0] : ((~old(X0) | funny(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [flattening 63]
65. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 12]
81. tall(X0) | calm(X0) | ~patient(X0) [cnf transformation 31]
82. tall(X0) | calm(X0) | patient(X0) [cnf transformation 31]
93. ~tall(paul) | ~old(paul) [cnf transformation 46]
105. funny(X0) | old(X0) [cnf transformation 57]
106. funny(X0) | humble(X0) [cnf transformation 57]
112. ~humble(sK4) | funny(sK4) | ~calm(X1) | ~brave(X1) [cnf transformation 62]
118. ~funny(X0) | ~strong(X0) [cnf transformation 64]
125. ~funny(X0) | strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
126. ~funny(X0) | strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
127. funny(X0) | ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
128. funny(X0) | ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
143. brave(paul) [cnf transformation 23]
144. ~funny(X0) | strong(X0) | tall(X0) [duplicate literal removal 125]
145. ~funny(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 126]
146. funny(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 127]
147. funny(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 128]
148. tall(X0) | calm(X0) [subsumption resolution 81,82]
164. 4 <=> tall(paul) [avatar definition]
165. ~tall(paul) <- (~4) [avatar component clause 164]
172. 6 <=> old(paul) [avatar definition]
173. ~old(paul) <- (~6) [avatar component clause 172]
176. ~6 | ~4 [avatar split clause 93,164,172]
252. 23 <=> ! [X1] : (~calm(X1) | ~brave(X1)) [avatar definition]
253. ~brave(X1) | ~calm(X1) <- (23) [avatar component clause 252]
257. 24 <=> funny(sK4) [avatar definition]
259. funny(sK4) <- (24) [avatar component clause 257]
261. funny(sK4) | ~calm(X1) | ~brave(X1) [subsumption resolution 112,106]
262. 23 | 24 [avatar split clause 261,257,252]
277. ~strong(X0) | ~tall(X0) [subsumption resolution 147,118]
278. ~strong(X0) | tall(X0) [subsumption resolution 146,118]
279. ~strong(X0) [subsumption resolution 278,277]
280. ~funny(X0) | ~tall(X0) [subsumption resolution 145,279]
281. ~funny(X0) | tall(X0) [subsumption resolution 144,279]
282. ~funny(X0) [subsumption resolution 281,280]
347. old(X0) [resolution 105,282]
348. $false <- (~6) [resolution 347,173]
349. 6 [avatar contradiction clause 348]
360. calm(paul) <- (~4) [resolution 148,165]
366. $false <- (24) [subsumption resolution 259,282]
367. ~24 [avatar contradiction clause 366]
369. ~calm(paul) <- (23) [resolution 253,143]
372. $false <- (~4, 23) [subsumption resolution 369,360]
373. 4 | ~23 [avatar contradiction clause 372]
374. $false [avatar sat refutation 176,262,349,367,373]
% SZS output end Proof for 7816841809406352948978479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is either old or creative.
Everyone who is not brave or curious is both strong and not kind.
Everyone who is humble or not generous is both not curious and happy.
If someone is not rich or patient then mary is brave.
Everyone who is either quiet or wise is not quiet and vice versa.
If fred is both not curious and not calm then someone is either not humble or not tall.
Everyone who is happy is either not generous or not rich.
If lucy is humble then someone is either creative or not generous and vice versa.
Everyone who is not patient is either not wise or old.
If paul is both not brave and creative then susan is old and vice versa.
If paul is both curious and humble then susan is either not kind or patient and vice versa.
Everyone who is not tall or not old is either not humble or rich.
If someone is not old or patient then alice is tall and vice versa.
If fred is either not wise or creative then alice is not rich or humble.
Everyone who is calm or not rich is not humble and vice versa.
If someone is humble or not happy then alice is both quiet and not creative.
Fred is not quiet or not curious.
Someone is humble.
Susan is old or not creative.
Someone is either not quiet or humble.
Susan is creative or brave.
John is both generous and not kind.
Paul is rich.
Someone is not old or creative. | Alice is not tall. | contradiction | (![X]:((strong(X)|~wise(X))=>(old(X)<~>creative(X))))&
(![X]:((~brave(X)|curious(X))=>(strong(X)&~kind(X))))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)&happy(X))))&
((?[X]:((~rich(X)|patient(X))))=>(brave(mary)))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
((humble(lucy))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~patient(X)=>(~wise(X)<~>old(X))))&
(((~brave(paul)&creative(paul)))<=>(old(susan)))&
(((curious(paul)&humble(paul)))<=>((~kind(susan)<~>patient(susan))))&
(![X]:((~tall(X)|~old(X))=>(~humble(X)<~>rich(X))))&
((?[X]:((~old(X)|patient(X))))<=>(tall(alice)))&
(((~wise(fred)<~>creative(fred)))=>((~rich(alice)|humble(alice))))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
((?[X]:((humble(X)|~happy(X))))=>((quiet(alice)&~creative(alice))))&
((~quiet(fred)|~curious(fred)))&
(?[X]:(humble(X)))&
((old(susan)|~creative(susan)))&
(?[X]:((~quiet(X)<~>humble(X))))&
((creative(susan)|brave(susan)))&
((generous(john)&~kind(john)))&
(rich(paul))&
(?[X]:((~old(X)|creative(X)))) | ~tall(alice) | [
"p0",
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 668560748751771011610109
% SZS output start Proof for 668560748751771011610109
1. ! [X0] : ((~wise(X0) | strong(X0)) => (old(X0) <~> creative(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~brave(X0)) => (~kind(X0) & strong(X0))) [input p1]
10. (creative(paul) & ~brave(paul)) <=> old(susan) [input p9]
13. ? [X0] : (patient(X0) | ~old(X0)) <=> tall(alice) [input p12]
25. ~tall(alice) [input hypothesis]
26. ! [X0] : ((old(X0) <~> creative(X0)) | (wise(X0) & ~strong(X0))) [ennf transformation 1]
27. ! [X0] : ((~kind(X0) & strong(X0)) | (~curious(X0) & brave(X0))) [ennf transformation 2]
38. ! [X0] : (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | (wise(X0) & ~strong(X0))) [nnf transformation 26]
49. ((creative(paul) & ~brave(paul)) | ~old(susan)) & (old(susan) | (~creative(paul) | brave(paul))) [nnf transformation 10]
50. ((creative(paul) & ~brave(paul)) | ~old(susan)) & (old(susan) | ~creative(paul) | brave(paul)) [flattening 49]
54. (? [X0] : (patient(X0) | ~old(X0)) | ~tall(alice)) & (tall(alice) | ! [X0] : (~patient(X0) & old(X0))) [nnf transformation 13]
55. (? [X0] : (patient(X0) | ~old(X0)) | ~tall(alice)) & (tall(alice) | ! [X1] : (~patient(X1) & old(X1))) [rectify 54]
56. ? [X0] : (patient(X0) | ~old(X0)) => (patient(sK2) | ~old(sK2)) [choice axiom]
57. ((patient(sK2) | ~old(sK2)) | ~tall(alice)) & (tall(alice) | ! [X1] : (~patient(X1) & old(X1))) [skolemisation 55,56]
70. ~creative(X0) | ~old(X0) | ~strong(X0) [cnf transformation 38]
72. brave(X0) | strong(X0) [cnf transformation 27]
97. ~brave(paul) | ~old(susan) [cnf transformation 50]
98. creative(paul) | ~old(susan) [cnf transformation 50]
109. tall(alice) | old(X1) [cnf transformation 57]
131. ~tall(alice) [cnf transformation 25]
190. 13 <=> old(susan) [avatar definition]
192. ~old(susan) <- (~13) [avatar component clause 190]
194. 14 <=> creative(paul) [avatar definition]
196. creative(paul) <- (14) [avatar component clause 194]
197. ~13 | 14 [avatar split clause 98,194,190]
199. 15 <=> brave(paul) [avatar definition]
201. ~brave(paul) <- (~15) [avatar component clause 199]
202. ~13 | ~15 [avatar split clause 97,199,190]
226. 20 <=> tall(alice) [avatar definition]
236. 22 <=> ! [X1] : old(X1) [avatar definition]
237. old(X1) <- (22) [avatar component clause 236]
238. 22 | 20 [avatar split clause 109,226,236]
305. ~20 [avatar split clause 131,226]
316. strong(paul) <- (~15) [resolution 72,201]
352. ~old(paul) | ~strong(paul) <- (14) [resolution 70,196]
356. ~strong(paul) <- (14, 22) [subsumption resolution 352,237]
357. $false <- (14, ~15, 22) [subsumption resolution 356,316]
358. ~14 | 15 | ~22 [avatar contradiction clause 357]
364. $false <- (~13, 22) [subsumption resolution 192,237]
365. 13 | ~22 [avatar contradiction clause 364]
366. $false [avatar sat refutation 197,202,238,305,358,365]
% SZS output end Proof for 668560748751771011610109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not quiet is not wise or not patient and vice versa.
If susan is not tall or humble then john is both rich and not brave.
Everyone who is both not creative and funny is either not strong or strong and vice versa.
Everyone who is not curious is rich.
If john is tall or patient then someone is patient or not wise.
If someone is not curious then susan is both humble and generous.
Everyone who is either kind or not quiet is both patient and not patient and vice versa.
Everyone who is both not old and tall is both not tall and not funny.
Everyone who is both strong and not strong is not quiet.
Everyone who is quiet or not happy is old or funny.
Everyone who is both not tall and not generous is both kind and not curious.
If alice is both not funny and not tall then mary is both not humble and curious and vice versa.
If someone is not humble then mary is both humble and not quiet and vice versa.
If someone is either calm or not old then susan is not old.
If lucy is humble then someone is not kind and vice versa.
Everyone who is tall or not old is not curious or generous and vice versa.
Paul is both not old and not strong.
Lucy is both wise and curious.
John is wise.
Someone is funny or kind.
Someone is not calm or curious.
John is not humble.
Someone is brave. | Susan is funny. | entailment | (![X]:((brave(X)&~quiet(X))<=>(~wise(X)|~patient(X))))&
(((~tall(susan)|humble(susan)))=>((rich(john)&~brave(john))))&
(![X]:((~creative(X)&funny(X))<=>(~strong(X)<~>strong(X))))&
(![X]:(~curious(X)=>rich(X)))&
(((tall(john)|patient(john)))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(~curious(X)))=>((humble(susan)&generous(susan))))&
(![X]:((kind(X)<~>~quiet(X))<=>(patient(X)&~patient(X))))&
(![X]:((~old(X)&tall(X))=>(~tall(X)&~funny(X))))&
(![X]:((strong(X)&~strong(X))=>~quiet(X)))&
(![X]:((quiet(X)|~happy(X))=>(old(X)|funny(X))))&
(![X]:((~tall(X)&~generous(X))=>(kind(X)&~curious(X))))&
(((~funny(alice)&~tall(alice)))<=>((~humble(mary)&curious(mary))))&
((?[X]:(~humble(X)))<=>((humble(mary)&~quiet(mary))))&
((?[X]:((calm(X)<~>~old(X))))=>(~old(susan)))&
((humble(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((tall(X)|~old(X))<=>(~curious(X)|generous(X))))&
((~old(paul)&~strong(paul)))&
((wise(lucy)&curious(lucy)))&
(wise(john))&
(?[X]:((funny(X)|kind(X))))&
(?[X]:((~calm(X)|curious(X))))&
(~humble(john))&
(?[X]:(brave(X))) | funny(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1382812297287227215612470
% SZS output start Proof for 1382812297287227215612470
3. ! [X0] : ((funny(X0) & ~creative(X0)) <=> (~strong(X0) <~> strong(X0))) [input p2]
24. ~funny(susan) [input hypothesis]
42. ! [X0] : (((funny(X0) & ~creative(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~funny(X0) | creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((funny(X0) & ~creative(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~funny(X0) | creative(X0))) [flattening 42]
79. funny(X0) | strong(X0) | strong(X0) [cnf transformation 43]
80. funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 43]
121. ~funny(susan) [cnf transformation 24]
125. funny(X0) | strong(X0) [duplicate literal removal 79]
126. funny(X0) | ~strong(X0) [duplicate literal removal 80]
141. funny(X0) [subsumption resolution 125,126]
237. $false [subsumption resolution 121,141]
% SZS output end Proof for 1382812297287227215612470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and humble is both not humble and not strong and vice versa. Everyone who is creative or patient is both patient and happy. Everyone who is not happy is not creative or not kind and vice versa. If alice is not tall or not creative then someone is both not humble and funny. Everyone who is creative or strong is both happy and not quiet. If paul is both not generous and tall then someone is rich or not old. If mary is both generous and not patient then someone is either old or happy. Everyone who is not creative or not tall is not kind or kind and vice versa. If john is humble or not old then paul is either brave or strong. Everyone who is both not humble and not tall is either not creative or not wise and vice versa. Everyone who is either funny or calm is either funny or tall. If mary is both not humble and curious then someone is not quiet or strong and vice versa. Everyone who is kind is old and vice versa. If someone is either rich or not happy then someone is happy and vice versa. Everyone who is not happy is old. If fred is both not humble and brave then someone is curious or not happy and vice versa. Someone is not calm or not quiet. Someone is old. Alice is brave. Someone is both not funny and not curious. Paul is not rich. Susan is funny. John is either not curious or old. | John is patient. | entailment | (![X]:((~strong(X)&humble(X))<=>(~humble(X)&~strong(X))))&
(![X]:((creative(X)|patient(X))=>(patient(X)&happy(X))))&
(![X]:(~happy(X)<=>(~creative(X)|~kind(X))))&
(((~tall(alice)|~creative(alice)))=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((creative(X)|strong(X))=>(happy(X)&~quiet(X))))&
(((~generous(paul)&tall(paul)))=>(?[X]:((rich(X)|~old(X)))))&
(((generous(mary)&~patient(mary)))=>(?[X]:((old(X)<~>happy(X)))))&
(![X]:((~creative(X)|~tall(X))<=>(~kind(X)|kind(X))))&
(((humble(john)|~old(john)))=>((brave(paul)<~>strong(paul))))&
(![X]:((~humble(X)&~tall(X))<=>(~creative(X)<~>~wise(X))))&
(![X]:((funny(X)<~>calm(X))=>(funny(X)<~>tall(X))))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:(kind(X)<=>old(X)))&
((?[X]:((rich(X)<~>~happy(X))))<=>(?[X]:(happy(X))))&
(![X]:(~happy(X)=>old(X)))&
(((~humble(fred)&brave(fred)))<=>(?[X]:((curious(X)|~happy(X)))))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:(old(X)))&
(brave(alice))&
(?[X]:((~funny(X)&~curious(X))))&
(~rich(paul))&
(funny(susan))&
((~curious(john)<~>old(john))) | patient(john) | [
"p0",
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 182112396049210344091998
% SZS output start Proof for 182112396049210344091998
1. ! [X0] : ((humble(X0) & ~strong(X0)) <=> (~strong(X0) & ~humble(X0))) [input p0]
2. ! [X0] : ((patient(X0) | creative(X0)) => (happy(X0) & patient(X0))) [input p1]
3. ! [X0] : (~happy(X0) <=> (~kind(X0) | ~creative(X0))) [input p2]
5. ! [X0] : ((strong(X0) | creative(X0)) => (~quiet(X0) & happy(X0))) [input p4]
24. ~patient(john) [input hypothesis]
26. ! [X0] : ((happy(X0) & patient(X0)) | (~patient(X0) & ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((~quiet(X0) & happy(X0)) | (~strong(X0) & ~creative(X0))) [ennf transformation 5]
36. ! [X0] : (((humble(X0) & ~strong(X0)) | (strong(X0) | humble(X0))) & ((~strong(X0) & ~humble(X0)) | (~humble(X0) | strong(X0)))) [nnf transformation 1]
37. ! [X0] : (((humble(X0) & ~strong(X0)) | strong(X0) | humble(X0)) & ((~strong(X0) & ~humble(X0)) | ~humble(X0) | strong(X0))) [flattening 36]
38. ! [X0] : ((~happy(X0) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | happy(X0))) [nnf transformation 3]
39. ! [X0] : ((~happy(X0) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | happy(X0))) [flattening 38]
76. ~humble(X0) | ~humble(X0) | strong(X0) [cnf transformation 37]
79. humble(X0) | strong(X0) | humble(X0) [cnf transformation 37]
80. ~creative(X0) | patient(X0) [cnf transformation 26]
85. ~happy(X0) | creative(X0) [cnf transformation 39]
92. happy(X0) | ~strong(X0) [cnf transformation 28]
142. ~patient(john) [cnf transformation 24]
145. ~humble(X0) | strong(X0) [duplicate literal removal 76]
146. humble(X0) | strong(X0) [duplicate literal removal 79]
147. strong(X0) [subsumption resolution 145,146]
169. happy(X0) [subsumption resolution 92,147]
251. creative(X0) [resolution 85,169]
253. patient(X1) [resolution 251,80]
256. $false [resolution 253,142]
% SZS output end Proof for 182112396049210344091998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet or not patient then mary is both not calm and not curious and vice versa.
If someone is strong then paul is either not quiet or curious and vice versa.
Everyone who is not humble or patient is both kind and funny and vice versa.
Everyone who is not kind or funny is both not generous and not rich and vice versa.
Everyone who is both happy and not strong is not generous and vice versa.
If someone is both rich and funny then someone is not funny.
Everyone who is not kind is either rich or humble and vice versa.
Everyone who is kind is not wise or not tall and vice versa.
Everyone who is humble is not rich or old.
If john is not rich then someone is either not old or patient and vice versa.
If mary is not rich or curious then alice is either not patient or not funny.
Everyone who is either funny or strong is not patient or curious and vice versa.
If fred is tall or not creative then mary is patient or strong.
Everyone who is both not generous and tall is either quiet or calm and vice versa.
Everyone who is either not funny or tall is both funny and kind.
If someone is wise or not happy then alice is both not quiet and not wise.
Someone is kind or generous.
Someone is both happy and generous.
Someone is not curious.
Someone is either not happy or not rich.
Someone is either not generous or not old.
John is not calm.
Someone is not calm or calm.
Someone is creative. | Alice is happy. | neutral | (((~quiet(paul)|~patient(paul)))<=>((~calm(mary)&~curious(mary))))&
((?[X]:(strong(X)))<=>((~quiet(paul)<~>curious(paul))))&
(![X]:((~humble(X)|patient(X))<=>(kind(X)&funny(X))))&
(![X]:((~kind(X)|funny(X))<=>(~generous(X)&~rich(X))))&
(![X]:((happy(X)&~strong(X))<=>~generous(X)))&
((?[X]:((rich(X)&funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(~kind(X)<=>(rich(X)<~>humble(X))))&
(![X]:(kind(X)<=>(~wise(X)|~tall(X))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~calm(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(creative(X))) | happy(alice) | [] | null | 0 |
If paul is not kind or wise then paul is either wise or strong.
Everyone who is either quiet or humble is not brave or humble and vice versa.
If someone is wise then someone is both not kind and not tall and vice versa.
Everyone who is creative or not generous is both not happy and not strong.
Everyone who is not rich or calm is either funny or humble and vice versa.
Everyone who is both not calm and not funny is not curious.
Everyone who is not funny is calm.
If fred is either humble or not curious then fred is either patient or not creative.
Everyone who is curious or not curious is both calm and brave and vice versa.
If fred is brave or not funny then mary is not funny or not curious and vice versa.
Everyone who is not wise is not kind and vice versa.
If mary is not curious then someone is both creative and not creative.
Everyone who is either old or kind is not strong or patient and vice versa.
Everyone who is either not generous or calm is happy or strong and vice versa.
If someone is both happy and not strong then fred is not happy or not humble and vice versa.
Alice is both kind and wise.
Someone is not quiet or strong.
Someone is either humble or creative.
Mary is not strong.
Someone is both not wise and not old.
Alice is both not rich and calm.
Mary is either tall or not strong.
Someone is curious. | Alice is not generous. | neutral | (((~kind(paul)|wise(paul)))=>((wise(paul)<~>strong(paul))))&
(![X]:((quiet(X)<~>humble(X))<=>(~brave(X)|humble(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:((creative(X)|~generous(X))=>(~happy(X)&~strong(X))))&
(![X]:((~rich(X)|calm(X))<=>(funny(X)<~>humble(X))))&
(![X]:((~calm(X)&~funny(X))=>~curious(X)))&
(![X]:(~funny(X)=>calm(X)))&
(((humble(fred)<~>~curious(fred)))=>((patient(fred)<~>~creative(fred))))&
(![X]:((curious(X)|~curious(X))<=>(calm(X)&brave(X))))&
(((brave(fred)|~funny(fred)))<=>((~funny(mary)|~curious(mary))))&
(![X]:(~wise(X)<=>~kind(X)))&
((~curious(mary))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((old(X)<~>kind(X))<=>(~strong(X)|patient(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(happy(X)|strong(X))))&
((?[X]:((happy(X)&~strong(X))))<=>((~happy(fred)|~humble(fred))))&
((kind(alice)&wise(alice)))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((humble(X)<~>creative(X))))&
(~strong(mary))&
(?[X]:((~wise(X)&~old(X))))&
((~rich(alice)&calm(alice)))&
((tall(mary)<~>~strong(mary)))&
(?[X]:(curious(X))) | ~generous(alice) | [] | null | 0 |
If john is both old and not wise then mary is both rich and not calm and vice versa.
Everyone who is either not old or not happy is not brave and vice versa.
Everyone who is calm or strong is both quiet and curious and vice versa.
Everyone who is both not strong and not kind is not happy or quiet.
Everyone who is both quiet and not tall is generous or calm.
Everyone who is calm is either not funny or not old and vice versa.
Everyone who is patient or humble is either funny or humble.
Everyone who is both calm and not quiet is both not brave and not strong and vice versa.
Everyone who is old is not quiet and vice versa.
Everyone who is old is not curious or not calm and vice versa.
Everyone who is not wise is either happy or not curious and vice versa.
Everyone who is calm or not humble is happy or not curious.
Everyone who is both creative and not brave is both not brave and not patient.
Everyone who is either not rich or not old is humble.
Everyone who is brave or not wise is both quiet and strong.
If someone is both not generous and creative then lucy is rich or not old and vice versa.
Someone is not calm or not kind.
John is tall or creative.
Someone is calm.
Susan is happy or not creative.
Mary is either not curious or curious.
Someone is kind.
Paul is calm or kind.
Alice is tall. | Mary is funny. | entailment | (((old(john)&~wise(john)))<=>((rich(mary)&~calm(mary))))&
(![X]:((~old(X)<~>~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|strong(X))<=>(quiet(X)&curious(X))))&
(![X]:((~strong(X)&~kind(X))=>(~happy(X)|quiet(X))))&
(![X]:((quiet(X)&~tall(X))=>(generous(X)|calm(X))))&
(![X]:(calm(X)<=>(~funny(X)<~>~old(X))))&
(![X]:((patient(X)|humble(X))=>(funny(X)<~>humble(X))))&
(![X]:((calm(X)&~quiet(X))<=>(~brave(X)&~strong(X))))&
(![X]:(old(X)<=>~quiet(X)))&
(![X]:(old(X)<=>(~curious(X)|~calm(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((calm(X)|~humble(X))=>(happy(X)|~curious(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)<~>~old(X))=>humble(X)))&
(![X]:((brave(X)|~wise(X))=>(quiet(X)&strong(X))))&
((?[X]:((~generous(X)&creative(X))))<=>((rich(lucy)|~old(lucy))))&
(?[X]:((~calm(X)|~kind(X))))&
((tall(john)|creative(john)))&
(?[X]:(calm(X)))&
((happy(susan)|~creative(susan)))&
((~curious(mary)<~>curious(mary)))&
(?[X]:(kind(X)))&
((calm(paul)|kind(paul)))&
(tall(alice)) | funny(mary) | [
"p2",
"p5",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6833206274885923170119103
% SZS output start Proof for 6833206274885923170119103
3. ! [X0] : ((strong(X0) | calm(X0)) <=> (curious(X0) & quiet(X0))) [input p2]
6. ! [X0] : (calm(X0) <=> (~funny(X0) <~> ~old(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) & calm(X0)) <=> (~strong(X0) & ~brave(X0))) [input p7]
9. ! [X0] : (old(X0) <=> ~quiet(X0)) [input p8]
10. ! [X0] : (old(X0) <=> (~calm(X0) | ~curious(X0))) [input p9]
15. ! [X0] : ((~wise(X0) | brave(X0)) => (strong(X0) & quiet(X0))) [input p14]
25. ~funny(mary) [input hypothesis]
39. ! [X0] : ((strong(X0) & quiet(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 15]
43. ! [X0] : (((strong(X0) | calm(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((strong(X0) | calm(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : ((calm(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ~calm(X0))) [nnf transformation 6]
47. ! [X0] : (((~quiet(X0) & calm(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (quiet(X0) | ~calm(X0)))) [nnf transformation 8]
48. ! [X0] : (((~quiet(X0) & calm(X0)) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | quiet(X0) | ~calm(X0))) [flattening 47]
49. ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))) [nnf transformation 9]
50. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & ((~calm(X0) | ~curious(X0)) | ~old(X0))) [nnf transformation 10]
51. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & (~calm(X0) | ~curious(X0) | ~old(X0))) [flattening 50]
74. ~calm(X0) | quiet(X0) [cnf transformation 44]
75. ~strong(X0) | quiet(X0) [cnf transformation 44]
81. ~calm(X0) | funny(X0) | old(X0) [cnf transformation 45]
88. strong(X0) | calm(X0) | brave(X0) [cnf transformation 48]
90. ~quiet(X0) | ~old(X0) [cnf transformation 49]
94. calm(X0) | old(X0) [cnf transformation 51]
104. ~brave(X0) | quiet(X0) [cnf transformation 39]
120. ~funny(mary) [cnf transformation 25]
226. funny(X0) | old(X0) | old(X0) [resolution 81,94]
227. funny(X0) | old(X0) [duplicate literal removal 226]
239. calm(X1) | brave(X1) | quiet(X1) [resolution 88,75]
241. calm(X1) | quiet(X1) [subsumption resolution 239,104]
242. quiet(X1) [subsumption resolution 241,74]
243. ~old(X0) [resolution 242,90]
295. old(mary) [resolution 227,120]
299. $false [subsumption resolution 295,243]
% SZS output end Proof for 6833206274885923170119103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or brave is either strong or generous and vice versa.
Everyone who is wise is not humble and vice versa.
If john is humble or not calm then someone is both not strong and brave and vice versa.
Everyone who is tall or strong is both curious and not patient.
If someone is calm or not wise then alice is both not humble and kind and vice versa.
If paul is funny then alice is old and vice versa.
Everyone who is not patient is both curious and not generous and vice versa.
Everyone who is happy or quiet is brave or funny and vice versa.
Everyone who is old or wise is old or not funny.
Everyone who is not calm or not rich is both not generous and funny and vice versa.
Everyone who is either not quiet or not wise is not generous or not patient and vice versa.
Everyone who is either old or not tall is not funny or not humble.
Everyone who is both not generous and rich is either not patient or not brave and vice versa.
Everyone who is both not old and curious is patient or not funny.
If lucy is not curious then someone is both happy and not rich and vice versa.
If paul is not kind then someone is both brave and not humble and vice versa.
Someone is both not patient and not quiet.
Someone is either not brave or not quiet.
Someone is both generous and not creative.
Lucy is both not happy and quiet.
Mary is calm.
John is either patient or humble.
Someone is patient. | Lucy is quiet. | entailment | (![X]:((creative(X)<~>brave(X))<=>(strong(X)<~>generous(X))))&
(![X]:(wise(X)<=>~humble(X)))&
(((humble(john)|~calm(john)))<=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((tall(X)|strong(X))=>(curious(X)&~patient(X))))&
((?[X]:((calm(X)|~wise(X))))<=>((~humble(alice)&kind(alice))))&
((funny(paul))<=>(old(alice)))&
(![X]:(~patient(X)<=>(curious(X)&~generous(X))))&
(![X]:((happy(X)|quiet(X))<=>(brave(X)|funny(X))))&
(![X]:((old(X)|wise(X))=>(old(X)|~funny(X))))&
(![X]:((~calm(X)|~rich(X))<=>(~generous(X)&funny(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~generous(X)|~patient(X))))&
(![X]:((old(X)<~>~tall(X))=>(~funny(X)|~humble(X))))&
(![X]:((~generous(X)&rich(X))<=>(~patient(X)<~>~brave(X))))&
(![X]:((~old(X)&curious(X))=>(patient(X)|~funny(X))))&
((~curious(lucy))<=>(?[X]:((happy(X)&~rich(X)))))&
((~kind(paul))<=>(?[X]:((brave(X)&~humble(X)))))&
(?[X]:((~patient(X)&~quiet(X))))&
(?[X]:((~brave(X)<~>~quiet(X))))&
(?[X]:((generous(X)&~creative(X))))&
((~happy(lucy)&quiet(lucy)))&
(calm(mary))&
((patient(john)<~>humble(john)))&
(?[X]:(patient(X))) | quiet(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5822137537397109832677749
% SZS output start Proof for 5822137537397109832677749
20. quiet(lucy) & ~happy(lucy) [input p19]
24. ~quiet(lucy) [input hypothesis]
142. quiet(lucy) [cnf transformation 20]
147. ~quiet(lucy) [cnf transformation 24]
266. $false [subsumption resolution 147,142]
% SZS output end Proof for 5822137537397109832677749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then lucy is either not generous or kind.
If someone is tall then fred is patient and vice versa.
If someone is both humble and not patient then someone is both not brave and kind.
If someone is either brave or creative then mary is not brave or not patient and vice versa.
If someone is both not curious and not quiet then someone is calm or not brave and vice versa.
Everyone who is either not patient or not generous is not wise and vice versa.
Everyone who is creative or funny is either humble or creative.
Everyone who is patient or funny is either not quiet or not old and vice versa.
Everyone who is either curious or not quiet is not wise or not creative.
If someone is both generous and quiet then someone is not wise and vice versa.
Everyone who is either patient or old is both wise and not calm.
Everyone who is rich is either not rich or strong and vice versa.
Everyone who is calm or not creative is not strong or happy.
Everyone who is brave or patient is either not wise or not old.
Everyone who is either happy or humble is patient.
Everyone who is not creative or not humble is both not generous and not quiet.
Fred is curious or wise.
Someone is either not strong or brave.
Susan is either humble or rich.
Someone is not quiet or quiet.
Alice is generous or old. | Alice is brave. | contradiction | ((?[X]:(rich(X)))=>((~generous(lucy)<~>kind(lucy))))&
((?[X]:(tall(X)))<=>(patient(fred)))&
((?[X]:((humble(X)&~patient(X))))=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>((~brave(mary)|~patient(mary))))&
((?[X]:((~curious(X)&~quiet(X))))<=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~patient(X)<~>~generous(X))<=>~wise(X)))&
(![X]:((creative(X)|funny(X))=>(humble(X)<~>creative(X))))&
(![X]:((patient(X)|funny(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((curious(X)<~>~quiet(X))=>(~wise(X)|~creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((patient(X)<~>old(X))=>(wise(X)&~calm(X))))&
(![X]:(rich(X)<=>(~rich(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))=>(~strong(X)|happy(X))))&
(![X]:((brave(X)|patient(X))=>(~wise(X)<~>~old(X))))&
(![X]:((happy(X)<~>humble(X))=>patient(X)))&
(![X]:((~creative(X)|~humble(X))=>(~generous(X)&~quiet(X))))&
((curious(fred)|wise(fred)))&
(?[X]:((~strong(X)<~>brave(X))))&
((humble(susan)<~>rich(susan)))&
(?[X]:((~quiet(X)|quiet(X))))&
((generous(alice)|old(alice))) | brave(alice) | [
"p6",
"p9",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6076234812491248417699939
% SZS output start Proof for 6076234812491248417699939
7. ! [X0] : ((funny(X0) | creative(X0)) => (humble(X0) <~> creative(X0))) [input p6]
10. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X0] : ~wise(X0) [input p9]
14. ! [X0] : ((patient(X0) | brave(X0)) => (~wise(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~quiet(X0) & ~generous(X0))) [input p15]
21. old(alice) | generous(alice) [input p20]
22. brave(alice) [input hypothesis]
25. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X1] : ~wise(X1) [rectify 10]
28. ! [X0] : ((humble(X0) <~> creative(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 7]
34. ! [X0] : ((~wise(X0) <~> ~old(X0)) | (~patient(X0) & ~brave(X0))) [ennf transformation 14]
36. ! [X0] : ((~quiet(X0) & ~generous(X0)) | (humble(X0) & creative(X0))) [ennf transformation 16]
56. ! [X0] : (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~funny(X0) & ~creative(X0))) [nnf transformation 28]
60. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~quiet(X0) | ~generous(X0))) [nnf transformation 25]
61. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~quiet(X3) | ~generous(X3))) [rectify 60]
62. ? [X0] : (quiet(X0) & generous(X0)) => (quiet(sK5) & generous(sK5)) [choice axiom]
63. ? [X2] : ~wise(X2) => ~wise(sK6) [choice axiom]
64. ((quiet(sK5) & generous(sK5)) | ! [X1] : wise(X1)) & (~wise(sK6) | ! [X3] : (~quiet(X3) | ~generous(X3))) [skolemisation 61,63,62]
67. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~patient(X0) & ~brave(X0))) [nnf transformation 34]
98. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 56]
109. generous(sK5) | wise(X1) [cnf transformation 64]
121. ~old(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 67]
127. ~generous(X0) | creative(X0) [cnf transformation 36]
128. ~generous(X0) | humble(X0) [cnf transformation 36]
137. old(alice) | generous(alice) [cnf transformation 21]
138. brave(alice) [cnf transformation 22]
141. ~creative(X0) | ~humble(X0) [duplicate literal removal 98]
240. 23 <=> ! [X1] : wise(X1) [avatar definition]
241. wise(X1) <- (23) [avatar component clause 240]
248. 25 <=> generous(sK5) [avatar definition]
250. generous(sK5) <- (25) [avatar component clause 248]
251. 23 | 25 [avatar split clause 109,248,240]
284. 32 <=> generous(alice) [avatar definition]
286. generous(alice) <- (32) [avatar component clause 284]
288. 33 <=> old(alice) [avatar definition]
290. old(alice) <- (33) [avatar component clause 288]
291. 32 | 33 [avatar split clause 137,288,284]
294. creative(sK5) <- (25) [resolution 127,250]
295. creative(alice) <- (32) [resolution 127,286]
296. humble(sK5) <- (25) [resolution 128,250]
297. humble(alice) <- (32) [resolution 128,286]
300. ~humble(sK5) <- (25) [resolution 141,294]
301. ~humble(alice) <- (32) [resolution 141,295]
302. $false <- (25) [subsumption resolution 300,296]
303. ~25 [avatar contradiction clause 302]
304. $false <- (32) [subsumption resolution 301,297]
305. ~32 [avatar contradiction clause 304]
363. ~wise(alice) | ~brave(alice) <- (33) [resolution 121,290]
364. ~brave(alice) <- (23, 33) [subsumption resolution 363,241]
365. $false <- (23, 33) [subsumption resolution 364,138]
366. ~23 | ~33 [avatar contradiction clause 365]
367. $false [avatar sat refutation 251,291,303,305,366]
% SZS output end Proof for 6076234812491248417699939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or curious then alice is tall or happy and vice versa.
Everyone who is both not happy and happy is not curious.
Everyone who is humble is both not old and not tall and vice versa.
Everyone who is not brave or humble is both not funny and brave and vice versa.
If someone is patient then paul is both not rich and creative and vice versa.
Everyone who is both not old and kind is both quiet and not calm.
Everyone who is not funny or wise is both not calm and not rich and vice versa.
Everyone who is either not happy or not curious is patient and vice versa.
If someone is both patient and wise then someone is not curious.
Everyone who is either old or not tall is both not creative and not tall and vice versa.
If paul is either kind or not curious then paul is not generous.
Everyone who is old is rich or funny.
Everyone who is old or not strong is both not wise and not calm and vice versa.
Everyone who is not old is both not creative and not rich.
Everyone who is not humble is old and vice versa.
If john is either kind or quiet then john is either funny or not tall.
Someone is patient or not curious.
Someone is either not creative or curious.
Lucy is either not rich or curious.
Someone is both not curious and not humble.
Someone is both humble and not tall.
Mary is creative or not curious. | Alice is not patient. | entailment | ((?[X]:((~brave(X)|curious(X))))<=>((tall(alice)|happy(alice))))&
(![X]:((~happy(X)&happy(X))=>~curious(X)))&
(![X]:(humble(X)<=>(~old(X)&~tall(X))))&
(![X]:((~brave(X)|humble(X))<=>(~funny(X)&brave(X))))&
((?[X]:(patient(X)))<=>((~rich(paul)&creative(paul))))&
(![X]:((~old(X)&kind(X))=>(quiet(X)&~calm(X))))&
(![X]:((~funny(X)|wise(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>patient(X)))&
((?[X]:((patient(X)&wise(X))))=>(?[X]:(~curious(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~creative(X)&~tall(X))))&
(((kind(paul)<~>~curious(paul)))=>(~generous(paul)))&
(![X]:(old(X)=>(rich(X)|funny(X))))&
(![X]:((old(X)|~strong(X))<=>(~wise(X)&~calm(X))))&
(![X]:(~old(X)=>(~creative(X)&~rich(X))))&
(![X]:(~humble(X)<=>old(X)))&
(((kind(john)<~>quiet(john)))=>((funny(john)<~>~tall(john))))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:((~creative(X)<~>curious(X))))&
((~rich(lucy)<~>curious(lucy)))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((humble(X)&~tall(X))))&
((creative(mary)|~curious(mary))) | ~patient(alice) | [
"p2",
"p4",
"p6",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8802670420972279231860600
% SZS output start Proof for 8802670420972279231860600
3. ! [X0] : (humble(X0) <=> (~tall(X0) & ~old(X0))) [input p2]
5. ? [X0] : patient(X0) <=> (creative(paul) & ~rich(paul)) [input p4]
7. ! [X0] : ((wise(X0) | ~funny(X0)) <=> (~rich(X0) & ~calm(X0))) [input p6]
10. ! [X0] : ((old(X0) <~> ~tall(X0)) <=> (~tall(X0) & ~creative(X0))) [input p9]
12. ! [X0] : (old(X0) => (funny(X0) | rich(X0))) [input p11]
13. ! [X0] : ((~strong(X0) | old(X0)) <=> (~calm(X0) & ~wise(X0))) [input p12]
15. ! [X0] : (~humble(X0) <=> old(X0)) [input p14]
23. patient(alice) [input hypothesis]
31. ! [X0] : ((funny(X0) | rich(X0)) | ~old(X0)) [ennf transformation 12]
32. ! [X0] : (funny(X0) | rich(X0) | ~old(X0)) [flattening 31]
40. ! [X0] : ((humble(X0) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ~humble(X0))) [nnf transformation 3]
41. ! [X0] : ((humble(X0) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ~humble(X0))) [flattening 40]
44. (? [X0] : patient(X0) | (~creative(paul) | rich(paul))) & ((creative(paul) & ~rich(paul)) | ! [X0] : ~patient(X0)) [nnf transformation 5]
45. (? [X0] : patient(X0) | ~creative(paul) | rich(paul)) & ((creative(paul) & ~rich(paul)) | ! [X0] : ~patient(X0)) [flattening 44]
46. (? [X0] : patient(X0) | ~creative(paul) | rich(paul)) & ((creative(paul) & ~rich(paul)) | ! [X1] : ~patient(X1)) [rectify 45]
47. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
48. (patient(sK1) | ~creative(paul) | rich(paul)) & ((creative(paul) & ~rich(paul)) | ! [X1] : ~patient(X1)) [skolemisation 46,47]
49. ! [X0] : (((wise(X0) | ~funny(X0)) | (rich(X0) | calm(X0))) & ((~rich(X0) & ~calm(X0)) | (~wise(X0) & funny(X0)))) [nnf transformation 7]
50. ! [X0] : ((wise(X0) | ~funny(X0) | rich(X0) | calm(X0)) & ((~rich(X0) & ~calm(X0)) | (~wise(X0) & funny(X0)))) [flattening 49]
55. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (tall(X0) | creative(X0))) & ((~tall(X0) & ~creative(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [nnf transformation 10]
56. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | tall(X0) | creative(X0)) & ((~tall(X0) & ~creative(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [flattening 55]
57. ! [X0] : (((~strong(X0) | old(X0)) | (calm(X0) | wise(X0))) & ((~calm(X0) & ~wise(X0)) | (strong(X0) & ~old(X0)))) [nnf transformation 13]
58. ! [X0] : ((~strong(X0) | old(X0) | calm(X0) | wise(X0)) & ((~calm(X0) & ~wise(X0)) | (strong(X0) & ~old(X0)))) [flattening 57]
59. ! [X0] : ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))) [nnf transformation 15]
77. ~humble(X0) | ~tall(X0) [cnf transformation 41]
84. ~rich(paul) | ~patient(X1) [cnf transformation 48]
85. creative(paul) | ~patient(X1) [cnf transformation 48]
91. ~rich(X0) | funny(X0) [cnf transformation 50]
93. ~funny(X0) | wise(X0) | rich(X0) | calm(X0) [cnf transformation 50]
100. ~creative(X0) | old(X0) | tall(X0) [cnf transformation 56]
101. ~tall(X0) | ~tall(X0) | ~old(X0) [cnf transformation 56]
105. funny(X0) | rich(X0) | ~old(X0) [cnf transformation 32]
106. ~wise(X0) | ~old(X0) [cnf transformation 58]
108. ~calm(X0) | ~old(X0) [cnf transformation 58]
113. old(X0) | humble(X0) [cnf transformation 59]
129. patient(alice) [cnf transformation 23]
130. ~old(X0) | ~tall(X0) [duplicate literal removal 101]
162. 7 <=> rich(paul) [avatar definition]
163. ~rich(paul) <- (~7) [avatar component clause 162]
166. 8 <=> creative(paul) [avatar definition]
167. creative(paul) <- (8) [avatar component clause 166]
175. 10 <=> ! [X1] : ~patient(X1) [avatar definition]
176. ~patient(X1) <- (10) [avatar component clause 175]
177. 10 | 8 [avatar split clause 85,166,175]
178. 10 | ~7 [avatar split clause 84,162,175]
187. ~old(X0) | funny(X0) [subsumption resolution 105,91]
254. ~tall(X0) | humble(X0) [resolution 130,113]
255. ~tall(X0) [subsumption resolution 254,77]
318. 30 <=> calm(paul) [avatar definition]
320. calm(paul) <- (30) [avatar component clause 318]
322. 31 <=> wise(paul) [avatar definition]
324. wise(paul) <- (31) [avatar component clause 322]
326. $false <- (10) [resolution 176,129]
329. ~10 [avatar contradiction clause 326]
330. old(paul) | tall(paul) <- (8) [resolution 167,100]
332. old(paul) <- (8) [subsumption resolution 330,255]
334. funny(paul) <- (8) [resolution 332,187]
337. wise(paul) | rich(paul) | calm(paul) <- (8) [resolution 334,93]
347. ~old(paul) <- (30) [resolution 320,108]
349. $false <- (8, 30) [subsumption resolution 347,332]
350. ~8 | ~30 [avatar contradiction clause 349]
351. wise(paul) | calm(paul) <- (~7, 8) [subsumption resolution 337,163]
352. 30 | 31 | 7 | ~8 [avatar split clause 351,166,162,322,318]
361. ~old(paul) <- (31) [resolution 324,106]
364. $false <- (8, 31) [subsumption resolution 361,332]
365. ~8 | ~31 [avatar contradiction clause 364]
366. $false [avatar sat refutation 177,178,329,350,352,365]
% SZS output end Proof for 8802670420972279231860600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both not strong and not happy.
Everyone who is both brave and patient is not curious.
Everyone who is both brave and funny is strong.
Everyone who is not patient or quiet is happy or patient.
If someone is either not strong or brave then fred is patient or kind.
If someone is not rich then someone is either curious or patient and vice versa.
If someone is both not kind and curious then someone is both not happy and wise.
Everyone who is not patient or not quiet is tall or not quiet and vice versa.
If paul is either happy or not quiet then someone is not calm or not tall and vice versa.
If mary is strong then lucy is quiet and vice versa.
If someone is both tall and not kind then mary is both curious and not curious and vice versa.
If someone is not wise or happy then lucy is not generous or not rich and vice versa.
If lucy is calm then mary is both creative and wise.
Everyone who is both generous and kind is patient.
If fred is not quiet or not strong then someone is both brave and not generous.
Everyone who is quiet or not creative is either not tall or rich and vice versa.
Someone is both calm and humble.
Susan is not creative or rich.
Someone is not humble.
Someone is both not humble and creative.
Lucy is humble or not creative.
Someone is either not strong or rich.
Susan is not curious or not old. | Paul is happy. | contradiction | (![X]:(happy(X)=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&patient(X))=>~curious(X)))&
(![X]:((brave(X)&funny(X))=>strong(X)))&
(![X]:((~patient(X)|quiet(X))=>(happy(X)|patient(X))))&
((?[X]:((~strong(X)<~>brave(X))))=>((patient(fred)|kind(fred))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)<~>patient(X)))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(tall(X)|~quiet(X))))&
(((happy(paul)<~>~quiet(paul)))<=>(?[X]:((~calm(X)|~tall(X)))))&
((strong(mary))<=>(quiet(lucy)))&
((?[X]:((tall(X)&~kind(X))))<=>((curious(mary)&~curious(mary))))&
((?[X]:((~wise(X)|happy(X))))<=>((~generous(lucy)|~rich(lucy))))&
((calm(lucy))=>((creative(mary)&wise(mary))))&
(![X]:((generous(X)&kind(X))=>patient(X)))&
(((~quiet(fred)|~strong(fred)))=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:((quiet(X)|~creative(X))<=>(~tall(X)<~>rich(X))))&
(?[X]:((calm(X)&humble(X))))&
((~creative(susan)|rich(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)&creative(X))))&
((humble(lucy)|~creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
((~curious(susan)|~old(susan))) | happy(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7897187743941880370867282
% SZS output start Proof for 7897187743941880370867282
1. ! [X0] : (happy(X0) => (~happy(X0) & ~strong(X0))) [input p0]
24. happy(paul) [input hypothesis]
29. ! [X0] : ((~happy(X0) & ~strong(X0)) | ~happy(X0)) [ennf transformation 1]
81. ~happy(X0) | ~happy(X0) [cnf transformation 29]
135. happy(paul) [cnf transformation 24]
137. ~happy(X0) [duplicate literal removal 81]
294. $false [subsumption resolution 135,137]
% SZS output end Proof for 7897187743941880370867282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then paul is quiet or not brave.
Everyone who is both not humble and curious is both humble and not calm.
Everyone who is not wise is either not happy or patient.
If someone is generous then susan is both not calm and old.
Everyone who is either old or strong is generous and vice versa.
Everyone who is either not wise or not quiet is kind or wise.
Everyone who is humble is not tall and vice versa.
Everyone who is both not brave and humble is brave and vice versa.
Everyone who is patient is creative.
Everyone who is wise is humble or tall and vice versa.
If someone is not wise then someone is old and vice versa.
If someone is not curious then someone is either tall or not calm.
If someone is not creative or not happy then someone is either not rich or creative.
If mary is either not kind or happy then someone is funny and vice versa.
Everyone who is both not strong and not rich is not quiet and vice versa.
Everyone who is either rich or not humble is both not brave and wise and vice versa.
Paul is patient or old.
John is either not rich or old.
Someone is either not wise or not kind.
Someone is kind or patient.
Someone is funny.
Someone is both not strong and creative. | Susan is quiet. | contradiction | ((?[X]:(~calm(X)))=>((quiet(paul)|~brave(paul))))&
(![X]:((~humble(X)&curious(X))=>(humble(X)&~calm(X))))&
(![X]:(~wise(X)=>(~happy(X)<~>patient(X))))&
((?[X]:(generous(X)))=>((~calm(susan)&old(susan))))&
(![X]:((old(X)<~>strong(X))<=>generous(X)))&
(![X]:((~wise(X)<~>~quiet(X))=>(kind(X)|wise(X))))&
(![X]:(humble(X)<=>~tall(X)))&
(![X]:((~brave(X)&humble(X))<=>brave(X)))&
(![X]:(patient(X)=>creative(X)))&
(![X]:(wise(X)<=>(humble(X)|tall(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(old(X))))&
((?[X]:(~curious(X)))=>(?[X]:((tall(X)<~>~calm(X)))))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:((~rich(X)<~>creative(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(?[X]:(funny(X))))&
(![X]:((~strong(X)&~rich(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~humble(X))<=>(~brave(X)&wise(X))))&
((patient(paul)|old(paul)))&
((~rich(john)<~>old(john)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)&creative(X)))) | quiet(susan) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2324934715569285333892377
% SZS output start Proof for 2324934715569285333892377
4. ? [X0] : generous(X0) => (old(susan) & ~calm(susan)) [input p3]
5. ! [X0] : ((old(X0) <~> strong(X0)) <=> generous(X0)) [input p4]
7. ! [X0] : (humble(X0) <=> ~tall(X0)) [input p6]
8. ! [X0] : ((humble(X0) & ~brave(X0)) <=> brave(X0)) [input p7]
10. ! [X0] : (wise(X0) <=> (tall(X0) | humble(X0))) [input p9]
11. ? [X0] : ~wise(X0) <=> ? [X0] : old(X0) [input p10]
15. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> ~quiet(X0)) [input p14]
16. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> (wise(X0) & ~brave(X0))) [input p15]
23. quiet(susan) [input hypothesis]
24. ? [X0] : ~wise(X0) <=> ? [X1] : old(X1) [rectify 11]
27. ! [X0] : ((old(X0) <~> strong(X0)) => generous(X0)) [unused predicate definition removal 5]
33. (old(susan) & ~calm(susan)) | ! [X0] : ~generous(X0) [ennf transformation 4]
34. ! [X0] : (generous(X0) | (old(X0) <=> strong(X0))) [ennf transformation 27]
41. ! [X0] : (generous(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [nnf transformation 34]
43. ! [X0] : ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0))) [nnf transformation 7]
44. ! [X0] : (((humble(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~humble(X0) | brave(X0)))) [nnf transformation 8]
45. ! [X0] : (((humble(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~humble(X0) | brave(X0))) [flattening 44]
46. ! [X0] : ((wise(X0) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | ~wise(X0))) [nnf transformation 10]
47. ! [X0] : ((wise(X0) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ~wise(X0))) [flattening 46]
48. (? [X0] : ~wise(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : wise(X0)) [nnf transformation 24]
49. (? [X0] : ~wise(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : wise(X3)) [rectify 48]
50. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
51. ? [X2] : old(X2) => old(sK1) [choice axiom]
52. (~wise(sK0) | ! [X1] : ~old(X1)) & (old(sK1) | ! [X3] : wise(X3)) [skolemisation 49,51,50]
65. ! [X0] : (((~rich(X0) & ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (rich(X0) | strong(X0)))) [nnf transformation 15]
66. ! [X0] : (((~rich(X0) & ~strong(X0)) | quiet(X0)) & (~quiet(X0) | rich(X0) | strong(X0))) [flattening 65]
67. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 16]
68. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [flattening 67]
85. old(susan) | ~generous(X0) [cnf transformation 33]
87. ~strong(X0) | old(X0) | generous(X0) [cnf transformation 41]
91. tall(X0) | humble(X0) [cnf transformation 43]
92. brave(X0) | ~humble(X0) | brave(X0) [cnf transformation 45]
93. ~brave(X0) | ~brave(X0) [cnf transformation 45]
98. ~tall(X0) | wise(X0) [cnf transformation 47]
100. ~wise(sK0) | ~old(X1) [cnf transformation 52]
111. ~quiet(X0) | rich(X0) | strong(X0) [cnf transformation 66]
119. humble(X0) | ~rich(X0) | ~wise(X0) | brave(X0) [cnf transformation 68]
129. quiet(susan) [cnf transformation 23]
130. brave(X0) | ~humble(X0) [duplicate literal removal 92]
131. ~brave(X0) [duplicate literal removal 93]
147. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
148. ~generous(X0) <- (4) [avatar component clause 147]
150. 5 <=> old(susan) [avatar definition]
152. old(susan) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 85,150,147]
159. ~humble(X0) [subsumption resolution 130,131]
161. 7 <=> ! [X1] : ~old(X1) [avatar definition]
162. ~old(X1) <- (7) [avatar component clause 161]
164. 8 <=> wise(sK0) [avatar definition]
166. ~wise(sK0) <- (~8) [avatar component clause 164]
167. 7 | ~8 [avatar split clause 100,164,161]
169. 9 <=> ! [X3] : wise(X3) [avatar definition]
170. wise(X3) <- (9) [avatar component clause 169]
226. ~rich(X0) | ~wise(X0) | brave(X0) [subsumption resolution 119,159]
227. ~rich(X0) | ~wise(X0) [subsumption resolution 226,131]
267. $false <- (~8, 9) [subsumption resolution 166,170]
268. 8 | ~9 [avatar contradiction clause 267]
277. wise(X0) | humble(X0) [resolution 98,91]
287. rich(susan) | strong(susan) [resolution 111,129]
289. 30 <=> strong(susan) [avatar definition]
291. strong(susan) <- (30) [avatar component clause 289]
293. 31 <=> rich(susan) [avatar definition]
295. rich(susan) <- (31) [avatar component clause 293]
296. 30 | 31 [avatar split clause 287,293,289]
298. ~wise(susan) <- (31) [resolution 295,227]
300. $false <- (9, 31) [subsumption resolution 298,170]
301. ~9 | ~31 [avatar contradiction clause 300]
312. wise(X0) [subsumption resolution 277,159]
313. 9 [avatar split clause 312,169]
325. old(susan) | generous(susan) <- (30) [resolution 291,87]
327. generous(susan) <- (7, 30) [subsumption resolution 325,162]
328. $false <- (4, 7, 30) [subsumption resolution 327,148]
329. ~4 | ~7 | ~30 [avatar contradiction clause 328]
330. $false <- (5, 7) [subsumption resolution 152,162]
331. ~5 | ~7 [avatar contradiction clause 330]
332. $false [avatar sat refutation 153,167,268,296,301,313,329,331]
% SZS output end Proof for 2324934715569285333892377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not generous is both not patient and brave and vice versa. Everyone who is either not calm or rich is both quiet and not patient. Everyone who is both not curious and funny is not humble and vice versa. If someone is either not funny or not brave then paul is funny. If someone is curious or not tall then someone is happy or not creative. If paul is either not creative or quiet then paul is both not rich and quiet. If someone is either creative or calm then fred is either not patient or not creative. If someone is not wise then someone is both rich and generous. Everyone who is humble or not wise is generous or not tall. Everyone who is both not patient and brave is not curious or kind. Everyone who is not creative or happy is not wise and vice versa. Everyone who is humble or brave is not funny. Everyone who is not curious or funny is old. Everyone who is strong is either curious or not wise. Everyone who is not brave is either tall or not funny and vice versa. If fred is both not humble and not happy then someone is not creative or humble and vice versa. Alice is generous. Someone is wise or creative. Paul is not calm or not quiet. Paul is not calm or humble. Paul is rich or generous. Susan is either not brave or patient. Someone is happy. Someone is both patient and funny. | Susan is brave. | neutral | (![X]:((curious(X)<~>~generous(X))<=>(~patient(X)&brave(X))))&
(![X]:((~calm(X)<~>rich(X))=>(quiet(X)&~patient(X))))&
(![X]:((~curious(X)&funny(X))<=>~humble(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(funny(paul)))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((happy(X)|~creative(X)))))&
(((~creative(paul)<~>quiet(paul)))=>((~rich(paul)&quiet(paul))))&
((?[X]:((creative(X)<~>calm(X))))=>((~patient(fred)<~>~creative(fred))))&
((?[X]:(~wise(X)))=>(?[X]:((rich(X)&generous(X)))))&
(![X]:((humble(X)|~wise(X))=>(generous(X)|~tall(X))))&
(![X]:((~patient(X)&brave(X))=>(~curious(X)|kind(X))))&
(![X]:((~creative(X)|happy(X))<=>~wise(X)))&
(![X]:((humble(X)|brave(X))=>~funny(X)))&
(![X]:((~curious(X)|funny(X))=>old(X)))&
(![X]:(strong(X)=>(curious(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~funny(X))))&
(((~humble(fred)&~happy(fred)))<=>(?[X]:((~creative(X)|humble(X)))))&
(generous(alice))&
(?[X]:((wise(X)|creative(X))))&
((~calm(paul)|~quiet(paul)))&
((~calm(paul)|humble(paul)))&
((rich(paul)|generous(paul)))&
((~brave(susan)<~>patient(susan)))&
(?[X]:(happy(X)))&
(?[X]:((patient(X)&funny(X)))) | brave(susan) | [] | null | 0 |
Everyone who is both wise and kind is both curious and humble and vice versa.
Everyone who is not funny is not calm and vice versa.
If paul is either not brave or kind then paul is both not old and not funny.
Everyone who is not rich is tall or not wise.
If someone is funny or brave then someone is strong.
Everyone who is not quiet or not humble is both not patient and not strong.
Everyone who is not wise is both wise and not kind.
If john is not curious then someone is both strong and tall.
Everyone who is strong is happy and vice versa.
If someone is either kind or not calm then someone is either not quiet or not funny.
Everyone who is both not tall and brave is not patient or old.
Everyone who is either not rich or not tall is wise or strong and vice versa.
Everyone who is either calm or not old is both quiet and tall.
Everyone who is both wise and calm is quiet or humble and vice versa.
Everyone who is both not tall and not strong is both not strong and not funny and vice versa.
Everyone who is not creative is both old and not creative.
John is both not curious and happy.
Someone is quiet or creative.
Someone is not old or not happy.
Someone is either wise or not humble.
Someone is both kind and patient.
Mary is both kind and funny.
Lucy is tall or not humble.
Paul is calm or not creative. | John is not brave. | neutral | (![X]:((wise(X)&kind(X))<=>(curious(X)&humble(X))))&
(![X]:(~funny(X)<=>~calm(X)))&
(((~brave(paul)<~>kind(paul)))=>((~old(paul)&~funny(paul))))&
(![X]:(~rich(X)=>(tall(X)|~wise(X))))&
((?[X]:((funny(X)|brave(X))))=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)|~humble(X))=>(~patient(X)&~strong(X))))&
(![X]:(~wise(X)=>(wise(X)&~kind(X))))&
((~curious(john))=>(?[X]:((strong(X)&tall(X)))))&
(![X]:(strong(X)<=>happy(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(![X]:((~tall(X)&brave(X))=>(~patient(X)|old(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>(wise(X)|strong(X))))&
(![X]:((calm(X)<~>~old(X))=>(quiet(X)&tall(X))))&
(![X]:((wise(X)&calm(X))<=>(quiet(X)|humble(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~strong(X)&~funny(X))))&
(![X]:(~creative(X)=>(old(X)&~creative(X))))&
((~curious(john)&happy(john)))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~old(X)|~happy(X))))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:((kind(X)&patient(X))))&
((kind(mary)&funny(mary)))&
((tall(lucy)|~humble(lucy)))&
((calm(paul)|~creative(paul))) | ~brave(john) | [] | null | 0 |
If lucy is not strong or creative then lucy is not wise or not happy and vice versa.
If mary is calm then someone is both not patient and not calm and vice versa.
If someone is not old then someone is not calm or kind.
Everyone who is calm or generous is quiet or curious and vice versa.
Everyone who is either wise or not patient is rich.
Everyone who is both not rich and patient is either not kind or strong.
If someone is both not kind and not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is not strong is patient or not tall.
Someone is rich or not happy.
Someone is either happy or not tall.
Someone is not curious.
Susan is calm or kind.
Someone is generous or brave.
Susan is either not rich or not kind. | Lucy is not old. | neutral | (((~strong(lucy)|creative(lucy)))<=>((~wise(lucy)|~happy(lucy))))&
((calm(mary))<=>(?[X]:((~patient(X)&~calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((calm(X)|generous(X))<=>(quiet(X)|curious(X))))&
(![X]:((wise(X)<~>~patient(X))=>rich(X)))&
(![X]:((~rich(X)&patient(X))=>(~kind(X)<~>strong(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:(~curious(X)))&
((calm(susan)|kind(susan)))&
(?[X]:((generous(X)|brave(X))))&
((~rich(susan)<~>~kind(susan))) | ~old(lucy) | [] | null | 0 |
Everyone who is both generous and not patient is both not strong and strong.
If someone is rich then paul is not calm.
Everyone who is both not quiet and not tall is both rich and not curious.
If someone is either rich or old then alice is tall and vice versa.
If someone is either not old or rich then paul is both brave and wise.
Everyone who is brave is not calm and vice versa.
Everyone who is either old or strong is generous.
Everyone who is either not quiet or not kind is either old or not happy and vice versa.
If lucy is both kind and not strong then mary is not funny and vice versa.
If someone is not creative or funny then someone is either not patient or rich and vice versa.
Everyone who is brave is humble or strong and vice versa.
Everyone who is not creative or not funny is not wise.
Everyone who is not tall or not patient is tall.
If someone is not creative then john is either not strong or not quiet.
Everyone who is not humble or wise is both kind and calm and vice versa.
Everyone who is either generous or not kind is kind.
Someone is not curious.
Susan is either not brave or old.
John is either brave or quiet.
Someone is not strong or not generous.
Fred is generous.
Someone is not curious or creative.
Someone is kind.
Someone is not patient or not curious. | Alice is tall. | entailment | (![X]:((generous(X)&~patient(X))=>(~strong(X)&strong(X))))&
((?[X]:(rich(X)))=>(~calm(paul)))&
(![X]:((~quiet(X)&~tall(X))=>(rich(X)&~curious(X))))&
((?[X]:((rich(X)<~>old(X))))<=>(tall(alice)))&
((?[X]:((~old(X)<~>rich(X))))=>((brave(paul)&wise(paul))))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:((old(X)<~>strong(X))=>generous(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(old(X)<~>~happy(X))))&
(((kind(lucy)&~strong(lucy)))<=>(~funny(mary)))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:(brave(X)<=>(humble(X)|strong(X))))&
(![X]:((~creative(X)|~funny(X))=>~wise(X)))&
(![X]:((~tall(X)|~patient(X))=>tall(X)))&
((?[X]:(~creative(X)))=>((~strong(john)<~>~quiet(john))))&
(![X]:((~humble(X)|wise(X))<=>(kind(X)&calm(X))))&
(![X]:((generous(X)<~>~kind(X))=>kind(X)))&
(?[X]:(~curious(X)))&
((~brave(susan)<~>old(susan)))&
((brave(john)<~>quiet(john)))&
(?[X]:((~strong(X)|~generous(X))))&
(generous(fred))&
(?[X]:((~curious(X)|creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((~patient(X)|~curious(X)))) | tall(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 738237796566775833033145
% SZS output start Proof for 738237796566775833033145
13. ! [X0] : ((~patient(X0) | ~tall(X0)) => tall(X0)) [input p12]
25. ~tall(alice) [input hypothesis]
39. ! [X0] : (tall(X0) | (patient(X0) & tall(X0))) [ennf transformation 13]
107. tall(X0) | tall(X0) [cnf transformation 39]
125. ~tall(alice) [cnf transformation 25]
127. tall(X0) [duplicate literal removal 107]
261. $false [subsumption resolution 125,127]
% SZS output end Proof for 738237796566775833033145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not brave is both rich and not funny.
Everyone who is either tall or creative is not patient.
Everyone who is brave is calm or strong.
Everyone who is both not old and not kind is either not creative or calm and vice versa.
If susan is strong then someone is both brave and not kind and vice versa.
If someone is both quiet and generous then alice is both patient and strong and vice versa.
If someone is wise then susan is both generous and not generous and vice versa.
Everyone who is either not tall or strong is either rich or funny and vice versa.
Everyone who is both not curious and not generous is not curious or not wise and vice versa.
If someone is not quiet then mary is either strong or rich.
If alice is brave then paul is either not kind or tall and vice versa.
Everyone who is both rich and not old is both tall and generous and vice versa.
Everyone who is either not old or not patient is wise or not happy.
Everyone who is happy is not generous and vice versa.
Everyone who is not quiet is either not happy or not calm.
John is either not creative or creative.
Fred is old.
Paul is either quiet or happy.
Someone is both happy and brave.
Someone is wise or not calm.
Someone is not rich or brave. | Paul is tall. | entailment | (![X]:((~quiet(X)|~brave(X))=>(rich(X)&~funny(X))))&
(![X]:((tall(X)<~>creative(X))=>~patient(X)))&
(![X]:(brave(X)=>(calm(X)|strong(X))))&
(![X]:((~old(X)&~kind(X))<=>(~creative(X)<~>calm(X))))&
((strong(susan))<=>(?[X]:((brave(X)&~kind(X)))))&
((?[X]:((quiet(X)&generous(X))))<=>((patient(alice)&strong(alice))))&
((?[X]:(wise(X)))<=>((generous(susan)&~generous(susan))))&
(![X]:((~tall(X)<~>strong(X))<=>(rich(X)<~>funny(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~curious(X)|~wise(X))))&
((?[X]:(~quiet(X)))=>((strong(mary)<~>rich(mary))))&
((brave(alice))<=>((~kind(paul)<~>tall(paul))))&
(![X]:((rich(X)&~old(X))<=>(tall(X)&generous(X))))&
(![X]:((~old(X)<~>~patient(X))=>(wise(X)|~happy(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:(~quiet(X)=>(~happy(X)<~>~calm(X))))&
((~creative(john)<~>creative(john)))&
(old(fred))&
((quiet(paul)<~>happy(paul)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((~rich(X)|brave(X)))) | tall(paul) | [
"p0",
"p1",
"p3",
"p6",
"p8",
"p11",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1284672133014742357721237
% SZS output start Proof for 1284672133014742357721237
1. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (~funny(X0) & rich(X0))) [input p0]
2. ! [X0] : ((tall(X0) <~> creative(X0)) => ~patient(X0)) [input p1]
4. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~creative(X0) <~> calm(X0))) [input p3]
7. ? [X0] : wise(X0) <=> (~generous(susan) & generous(susan)) [input p6]
9. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> (~wise(X0) | ~curious(X0))) [input p8]
12. ! [X0] : ((~old(X0) & rich(X0)) <=> (generous(X0) & tall(X0))) [input p11]
13. ! [X0] : ((~old(X0) <~> ~patient(X0)) => (~happy(X0) | wise(X0))) [input p12]
14. ! [X0] : (happy(X0) <=> ~generous(X0)) [input p13]
15. ! [X0] : (~quiet(X0) => (~happy(X0) <~> ~calm(X0))) [input p14]
18. quiet(paul) <~> happy(paul) [input p17]
22. ~tall(paul) [input hypothesis]
23. ! [X0] : ((~funny(X0) & rich(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 1]
24. ! [X0] : (~patient(X0) | (tall(X0) <=> creative(X0))) [ennf transformation 2]
28. ! [X0] : ((~happy(X0) | wise(X0)) | (~old(X0) <=> ~patient(X0))) [ennf transformation 13]
29. ! [X0] : (~happy(X0) | wise(X0) | (~old(X0) <=> ~patient(X0))) [flattening 28]
30. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | quiet(X0)) [ennf transformation 15]
31. ! [X0] : (~patient(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) [nnf transformation 24]
32. ! [X0] : (((~kind(X0) & ~old(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) & (((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | (kind(X0) | old(X0)))) [nnf transformation 4]
33. ! [X0] : (((~kind(X0) & ~old(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) & (((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | kind(X0) | old(X0))) [flattening 32]
43. (? [X0] : wise(X0) | (generous(susan) | ~generous(susan))) & ((~generous(susan) & generous(susan)) | ! [X0] : ~wise(X0)) [nnf transformation 7]
44. (? [X0] : wise(X0) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X0] : ~wise(X0)) [flattening 43]
45. (? [X0] : wise(X0) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X1] : ~wise(X1)) [rectify 44]
46. ? [X0] : wise(X0) => wise(sK2) [choice axiom]
47. (wise(sK2) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X1] : ~wise(X1)) [skolemisation 45,46]
49. ! [X0] : (((~generous(X0) & ~curious(X0)) | (wise(X0) & curious(X0))) & ((~wise(X0) | ~curious(X0)) | (generous(X0) | curious(X0)))) [nnf transformation 9]
50. ! [X0] : (((~generous(X0) & ~curious(X0)) | (wise(X0) & curious(X0))) & (~wise(X0) | ~curious(X0) | generous(X0) | curious(X0))) [flattening 49]
53. ! [X0] : (((~old(X0) & rich(X0)) | (~generous(X0) | ~tall(X0))) & ((generous(X0) & tall(X0)) | (old(X0) | ~rich(X0)))) [nnf transformation 12]
54. ! [X0] : (((~old(X0) & rich(X0)) | ~generous(X0) | ~tall(X0)) & ((generous(X0) & tall(X0)) | old(X0) | ~rich(X0))) [flattening 53]
55. ! [X0] : (~happy(X0) | wise(X0) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) [nnf transformation 29]
56. ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))) [nnf transformation 14]
57. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | quiet(X0)) [nnf transformation 30]
59. (~happy(paul) | ~quiet(paul)) & (happy(paul) | quiet(paul)) [nnf transformation 18]
66. rich(X0) | quiet(X0) [cnf transformation 23]
71. ~patient(X0) | tall(X0) | ~creative(X0) [cnf transformation 31]
75. ~old(X0) | calm(X0) | creative(X0) [cnf transformation 33]
86. generous(susan) | ~wise(X1) [cnf transformation 47]
87. ~generous(susan) | ~wise(X1) [cnf transformation 47]
101. ~generous(X0) | wise(X0) [cnf transformation 50]
108. ~rich(X0) | old(X0) | tall(X0) [cnf transformation 54]
113. ~happy(X0) | wise(X0) | ~old(X0) | patient(X0) [cnf transformation 55]
115. happy(X0) | generous(X0) [cnf transformation 56]
116. ~happy(X0) | ~calm(X0) | quiet(X0) [cnf transformation 57]
122. ~happy(paul) | ~quiet(paul) [cnf transformation 59]
127. ~tall(paul) [cnf transformation 22]
170. 10 <=> ! [X1] : ~wise(X1) [avatar definition]
171. ~wise(X1) <- (10) [avatar component clause 170]
173. 11 <=> generous(susan) [avatar definition]
176. 10 | ~11 [avatar split clause 87,173,170]
177. 10 | 11 [avatar split clause 86,173,170]
192. 15 <=> tall(paul) [avatar definition]
194. ~tall(paul) <- (~15) [avatar component clause 192]
208. 18 <=> quiet(paul) [avatar definition]
210. ~quiet(paul) <- (~18) [avatar component clause 208]
212. 19 <=> happy(paul) [avatar definition]
213. happy(paul) <- (19) [avatar component clause 212]
214. ~happy(paul) <- (~19) [avatar component clause 212]
215. ~18 | ~19 [avatar split clause 122,212,208]
227. ~15 [avatar split clause 127,192]
234. generous(paul) <- (~19) [resolution 115,214]
241. wise(paul) <- (~19) [resolution 234,101]
245. $false <- (10, ~19) [subsumption resolution 241,171]
246. ~10 | 19 [avatar contradiction clause 245]
307. 32 <=> creative(paul) [avatar definition]
308. ~creative(paul) <- (~32) [avatar component clause 307]
311. 33 <=> calm(paul) [avatar definition]
319. old(X1) | tall(X1) | quiet(X1) [resolution 108,66]
324. ~calm(paul) | quiet(paul) <- (19) [resolution 116,213]
368. 39 <=> old(paul) [avatar definition]
369. ~old(paul) <- (~39) [avatar component clause 368]
370. old(paul) <- (39) [avatar component clause 368]
503. wise(paul) | ~old(paul) | patient(paul) <- (19) [resolution 113,213]
509. ~old(paul) | patient(paul) <- (10, 19) [subsumption resolution 503,171]
510. patient(paul) <- (10, 19, 39) [subsumption resolution 509,370]
511. tall(paul) | ~creative(paul) <- (10, 19, 39) [resolution 510,71]
513. ~creative(paul) <- (10, ~15, 19, 39) [subsumption resolution 511,194]
516. ~32 | ~10 | 15 | ~19 | ~39 [avatar split clause 513,368,212,192,170,307]
521. calm(paul) | creative(paul) <- (39) [resolution 370,75]
525. calm(paul) <- (~32, 39) [subsumption resolution 521,308]
526. 33 | 32 | ~39 [avatar split clause 525,368,307,311]
527. ~calm(paul) <- (~18, 19) [subsumption resolution 324,210]
528. ~33 | 18 | ~19 [avatar split clause 527,212,208,311]
553. tall(paul) | quiet(paul) <- (~39) [resolution 369,319]
555. quiet(paul) <- (~15, ~39) [subsumption resolution 553,194]
556. $false <- (~15, ~18, ~39) [subsumption resolution 555,210]
557. 15 | 18 | 39 [avatar contradiction clause 556]
559. $false [avatar sat refutation 176,177,215,227,246,516,526,528,557]
% SZS output end Proof for 1284672133014742357721237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not calm then susan is both funny and not quiet.
If paul is brave then mary is happy.
Everyone who is strong is kind and vice versa.
If someone is both calm and not kind then john is both not happy and not tall.
If fred is old then someone is either not patient or not curious.
Everyone who is both not generous and not calm is both funny and not old.
If someone is either not patient or not brave then fred is not old and vice versa.
If someone is either old or curious then someone is not humble and vice versa.
Everyone who is not calm or not patient is not calm or not strong.
If fred is both not calm and old then someone is not wise and vice versa.
If paul is both not tall and curious then someone is strong or patient and vice versa.
Everyone who is quiet is not patient or patient and vice versa.
Everyone who is generous or not funny is not creative or not strong and vice versa.
Everyone who is not brave or not funny is not quiet.
Everyone who is wise or not patient is either not old or humble.
Everyone who is both kind and tall is not patient.
Someone is either humble or not tall.
Someone is calm.
Someone is patient or strong.
Lucy is either not happy or wise.
Someone is not tall or not kind.
Someone is both humble and creative.
Someone is not creative or not rich. | Susan is calm. | entailment | ((~calm(susan))=>((funny(susan)&~quiet(susan))))&
((brave(paul))=>(happy(mary)))&
(![X]:(strong(X)<=>kind(X)))&
((?[X]:((calm(X)&~kind(X))))=>((~happy(john)&~tall(john))))&
((old(fred))=>(?[X]:((~patient(X)<~>~curious(X)))))&
(![X]:((~generous(X)&~calm(X))=>(funny(X)&~old(X))))&
((?[X]:((~patient(X)<~>~brave(X))))<=>(~old(fred)))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~calm(X)|~patient(X))=>(~calm(X)|~strong(X))))&
(((~calm(fred)&old(fred)))<=>(?[X]:(~wise(X))))&
(((~tall(paul)&curious(paul)))<=>(?[X]:((strong(X)|patient(X)))))&
(![X]:(quiet(X)<=>(~patient(X)|patient(X))))&
(![X]:((generous(X)|~funny(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~brave(X)|~funny(X))=>~quiet(X)))&
(![X]:((wise(X)|~patient(X))=>(~old(X)<~>humble(X))))&
(![X]:((kind(X)&tall(X))=>~patient(X)))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:(calm(X)))&
(?[X]:((patient(X)|strong(X))))&
((~happy(lucy)<~>wise(lucy)))&
(?[X]:((~tall(X)|~kind(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~creative(X)|~rich(X)))) | calm(susan) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2670636899629516991358682
% SZS output start Proof for 2670636899629516991358682
1. ~calm(susan) => (~quiet(susan) & funny(susan)) [input p0]
12. ! [X0] : (quiet(X0) <=> (patient(X0) | ~patient(X0))) [input p11]
24. ~calm(susan) [input hypothesis]
26. ! [X0] : ((patient(X0) | ~patient(X0)) => quiet(X0)) [unused predicate definition removal 12]
28. (~quiet(susan) & funny(susan)) | calm(susan) [ennf transformation 1]
36. ! [X0] : (quiet(X0) | (~patient(X0) & patient(X0))) [ennf transformation 26]
80. ~quiet(susan) | calm(susan) [cnf transformation 28]
108. quiet(X0) | patient(X0) [cnf transformation 36]
109. quiet(X0) | ~patient(X0) [cnf transformation 36]
130. ~calm(susan) [cnf transformation 24]
132. 1 <=> calm(susan) [avatar definition]
136. 2 <=> quiet(susan) [avatar definition]
138. ~quiet(susan) <- (~2) [avatar component clause 136]
139. 1 | ~2 [avatar split clause 80,136,132]
265. quiet(X0) [subsumption resolution 108,109]
306. ~1 [avatar split clause 130,132]
314. $false <- (~2) [subsumption resolution 138,265]
315. 2 [avatar contradiction clause 314]
316. $false [avatar sat refutation 139,306,315]
% SZS output end Proof for 2670636899629516991358682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not strong or not humble then someone is patient or happy.
Everyone who is both brave and creative is not humble and vice versa.
Everyone who is not funny is funny or calm and vice versa.
Everyone who is not funny is creative or rich and vice versa.
If someone is both curious and wise then mary is either happy or strong and vice versa.
If paul is calm or wise then someone is not funny and vice versa.
Everyone who is either not patient or wise is both not old and kind.
Everyone who is both not funny and not creative is happy and vice versa.
If alice is either happy or not wise then someone is both not creative and quiet and vice versa.
Everyone who is both not patient and happy is either not calm or creative and vice versa.
If someone is not kind then someone is tall and vice versa.
Everyone who is both creative and not happy is either generous or patient and vice versa.
Everyone who is either not curious or funny is either generous or not quiet and vice versa.
If john is either not happy or happy then susan is either not happy or generous and vice versa.
If someone is creative or curious then paul is not strong or not happy.
Everyone who is not kind is both patient and not quiet.
Fred is not strong or not patient.
Fred is either not brave or not kind.
Someone is not wise.
Fred is either not patient or quiet.
Susan is both not strong and humble.
Someone is either not brave or not generous.
Mary is kind. | Alice is not curious. | neutral | (((~strong(lucy)|~humble(lucy)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((brave(X)&creative(X))<=>~humble(X)))&
(![X]:(~funny(X)<=>(funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(creative(X)|rich(X))))&
((?[X]:((curious(X)&wise(X))))<=>((happy(mary)<~>strong(mary))))&
(((calm(paul)|wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)<~>wise(X))=>(~old(X)&kind(X))))&
(![X]:((~funny(X)&~creative(X))<=>happy(X)))&
(((happy(alice)<~>~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~happy(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(generous(X)<~>~quiet(X))))&
(((~happy(john)<~>happy(john)))<=>((~happy(susan)<~>generous(susan))))&
((?[X]:((creative(X)|curious(X))))=>((~strong(paul)|~happy(paul))))&
(![X]:(~kind(X)=>(patient(X)&~quiet(X))))&
((~strong(fred)|~patient(fred)))&
((~brave(fred)<~>~kind(fred)))&
(?[X]:(~wise(X)))&
((~patient(fred)<~>quiet(fred)))&
((~strong(susan)&humble(susan)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(kind(mary)) | ~curious(alice) | [] | null | 0 |
If alice is either not quiet or funny then someone is either old or funny.
If alice is both old and brave then paul is both patient and not quiet.
If someone is strong then mary is wise or not humble and vice versa.
If someone is either curious or kind then mary is both not strong and not funny.
Everyone who is not brave is both humble and not brave and vice versa.
Everyone who is rich is not humble or not calm and vice versa.
If someone is tall then someone is both not wise and not calm.
If someone is both not patient and brave then paul is not happy or not generous and vice versa.
Everyone who is not kind is humble or not generous and vice versa.
Everyone who is both funny and not kind is either strong or kind and vice versa.
If someone is both creative and humble then someone is funny or kind.
Everyone who is both quiet and humble is both not wise and kind and vice versa.
Everyone who is patient or kind is not creative.
If someone is either not happy or not curious then susan is not happy or not wise.
Everyone who is both humble and quiet is either tall or not funny and vice versa.
Everyone who is either kind or brave is humble and vice versa.
Someone is either not brave or not creative.
Someone is both not quiet and not rich.
Susan is strong.
Susan is not patient.
Susan is not wise or not curious.
Someone is both not creative and not rich.
Alice is not strong.
Mary is either not calm or creative. | Alice is not patient. | neutral | (((~quiet(alice)<~>funny(alice)))=>(?[X]:((old(X)<~>funny(X)))))&
(((old(alice)&brave(alice)))=>((patient(paul)&~quiet(paul))))&
((?[X]:(strong(X)))<=>((wise(mary)|~humble(mary))))&
((?[X]:((curious(X)<~>kind(X))))=>((~strong(mary)&~funny(mary))))&
(![X]:(~brave(X)<=>(humble(X)&~brave(X))))&
(![X]:(rich(X)<=>(~humble(X)|~calm(X))))&
((?[X]:(tall(X)))=>(?[X]:((~wise(X)&~calm(X)))))&
((?[X]:((~patient(X)&brave(X))))<=>((~happy(paul)|~generous(paul))))&
(![X]:(~kind(X)<=>(humble(X)|~generous(X))))&
(![X]:((funny(X)&~kind(X))<=>(strong(X)<~>kind(X))))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~wise(X)&kind(X))))&
(![X]:((patient(X)|kind(X))=>~creative(X)))&
((?[X]:((~happy(X)<~>~curious(X))))=>((~happy(susan)|~wise(susan))))&
(![X]:((humble(X)&quiet(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((kind(X)<~>brave(X))<=>humble(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((~quiet(X)&~rich(X))))&
(strong(susan))&
(~patient(susan))&
((~wise(susan)|~curious(susan)))&
(?[X]:((~creative(X)&~rich(X))))&
(~strong(alice))&
((~calm(mary)<~>creative(mary))) | ~patient(alice) | [] | null | 0 |
Everyone who is both brave and old is brave or generous and vice versa.
Everyone who is brave is wise or quiet.
If someone is either not rich or patient then paul is not old.
Everyone who is not wise or quiet is brave and vice versa.
Everyone who is both not strong and not calm is both tall and calm.
If lucy is not brave then someone is either patient or not creative.
If someone is both not old and strong then mary is either not strong or not calm and vice versa.
Everyone who is either not rich or creative is either not old or patient.
If someone is either kind or generous then someone is creative or funny.
If paul is not happy then someone is either not rich or brave and vice versa.
If someone is not wise then paul is not creative.
Everyone who is not quiet or quiet is not curious.
If fred is either not patient or calm then someone is both wise and curious.
If someone is either happy or curious then someone is humble and vice versa.
If someone is not quiet or not brave then paul is not quiet and vice versa.
Everyone who is not funny is both brave and rich and vice versa.
Lucy is not rich.
Someone is calm or not creative.
Paul is quiet.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich.
Mary is not happy. | Alice is not old. | contradiction | (![X]:((brave(X)&old(X))<=>(brave(X)|generous(X))))&
(![X]:(brave(X)=>(wise(X)|quiet(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>(~old(paul)))&
(![X]:((~wise(X)|quiet(X))<=>brave(X)))&
(![X]:((~strong(X)&~calm(X))=>(tall(X)&calm(X))))&
((~brave(lucy))=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((~old(X)&strong(X))))<=>((~strong(mary)<~>~calm(mary))))&
(![X]:((~rich(X)<~>creative(X))=>(~old(X)<~>patient(X))))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:((creative(X)|funny(X)))))&
((~happy(paul))<=>(?[X]:((~rich(X)<~>brave(X)))))&
((?[X]:(~wise(X)))=>(~creative(paul)))&
(![X]:((~quiet(X)|quiet(X))=>~curious(X)))&
(((~patient(fred)<~>calm(fred)))=>(?[X]:((wise(X)&curious(X)))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(~quiet(paul)))&
(![X]:(~funny(X)<=>(brave(X)&rich(X))))&
(~rich(lucy))&
(?[X]:((calm(X)|~creative(X))))&
(quiet(paul))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X))))&
(~happy(mary)) | ~old(alice) | [
"p0",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 459922289730241225367687
% SZS output start Proof for 459922289730241225367687
1. ! [X0] : ((old(X0) & brave(X0)) <=> (generous(X0) | brave(X0))) [input p0]
15. ? [X0] : (~brave(X0) | ~quiet(X0)) <=> ~quiet(paul) [input p14]
19. quiet(paul) [input p18]
25. ~old(alice) [input hypothesis]
43. ! [X0] : (((old(X0) & brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~old(X0) | ~brave(X0)))) [nnf transformation 1]
44. ! [X0] : (((old(X0) & brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~old(X0) | ~brave(X0))) [flattening 43]
72. (? [X0] : (~brave(X0) | ~quiet(X0)) | quiet(paul)) & (~quiet(paul) | ! [X0] : (brave(X0) & quiet(X0))) [nnf transformation 15]
73. (? [X0] : (~brave(X0) | ~quiet(X0)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (brave(X1) & quiet(X1))) [rectify 72]
74. ? [X0] : (~brave(X0) | ~quiet(X0)) => (~brave(sK7) | ~quiet(sK7)) [choice axiom]
75. ((~brave(sK7) | ~quiet(sK7)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (brave(X1) & quiet(X1))) [skolemisation 73,74]
84. ~brave(X0) | old(X0) [cnf transformation 44]
123. ~quiet(paul) | brave(X1) [cnf transformation 75]
128. quiet(paul) [cnf transformation 19]
135. ~old(alice) [cnf transformation 25]
277. 30 <=> quiet(paul) [avatar definition]
286. 32 <=> ! [X1] : brave(X1) [avatar definition]
287. brave(X1) <- (32) [avatar component clause 286]
288. 32 | ~30 [avatar split clause 123,277,286]
302. 30 [avatar split clause 128,277]
320. old(X0) <- (32) [resolution 84,287]
321. $false <- (32) [resolution 320,135]
326. ~32 [avatar contradiction clause 321]
327. $false [avatar sat refutation 288,302,326]
% SZS output end Proof for 459922289730241225367687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not old.
Everyone who is patient or not brave is humble.
Everyone who is humble or not funny is either wise or not kind.
If paul is either old or wise then someone is both wise and not strong.
If susan is both funny and brave then paul is not happy or calm and vice versa.
Everyone who is kind or brave is either not brave or not quiet.
If paul is both not old and calm then someone is both not brave and not calm and vice versa.
Everyone who is both not quiet and not kind is happy.
Everyone who is patient or humble is funny.
Everyone who is patient is not old and vice versa.
Everyone who is creative or not old is generous or not curious and vice versa.
If fred is either brave or curious then fred is patient and vice versa.
If someone is either not tall or happy then someone is both not wise and not kind.
If someone is either not kind or strong then lucy is tall.
Everyone who is either not curious or calm is quiet.
Everyone who is not wise or not humble is either generous or not kind and vice versa.
Someone is both calm and brave.
Someone is not tall or not happy.
Lucy is both not calm and creative.
Fred is either not old or curious.
Someone is strong.
Someone is not strong.
Someone is both not old and humble. | Paul is not funny. | contradiction | (![X]:((generous(X)|kind(X))=>~old(X)))&
(![X]:((patient(X)|~brave(X))=>humble(X)))&
(![X]:((humble(X)|~funny(X))=>(wise(X)<~>~kind(X))))&
(((old(paul)<~>wise(paul)))=>(?[X]:((wise(X)&~strong(X)))))&
(((funny(susan)&brave(susan)))<=>((~happy(paul)|calm(paul))))&
(![X]:((kind(X)|brave(X))=>(~brave(X)<~>~quiet(X))))&
(((~old(paul)&calm(paul)))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(![X]:((patient(X)|humble(X))=>funny(X)))&
(![X]:(patient(X)<=>~old(X)))&
(![X]:((creative(X)|~old(X))<=>(generous(X)|~curious(X))))&
(((brave(fred)<~>curious(fred)))<=>(patient(fred)))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:((~wise(X)&~kind(X)))))&
((?[X]:((~kind(X)<~>strong(X))))=>(tall(lucy)))&
(![X]:((~curious(X)<~>calm(X))=>quiet(X)))&
(![X]:((~wise(X)|~humble(X))<=>(generous(X)<~>~kind(X))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:((~tall(X)|~happy(X))))&
((~calm(lucy)&creative(lucy)))&
((~old(fred)<~>curious(fred)))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&humble(X)))) | ~funny(paul) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p8",
"p9",
"p10",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9076466909254008794666854
% SZS output start Proof for 9076466909254008794666854
1. ! [X0] : ((kind(X0) | generous(X0)) => ~old(X0)) [input p0]
2. ! [X0] : ((~brave(X0) | patient(X0)) => humble(X0)) [input p1]
3. ! [X0] : ((~funny(X0) | humble(X0)) => (wise(X0) <~> ~kind(X0))) [input p2]
6. ! [X0] : ((brave(X0) | kind(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p5]
7. (calm(paul) & ~old(paul)) <=> ? [X0] : (~calm(X0) & ~brave(X0)) [input p6]
9. ! [X0] : ((humble(X0) | patient(X0)) => funny(X0)) [input p8]
10. ! [X0] : (patient(X0) <=> ~old(X0)) [input p9]
11. ! [X0] : ((~old(X0) | creative(X0)) <=> (~curious(X0) | generous(X0))) [input p10]
15. ! [X0] : ((~curious(X0) <~> calm(X0)) => quiet(X0)) [input p14]
16. ! [X0] : ((~humble(X0) | ~wise(X0)) <=> (generous(X0) <~> ~kind(X0))) [input p15]
19. creative(lucy) & ~calm(lucy) [input p18]
24. ~funny(paul) [input hypothesis]
26. ! [X0] : (~old(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 1]
27. ! [X0] : (humble(X0) | (brave(X0) & ~patient(X0))) [ennf transformation 2]
28. ! [X0] : ((wise(X0) <~> ~kind(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 3]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 6]
33. ! [X0] : (funny(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 9]
36. ! [X0] : (quiet(X0) | (~curious(X0) <=> calm(X0))) [ennf transformation 15]
37. ! [X0] : (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | (funny(X0) & ~humble(X0))) [nnf transformation 28]
43. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~brave(X0) & ~kind(X0))) [nnf transformation 30]
44. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X0] : (~calm(X0) & ~brave(X0)) | (~calm(paul) | old(paul))) [nnf transformation 7]
45. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X0] : (~calm(X0) & ~brave(X0)) | ~calm(paul) | old(paul)) [flattening 44]
46. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X1] : (~calm(X1) & ~brave(X1)) | ~calm(paul) | old(paul)) [rectify 45]
47. ? [X1] : (~calm(X1) & ~brave(X1)) => (~calm(sK1) & ~brave(sK1)) [choice axiom]
48. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & ((~calm(sK1) & ~brave(sK1)) | ~calm(paul) | old(paul)) [skolemisation 46,47]
49. ! [X0] : ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))) [nnf transformation 10]
50. ! [X0] : (((~old(X0) | creative(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (old(X0) & ~creative(X0)))) [nnf transformation 11]
51. ! [X0] : ((~old(X0) | creative(X0) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | (old(X0) & ~creative(X0)))) [flattening 50]
58. ! [X0] : (quiet(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 36]
59. ! [X0] : (((~humble(X0) | ~wise(X0)) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0)))) & (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (humble(X0) & wise(X0)))) [nnf transformation 16]
60. ! [X0] : ((~humble(X0) | ~wise(X0) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0)))) & (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (humble(X0) & wise(X0)))) [flattening 59]
72. ~old(X0) | ~generous(X0) [cnf transformation 26]
73. ~old(X0) | ~kind(X0) [cnf transformation 26]
74. ~patient(X0) | humble(X0) [cnf transformation 27]
76. ~humble(X0) | wise(X0) | ~kind(X0) [cnf transformation 37]
78. ~wise(X0) | kind(X0) | ~humble(X0) [cnf transformation 37]
90. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 43]
95. ~old(paul) | calm(X0) | brave(X0) [cnf transformation 48]
98. ~patient(X0) | funny(X0) [cnf transformation 33]
101. patient(X0) | old(X0) [cnf transformation 49]
102. ~curious(X0) | generous(X0) | ~creative(X0) [cnf transformation 51]
116. curious(X0) | calm(X0) | quiet(X0) [cnf transformation 58]
120. ~generous(X0) | kind(X0) | wise(X0) [cnf transformation 60]
122. ~humble(X0) | ~wise(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 60]
127. ~calm(lucy) [cnf transformation 19]
128. creative(lucy) [cnf transformation 19]
135. ~funny(paul) [cnf transformation 24]
136. ~quiet(X0) | ~brave(X0) [duplicate literal removal 90]
142. 2 <=> old(paul) [avatar definition]
179. 9 <=> ! [X0] : (calm(X0) | brave(X0)) [avatar definition]
180. calm(X0) | brave(X0) <- (9) [avatar component clause 179]
182. 9 | ~2 [avatar split clause 95,142,179]
239. ~wise(X0) | ~humble(X0) | ~generous(X0) [subsumption resolution 122,78]
259. funny(X1) | old(X1) [resolution 101,98]
260. humble(X2) | old(X2) [resolution 101,74]
290. old(paul) [resolution 259,135]
293. 2 [avatar split clause 290,142]
320. brave(lucy) <- (9) [resolution 180,127]
336. ~creative(X1) | quiet(X1) | generous(X1) | calm(X1) [resolution 116,102]
376. old(X0) | wise(X0) | ~kind(X0) [resolution 260,76]
379. ~kind(X0) | wise(X0) [subsumption resolution 376,73]
409. 41 <=> kind(lucy) [avatar definition]
410. ~kind(lucy) <- (~41) [avatar component clause 409]
411. kind(lucy) <- (41) [avatar component clause 409]
483. quiet(lucy) | generous(lucy) | calm(lucy) [resolution 336,128]
484. quiet(lucy) | generous(lucy) [subsumption resolution 483,127]
486. 51 <=> generous(lucy) [avatar definition]
488. generous(lucy) <- (51) [avatar component clause 486]
490. 52 <=> quiet(lucy) [avatar definition]
492. quiet(lucy) <- (52) [avatar component clause 490]
493. 51 | 52 [avatar split clause 484,490,486]
504. 54 <=> wise(lucy) [avatar definition]
506. wise(lucy) <- (54) [avatar component clause 504]
535. kind(lucy) | wise(lucy) <- (51) [resolution 488,120]
537. wise(lucy) <- (~41, 51) [subsumption resolution 535,410]
538. 54 | 41 | ~51 [avatar split clause 537,486,409,504]
539. ~brave(lucy) <- (52) [resolution 492,136]
540. $false <- (9, 52) [subsumption resolution 539,320]
541. ~9 | ~52 [avatar contradiction clause 540]
552. wise(lucy) <- (41) [resolution 379,411]
553. 54 | ~41 [avatar split clause 552,409,504]
563. ~humble(lucy) | ~generous(lucy) <- (54) [resolution 506,239]
566. ~humble(lucy) <- (51, 54) [subsumption resolution 563,488]
573. old(lucy) <- (51, 54) [resolution 566,260]
577. ~generous(lucy) <- (51, 54) [resolution 573,72]
580. $false <- (51, 54) [subsumption resolution 577,488]
581. ~51 | ~54 [avatar contradiction clause 580]
582. $false [avatar sat refutation 182,293,493,538,541,553,581]
% SZS output end Proof for 9076466909254008794666854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is humble or generous then mary is quiet or curious and vice versa.
If john is tall or rich then fred is not creative or old.
If someone is not curious then lucy is funny or patient and vice versa.
If alice is both not kind and not happy then someone is calm or not curious and vice versa.
Everyone who is both old and not wise is either rich or not quiet and vice versa.
Everyone who is funny is creative.
Everyone who is either not generous or strong is both funny and happy and vice versa.
If susan is both calm and not humble then someone is both creative and strong.
Everyone who is both not happy and not strong is not funny or not rich and vice versa.
Everyone who is either quiet or creative is wise or kind.
Everyone who is either not kind or not old is either not generous or not curious and vice versa.
Everyone who is not funny or generous is humble.
If someone is not wise then susan is creative or not patient and vice versa.
Everyone who is not wise or generous is either not tall or funny and vice versa.
If john is either patient or old then lucy is both not calm and generous and vice versa.
Everyone who is brave is either not generous or not brave.
Someone is not wise or not rich.
Someone is calm or not strong.
Someone is both curious and not humble.
Someone is both not old and not wise.
Someone is either strong or not creative.
Mary is both not creative and not tall.
Someone is not strong or curious. | Lucy is generous. | neutral | (((humble(mary)|generous(mary)))<=>((quiet(mary)|curious(mary))))&
(((tall(john)|rich(john)))=>((~creative(fred)|old(fred))))&
((?[X]:(~curious(X)))<=>((funny(lucy)|patient(lucy))))&
(((~kind(alice)&~happy(alice)))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((old(X)&~wise(X))<=>(rich(X)<~>~quiet(X))))&
(![X]:(funny(X)=>creative(X)))&
(![X]:((~generous(X)<~>strong(X))<=>(funny(X)&happy(X))))&
(((calm(susan)&~humble(susan)))=>(?[X]:((creative(X)&strong(X)))))&
(![X]:((~happy(X)&~strong(X))<=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)<~>creative(X))=>(wise(X)|kind(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:((~funny(X)|generous(X))=>humble(X)))&
((?[X]:(~wise(X)))<=>((creative(susan)|~patient(susan))))&
(![X]:((~wise(X)|generous(X))<=>(~tall(X)<~>funny(X))))&
(((patient(john)<~>old(john)))<=>((~calm(lucy)&generous(lucy))))&
(![X]:(brave(X)=>(~generous(X)<~>~brave(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((curious(X)&~humble(X))))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((~creative(mary)&~tall(mary)))&
(?[X]:((~strong(X)|curious(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is both not creative and not happy is old or kind and vice versa. Everyone who is rich or tall is either not curious or kind and vice versa. Everyone who is either calm or patient is either not calm or humble. Everyone who is funny or not happy is not creative and vice versa. Everyone who is happy or not creative is either patient or not funny. Everyone who is patient is curious or not quiet and vice versa. If lucy is both not humble and not funny then lucy is both quiet and not rich and vice versa. Everyone who is either brave or not rich is curious and vice versa. Everyone who is not old or creative is either not quiet or curious. Everyone who is both not happy and not creative is curious and vice versa. If john is either not happy or not generous then someone is not quiet. Everyone who is either not happy or quiet is calm or humble and vice versa. If someone is old or wise then alice is old. If someone is funny or not kind then someone is not humble or not strong. Everyone who is either not generous or rich is both not quiet and not rich. Everyone who is old or not brave is not patient. Susan is either rich or not creative. Someone is either not kind or not creative. Mary is both funny and not strong. Someone is not rich or not funny. Alice is tall or not brave. Mary is not wise. | Lucy is funny. | entailment | (![X]:((~creative(X)&~happy(X))<=>(old(X)|kind(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((calm(X)<~>patient(X))=>(~calm(X)<~>humble(X))))&
(![X]:((funny(X)|~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|~creative(X))=>(patient(X)<~>~funny(X))))&
(![X]:(patient(X)<=>(curious(X)|~quiet(X))))&
(((~humble(lucy)&~funny(lucy)))<=>((quiet(lucy)&~rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))<=>curious(X)))&
(![X]:((~old(X)|creative(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((~happy(X)&~creative(X))<=>curious(X)))&
(((~happy(john)<~>~generous(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(calm(X)|humble(X))))&
((?[X]:((old(X)|wise(X))))=>(old(alice)))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((~generous(X)<~>rich(X))=>(~quiet(X)&~rich(X))))&
(![X]:((old(X)|~brave(X))=>~patient(X)))&
((rich(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((funny(mary)&~strong(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
((tall(alice)|~brave(alice)))&
(~wise(mary)) | funny(lucy) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3396410332810090335513630
% SZS output start Proof for 3396410332810090335513630
1. ! [X0] : ((~happy(X0) & ~creative(X0)) <=> (kind(X0) | old(X0))) [input p0]
4. ! [X0] : ((~happy(X0) | funny(X0)) <=> ~creative(X0)) [input p3]
5. ! [X0] : ((~creative(X0) | happy(X0)) => (patient(X0) <~> ~funny(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (~quiet(X0) | curious(X0))) [input p5]
9. ! [X0] : ((creative(X0) | ~old(X0)) => (~quiet(X0) <~> curious(X0))) [input p8]
10. ! [X0] : ((~creative(X0) & ~happy(X0)) <=> curious(X0)) [input p9]
16. ! [X0] : ((~brave(X0) | old(X0)) => ~patient(X0)) [input p15]
23. ~funny(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~funny(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 5]
31. ! [X0] : ((~quiet(X0) <~> curious(X0)) | (~creative(X0) & old(X0))) [ennf transformation 9]
35. ! [X0] : (~patient(X0) | (brave(X0) & ~old(X0))) [ennf transformation 16]
36. ! [X0] : (((~happy(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | (happy(X0) | creative(X0)))) [nnf transformation 1]
37. ! [X0] : (((~happy(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | happy(X0) | creative(X0))) [flattening 36]
41. ! [X0] : (((~happy(X0) | funny(X0)) | creative(X0)) & (~creative(X0) | (happy(X0) & ~funny(X0)))) [nnf transformation 4]
42. ! [X0] : ((~happy(X0) | funny(X0) | creative(X0)) & (~creative(X0) | (happy(X0) & ~funny(X0)))) [flattening 41]
43. ! [X0] : (((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | (creative(X0) & ~happy(X0))) [nnf transformation 30]
44. ! [X0] : ((patient(X0) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ~patient(X0))) [nnf transformation 6]
45. ! [X0] : ((patient(X0) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ~patient(X0))) [flattening 44]
49. ! [X0] : (((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | (~creative(X0) & old(X0))) [nnf transformation 31]
50. ! [X0] : (((~creative(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | happy(X0)))) [nnf transformation 10]
51. ! [X0] : (((~creative(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | happy(X0))) [flattening 50]
67. ~old(X0) | ~happy(X0) [cnf transformation 37]
80. ~creative(X0) | happy(X0) [cnf transformation 42]
84. ~patient(X0) | funny(X0) | ~happy(X0) [cnf transformation 43]
85. ~patient(X0) | funny(X0) | creative(X0) [cnf transformation 43]
87. ~curious(X0) | patient(X0) [cnf transformation 45]
88. quiet(X0) | patient(X0) [cnf transformation 45]
97. ~quiet(X0) | curious(X0) | old(X0) [cnf transformation 49]
101. curious(X0) | creative(X0) | happy(X0) [cnf transformation 51]
103. ~curious(X0) | ~creative(X0) [cnf transformation 51]
117. ~patient(X0) | ~old(X0) [cnf transformation 35]
126. ~funny(lucy) [cnf transformation 23]
132. 1 <=> quiet(lucy) [avatar definition]
133. quiet(lucy) <- (1) [avatar component clause 132]
134. ~quiet(lucy) <- (~1) [avatar component clause 132]
140. 3 <=> funny(lucy) [avatar definition]
142. ~funny(lucy) <- (~3) [avatar component clause 140]
151. curious(X0) | happy(X0) [subsumption resolution 101,80]
167. 8 <=> ! [X0] : ~old(X0) [avatar definition]
168. ~old(X0) <- (8) [avatar component clause 167]
211. ~3 [avatar split clause 126,140]
216. patient(lucy) <- (~1) [resolution 88,134]
227. patient(X2) | happy(X2) [resolution 151,87]
230. happy(X1) | ~old(X1) [resolution 227,117]
254. funny(lucy) | ~happy(lucy) <- (~1) [resolution 84,216]
257. ~happy(lucy) <- (~1, ~3) [subsumption resolution 254,142]
268. funny(lucy) | creative(lucy) <- (~1) [resolution 85,216]
272. creative(lucy) <- (~1, ~3) [subsumption resolution 268,142]
285. 25 <=> curious(lucy) [avatar definition]
287. curious(lucy) <- (25) [avatar component clause 285]
326. happy(lucy) <- (~1, ~3) [resolution 272,80]
327. $false <- (~1, ~3) [subsumption resolution 326,257]
328. 1 | 3 [avatar contradiction clause 327]
331. 31 <=> patient(lucy) [avatar definition]
332. patient(lucy) <- (31) [avatar component clause 331]
336. curious(lucy) | old(lucy) <- (1) [resolution 97,133]
339. curious(lucy) <- (1, 8) [subsumption resolution 336,168]
340. 25 | ~1 | ~8 [avatar split clause 339,167,132,285]
347. ~old(X1) [subsumption resolution 230,67]
348. 8 [avatar split clause 347,167]
365. patient(lucy) <- (25) [resolution 287,87]
370. ~creative(lucy) <- (25) [resolution 287,103]
386. 31 | ~25 [avatar split clause 365,285,331]
390. funny(lucy) | creative(lucy) <- (31) [resolution 332,85]
394. creative(lucy) <- (~3, 31) [subsumption resolution 390,142]
395. $false <- (~3, 25, 31) [subsumption resolution 394,370]
396. 3 | ~25 | ~31 [avatar contradiction clause 395]
397. $false [avatar sat refutation 211,328,340,348,386,396]
% SZS output end Proof for 3396410332810090335513630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not rich and vice versa. If someone is either not kind or strong then paul is not generous. If susan is rich or not calm then fred is either calm or wise. Everyone who is not funny or rich is either not rich or not funny. Everyone who is either strong or not funny is both quiet and happy. If susan is both curious and kind then fred is either curious or not patient. Everyone who is both kind and not rich is either kind or not rich. If someone is old or generous then someone is creative or not funny. Everyone who is not wise is not rich and vice versa. If someone is both wise and old then someone is quiet or strong. Everyone who is both curious and not wise is either calm or patient and vice versa. If susan is not calm then someone is curious or rich. If john is happy or not humble then someone is not happy or not tall and vice versa. If someone is quiet or happy then someone is not wise or not quiet and vice versa. Everyone who is both not humble and old is generous. If someone is wise or calm then paul is humble or happy and vice versa. Someone is not humble. Fred is both old and quiet. John is both not happy and curious. Someone is either wise or happy. Someone is both tall and not brave. Fred is not generous or not quiet. Someone is not rich. Paul is curious or kind. | Paul is happy. | neutral | (![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~kind(X)<~>strong(X))))=>(~generous(paul)))&
(((rich(susan)|~calm(susan)))=>((calm(fred)<~>wise(fred))))&
(![X]:((~funny(X)|rich(X))=>(~rich(X)<~>~funny(X))))&
(![X]:((strong(X)<~>~funny(X))=>(quiet(X)&happy(X))))&
(((curious(susan)&kind(susan)))=>((curious(fred)<~>~patient(fred))))&
(![X]:((kind(X)&~rich(X))=>(kind(X)<~>~rich(X))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:(~wise(X)<=>~rich(X)))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
(![X]:((curious(X)&~wise(X))<=>(calm(X)<~>patient(X))))&
((~calm(susan))=>(?[X]:((curious(X)|rich(X)))))&
(((happy(john)|~humble(john)))<=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((quiet(X)|happy(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&old(X))=>generous(X)))&
((?[X]:((wise(X)|calm(X))))<=>((humble(paul)|happy(paul))))&
(?[X]:(~humble(X)))&
((old(fred)&quiet(fred)))&
((~happy(john)&curious(john)))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((tall(X)&~brave(X))))&
((~generous(fred)|~quiet(fred)))&
(?[X]:(~rich(X)))&
((curious(paul)|kind(paul))) | happy(paul) | [] | null | 0 |
If mary is strong then fred is both not strong and not curious. Everyone who is either brave or strong is either not strong or not rich. Everyone who is tall is both not rich and happy. Everyone who is not funny or strong is both creative and not brave. Everyone who is not brave or not quiet is both not humble and not calm and vice versa. If someone is either humble or not kind then someone is both not humble and rich and vice versa. If someone is not strong or not calm then someone is not generous. If fred is wise or quiet then john is wise. If fred is creative or not rich then susan is either calm or not quiet. Everyone who is either not rich or not humble is not tall or not quiet. Everyone who is either tall or generous is not quiet and vice versa. Everyone who is both not kind and not creative is either rich or wise and vice versa. Everyone who is kind is patient. If mary is old then susan is not wise or not calm. Everyone who is not generous is not kind and vice versa. Paul is funny. Someone is calm. Someone is not humble or not curious. Lucy is not rich or not kind. John is not kind or not creative. Someone is not funny. Susan is humble. John is curious. | Susan is patient. | neutral | ((strong(mary))=>((~strong(fred)&~curious(fred))))&
(![X]:((brave(X)<~>strong(X))=>(~strong(X)<~>~rich(X))))&
(![X]:(tall(X)=>(~rich(X)&happy(X))))&
(![X]:((~funny(X)|strong(X))=>(creative(X)&~brave(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~generous(X))))&
(((wise(fred)|quiet(fred)))=>(wise(john)))&
(((creative(fred)|~rich(fred)))=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
(funny(paul))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)|~curious(X))))&
((~rich(lucy)|~kind(lucy)))&
((~kind(john)|~creative(john)))&
(?[X]:(~funny(X)))&
(humble(susan))&
(curious(john)) | patient(susan) | [] | null | 0 |
If someone is old or generous then someone is not funny or funny.
Everyone who is quiet is not brave or calm.
If mary is either wise or not calm then someone is either humble or creative.
Everyone who is not brave or generous is both not humble and not curious.
Everyone who is both curious and not patient is not wise or not brave and vice versa.
Everyone who is either not tall or strong is both strong and funny.
Everyone who is humble or not brave is both not generous and calm.
Everyone who is brave is creative or brave.
Everyone who is both tall and calm is either not patient or patient and vice versa.
If susan is both creative and humble then someone is not funny or not rich.
If someone is either not funny or not rich then someone is both not funny and quiet and vice versa.
If susan is rich then someone is both kind and not wise and vice versa.
If fred is both generous and not tall then paul is both curious and not calm and vice versa.
Everyone who is either not kind or generous is not quiet.
Everyone who is both not strong and humble is not strong and vice versa.
Mary is not happy or not old.
Someone is either not kind or not creative.
Fred is both not generous and not humble.
Someone is either not humble or humble.
Someone is either not happy or strong.
Someone is not happy or generous.
Someone is both tall and not generous. | Fred is creative. | neutral | ((?[X]:((old(X)|generous(X))))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:(quiet(X)=>(~brave(X)|calm(X))))&
(((wise(mary)<~>~calm(mary)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~brave(X)|generous(X))=>(~humble(X)&~curious(X))))&
(![X]:((curious(X)&~patient(X))<=>(~wise(X)|~brave(X))))&
(![X]:((~tall(X)<~>strong(X))=>(strong(X)&funny(X))))&
(![X]:((humble(X)|~brave(X))=>(~generous(X)&calm(X))))&
(![X]:(brave(X)=>(creative(X)|brave(X))))&
(![X]:((tall(X)&calm(X))<=>(~patient(X)<~>patient(X))))&
(((creative(susan)&humble(susan)))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:((~funny(X)&quiet(X)))))&
((rich(susan))<=>(?[X]:((kind(X)&~wise(X)))))&
(((generous(fred)&~tall(fred)))<=>((curious(paul)&~calm(paul))))&
(![X]:((~kind(X)<~>generous(X))=>~quiet(X)))&
(![X]:((~strong(X)&humble(X))<=>~strong(X)))&
((~happy(mary)|~old(mary)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~generous(fred)&~humble(fred)))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:((tall(X)&~generous(X)))) | creative(fred) | [] | null | 0 |
If john is both generous and rich then john is either not curious or not old.
If alice is not humble or not strong then alice is either not brave or not strong and vice versa.
Everyone who is both not happy and happy is either humble or strong and vice versa.
Everyone who is happy is not quiet or wise and vice versa.
If someone is not generous or quiet then susan is either not patient or not happy and vice versa.
If lucy is both not humble and happy then someone is not patient or not tall and vice versa.
Everyone who is not quiet or not strong is not rich or quiet.
Everyone who is strong or not generous is not quiet or not tall and vice versa.
Everyone who is either not creative or brave is happy.
Everyone who is strong or happy is either humble or calm.
If someone is both happy and quiet then someone is both tall and not tall.
If someone is both not tall and kind then alice is either not generous or happy and vice versa.
If lucy is not funny or strong then someone is not calm or curious and vice versa.
Everyone who is both quiet and curious is not quiet and vice versa.
If lucy is not patient or not brave then someone is kind and vice versa.
Everyone who is both not wise and brave is both rich and not humble.
Someone is not wise or not tall.
Someone is rich or brave.
Mary is either not happy or strong.
Fred is either happy or not happy.
Fred is not strong or wise.
Mary is either happy or not old. | Alice is strong. | contradiction | (((generous(john)&rich(john)))=>((~curious(john)<~>~old(john))))&
(((~humble(alice)|~strong(alice)))<=>((~brave(alice)<~>~strong(alice))))&
(![X]:((~happy(X)&happy(X))<=>(humble(X)<~>strong(X))))&
(![X]:(happy(X)<=>(~quiet(X)|wise(X))))&
((?[X]:((~generous(X)|quiet(X))))<=>((~patient(susan)<~>~happy(susan))))&
(((~humble(lucy)&happy(lucy)))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~quiet(X)|~strong(X))=>(~rich(X)|quiet(X))))&
(![X]:((strong(X)|~generous(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((~creative(X)<~>brave(X))=>happy(X)))&
(![X]:((strong(X)|happy(X))=>(humble(X)<~>calm(X))))&
((?[X]:((happy(X)&quiet(X))))=>(?[X]:((tall(X)&~tall(X)))))&
((?[X]:((~tall(X)&kind(X))))<=>((~generous(alice)<~>happy(alice))))&
(((~funny(lucy)|strong(lucy)))<=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:((quiet(X)&curious(X))<=>~quiet(X)))&
(((~patient(lucy)|~brave(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)&brave(X))=>(rich(X)&~humble(X))))&
(?[X]:((~wise(X)|~tall(X))))&
(?[X]:((rich(X)|brave(X))))&
((~happy(mary)<~>strong(mary)))&
((happy(fred)<~>~happy(fred)))&
((~strong(fred)|wise(fred)))&
((happy(mary)<~>~old(mary))) | strong(alice) | [
"p5",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 893168985864160369922187
% SZS output start Proof for 893168985864160369922187
6. (happy(lucy) & ~humble(lucy)) <=> ? [X0] : (~tall(X0) | ~patient(X0)) [input p5]
8. ! [X0] : ((~generous(X0) | strong(X0)) <=> (~tall(X0) | ~quiet(X0))) [input p7]
11. ? [X0] : (quiet(X0) & happy(X0)) => ? [X0] : (~tall(X0) & tall(X0)) [input p10]
14. ! [X0] : ((curious(X0) & quiet(X0)) <=> ~quiet(X0)) [input p13]
23. strong(alice) [input hypothesis]
24. ? [X0] : (quiet(X0) & happy(X0)) => ? [X1] : (~tall(X1) & tall(X1)) [rectify 11]
31. ? [X1] : (~tall(X1) & tall(X1)) | ! [X0] : (~quiet(X0) | ~happy(X0)) [ennf transformation 24]
45. ((happy(lucy) & ~humble(lucy)) | ! [X0] : (tall(X0) & patient(X0))) & (? [X0] : (~tall(X0) | ~patient(X0)) | (~happy(lucy) | humble(lucy))) [nnf transformation 6]
46. ((happy(lucy) & ~humble(lucy)) | ! [X0] : (tall(X0) & patient(X0))) & (? [X0] : (~tall(X0) | ~patient(X0)) | ~happy(lucy) | humble(lucy)) [flattening 45]
47. ((happy(lucy) & ~humble(lucy)) | ! [X0] : (tall(X0) & patient(X0))) & (? [X1] : (~tall(X1) | ~patient(X1)) | ~happy(lucy) | humble(lucy)) [rectify 46]
48. ? [X1] : (~tall(X1) | ~patient(X1)) => (~tall(sK1) | ~patient(sK1)) [choice axiom]
49. ((happy(lucy) & ~humble(lucy)) | ! [X0] : (tall(X0) & patient(X0))) & ((~tall(sK1) | ~patient(sK1)) | ~happy(lucy) | humble(lucy)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) | strong(X0)) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | (generous(X0) & ~strong(X0)))) [nnf transformation 8]
51. ! [X0] : ((~generous(X0) | strong(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | (generous(X0) & ~strong(X0)))) [flattening 50]
54. ? [X0] : (~tall(X0) & tall(X0)) | ! [X1] : (~quiet(X1) | ~happy(X1)) [rectify 31]
55. ? [X0] : (~tall(X0) & tall(X0)) => (~tall(sK2) & tall(sK2)) [choice axiom]
56. (~tall(sK2) & tall(sK2)) | ! [X1] : (~quiet(X1) | ~happy(X1)) [skolemisation 54,55]
66. ! [X0] : (((curious(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 14]
67. ! [X0] : (((curious(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | ~curious(X0) | ~quiet(X0))) [flattening 66]
107. happy(lucy) | tall(X0) [cnf transformation 49]
110. ~tall(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 51]
120. tall(sK2) | ~quiet(X1) | ~happy(X1) [cnf transformation 56]
121. ~tall(sK2) | ~quiet(X1) | ~happy(X1) [cnf transformation 56]
133. quiet(X0) | quiet(X0) [cnf transformation 67]
149. strong(alice) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 133]
182. 7 <=> strong(alice) [avatar definition]
183. strong(alice) <- (7) [avatar component clause 182]
220. 14 <=> ! [X0] : tall(X0) [avatar definition]
221. tall(X0) <- (14) [avatar component clause 220]
223. 15 <=> happy(lucy) [avatar definition]
225. happy(lucy) <- (15) [avatar component clause 223]
226. 14 | 15 [avatar split clause 107,223,220]
248. 20 <=> ! [X1] : (~quiet(X1) | ~happy(X1)) [avatar definition]
249. ~quiet(X1) | ~happy(X1) <- (20) [avatar component clause 248]
251. 21 <=> tall(sK2) [avatar definition]
254. 20 | ~21 [avatar split clause 121,251,248]
255. 20 | 21 [avatar split clause 120,251,248]
370. 7 [avatar split clause 149,182]
373. ~happy(X1) <- (20) [subsumption resolution 249,151]
374. $false <- (15, 20) [subsumption resolution 225,373]
375. ~15 | ~20 [avatar contradiction clause 374]
396. ~quiet(X0) | ~strong(X0) <- (14) [resolution 110,221]
397. ~strong(X0) <- (14) [subsumption resolution 396,151]
409. $false <- (7, 14) [resolution 397,183]
410. ~7 | ~14 [avatar contradiction clause 409]
411. $false [avatar sat refutation 226,254,255,370,375,410]
% SZS output end Proof for 893168985864160369922187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is creative then fred is kind.
Everyone who is not happy is creative or quiet and vice versa.
If mary is not creative or old then mary is both not tall and not old.
Everyone who is not calm is tall or kind.
Everyone who is curious or tall is both generous and creative.
If alice is either not happy or creative then someone is either not kind or rich.
Everyone who is brave is both brave and not tall and vice versa.
Everyone who is strong is funny and vice versa.
Everyone who is either funny or not quiet is either quiet or curious and vice versa.
If mary is both brave and not happy then mary is both happy and generous.
If fred is either wise or humble then someone is both tall and not creative.
Everyone who is humble or strong is either creative or kind.
If paul is either not generous or not calm then someone is either not kind or not happy and vice versa.
Everyone who is not happy is both not humble and not curious and vice versa.
If someone is both not old and humble then someone is old and vice versa.
If susan is both not tall and not funny then lucy is tall and vice versa.
Fred is quiet or brave.
Someone is both kind and old.
Fred is calm.
Someone is both not humble and not rich.
Someone is either kind or not humble.
Paul is strong or not generous.
Fred is creative or rich. | Mary is old. | contradiction | ((creative(susan))=>(kind(fred)))&
(![X]:(~happy(X)<=>(creative(X)|quiet(X))))&
(((~creative(mary)|old(mary)))=>((~tall(mary)&~old(mary))))&
(![X]:(~calm(X)=>(tall(X)|kind(X))))&
(![X]:((curious(X)|tall(X))=>(generous(X)&creative(X))))&
(((~happy(alice)<~>creative(alice)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:(brave(X)<=>(brave(X)&~tall(X))))&
(![X]:(strong(X)<=>funny(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>(quiet(X)<~>curious(X))))&
(((brave(mary)&~happy(mary)))=>((happy(mary)&generous(mary))))&
(((wise(fred)<~>humble(fred)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((humble(X)|strong(X))=>(creative(X)<~>kind(X))))&
(((~generous(paul)<~>~calm(paul)))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:(~happy(X)<=>(~humble(X)&~curious(X))))&
((?[X]:((~old(X)&humble(X))))<=>(?[X]:(old(X))))&
(((~tall(susan)&~funny(susan)))<=>(tall(lucy)))&
((quiet(fred)|brave(fred)))&
(?[X]:((kind(X)&old(X))))&
(calm(fred))&
(?[X]:((~humble(X)&~rich(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((strong(paul)|~generous(paul)))&
((creative(fred)|rich(fred))) | old(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 638717831222389806466727
% SZS output start Proof for 638717831222389806466727
3. (old(mary) | ~creative(mary)) => (~old(mary) & ~tall(mary)) [input p2]
24. old(mary) [input hypothesis]
27. (~old(mary) & ~tall(mary)) | (~old(mary) & creative(mary)) [ennf transformation 3]
76. ~old(mary) | ~old(mary) [cnf transformation 27]
136. old(mary) [cnf transformation 24]
142. ~old(mary) [duplicate literal removal 76]
314. $false [subsumption resolution 136,142]
% SZS output end Proof for 638717831222389806466727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or not old then susan is not calm and vice versa.
If someone is not humble then someone is both not wise and not happy and vice versa.
If someone is tall then someone is not rich or curious and vice versa.
Everyone who is both wise and not brave is both not strong and happy.
Everyone who is either not kind or strong is both rich and old.
If someone is both not rich and not patient then mary is either not kind or not old and vice versa.
Everyone who is humble is both not creative and tall.
If lucy is either not strong or creative then someone is either not old or wise.
If john is both patient and happy then lucy is not tall or not quiet.
Everyone who is patient is both not creative and wise.
If alice is happy then someone is either not patient or brave and vice versa.
Everyone who is rich is quiet or humble and vice versa.
Everyone who is either not kind or not strong is both wise and happy.
Everyone who is either calm or not generous is not generous.
Everyone who is patient is old or not patient and vice versa.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Someone is curious or creative.
Alice is either not calm or not rich.
Someone is rich.
Someone is either not quiet or kind.
Someone is not brave or not wise.
Someone is not creative.
Lucy is old. | Lucy is rich. | entailment | ((?[X]:((wise(X)|~old(X))))<=>(~calm(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)&~happy(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))=>(~strong(X)&happy(X))))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&old(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>((~kind(mary)<~>~old(mary))))&
(![X]:(humble(X)=>(~creative(X)&tall(X))))&
(((~strong(lucy)<~>creative(lucy)))=>(?[X]:((~old(X)<~>wise(X)))))&
(((patient(john)&happy(john)))=>((~tall(lucy)|~quiet(lucy))))&
(![X]:(patient(X)=>(~creative(X)&wise(X))))&
((happy(alice))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:(rich(X)<=>(quiet(X)|humble(X))))&
(![X]:((~kind(X)<~>~strong(X))=>(wise(X)&happy(X))))&
(![X]:((calm(X)<~>~generous(X))=>~generous(X)))&
(![X]:(patient(X)<=>(old(X)|~patient(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(?[X]:((curious(X)|creative(X))))&
((~calm(alice)<~>~rich(alice)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:(~creative(X)))&
(old(lucy)) | rich(lucy) | [
"p1",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8292794837372718659877815
% SZS output start Proof for 8292794837372718659877815
2. ? [X0] : ~humble(X0) <=> ? [X0] : (~happy(X0) & ~wise(X0)) [input p1]
10. ! [X0] : (patient(X0) => (wise(X0) & ~creative(X0))) [input p9]
12. ! [X0] : (rich(X0) <=> (humble(X0) | quiet(X0))) [input p11]
15. ! [X0] : (patient(X0) <=> (~patient(X0) | old(X0))) [input p14]
24. ~rich(lucy) [input hypothesis]
25. ? [X0] : ~humble(X0) <=> ? [X1] : (~happy(X1) & ~wise(X1)) [rectify 2]
34. ! [X0] : ((wise(X0) & ~creative(X0)) | ~patient(X0)) [ennf transformation 10]
41. (? [X0] : ~humble(X0) | ! [X1] : (happy(X1) | wise(X1))) & (? [X1] : (~happy(X1) & ~wise(X1)) | ! [X0] : humble(X0)) [nnf transformation 25]
42. (? [X0] : ~humble(X0) | ! [X1] : (happy(X1) | wise(X1))) & (? [X2] : (~happy(X2) & ~wise(X2)) | ! [X3] : humble(X3)) [rectify 41]
43. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
44. ? [X2] : (~happy(X2) & ~wise(X2)) => (~happy(sK2) & ~wise(sK2)) [choice axiom]
45. (~humble(sK1) | ! [X1] : (happy(X1) | wise(X1))) & ((~happy(sK2) & ~wise(sK2)) | ! [X3] : humble(X3)) [skolemisation 42,44,43]
63. ! [X0] : ((rich(X0) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | ~rich(X0))) [nnf transformation 12]
64. ! [X0] : ((rich(X0) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | ~rich(X0))) [flattening 63]
67. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | ~patient(X0))) [nnf transformation 15]
68. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~patient(X0))) [flattening 67]
85. ~wise(sK2) | humble(X3) [cnf transformation 45]
111. ~patient(X0) | wise(X0) [cnf transformation 34]
118. ~humble(X0) | rich(X0) [cnf transformation 64]
127. patient(X0) | patient(X0) [cnf transformation 68]
145. ~rich(lucy) [cnf transformation 24]
151. patient(X0) [duplicate literal removal 127]
183. 8 <=> ! [X3] : humble(X3) [avatar definition]
184. humble(X3) <- (8) [avatar component clause 183]
191. 10 <=> wise(sK2) [avatar definition]
193. ~wise(sK2) <- (~10) [avatar component clause 191]
194. 8 | ~10 [avatar split clause 85,191,183]
204. 13 <=> ! [X1] : rich(X1) [avatar definition]
205. rich(X1) <- (13) [avatar component clause 204]
358. wise(X0) [resolution 111,151]
362. $false <- (~10) [resolution 358,193]
363. 10 [avatar contradiction clause 362]
368. rich(X0) <- (8) [resolution 118,184]
369. 13 | ~8 [avatar split clause 368,183,204]
370. $false <- (13) [resolution 205,145]
377. ~13 [avatar contradiction clause 370]
378. $false [avatar sat refutation 194,363,369,377]
% SZS output end Proof for 8292794837372718659877815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or funny then susan is either not tall or quiet. If someone is not old or not funny then john is happy or old and vice versa. Everyone who is either curious or not kind is old or not curious. Everyone who is both not strong and not generous is both not happy and funny and vice versa. Everyone who is happy is not creative and vice versa. If someone is either patient or not patient then lucy is either brave or humble. If someone is not happy or kind then fred is both kind and humble and vice versa. Everyone who is both not happy and curious is either quiet or not tall and vice versa. If lucy is either not calm or humble then someone is generous and vice versa. Everyone who is both not creative and not old is not happy or wise and vice versa. If someone is not funny then someone is not patient. Everyone who is not curious or wise is not happy or not old. If lucy is not funny or not rich then john is either not funny or kind. Everyone who is both rich and happy is creative or brave. Everyone who is either kind or not generous is either funny or not calm. If someone is either not rich or not humble then alice is not quiet. Someone is not rich. Mary is either generous or patient. Someone is funny or not quiet. Someone is not generous or calm. Someone is either not old or kind. | Susan is happy. | entailment | ((?[X]:((~brave(X)|funny(X))))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((~old(X)|~funny(X))))<=>((happy(john)|old(john))))&
(![X]:((curious(X)<~>~kind(X))=>(old(X)|~curious(X))))&
(![X]:((~strong(X)&~generous(X))<=>(~happy(X)&funny(X))))&
(![X]:(happy(X)<=>~creative(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((brave(lucy)<~>humble(lucy))))&
((?[X]:((~happy(X)|kind(X))))<=>((kind(fred)&humble(fred))))&
(![X]:((~happy(X)&curious(X))<=>(quiet(X)<~>~tall(X))))&
(((~calm(lucy)<~>humble(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((~creative(X)&~old(X))<=>(~happy(X)|wise(X))))&
((?[X]:(~funny(X)))=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|wise(X))=>(~happy(X)|~old(X))))&
(((~funny(lucy)|~rich(lucy)))=>((~funny(john)<~>kind(john))))&
(![X]:((rich(X)&happy(X))=>(creative(X)|brave(X))))&
(![X]:((kind(X)<~>~generous(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(~quiet(alice)))&
(?[X]:(~rich(X)))&
((generous(mary)<~>patient(mary)))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~generous(X)|calm(X))))&
(?[X]:((~old(X)<~>kind(X)))) | happy(susan) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6653825786338239757958830
% SZS output start Proof for 6653825786338239757958830
5. ! [X0] : (happy(X0) <=> ~creative(X0)) [input p4]
10. ! [X0] : ((~old(X0) & ~creative(X0)) <=> (wise(X0) | ~happy(X0))) [input p9]
22. ~happy(susan) [input hypothesis]
45. ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))) [nnf transformation 5]
58. ! [X0] : (((~old(X0) & ~creative(X0)) | (~wise(X0) & happy(X0))) & ((wise(X0) | ~happy(X0)) | (old(X0) | creative(X0)))) [nnf transformation 10]
59. ! [X0] : (((~old(X0) & ~creative(X0)) | (~wise(X0) & happy(X0))) & (wise(X0) | ~happy(X0) | old(X0) | creative(X0))) [flattening 58]
90. ~creative(X0) | ~happy(X0) [cnf transformation 45]
91. creative(X0) | happy(X0) [cnf transformation 45]
112. ~creative(X0) | happy(X0) [cnf transformation 59]
137. ~happy(susan) [cnf transformation 22]
227. 20 <=> ! [X1] : happy(X1) [avatar definition]
228. happy(X1) <- (20) [avatar component clause 227]
247. ~creative(X0) [subsumption resolution 112,90]
329. happy(X1) [resolution 91,247]
330. 20 [avatar split clause 329,227]
331. $false <- (20) [resolution 228,137]
334. ~20 [avatar contradiction clause 331]
335. $false [avatar sat refutation 330,334]
% SZS output end Proof for 6653825786338239757958830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not humble is not kind or not creative and vice versa.
Everyone who is either not rich or not generous is both not kind and not brave.
If john is old or calm then someone is not strong or curious and vice versa.
If someone is strong or wise then fred is not tall or not patient and vice versa.
If someone is funny or quiet then mary is not calm and vice versa.
Everyone who is either kind or not wise is either rich or kind and vice versa.
If mary is both generous and not brave then lucy is wise or quiet.
Everyone who is brave or creative is patient or not strong and vice versa.
Everyone who is both not old and creative is both happy and not old and vice versa.
If susan is either humble or not tall then someone is both wise and not brave and vice versa.
Everyone who is wise is generous and vice versa.
If fred is not quiet then john is rich.
Everyone who is both not calm and not curious is both not kind and happy and vice versa.
If fred is not strong or humble then someone is not funny or not quiet.
If someone is not strong or not old then someone is either not humble or quiet.
Everyone who is patient is not patient.
Someone is either wise or brave.
Alice is rich or not wise.
Someone is either not happy or not kind.
Someone is old or patient.
Someone is creative or humble.
Mary is either kind or happy.
Mary is creative. | John is patient. | contradiction | (![X]:((patient(X)<~>~humble(X))<=>(~kind(X)|~creative(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~kind(X)&~brave(X))))&
(((old(john)|calm(john)))<=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:((strong(X)|wise(X))))<=>((~tall(fred)|~patient(fred))))&
((?[X]:((funny(X)|quiet(X))))<=>(~calm(mary)))&
(![X]:((kind(X)<~>~wise(X))<=>(rich(X)<~>kind(X))))&
(((generous(mary)&~brave(mary)))=>((wise(lucy)|quiet(lucy))))&
(![X]:((brave(X)|creative(X))<=>(patient(X)|~strong(X))))&
(![X]:((~old(X)&creative(X))<=>(happy(X)&~old(X))))&
(((humble(susan)<~>~tall(susan)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(wise(X)<=>generous(X)))&
((~quiet(fred))=>(rich(john)))&
(![X]:((~calm(X)&~curious(X))<=>(~kind(X)&happy(X))))&
(((~strong(fred)|humble(fred)))=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(patient(X)=>~patient(X)))&
(?[X]:((wise(X)<~>brave(X))))&
((rich(alice)|~wise(alice)))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((creative(X)|humble(X))))&
((kind(mary)<~>happy(mary)))&
(creative(mary)) | patient(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8062609828489364220538584
% SZS output start Proof for 8062609828489364220538584
16. ! [X0] : (patient(X0) => ~patient(X0)) [input p15]
24. patient(john) [input hypothesis]
32. ! [X0] : (~patient(X0) | ~patient(X0)) [ennf transformation 16]
136. ~patient(X0) | ~patient(X0) [cnf transformation 32]
147. patient(john) [cnf transformation 24]
148. ~patient(X0) [duplicate literal removal 136]
353. $false [subsumption resolution 147,148]
% SZS output end Proof for 8062609828489364220538584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is rich and vice versa.
Everyone who is not brave is strong.
Everyone who is not patient is not creative or not wise.
If someone is creative or tall then someone is curious or brave.
Everyone who is generous or kind is not brave and vice versa.
Everyone who is both not brave and humble is not wise and vice versa.
If someone is both rich and quiet then susan is either strong or not strong.
If someone is both not calm and tall then lucy is both not humble and not kind and vice versa.
If lucy is not wise then someone is not quiet and vice versa.
If alice is either old or tall then someone is not funny or kind.
Everyone who is not old is either calm or not happy and vice versa.
If paul is not strong or not brave then alice is both not tall and humble and vice versa.
Everyone who is either old or not rich is either not funny or not brave and vice versa.
Everyone who is both brave and not generous is not curious and vice versa.
If someone is both not old and old then someone is funny or creative and vice versa.
If susan is brave or not wise then paul is either not wise or tall and vice versa.
Someone is both patient and not creative.
John is either curious or funny.
Someone is quiet or not funny.
Someone is not patient.
Susan is quiet or not strong.
Mary is generous. | Lucy is not quiet. | neutral | (![X]:(tall(X)<=>rich(X)))&
(![X]:(~brave(X)=>strong(X)))&
(![X]:(~patient(X)=>(~creative(X)|~wise(X))))&
((?[X]:((creative(X)|tall(X))))=>(?[X]:((curious(X)|brave(X)))))&
(![X]:((generous(X)|kind(X))<=>~brave(X)))&
(![X]:((~brave(X)&humble(X))<=>~wise(X)))&
((?[X]:((rich(X)&quiet(X))))=>((strong(susan)<~>~strong(susan))))&
((?[X]:((~calm(X)&tall(X))))<=>((~humble(lucy)&~kind(lucy))))&
((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(((old(alice)<~>tall(alice)))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:(~old(X)<=>(calm(X)<~>~happy(X))))&
(((~strong(paul)|~brave(paul)))<=>((~tall(alice)&humble(alice))))&
(![X]:((old(X)<~>~rich(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:((brave(X)&~generous(X))<=>~curious(X)))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(((brave(susan)|~wise(susan)))<=>((~wise(paul)<~>tall(paul))))&
(?[X]:((patient(X)&~creative(X))))&
((curious(john)<~>funny(john)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:(~patient(X)))&
((quiet(susan)|~strong(susan)))&
(generous(mary)) | ~quiet(lucy) | [] | null | 0 |
If someone is not tall then someone is funny.
Everyone who is not calm is both rich and old.
Everyone who is not old is not happy.
Everyone who is strong or not curious is old.
If someone is both wise and not generous then lucy is not patient or not quiet and vice versa.
Everyone who is not calm or not humble is both not kind and tall.
Everyone who is humble or not generous is not rich or not tall.
Everyone who is not tall or calm is either not patient or humble and vice versa.
Everyone who is both not happy and not old is tall and vice versa.
Everyone who is either creative or rich is generous or not rich and vice versa.
If someone is not humble or not wise then someone is quiet.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
Someone is both not patient and brave.
Fred is not tall.
Paul is both calm and strong.
Fred is either strong or not generous.
Someone is rich or not kind.
Someone is either not rich or happy.
Paul is patient or tall. | Lucy is not old. | contradiction | ((?[X]:(~tall(X)))=>(?[X]:(funny(X))))&
(![X]:(~calm(X)=>(rich(X)&old(X))))&
(![X]:(~old(X)=>~happy(X)))&
(![X]:((strong(X)|~curious(X))=>old(X)))&
((?[X]:((wise(X)&~generous(X))))<=>((~patient(lucy)|~quiet(lucy))))&
(![X]:((~calm(X)|~humble(X))=>(~kind(X)&tall(X))))&
(![X]:((humble(X)|~generous(X))=>(~rich(X)|~tall(X))))&
(![X]:((~tall(X)|calm(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((~happy(X)&~old(X))<=>tall(X)))&
(![X]:((creative(X)<~>rich(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(?[X]:((~patient(X)&brave(X))))&
(~tall(fred))&
((calm(paul)&strong(paul)))&
((strong(fred)<~>~generous(fred)))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
((patient(paul)|tall(paul))) | ~old(lucy) | [
"p2",
"p3",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7624858791130894822585573
% SZS output start Proof for 7624858791130894822585573
3. ! [X0] : (~old(X0) => ~happy(X0)) [input p2]
4. ! [X0] : ((~curious(X0) | strong(X0)) => old(X0)) [input p3]
14. (~brave(lucy) & happy(lucy)) <=> ? [X0] : (~calm(X0) | ~rich(X0)) [input p13]
16. ! [X0] : (old(X0) <=> ~rich(X0)) [input p15]
19. strong(paul) & calm(paul) [input p18]
24. ~old(lucy) [input hypothesis]
29. ! [X0] : (strong(X0) => old(X0)) [pure predicate removal 4]
32. ! [X0] : (~happy(X0) | old(X0)) [ennf transformation 3]
33. ! [X0] : (old(X0) | ~strong(X0)) [ennf transformation 29]
63. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | (brave(lucy) | ~happy(lucy))) [nnf transformation 14]
64. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | brave(lucy) | ~happy(lucy)) [flattening 63]
65. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X1] : (~calm(X1) | ~rich(X1)) | brave(lucy) | ~happy(lucy)) [rectify 64]
66. ? [X1] : (~calm(X1) | ~rich(X1)) => (~calm(sK4) | ~rich(sK4)) [choice axiom]
67. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & ((~calm(sK4) | ~rich(sK4)) | brave(lucy) | ~happy(lucy)) [skolemisation 65,66]
72. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 16]
83. ~happy(X0) | old(X0) [cnf transformation 32]
84. ~strong(X0) | old(X0) [cnf transformation 33]
121. happy(lucy) | rich(X0) [cnf transformation 67]
127. ~old(X0) | ~rich(X0) [cnf transformation 72]
133. strong(paul) [cnf transformation 19]
140. ~old(lucy) [cnf transformation 24]
232. 20 <=> ! [X0] : rich(X0) [avatar definition]
233. rich(X0) <- (20) [avatar component clause 232]
236. 21 <=> happy(lucy) [avatar definition]
238. happy(lucy) <- (21) [avatar component clause 236]
240. 20 | 21 [avatar split clause 121,236,232]
300. old(lucy) <- (21) [resolution 83,238]
301. $false <- (21) [subsumption resolution 300,140]
302. ~21 [avatar contradiction clause 301]
304. old(paul) [resolution 84,133]
313. ~rich(paul) [resolution 127,304]
316. $false <- (20) [subsumption resolution 313,233]
317. ~20 [avatar contradiction clause 316]
318. $false [avatar sat refutation 240,302,317]
% SZS output end Proof for 7624858791130894822585573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is funny then alice is not rich.
Everyone who is generous is both curious and funny.
Everyone who is generous is both not tall and quiet and vice versa.
If someone is both funny and not wise then someone is funny.
Everyone who is kind is not creative or happy and vice versa.
If someone is both curious and not creative then john is either wise or not generous.
If someone is not funny then someone is kind.
Everyone who is not humble or tall is patient or not patient and vice versa.
If someone is not funny then someone is wise or creative.
Everyone who is either wise or humble is both not calm and not curious and vice versa.
If john is not kind then someone is both wise and patient.
Everyone who is both creative and not happy is not kind or not curious and vice versa.
Everyone who is rich is both not humble and patient.
If paul is not happy or curious then someone is either quiet or curious.
If someone is both creative and happy then someone is patient and vice versa.
Everyone who is not brave or kind is both not creative and not patient.
Someone is not brave or not curious.
Someone is either not curious or not funny.
Alice is not kind or rich.
Lucy is not humble or not funny.
Someone is humble.
Someone is both happy and not funny.
Fred is wise. | John is not brave. | neutral | ((funny(alice))=>(~rich(alice)))&
(![X]:(generous(X)=>(curious(X)&funny(X))))&
(![X]:(generous(X)<=>(~tall(X)&quiet(X))))&
((?[X]:((funny(X)&~wise(X))))=>(?[X]:(funny(X))))&
(![X]:(kind(X)<=>(~creative(X)|happy(X))))&
((?[X]:((curious(X)&~creative(X))))=>((wise(john)<~>~generous(john))))&
((?[X]:(~funny(X)))=>(?[X]:(kind(X))))&
(![X]:((~humble(X)|tall(X))<=>(patient(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
((~kind(john))=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((creative(X)&~happy(X))<=>(~kind(X)|~curious(X))))&
(![X]:(rich(X)=>(~humble(X)&patient(X))))&
(((~happy(paul)|curious(paul)))=>(?[X]:((quiet(X)<~>curious(X)))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:(patient(X))))&
(![X]:((~brave(X)|kind(X))=>(~creative(X)&~patient(X))))&
(?[X]:((~brave(X)|~curious(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~kind(alice)|rich(alice)))&
((~humble(lucy)|~funny(lucy)))&
(?[X]:(humble(X)))&
(?[X]:((happy(X)&~funny(X))))&
(wise(fred)) | ~brave(john) | [] | null | 0 |
Everyone who is both not wise and generous is either not generous or not old.
If someone is tall or funny then paul is humble or happy.
Everyone who is not wise or wise is both not tall and curious.
If someone is either tall or not strong then alice is not patient.
If someone is quiet then someone is kind and vice versa.
If john is patient then fred is rich or quiet and vice versa.
Everyone who is both strong and not wise is both not curious and brave and vice versa.
Everyone who is patient is humble and vice versa.
Everyone who is either not rich or humble is either not wise or generous.
Everyone who is creative or curious is quiet or brave.
If mary is either quiet or generous then alice is generous or rich and vice versa.
Everyone who is not old or old is both not generous and happy and vice versa.
Everyone who is both not calm and not strong is not kind.
Everyone who is not old or not rich is either not tall or not humble and vice versa.
Everyone who is quiet or strong is wise or happy and vice versa.
Paul is either patient or not wise.
Mary is either not rich or not old.
Someone is either old or not calm.
Someone is not generous or not curious.
Paul is either curious or not creative.
Someone is strong. | Alice is not strong. | neutral | (![X]:((~wise(X)&generous(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((tall(X)|funny(X))))=>((humble(paul)|happy(paul))))&
(![X]:((~wise(X)|wise(X))=>(~tall(X)&curious(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>(~patient(alice)))&
((?[X]:(quiet(X)))<=>(?[X]:(kind(X))))&
((patient(john))<=>((rich(fred)|quiet(fred))))&
(![X]:((strong(X)&~wise(X))<=>(~curious(X)&brave(X))))&
(![X]:(patient(X)<=>humble(X)))&
(![X]:((~rich(X)<~>humble(X))=>(~wise(X)<~>generous(X))))&
(![X]:((creative(X)|curious(X))=>(quiet(X)|brave(X))))&
(((quiet(mary)<~>generous(mary)))<=>((generous(alice)|rich(alice))))&
(![X]:((~old(X)|old(X))<=>(~generous(X)&happy(X))))&
(![X]:((~calm(X)&~strong(X))=>~kind(X)))&
(![X]:((~old(X)|~rich(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((quiet(X)|strong(X))<=>(wise(X)|happy(X))))&
((patient(paul)<~>~wise(paul)))&
((~rich(mary)<~>~old(mary)))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~generous(X)|~curious(X))))&
((curious(paul)<~>~creative(paul)))&
(?[X]:(strong(X))) | ~strong(alice) | [] | null | 0 |
Everyone who is not calm or brave is either not funny or happy and vice versa.
Everyone who is not tall or not quiet is generous and vice versa.
Everyone who is not funny or not strong is wise and vice versa.
Everyone who is either not humble or happy is not generous.
Everyone who is both not curious and not kind is both not humble and not happy and vice versa.
Everyone who is not humble is kind.
If mary is not humble or calm then john is curious.
Everyone who is both patient and wise is both kind and calm.
If someone is both brave and not patient then susan is generous or not generous and vice versa.
If john is not rich then someone is creative and vice versa.
If john is not wise or generous then paul is either generous or not generous and vice versa.
Everyone who is strong is both tall and not generous and vice versa.
Everyone who is either not creative or old is both not tall and patient and vice versa.
Everyone who is quiet or not quiet is either not rich or old and vice versa.
If lucy is not creative then alice is curious or generous.
Everyone who is quiet or not old is not patient or not strong.
Fred is funny.
Someone is both generous and not quiet.
Someone is either quiet or not strong.
Lucy is not strong or calm.
Someone is either calm or curious.
Lucy is strong or not generous.
Susan is generous. | Fred is not brave. | neutral | (![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~funny(X)|~strong(X))<=>wise(X)))&
(![X]:((~humble(X)<~>happy(X))=>~generous(X)))&
(![X]:((~curious(X)&~kind(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~humble(mary)|calm(mary)))=>(curious(john)))&
(![X]:((patient(X)&wise(X))=>(kind(X)&calm(X))))&
((?[X]:((brave(X)&~patient(X))))<=>((generous(susan)|~generous(susan))))&
((~rich(john))<=>(?[X]:(creative(X))))&
(((~wise(john)|generous(john)))<=>((generous(paul)<~>~generous(paul))))&
(![X]:(strong(X)<=>(tall(X)&~generous(X))))&
(![X]:((~creative(X)<~>old(X))<=>(~tall(X)&patient(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)<~>old(X))))&
((~creative(lucy))=>((curious(alice)|generous(alice))))&
(![X]:((quiet(X)|~old(X))=>(~patient(X)|~strong(X))))&
(funny(fred))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
((~strong(lucy)|calm(lucy)))&
(?[X]:((calm(X)<~>curious(X))))&
((strong(lucy)|~generous(lucy)))&
(generous(susan)) | ~brave(fred) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is rich is not kind and vice versa.
If someone is not brave or not happy then someone is both creative and not humble.
If mary is not curious or generous then someone is either creative or not calm and vice versa.
If someone is either curious or creative then susan is either calm or creative.
If mary is generous then someone is not brave or not patient and vice versa.
Everyone who is either not wise or not happy is kind or patient and vice versa.
Everyone who is either not tall or not calm is not rich.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Someone is quiet or not funny.
Someone is not patient or patient.
Lucy is strong.
Someone is wise.
Lucy is both not humble and generous.
John is not brave or creative.
Someone is either old or not patient.
Mary is brave or curious. | Lucy is happy. | contradiction | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(rich(X)<=>~kind(X)))&
((?[X]:((~brave(X)|~happy(X))))=>(?[X]:((creative(X)&~humble(X)))))&
(((~curious(mary)|generous(mary)))<=>(?[X]:((creative(X)<~>~calm(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>((calm(susan)<~>creative(susan))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((~patient(X)|patient(X))))&
(strong(lucy))&
(?[X]:(wise(X)))&
((~humble(lucy)&generous(lucy)))&
((~brave(john)|creative(john)))&
(?[X]:((old(X)<~>~patient(X))))&
((brave(mary)|curious(mary))) | happy(lucy) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1755475320924736218661044
% SZS output start Proof for 1755475320924736218661044
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
15. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p14]
24. happy(lucy) [input hypothesis]
43. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
44. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 43]
67. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 15]
68. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 67]
77. ~happy(X0) | ~curious(X0) [cnf transformation 44]
115. curious(X0) | curious(X0) [cnf transformation 68]
126. happy(lucy) [cnf transformation 24]
127. curious(X0) [duplicate literal removal 115]
257. ~curious(lucy) [resolution 77,126]
258. $false [subsumption resolution 257,127]
% SZS output end Proof for 1755475320924736218661044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or happy then someone is happy. Everyone who is happy or calm is not old and vice versa. Everyone who is both curious and not patient is not kind or not generous and vice versa. If lucy is both not rich and not old then john is either not quiet or generous and vice versa. If someone is not curious or not brave then alice is both not brave and not quiet and vice versa. Everyone who is not kind is both wise and not happy. If alice is brave or not strong then john is either not tall or curious and vice versa. If someone is either humble or wise then someone is strong or not kind and vice versa. Everyone who is either not funny or not creative is both not patient and calm. If paul is not funny or rich then lucy is quiet or not kind. If someone is either not humble or not generous then someone is both rich and not creative and vice versa. Everyone who is not rich is both not calm and not generous and vice versa. Everyone who is not generous is both old and funny. Everyone who is either kind or calm is either not happy or strong. If someone is either not quiet or patient then someone is both old and not creative and vice versa. Everyone who is both rich and not brave is either not rich or not funny and vice versa. Paul is not calm or quiet. Someone is either kind or not old. Someone is not quiet. Someone is not calm or not quiet. Lucy is both patient and rich. Someone is not funny or generous. | Alice is strong. | neutral | ((?[X]:((~happy(X)|happy(X))))=>(?[X]:(happy(X))))&
(![X]:((happy(X)|calm(X))<=>~old(X)))&
(![X]:((curious(X)&~patient(X))<=>(~kind(X)|~generous(X))))&
(((~rich(lucy)&~old(lucy)))<=>((~quiet(john)<~>generous(john))))&
((?[X]:((~curious(X)|~brave(X))))<=>((~brave(alice)&~quiet(alice))))&
(![X]:(~kind(X)=>(wise(X)&~happy(X))))&
(((brave(alice)|~strong(alice)))<=>((~tall(john)<~>curious(john))))&
((?[X]:((humble(X)<~>wise(X))))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~patient(X)&calm(X))))&
(((~funny(paul)|rich(paul)))=>((quiet(lucy)|~kind(lucy))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(~rich(X)<=>(~calm(X)&~generous(X))))&
(![X]:(~generous(X)=>(old(X)&funny(X))))&
(![X]:((kind(X)<~>calm(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((~calm(paul)|quiet(paul)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
((patient(lucy)&rich(lucy)))&
(?[X]:((~funny(X)|generous(X)))) | strong(alice) | [] | null | 0 |
Everyone who is happy or brave is curious.
Everyone who is tall is both quiet and not kind and vice versa.
Everyone who is not strong or kind is not old and vice versa.
If fred is creative then someone is either not rich or funny.
Everyone who is not happy or rich is not kind and vice versa.
If someone is both not quiet and quiet then someone is both calm and not old.
Everyone who is not creative is not kind or not patient and vice versa.
If someone is both happy and not wise then someone is not calm.
If someone is happy then mary is both curious and strong and vice versa.
Everyone who is not strong or kind is both not kind and kind and vice versa.
If mary is either not humble or not brave then john is either kind or humble.
Everyone who is either not wise or not generous is both not calm and strong and vice versa.
If john is wise then paul is both not humble and wise.
If john is not quiet then someone is both generous and calm and vice versa.
If alice is wise then someone is both not rich and not generous and vice versa.
If someone is tall or creative then someone is either brave or not calm and vice versa.
Paul is either happy or not patient.
Someone is both not patient and calm.
Someone is not kind.
Someone is both quiet and wise.
Lucy is either strong or happy.
Mary is not kind.
Someone is strong or patient.
John is not curious or not generous. | Fred is strong. | entailment | (![X]:((happy(X)|brave(X))=>curious(X)))&
(![X]:(tall(X)<=>(quiet(X)&~kind(X))))&
(![X]:((~strong(X)|kind(X))<=>~old(X)))&
((creative(fred))=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((~happy(X)|rich(X))<=>~kind(X)))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:((calm(X)&~old(X)))))&
(![X]:(~creative(X)<=>(~kind(X)|~patient(X))))&
((?[X]:((happy(X)&~wise(X))))=>(?[X]:(~calm(X))))&
((?[X]:(happy(X)))<=>((curious(mary)&strong(mary))))&
(![X]:((~strong(X)|kind(X))<=>(~kind(X)&kind(X))))&
(((~humble(mary)<~>~brave(mary)))=>((kind(john)<~>humble(john))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~calm(X)&strong(X))))&
((wise(john))=>((~humble(paul)&wise(paul))))&
((~quiet(john))<=>(?[X]:((generous(X)&calm(X)))))&
((wise(alice))<=>(?[X]:((~rich(X)&~generous(X)))))&
((?[X]:((tall(X)|creative(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
((happy(paul)<~>~patient(paul)))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)&wise(X))))&
((strong(lucy)<~>happy(lucy)))&
(~kind(mary))&
(?[X]:((strong(X)|patient(X))))&
((~curious(john)|~generous(john))) | strong(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1000126760429271851987976
% SZS output start Proof for 1000126760429271851987976
10. ! [X0] : ((kind(X0) | ~strong(X0)) <=> (kind(X0) & ~kind(X0))) [input p9]
25. ~strong(fred) [input hypothesis]
58. ! [X0] : (((kind(X0) | ~strong(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (~kind(X0) & strong(X0)))) [nnf transformation 10]
59. ! [X0] : ((kind(X0) | ~strong(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | (~kind(X0) & strong(X0)))) [flattening 58]
107. ~kind(X0) | ~kind(X0) [cnf transformation 59]
108. strong(X0) | kind(X0) [cnf transformation 59]
147. ~strong(fred) [cnf transformation 25]
148. ~kind(X0) [duplicate literal removal 107]
330. kind(fred) [resolution 108,147]
331. $false [subsumption resolution 330,148]
% SZS output end Proof for 1000126760429271851987976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or calm is both not wise and not kind and vice versa. Everyone who is quiet is not humble or kind. Everyone who is either not brave or not strong is either tall or creative. Everyone who is both not tall and not humble is both not humble and generous. If lucy is kind then paul is either happy or curious. If someone is not humble or brave then someone is both wise and calm and vice versa. If someone is old then fred is either strong or not tall. If someone is both brave and quiet then someone is not tall and vice versa. Everyone who is both tall and not wise is generous and vice versa. Everyone who is either not strong or not kind is not wise or not patient and vice versa. Everyone who is either not happy or old is either not calm or brave and vice versa. If someone is either old or humble then alice is not brave or kind and vice versa. Everyone who is rich is either not curious or quiet. If paul is quiet or patient then paul is not brave or patient and vice versa. Everyone who is both funny and generous is happy and vice versa. Everyone who is humble or not creative is calm. Mary is kind or not wise. Susan is not strong or not rich. Someone is not wise. Someone is not generous or humble. Susan is either not calm or not patient. John is either quiet or happy. Someone is curious or brave. Someone is not curious. | Alice is not generous. | contradiction | (![X]:((kind(X)|calm(X))<=>(~wise(X)&~kind(X))))&
(![X]:(quiet(X)=>(~humble(X)|kind(X))))&
(![X]:((~brave(X)<~>~strong(X))=>(tall(X)<~>creative(X))))&
(![X]:((~tall(X)&~humble(X))=>(~humble(X)&generous(X))))&
((kind(lucy))=>((happy(paul)<~>curious(paul))))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:(old(X)))=>((strong(fred)<~>~tall(fred))))&
((?[X]:((brave(X)&quiet(X))))<=>(?[X]:(~tall(X))))&
(![X]:((tall(X)&~wise(X))<=>generous(X)))&
(![X]:((~strong(X)<~>~kind(X))<=>(~wise(X)|~patient(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:((old(X)<~>humble(X))))<=>((~brave(alice)|kind(alice))))&
(![X]:(rich(X)=>(~curious(X)<~>quiet(X))))&
(((quiet(paul)|patient(paul)))<=>((~brave(paul)|patient(paul))))&
(![X]:((funny(X)&generous(X))<=>happy(X)))&
(![X]:((humble(X)|~creative(X))=>calm(X)))&
((kind(mary)|~wise(mary)))&
((~strong(susan)|~rich(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((~generous(X)|humble(X))))&
((~calm(susan)<~>~patient(susan)))&
((quiet(john)<~>happy(john)))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:(~curious(X))) | ~generous(alice) | [
"p0",
"p1",
"p5",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7787041544268348602622704
% SZS output start Proof for 7787041544268348602622704
1. ! [X0] : ((calm(X0) | kind(X0)) <=> (~kind(X0) & ~wise(X0))) [input p0]
2. ! [X0] : (quiet(X0) => (kind(X0) | ~humble(X0))) [input p1]
6. ? [X0] : (brave(X0) | ~humble(X0)) <=> ? [X0] : (calm(X0) & wise(X0)) [input p5]
8. ? [X0] : (quiet(X0) & brave(X0)) <=> ? [X0] : ~tall(X0) [input p7]
9. ! [X0] : ((~wise(X0) & tall(X0)) <=> generous(X0)) [input p8]
16. ! [X0] : ((~creative(X0) | humble(X0)) => calm(X0)) [input p15]
25. ~generous(alice) [input hypothesis]
26. ? [X0] : (brave(X0) | ~humble(X0)) <=> ? [X1] : (calm(X1) & wise(X1)) [rectify 6]
27. ? [X0] : (quiet(X0) & brave(X0)) <=> ? [X1] : ~tall(X1) [rectify 8]
30. ! [X0] : ((kind(X0) | ~humble(X0)) | ~quiet(X0)) [ennf transformation 2]
31. ! [X0] : (kind(X0) | ~humble(X0) | ~quiet(X0)) [flattening 30]
37. ! [X0] : (calm(X0) | (creative(X0) & ~humble(X0))) [ennf transformation 16]
38. ! [X0] : (((calm(X0) | kind(X0)) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 1]
39. ! [X0] : ((calm(X0) | kind(X0) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 38]
42. (? [X0] : (brave(X0) | ~humble(X0)) | ! [X1] : (~calm(X1) | ~wise(X1))) & (? [X1] : (calm(X1) & wise(X1)) | ! [X0] : (~brave(X0) & humble(X0))) [nnf transformation 26]
43. (? [X0] : (brave(X0) | ~humble(X0)) | ! [X1] : (~calm(X1) | ~wise(X1))) & (? [X2] : (calm(X2) & wise(X2)) | ! [X3] : (~brave(X3) & humble(X3))) [rectify 42]
44. ? [X0] : (brave(X0) | ~humble(X0)) => (brave(sK0) | ~humble(sK0)) [choice axiom]
45. ? [X2] : (calm(X2) & wise(X2)) => (calm(sK1) & wise(sK1)) [choice axiom]
46. ((brave(sK0) | ~humble(sK0)) | ! [X1] : (~calm(X1) | ~wise(X1))) & ((calm(sK1) & wise(sK1)) | ! [X3] : (~brave(X3) & humble(X3))) [skolemisation 43,45,44]
48. (? [X0] : (quiet(X0) & brave(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (~quiet(X0) | ~brave(X0))) [nnf transformation 27]
49. (? [X0] : (quiet(X0) & brave(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (~quiet(X3) | ~brave(X3))) [rectify 48]
50. ? [X0] : (quiet(X0) & brave(X0)) => (quiet(sK2) & brave(sK2)) [choice axiom]
51. ? [X2] : ~tall(X2) => ~tall(sK3) [choice axiom]
52. ((quiet(sK2) & brave(sK2)) | ! [X1] : tall(X1)) & (~tall(sK3) | ! [X3] : (~quiet(X3) | ~brave(X3))) [skolemisation 49,51,50]
53. ! [X0] : (((~wise(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) | ~tall(X0)))) [nnf transformation 9]
54. ! [X0] : (((~wise(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | wise(X0) | ~tall(X0))) [flattening 53]
78. ~wise(X0) | ~calm(X0) [cnf transformation 39]
79. ~kind(X0) | ~kind(X0) [cnf transformation 39]
82. kind(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 31]
91. wise(sK1) | humble(X3) [cnf transformation 46]
93. calm(sK1) | humble(X3) [cnf transformation 46]
100. quiet(sK2) | tall(X1) [cnf transformation 52]
101. ~tall(X0) | wise(X0) | generous(X0) [cnf transformation 54]
131. ~humble(X0) | calm(X0) [cnf transformation 37]
142. ~generous(alice) [cnf transformation 25]
143. ~kind(X0) [duplicate literal removal 79]
145. ~humble(X0) | ~quiet(X0) [subsumption resolution 82,143]
150. 2 <=> calm(sK1) [avatar definition]
152. calm(sK1) <- (2) [avatar component clause 150]
155. 3 <=> ! [X3] : humble(X3) [avatar definition]
156. humble(X3) <- (3) [avatar component clause 155]
157. 3 | 2 [avatar split clause 93,150,155]
159. 4 <=> wise(sK1) [avatar definition]
161. wise(sK1) <- (4) [avatar component clause 159]
163. 3 | 4 [avatar split clause 91,159,155]
178. 8 <=> ! [X1] : tall(X1) [avatar definition]
179. tall(X1) <- (8) [avatar component clause 178]
181. 9 <=> quiet(sK2) [avatar definition]
183. quiet(sK2) <- (9) [avatar component clause 181]
184. 8 | 9 [avatar split clause 100,181,178]
284. ~calm(sK1) <- (4) [resolution 78,161]
285. $false <- (2, 4) [subsumption resolution 284,152]
286. ~2 | ~4 [avatar contradiction clause 285]
294. calm(X0) <- (3) [resolution 131,156]
298. ~quiet(X0) <- (3) [resolution 145,156]
300. $false <- (3, 9) [resolution 298,183]
305. ~3 | ~9 [avatar contradiction clause 300]
317. generous(X0) | wise(X0) <- (8) [resolution 101,179]
328. wise(alice) <- (8) [resolution 317,142]
355. ~calm(alice) <- (8) [resolution 328,78]
356. $false <- (3, 8) [subsumption resolution 355,294]
357. ~3 | ~8 [avatar contradiction clause 356]
358. $false [avatar sat refutation 157,163,184,286,305,357]
% SZS output end Proof for 7787041544268348602622704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not creative and generous then someone is both kind and not creative and vice versa. Everyone who is not patient or not funny is both not wise and not curious and vice versa. If someone is strong or not funny then someone is rich or not funny. Everyone who is not wise is not generous and vice versa. If john is both creative and humble then lucy is funny or not rich. If lucy is not quiet or kind then someone is both not patient and not curious and vice versa. Everyone who is not quiet or not happy is not curious. Everyone who is either not generous or not brave is either not calm or tall and vice versa. If someone is either not creative or not calm then someone is either quiet or not curious and vice versa. If someone is rich then someone is strong and vice versa. If susan is patient then someone is curious or not curious and vice versa. If susan is either brave or not wise then john is not kind and vice versa. Everyone who is not quiet is not rich. If susan is both creative and humble then john is not kind or not humble. Everyone who is humble is not patient or not calm. If susan is funny or brave then someone is both not quiet and not creative. Susan is both not old and not strong. Lucy is not humble or not kind. Lucy is not generous or old. Someone is not tall or patient. Paul is either kind or not generous. Paul is brave. Someone is both brave and not happy. Lucy is quiet or humble. | Susan is brave. | neutral | (((~creative(paul)&generous(paul)))<=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)&~curious(X))))&
((?[X]:((strong(X)|~funny(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:(~wise(X)<=>~generous(X)))&
(((creative(john)&humble(john)))=>((funny(lucy)|~rich(lucy))))&
(((~quiet(lucy)|kind(lucy)))<=>(?[X]:((~patient(X)&~curious(X)))))&
(![X]:((~quiet(X)|~happy(X))=>~curious(X)))&
(![X]:((~generous(X)<~>~brave(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:(rich(X)))<=>(?[X]:(strong(X))))&
((patient(susan))<=>(?[X]:((curious(X)|~curious(X)))))&
(((brave(susan)<~>~wise(susan)))<=>(~kind(john)))&
(![X]:(~quiet(X)=>~rich(X)))&
(((creative(susan)&humble(susan)))=>((~kind(john)|~humble(john))))&
(![X]:(humble(X)=>(~patient(X)|~calm(X))))&
(((funny(susan)|brave(susan)))=>(?[X]:((~quiet(X)&~creative(X)))))&
((~old(susan)&~strong(susan)))&
((~humble(lucy)|~kind(lucy)))&
((~generous(lucy)|old(lucy)))&
(?[X]:((~tall(X)|patient(X))))&
((kind(paul)<~>~generous(paul)))&
(brave(paul))&
(?[X]:((brave(X)&~happy(X))))&
((quiet(lucy)|humble(lucy))) | brave(susan) | [] | null | 0 |
If paul is either not happy or not kind then someone is either not creative or not calm.
If alice is funny then someone is not curious or rich and vice versa.
Everyone who is both happy and not patient is both not rich and quiet and vice versa.
If someone is not curious then someone is either not wise or not curious.
Everyone who is either brave or strong is either not strong or rich and vice versa.
Everyone who is both not wise and quiet is wise.
Everyone who is humble is both not funny and wise and vice versa.
Everyone who is both kind and humble is both not calm and creative.
If susan is not curious or not patient then john is not calm or not quiet and vice versa.
Everyone who is either not quiet or not old is both old and not kind and vice versa.
Everyone who is not happy is wise or funny and vice versa.
If someone is not calm or strong then someone is brave and vice versa.
Everyone who is not curious or kind is not generous and vice versa.
If fred is not curious then someone is not generous and vice versa.
If someone is either wise or not patient then fred is happy or calm.
If susan is not wise then mary is kind.
Susan is not brave or funny.
Paul is humble.
John is rich or brave.
Lucy is both not rich and brave.
Lucy is strong.
Someone is either brave or happy.
Fred is both brave and not tall. | Paul is not creative. | neutral | (((~happy(paul)<~>~kind(paul)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
((funny(alice))<=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~rich(X)&quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((brave(X)<~>strong(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~wise(X)&quiet(X))=>wise(X)))&
(![X]:(humble(X)<=>(~funny(X)&wise(X))))&
(![X]:((kind(X)&humble(X))=>(~calm(X)&creative(X))))&
(((~curious(susan)|~patient(susan)))<=>((~calm(john)|~quiet(john))))&
(![X]:((~quiet(X)<~>~old(X))<=>(old(X)&~kind(X))))&
(![X]:(~happy(X)<=>(wise(X)|funny(X))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)|kind(X))<=>~generous(X)))&
((~curious(fred))<=>(?[X]:(~generous(X))))&
((?[X]:((wise(X)<~>~patient(X))))=>((happy(fred)|calm(fred))))&
((~wise(susan))=>(kind(mary)))&
((~brave(susan)|funny(susan)))&
(humble(paul))&
((rich(john)|brave(john)))&
((~rich(lucy)&brave(lucy)))&
(strong(lucy))&
(?[X]:((brave(X)<~>happy(X))))&
((brave(fred)&~tall(fred))) | ~creative(paul) | [] | null | 0 |
Everyone who is rich or not calm is either quiet or not curious and vice versa. Everyone who is not calm is tall or rich and vice versa. If someone is old then someone is both strong and not happy. Everyone who is either not patient or not humble is patient and vice versa. Everyone who is strong or kind is either not wise or wise and vice versa. Everyone who is both not patient and not kind is either humble or not kind and vice versa. Everyone who is both not humble and calm is both funny and curious. If alice is both wise and humble then john is either rich or not kind and vice versa. If mary is either curious or calm then someone is both not curious and not creative and vice versa. If paul is not patient then john is not old. Everyone who is not tall or not humble is not kind. Everyone who is brave is either not funny or wise. If someone is patient or not humble then lucy is not generous or not creative and vice versa. If someone is kind or not humble then lucy is either strong or tall and vice versa. If someone is not strong or funny then someone is not humble or not happy and vice versa. Everyone who is strong or old is either not old or funny. Alice is either creative or curious. Someone is both not funny and not wise. Someone is not brave or not humble. Someone is either not patient or happy. Susan is strong. Fred is either creative or strong. Susan is either not wise or patient. Someone is either not old or not curious. | John is old. | contradiction | (![X]:((rich(X)|~calm(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(tall(X)|rich(X))))&
((?[X]:(old(X)))=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((~patient(X)<~>~humble(X))<=>patient(X)))&
(![X]:((strong(X)|kind(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((~patient(X)&~kind(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((~humble(X)&calm(X))=>(funny(X)&curious(X))))&
(((wise(alice)&humble(alice)))<=>((rich(john)<~>~kind(john))))&
(((curious(mary)<~>calm(mary)))<=>(?[X]:((~curious(X)&~creative(X)))))&
((~patient(paul))=>(~old(john)))&
(![X]:((~tall(X)|~humble(X))=>~kind(X)))&
(![X]:(brave(X)=>(~funny(X)<~>wise(X))))&
((?[X]:((patient(X)|~humble(X))))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:((kind(X)|~humble(X))))<=>((strong(lucy)<~>tall(lucy))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((strong(X)|old(X))=>(~old(X)<~>funny(X))))&
((creative(alice)<~>curious(alice)))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((~brave(X)|~humble(X))))&
(?[X]:((~patient(X)<~>happy(X))))&
(strong(susan))&
((creative(fred)<~>strong(fred)))&
((~wise(susan)<~>patient(susan)))&
(?[X]:((~old(X)<~>~curious(X)))) | old(john) | [
"p3",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3518325775611375740207278
% SZS output start Proof for 3518325775611375740207278
4. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> patient(X0)) [input p3]
6. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> (humble(X0) <~> ~kind(X0))) [input p5]
10. ~patient(paul) => ~old(john) [input p9]
11. ! [X0] : ((~humble(X0) | ~tall(X0)) => ~kind(X0)) [input p10]
25. old(john) [input hypothesis]
33. ~old(john) | patient(paul) [ennf transformation 10]
34. ! [X0] : (~kind(X0) | (humble(X0) & tall(X0))) [ennf transformation 11]
43. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 4]
46. ! [X0] : (((~kind(X0) & ~patient(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (kind(X0) | patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((~kind(X0) & ~patient(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | kind(X0) | patient(X0))) [flattening 46]
91. patient(X0) | ~humble(X0) | patient(X0) [cnf transformation 43]
93. ~humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 43]
104. ~patient(X0) | humble(X0) | kind(X0) [cnf transformation 47]
121. ~old(john) | patient(paul) [cnf transformation 33]
123. ~kind(X0) | humble(X0) [cnf transformation 34]
155. old(john) [cnf transformation 25]
161. patient(X0) | ~humble(X0) [duplicate literal removal 91]
162. ~humble(X0) | ~patient(X0) [duplicate literal removal 93]
176. ~humble(X0) [subsumption resolution 161,162]
178. ~patient(X0) | kind(X0) [subsumption resolution 104,176]
225. 12 <=> patient(paul) [avatar definition]
227. patient(paul) <- (12) [avatar component clause 225]
229. 13 <=> old(john) [avatar definition]
232. 12 | ~13 [avatar split clause 121,229,225]
233. ~kind(X0) [subsumption resolution 123,176]
324. 13 [avatar split clause 155,229]
334. kind(paul) <- (12) [resolution 178,227]
335. $false <- (12) [subsumption resolution 334,233]
336. ~12 [avatar contradiction clause 335]
337. $false [avatar sat refutation 232,324,336]
% SZS output end Proof for 3518325775611375740207278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and generous is funny or rich and vice versa. If someone is generous or humble then lucy is either not wise or strong and vice versa. Everyone who is both not curious and not brave is either not patient or not brave and vice versa. If someone is not calm or not patient then someone is old. If john is not funny then someone is either not brave or funny. Everyone who is wise is either creative or not happy and vice versa. Everyone who is both not rich and not curious is not generous or tall and vice versa. Everyone who is both not curious and not kind is not creative or not strong and vice versa. Everyone who is not quiet or not wise is either not wise or funny. Everyone who is both not tall and rich is rich. If someone is either not humble or not quiet then someone is not funny or not old. Everyone who is not calm is creative and vice versa. Everyone who is not funny or not old is either not quiet or not patient. Everyone who is not patient or not creative is not wise. If someone is curious or not curious then alice is not humble and vice versa. Everyone who is both happy and kind is old and vice versa. Lucy is both humble and not creative. Fred is strong. Someone is not kind or funny. Someone is not humble or not rich. Mary is not wise or not creative. Alice is either not wise or not tall. Someone is not old. | Alice is not quiet. | entailment | (![X]:((~patient(X)&generous(X))<=>(funny(X)|rich(X))))&
((?[X]:((generous(X)|humble(X))))<=>((~wise(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)&~brave(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:((~calm(X)|~patient(X))))=>(?[X]:(old(X))))&
((~funny(john))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:(wise(X)<=>(creative(X)<~>~happy(X))))&
(![X]:((~rich(X)&~curious(X))<=>(~generous(X)|tall(X))))&
(![X]:((~curious(X)&~kind(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~quiet(X)|~wise(X))=>(~wise(X)<~>funny(X))))&
(![X]:((~tall(X)&rich(X))=>rich(X)))&
((?[X]:((~humble(X)<~>~quiet(X))))=>(?[X]:((~funny(X)|~old(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
(![X]:((~funny(X)|~old(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((~patient(X)|~creative(X))=>~wise(X)))&
((?[X]:((curious(X)|~curious(X))))<=>(~humble(alice)))&
(![X]:((happy(X)&kind(X))<=>old(X)))&
((humble(lucy)&~creative(lucy)))&
(strong(fred))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:((~humble(X)|~rich(X))))&
((~wise(mary)|~creative(mary)))&
((~wise(alice)<~>~tall(alice)))&
(?[X]:(~old(X))) | ~quiet(alice) | [
"p0",
"p2",
"p6",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7948987496646685841683081
% SZS output start Proof for 7948987496646685841683081
1. ! [X0] : ((generous(X0) & ~patient(X0)) <=> (rich(X0) | funny(X0))) [input p0]
3. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~patient(X0) <~> ~brave(X0))) [input p2]
7. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (tall(X0) | ~generous(X0))) [input p6]
13. ! [X0] : ((~old(X0) | ~funny(X0)) => (~quiet(X0) <~> ~patient(X0))) [input p12]
14. ! [X0] : ((~creative(X0) | ~patient(X0)) => ~wise(X0)) [input p13]
22. ~wise(alice) <~> ~tall(alice) [input p21]
24. quiet(alice) [input hypothesis]
35. ! [X0] : ((~quiet(X0) <~> ~patient(X0)) | (old(X0) & funny(X0))) [ennf transformation 13]
36. ! [X0] : (~wise(X0) | (creative(X0) & patient(X0))) [ennf transformation 14]
37. ! [X0] : (((generous(X0) & ~patient(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~generous(X0) | patient(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & ~patient(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~generous(X0) | patient(X0))) [flattening 37]
43. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) | curious(X0)))) [nnf transformation 3]
44. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | brave(X0) | curious(X0))) [flattening 43]
52. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (curious(X0) | rich(X0)))) [nnf transformation 7]
53. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | curious(X0) | rich(X0))) [flattening 52]
61. ! [X0] : (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | (old(X0) & funny(X0))) [nnf transformation 35]
72. (tall(alice) | wise(alice)) & (~tall(alice) | ~wise(alice)) [nnf transformation 22]
76. ~funny(X0) | ~patient(X0) [cnf transformation 38]
87. brave(X0) | patient(X0) | brave(X0) | curious(X0) [cnf transformation 44]
90. ~brave(X0) | ~brave(X0) | patient(X0) [cnf transformation 44]
104. ~tall(X0) | ~curious(X0) [cnf transformation 53]
118. ~patient(X0) | ~quiet(X0) | funny(X0) [cnf transformation 61]
122. ~wise(X0) | patient(X0) [cnf transformation 36]
137. tall(alice) | wise(alice) [cnf transformation 72]
139. quiet(alice) [cnf transformation 24]
141. brave(X0) | patient(X0) | curious(X0) [duplicate literal removal 87]
142. ~brave(X0) | patient(X0) [duplicate literal removal 90]
171. curious(X0) | patient(X0) [subsumption resolution 141,142]
214. ~quiet(X0) | ~patient(X0) [subsumption resolution 118,76]
247. 24 <=> wise(alice) [avatar definition]
249. wise(alice) <- (24) [avatar component clause 247]
251. 25 <=> tall(alice) [avatar definition]
253. tall(alice) <- (25) [avatar component clause 251]
254. 24 | 25 [avatar split clause 137,251,247]
256. patient(alice) <- (24) [resolution 122,249]
266. ~patient(alice) [resolution 214,139]
267. $false <- (24) [subsumption resolution 266,256]
268. ~24 [avatar contradiction clause 267]
269. ~curious(alice) <- (25) [resolution 253,104]
272. patient(alice) <- (25) [resolution 269,171]
273. $false <- (25) [subsumption resolution 272,266]
274. ~25 [avatar contradiction clause 273]
275. $false [avatar sat refutation 254,268,274]
% SZS output end Proof for 7948987496646685841683081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or creative then someone is either not patient or old.
Everyone who is brave is not tall or generous and vice versa.
Everyone who is generous or calm is either happy or tall.
If someone is either not curious or rich then paul is creative or not curious and vice versa.
Everyone who is either creative or old is not patient or quiet.
If susan is curious or not generous then fred is both not patient and tall and vice versa.
Everyone who is either not generous or not happy is either not creative or brave and vice versa.
Everyone who is calm or rich is both not creative and not strong and vice versa.
Everyone who is not old or not generous is both happy and wise.
If someone is either kind or not kind then mary is either generous or not wise and vice versa.
Everyone who is either not patient or not funny is either creative or calm and vice versa.
If alice is either not wise or patient then john is not generous or not calm and vice versa.
Everyone who is either not patient or creative is both kind and strong and vice versa.
Everyone who is either not happy or not generous is patient or humble and vice versa.
Everyone who is not quiet or kind is not kind or quiet.
Everyone who is funny or not brave is rich.
Someone is funny.
Fred is not old or not funny.
Someone is either not brave or quiet.
Susan is either not creative or curious.
John is both curious and not quiet.
Someone is not kind.
Fred is curious or quiet.
Lucy is not happy. | Lucy is patient. | entailment | ((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((generous(mary)<~>~wise(mary))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((funny(X)|~brave(X))=>rich(X)))&
(?[X]:(funny(X)))&
((~old(fred)|~funny(fred)))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~creative(susan)<~>curious(susan)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X)))&
((curious(fred)|quiet(fred)))&
(~happy(lucy)) | patient(lucy) | [
"p1",
"p6",
"p7",
"p8",
"p10",
"p12",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2100313235969135802817
% SZS output start Proof for 2100313235969135802817
2. ! [X0] : (brave(X0) <=> (generous(X0) | ~tall(X0))) [input p1]
7. ! [X0] : ((~generous(X0) <~> ~happy(X0)) <=> (~creative(X0) <~> brave(X0))) [input p6]
8. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((~generous(X0) | ~old(X0)) => (wise(X0) & happy(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p12]
16. ! [X0] : ((~brave(X0) | funny(X0)) => rich(X0)) [input p15]
24. ~happy(lucy) [input p23]
25. ~patient(lucy) [input hypothesis]
31. ! [X0] : ((wise(X0) & happy(X0)) | (generous(X0) & old(X0))) [ennf transformation 9]
34. ! [X0] : (rich(X0) | (brave(X0) & ~funny(X0))) [ennf transformation 16]
39. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~brave(X0))) [flattening 39]
50. ! [X0] : ((((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))))) [nnf transformation 7]
51. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 51]
57. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 60]
78. ~generous(X0) | brave(X0) [cnf transformation 40]
99. ~brave(X0) | creative(X0) | ~generous(X0) | happy(X0) [cnf transformation 50]
102. happy(X0) | generous(X0) | brave(X0) | creative(X0) [cnf transformation 50]
104. ~calm(X0) | ~creative(X0) [cnf transformation 52]
105. ~rich(X0) | ~creative(X0) [cnf transformation 52]
107. ~strong(X0) | ~rich(X0) [cnf transformation 52]
110. happy(X0) | generous(X0) [cnf transformation 31]
127. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 57]
128. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
137. strong(X0) | creative(X0) | patient(X0) [cnf transformation 61]
149. ~funny(X0) | rich(X0) [cnf transformation 34]
161. ~happy(lucy) [cnf transformation 24]
162. ~patient(lucy) [cnf transformation 25]
236. happy(X0) | brave(X0) | creative(X0) [subsumption resolution 102,78]
238. ~generous(X0) | creative(X0) | happy(X0) [subsumption resolution 99,236]
262. ~calm(X0) | patient(X0) | funny(X0) [subsumption resolution 128,104]
263. ~creative(X0) | patient(X0) | funny(X0) [subsumption resolution 127,262]
328. generous(lucy) [resolution 110,161]
386. creative(X0) | patient(X0) | ~rich(X0) [resolution 137,107]
388. ~rich(X0) | patient(X0) [subsumption resolution 386,105]
450. creative(lucy) | happy(lucy) [resolution 238,328]
565. creative(lucy) [subsumption resolution 450,161]
643. patient(lucy) | funny(lucy) [resolution 565,263]
645. funny(lucy) [subsumption resolution 643,162]
739. rich(lucy) [resolution 645,149]
986. patient(lucy) [resolution 739,388]
988. $false [subsumption resolution 986,162]
% SZS output end Proof for 2100313235969135802817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is curious and vice versa. If susan is both happy and not patient then someone is not kind or not rich and vice versa. If alice is not humble or brave then someone is either not creative or patient and vice versa. Everyone who is not generous is either generous or happy. Everyone who is both not rich and calm is both old and not tall. Everyone who is rich or not happy is both not old and not strong and vice versa. Everyone who is either not creative or not kind is old or tall. Everyone who is either rich or creative is both generous and strong. Everyone who is either happy or not old is humble or not humble and vice versa. Everyone who is either happy or strong is both patient and brave. If someone is either not humble or not calm then someone is not patient or wise. Everyone who is not curious is not old or kind and vice versa. If someone is not old or happy then someone is either generous or tall and vice versa. Everyone who is curious is either not funny or not patient and vice versa. Everyone who is not happy or strong is old and vice versa. Everyone who is creative or brave is either generous or quiet and vice versa. Susan is both tall and not creative. Someone is both quiet and not humble. Mary is either not funny or not strong. Someone is either creative or not tall. Someone is brave or creative. Alice is either brave or strong. Fred is not creative. Someone is both not patient and curious. | Fred is not old. | contradiction | (![X]:(~brave(X)<=>curious(X)))&
(((happy(susan)&~patient(susan)))<=>(?[X]:((~kind(X)|~rich(X)))))&
(((~humble(alice)|brave(alice)))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:(~generous(X)=>(generous(X)<~>happy(X))))&
(![X]:((~rich(X)&calm(X))=>(old(X)&~tall(X))))&
(![X]:((rich(X)|~happy(X))<=>(~old(X)&~strong(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(old(X)|tall(X))))&
(![X]:((rich(X)<~>creative(X))=>(generous(X)&strong(X))))&
(![X]:((happy(X)<~>~old(X))<=>(humble(X)|~humble(X))))&
(![X]:((happy(X)<~>strong(X))=>(patient(X)&brave(X))))&
((?[X]:((~humble(X)<~>~calm(X))))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:(~curious(X)<=>(~old(X)|kind(X))))&
((?[X]:((~old(X)|happy(X))))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:(curious(X)<=>(~funny(X)<~>~patient(X))))&
(![X]:((~happy(X)|strong(X))<=>old(X)))&
(![X]:((creative(X)|brave(X))<=>(generous(X)<~>quiet(X))))&
((tall(susan)&~creative(susan)))&
(?[X]:((quiet(X)&~humble(X))))&
((~funny(mary)<~>~strong(mary)))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((brave(X)|creative(X))))&
((brave(alice)<~>strong(alice)))&
(~creative(fred))&
(?[X]:((~patient(X)&curious(X)))) | ~old(fred) | [
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5027270531601786985903584
% SZS output start Proof for 5027270531601786985903584
6. ! [X0] : ((~happy(X0) | rich(X0)) <=> (~strong(X0) & ~old(X0))) [input p5]
9. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (~humble(X0) | humble(X0))) [input p8]
15. ! [X0] : ((strong(X0) | ~happy(X0)) <=> old(X0)) [input p14]
25. ~old(fred) [input hypothesis]
47. ! [X0] : (((~happy(X0) | rich(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (happy(X0) & ~rich(X0)))) [nnf transformation 6]
48. ! [X0] : ((~happy(X0) | rich(X0) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | (happy(X0) & ~rich(X0)))) [flattening 47]
51. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 9]
52. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 51]
62. ! [X0] : (((strong(X0) | ~happy(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & happy(X0)))) [nnf transformation 15]
63. ! [X0] : ((strong(X0) | ~happy(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & happy(X0)))) [flattening 62]
93. ~old(X0) | happy(X0) [cnf transformation 48]
107. old(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 52]
108. old(X0) | ~happy(X0) | humble(X0) [cnf transformation 52]
126. old(X0) | happy(X0) [cnf transformation 63]
149. ~old(fred) [cnf transformation 25]
207. ~happy(X0) | old(X0) [subsumption resolution 107,108]
221. 16 <=> ! [X3] : old(X3) [avatar definition]
222. old(X3) <- (16) [avatar component clause 221]
227. happy(X0) [subsumption resolution 126,93]
269. old(X0) [resolution 207,227]
270. 16 [avatar split clause 269,221]
271. $false <- (16) [resolution 222,149]
274. ~16 [avatar contradiction clause 271]
275. $false [avatar sat refutation 270,274]
% SZS output end Proof for 5027270531601786985903584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not old or not happy and vice versa.
Everyone who is not humble is either not patient or not happy.
Everyone who is not curious is both not quiet and wise and vice versa.
Everyone who is not kind or patient is both not rich and not creative and vice versa.
Everyone who is not funny or happy is either tall or wise.
If someone is not funny then john is both not calm and funny and vice versa.
If someone is either not creative or kind then someone is not funny and vice versa.
If someone is not funny or patient then someone is both not creative and not happy and vice versa.
If susan is rich then paul is creative.
If someone is curious or not quiet then john is not creative or not wise and vice versa.
If lucy is calm then someone is humble.
Everyone who is rich or curious is wise.
If lucy is both not patient and not quiet then someone is not strong or funny and vice versa.
If someone is not wise or kind then lucy is patient.
Everyone who is happy is both not patient and not old.
Everyone who is generous or not strong is funny or not kind and vice versa.
Alice is old.
Fred is both quiet and curious.
Lucy is either not generous or rich.
Someone is brave.
Someone is both not rich and not creative.
Someone is funny.
Someone is either not tall or not curious. | Alice is not rich. | entailment | (![X]:(~strong(X)<=>(~old(X)|~happy(X))))&
(![X]:(~humble(X)=>(~patient(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(![X]:((~kind(X)|patient(X))<=>(~rich(X)&~creative(X))))&
(![X]:((~funny(X)|happy(X))=>(tall(X)<~>wise(X))))&
((?[X]:(~funny(X)))<=>((~calm(john)&funny(john))))&
((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:((~creative(X)&~happy(X)))))&
((rich(susan))=>(creative(paul)))&
((?[X]:((curious(X)|~quiet(X))))<=>((~creative(john)|~wise(john))))&
((calm(lucy))=>(?[X]:(humble(X))))&
(![X]:((rich(X)|curious(X))=>wise(X)))&
(((~patient(lucy)&~quiet(lucy)))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:((~wise(X)|kind(X))))=>(patient(lucy)))&
(![X]:(happy(X)=>(~patient(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))<=>(funny(X)|~kind(X))))&
(old(alice))&
((quiet(fred)&curious(fred)))&
((~generous(lucy)<~>rich(lucy)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~rich(alice) | [
"p3",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5372460914226258034629137
% SZS output start Proof for 5372460914226258034629137
4. ! [X0] : ((patient(X0) | ~kind(X0)) <=> (~creative(X0) & ~rich(X0))) [input p3]
6. ? [X0] : ~funny(X0) <=> (funny(john) & ~calm(john)) [input p5]
13. (~quiet(lucy) & ~patient(lucy)) <=> ? [X0] : (funny(X0) | ~strong(X0)) [input p12]
14. ? [X0] : (kind(X0) | ~wise(X0)) => patient(lucy) [input p13]
24. rich(alice) [input hypothesis]
33. patient(lucy) | ! [X0] : (~kind(X0) & wise(X0)) [ennf transformation 14]
39. ! [X0] : (((patient(X0) | ~kind(X0)) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | (~patient(X0) & kind(X0)))) [nnf transformation 4]
40. ! [X0] : ((patient(X0) | ~kind(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | (~patient(X0) & kind(X0)))) [flattening 39]
42. (? [X0] : ~funny(X0) | (~funny(john) | calm(john))) & ((funny(john) & ~calm(john)) | ! [X0] : funny(X0)) [nnf transformation 6]
43. (? [X0] : ~funny(X0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X0] : funny(X0)) [flattening 42]
44. (? [X0] : ~funny(X0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X1] : funny(X1)) [rectify 43]
45. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
46. (~funny(sK0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X1] : funny(X1)) [skolemisation 44,45]
62. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X0] : (funny(X0) | ~strong(X0)) | (quiet(lucy) | patient(lucy))) [nnf transformation 13]
63. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X0] : (funny(X0) | ~strong(X0)) | quiet(lucy) | patient(lucy)) [flattening 62]
64. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X1] : (funny(X1) | ~strong(X1)) | quiet(lucy) | patient(lucy)) [rectify 63]
65. ? [X1] : (funny(X1) | ~strong(X1)) => (funny(sK6) | ~strong(sK6)) [choice axiom]
66. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & ((funny(sK6) | ~strong(sK6)) | quiet(lucy) | patient(lucy)) [skolemisation 64,65]
83. ~rich(X0) | kind(X0) [cnf transformation 40]
93. funny(john) | funny(X1) [cnf transformation 46]
113. ~patient(lucy) | ~funny(X0) [cnf transformation 66]
117. patient(lucy) | ~kind(X0) [cnf transformation 33]
134. rich(alice) [cnf transformation 24]
140. 2 <=> funny(john) [avatar definition]
141. funny(john) <- (2) [avatar component clause 140]
149. 4 <=> ! [X1] : funny(X1) [avatar definition]
150. funny(X1) <- (4) [avatar component clause 149]
151. 4 | 2 [avatar split clause 93,140,149]
230. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
231. ~funny(X0) <- (22) [avatar component clause 230]
242. 25 <=> patient(lucy) [avatar definition]
245. 22 | ~25 [avatar split clause 113,242,230]
257. 28 <=> ! [X0] : ~kind(X0) [avatar definition]
258. ~kind(X0) <- (28) [avatar component clause 257]
259. 28 | 25 [avatar split clause 117,242,257]
280. $false <- (2, 22) [subsumption resolution 141,231]
281. ~2 | ~22 [avatar contradiction clause 280]
282. $false <- (4, 22) [subsumption resolution 150,231]
283. ~4 | ~22 [avatar contradiction clause 282]
295. kind(alice) [resolution 83,134]
296. $false <- (28) [subsumption resolution 295,258]
297. ~28 [avatar contradiction clause 296]
298. $false [avatar sat refutation 151,245,259,281,283,297]
% SZS output end Proof for 5372460914226258034629137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not kind is either not wise or wise and vice versa.
Everyone who is not wise or not brave is kind and vice versa.
If someone is both quiet and not wise then john is either tall or not rich and vice versa.
If someone is not calm or curious then lucy is either calm or not curious.
Everyone who is old is not kind and vice versa.
Everyone who is not brave or not rich is either not brave or not rich.
If someone is strong then fred is both not patient and funny and vice versa.
If paul is either not creative or not happy then alice is not wise and vice versa.
Everyone who is funny is not quiet and vice versa.
Everyone who is not strong or not quiet is not wise.
Everyone who is generous or not happy is both not brave and creative.
Everyone who is generous or not rich is strong and vice versa.
Everyone who is not strong or creative is either funny or quiet and vice versa.
Everyone who is not generous is both not generous and not old.
If fred is both humble and not old then fred is humble and vice versa.
If susan is creative then alice is either not kind or not quiet and vice versa.
Someone is not wise or generous.
Someone is either not curious or not generous.
Someone is not rich.
Someone is wise or tall.
Lucy is both not happy and not wise.
Someone is not generous.
Someone is either not brave or not quiet. | Alice is funny. | entailment | (![X]:((funny(X)<~>~kind(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((~wise(X)|~brave(X))<=>kind(X)))&
((?[X]:((quiet(X)&~wise(X))))<=>((tall(john)<~>~rich(john))))&
((?[X]:((~calm(X)|curious(X))))=>((calm(lucy)<~>~curious(lucy))))&
(![X]:(old(X)<=>~kind(X)))&
(![X]:((~brave(X)|~rich(X))=>(~brave(X)<~>~rich(X))))&
((?[X]:(strong(X)))<=>((~patient(fred)&funny(fred))))&
(((~creative(paul)<~>~happy(paul)))<=>(~wise(alice)))&
(![X]:(funny(X)<=>~quiet(X)))&
(![X]:((~strong(X)|~quiet(X))=>~wise(X)))&
(![X]:((generous(X)|~happy(X))=>(~brave(X)&creative(X))))&
(![X]:((generous(X)|~rich(X))<=>strong(X)))&
(![X]:((~strong(X)|creative(X))<=>(funny(X)<~>quiet(X))))&
(![X]:(~generous(X)=>(~generous(X)&~old(X))))&
(((humble(fred)&~old(fred)))<=>(humble(fred)))&
((creative(susan))<=>((~kind(alice)<~>~quiet(alice))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)|tall(X))))&
((~happy(lucy)&~wise(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((~brave(X)<~>~quiet(X)))) | funny(alice) | [
"p0",
"p1",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7821567316314646179485797
% SZS output start Proof for 7821567316314646179485797
1. ! [X0] : ((funny(X0) <~> ~kind(X0)) <=> (~wise(X0) <~> wise(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> kind(X0)) [input p1]
5. ! [X0] : (old(X0) <=> ~kind(X0)) [input p4]
11. ! [X0] : ((~happy(X0) | generous(X0)) => (creative(X0) & ~brave(X0))) [input p10]
14. ! [X0] : (~generous(X0) => (~old(X0) & ~generous(X0))) [input p13]
24. ~funny(alice) [input hypothesis]
28. ! [X0] : ((creative(X0) & ~brave(X0)) | (happy(X0) & ~generous(X0))) [ennf transformation 11]
29. ! [X0] : ((~old(X0) & ~generous(X0)) | generous(X0)) [ennf transformation 14]
30. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [nnf transformation 1]
31. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~kind(X0)) & (kind(X0) | (brave(X0) & wise(X0)))) [nnf transformation 2]
32. ! [X0] : ((~brave(X0) | ~wise(X0) | ~kind(X0)) & (kind(X0) | (brave(X0) & wise(X0)))) [flattening 31]
38. ! [X0] : ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))) [nnf transformation 5]
72. ~kind(X0) | funny(X0) | wise(X0) | wise(X0) [cnf transformation 30]
73. ~kind(X0) | funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 30]
77. brave(X0) | kind(X0) [cnf transformation 32]
90. old(X0) | kind(X0) [cnf transformation 38]
106. ~generous(X0) | ~brave(X0) [cnf transformation 28]
120. ~old(X0) | generous(X0) [cnf transformation 29]
138. ~funny(alice) [cnf transformation 24]
141. ~kind(X0) | funny(X0) | wise(X0) [duplicate literal removal 72]
142. ~wise(X0) | funny(X0) | ~kind(X0) [duplicate literal removal 73]
146. ~kind(X0) | funny(X0) [subsumption resolution 141,142]
240. 20 <=> kind(alice) [avatar definition]
241. kind(alice) <- (20) [avatar component clause 240]
242. ~kind(alice) <- (~20) [avatar component clause 240]
316. generous(X0) | kind(X0) [resolution 120,90]
324. funny(alice) <- (20) [resolution 146,241]
327. $false <- (20) [subsumption resolution 324,138]
328. ~20 [avatar contradiction clause 327]
475. kind(X2) | ~brave(X2) [resolution 316,106]
476. kind(X2) [subsumption resolution 475,77]
509. $false <- (~20) [resolution 476,242]
512. 20 [avatar contradiction clause 509]
513. $false [avatar sat refutation 328,512]
% SZS output end Proof for 7821567316314646179485797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not kind or strong and vice versa.
Everyone who is both not brave and old is both tall and calm.
If someone is not patient then mary is both patient and not brave.
Everyone who is both not funny and quiet is both not happy and rich and vice versa.
Everyone who is either not creative or creative is both not quiet and not curious and vice versa.
If fred is either patient or kind then alice is either strong or not humble.
Everyone who is not rich is not humble or rich and vice versa.
If someone is both not happy and not old then mary is either not strong or generous and vice versa.
Everyone who is both not wise and not generous is patient and vice versa.
Everyone who is not rich is both not quiet and not kind and vice versa.
If john is either old or not wise then someone is both not quiet and wise.
If someone is humble or not happy then someone is curious.
Everyone who is brave is not strong or tall and vice versa.
If john is not rich then someone is quiet or old and vice versa.
If lucy is not strong or not wise then mary is either not happy or creative.
Mary is not curious or not rich.
Someone is not brave or creative.
Someone is either quiet or not kind.
Fred is not kind.
Alice is both not kind and not quiet.
Someone is not tall or kind. | Lucy is not humble. | entailment | (![X]:(~creative(X)<=>(~kind(X)|strong(X))))&
(![X]:((~brave(X)&old(X))=>(tall(X)&calm(X))))&
((?[X]:(~patient(X)))=>((patient(mary)&~brave(mary))))&
(![X]:((~funny(X)&quiet(X))<=>(~happy(X)&rich(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~quiet(X)&~curious(X))))&
(((patient(fred)<~>kind(fred)))=>((strong(alice)<~>~humble(alice))))&
(![X]:(~rich(X)<=>(~humble(X)|rich(X))))&
((?[X]:((~happy(X)&~old(X))))<=>((~strong(mary)<~>generous(mary))))&
(![X]:((~wise(X)&~generous(X))<=>patient(X)))&
(![X]:(~rich(X)<=>(~quiet(X)&~kind(X))))&
(((old(john)<~>~wise(john)))=>(?[X]:((~quiet(X)&wise(X)))))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:(curious(X))))&
(![X]:(brave(X)<=>(~strong(X)|tall(X))))&
((~rich(john))<=>(?[X]:((quiet(X)|old(X)))))&
(((~strong(lucy)|~wise(lucy)))=>((~happy(mary)<~>creative(mary))))&
((~curious(mary)|~rich(mary)))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((quiet(X)<~>~kind(X))))&
(~kind(fred))&
((~kind(alice)&~quiet(alice)))&
(?[X]:((~tall(X)|kind(X)))) | ~humble(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8509287529796817550565607
% SZS output start Proof for 8509287529796817550565607
7. ! [X0] : (~rich(X0) <=> (rich(X0) | ~humble(X0))) [input p6]
22. humble(lucy) [input hypothesis]
39. ! [X0] : ((~rich(X0) | (~rich(X0) & humble(X0))) & ((rich(X0) | ~humble(X0)) | rich(X0))) [nnf transformation 7]
40. ! [X0] : ((~rich(X0) | (~rich(X0) & humble(X0))) & (rich(X0) | ~humble(X0) | rich(X0))) [flattening 39]
89. rich(X0) | ~humble(X0) | rich(X0) [cnf transformation 40]
91. ~rich(X0) | ~rich(X0) [cnf transformation 40]
128. humble(lucy) [cnf transformation 22]
129. rich(X0) | ~humble(X0) [duplicate literal removal 89]
130. ~rich(X0) [duplicate literal removal 91]
170. ~humble(X0) [subsumption resolution 129,130]
240. $false [subsumption resolution 128,170]
% SZS output end Proof for 8509287529796817550565607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not rich is either wise or strong and vice versa. If someone is not brave or not rich then lucy is curious and vice versa. Everyone who is either brave or not brave is either creative or not humble. Everyone who is either not rich or creative is either funny or happy. If fred is either not generous or not curious then lucy is rich and vice versa. Everyone who is both not rich and rich is not tall and vice versa. Everyone who is kind is either humble or not rich and vice versa. If someone is tall then paul is both not curious and not strong. Everyone who is brave is either not brave or patient. Everyone who is both not brave and kind is patient and vice versa. Everyone who is both funny and humble is both not patient and not humble. Everyone who is both old and not generous is both not creative and curious. Everyone who is humble or strong is both not creative and not funny. If john is brave or not funny then someone is either rich or not quiet and vice versa. Someone is calm or not wise. Fred is not patient. Someone is either strong or not calm. Someone is either old or not strong. Someone is both not old and curious. Someone is happy. Alice is not humble or not creative. | John is not strong. | neutral | (![X]:((~wise(X)|~rich(X))<=>(wise(X)<~>strong(X))))&
((?[X]:((~brave(X)|~rich(X))))<=>(curious(lucy)))&
(![X]:((brave(X)<~>~brave(X))=>(creative(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(funny(X)<~>happy(X))))&
(((~generous(fred)<~>~curious(fred)))<=>(rich(lucy)))&
(![X]:((~rich(X)&rich(X))<=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(![X]:((~brave(X)&kind(X))<=>patient(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)&~humble(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(?[X]:((calm(X)|~wise(X))))&
(~patient(fred))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:((~old(X)&curious(X))))&
(?[X]:(happy(X)))&
((~humble(alice)|~creative(alice))) | ~strong(john) | [] | null | 0 |
Everyone who is strong or not calm is not strong and vice versa. If someone is not happy then susan is not quiet and vice versa. Everyone who is brave is both not generous and not patient. Everyone who is either not old or generous is both calm and not strong. If paul is both strong and not calm then alice is not rich. Everyone who is both funny and patient is both generous and not kind. If mary is both not kind and brave then susan is tall and vice versa. Everyone who is both happy and not calm is either not tall or wise and vice versa. Everyone who is not quiet or not brave is patient or wise. If someone is not humble then someone is strong or not patient. Everyone who is both not patient and quiet is not rich or not wise and vice versa. Everyone who is either not rich or not funny is both calm and not funny and vice versa. If someone is either rich or calm then fred is happy and vice versa. Everyone who is both not generous and not rich is curious and vice versa. If fred is either not kind or quiet then someone is both rich and old and vice versa. Everyone who is not patient is either not humble or rich and vice versa. John is patient. John is strong or quiet. Someone is patient. Someone is both rich and wise. Paul is not funny. Susan is both rich and not generous. Someone is either kind or quiet. | Paul is humble. | contradiction | (![X]:((strong(X)|~calm(X))<=>~strong(X)))&
((?[X]:(~happy(X)))<=>(~quiet(susan)))&
(![X]:(brave(X)=>(~generous(X)&~patient(X))))&
(![X]:((~old(X)<~>generous(X))=>(calm(X)&~strong(X))))&
(((strong(paul)&~calm(paul)))=>(~rich(alice)))&
(![X]:((funny(X)&patient(X))=>(generous(X)&~kind(X))))&
(((~kind(mary)&brave(mary)))<=>(tall(susan)))&
(![X]:((happy(X)&~calm(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~quiet(X)|~brave(X))=>(patient(X)|wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
(((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:(~patient(X)<=>(~humble(X)<~>rich(X))))&
(patient(john))&
((strong(john)|quiet(john)))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)&wise(X))))&
(~funny(paul))&
((rich(susan)&~generous(susan)))&
(?[X]:((kind(X)<~>quiet(X)))) | humble(paul) | [
"p0",
"p10",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7997814372597996525447431
% SZS output start Proof for 7997814372597996525447431
1. ! [X0] : ((~calm(X0) | strong(X0)) <=> ~strong(X0)) [input p0]
11. ! [X0] : ((quiet(X0) & ~patient(X0)) <=> (~wise(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~funny(X0) & calm(X0))) [input p11]
16. ! [X0] : (~patient(X0) <=> (~humble(X0) <~> rich(X0))) [input p15]
21. ~funny(paul) [input p20]
24. humble(paul) [input hypothesis]
35. ! [X0] : (((~calm(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (calm(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((~calm(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (calm(X0) & ~strong(X0)))) [flattening 35]
49. ! [X0] : (((quiet(X0) & ~patient(X0)) | (wise(X0) & rich(X0))) & ((~wise(X0) | ~rich(X0)) | (~quiet(X0) | patient(X0)))) [nnf transformation 11]
50. ! [X0] : (((quiet(X0) & ~patient(X0)) | (wise(X0) & rich(X0))) & (~wise(X0) | ~rich(X0) | ~quiet(X0) | patient(X0))) [flattening 49]
51. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 12]
52. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [flattening 51]
61. ! [X0] : ((~patient(X0) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | patient(X0))) [nnf transformation 16]
69. ~strong(X0) | ~strong(X0) [cnf transformation 36]
71. ~calm(X0) | strong(X0) | strong(X0) [cnf transformation 36]
96. ~patient(X0) | rich(X0) [cnf transformation 50]
101. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 52]
116. rich(X0) | ~humble(X0) | patient(X0) [cnf transformation 61]
119. ~patient(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 61]
125. ~funny(paul) [cnf transformation 21]
130. humble(paul) [cnf transformation 24]
133. ~strong(X0) [duplicate literal removal 69]
134. ~calm(X0) | strong(X0) [duplicate literal removal 71]
219. ~humble(X0) | ~patient(X0) [subsumption resolution 119,96]
220. ~humble(X0) | rich(X0) [subsumption resolution 116,219]
245. rich(paul) [resolution 220,130]
326. calm(paul) | funny(paul) [resolution 101,245]
341. calm(paul) [subsumption resolution 326,125]
527. strong(paul) [resolution 341,134]
537. $false [subsumption resolution 527,133]
% SZS output end Proof for 7997814372597996525447431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not humble is not funny or not rich. Everyone who is creative is both humble and brave. If someone is both not strong and old then susan is not creative. Everyone who is not strong or quiet is either curious or old. Everyone who is both old and generous is not kind or not rich and vice versa. If alice is tall then someone is either not generous or not rich and vice versa. If fred is both funny and not quiet then lucy is either not generous or not wise. Everyone who is not quiet or old is either not calm or not creative and vice versa. Everyone who is both not old and curious is not wise or not brave and vice versa. Everyone who is wise or patient is both not generous and patient and vice versa. If someone is both not happy and not old then fred is strong or not curious. Everyone who is tall or not generous is brave. Everyone who is both not brave and kind is quiet or humble. If someone is not curious or curious then someone is not rich or not curious. Everyone who is both generous and patient is not humble and vice versa. If someone is both quiet and not old then someone is not happy or not kind. Someone is not wise or not patient. Alice is not happy or happy. Susan is either not wise or not generous. Someone is either not creative or not curious. Someone is either not quiet or calm. | Lucy is curious. | neutral | (![X]:((~rich(X)|~humble(X))=>(~funny(X)|~rich(X))))&
(![X]:(creative(X)=>(humble(X)&brave(X))))&
((?[X]:((~strong(X)&old(X))))=>(~creative(susan)))&
(![X]:((~strong(X)|quiet(X))=>(curious(X)<~>old(X))))&
(![X]:((old(X)&generous(X))<=>(~kind(X)|~rich(X))))&
((tall(alice))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((funny(fred)&~quiet(fred)))=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:((~quiet(X)|old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~old(X)&curious(X))<=>(~wise(X)|~brave(X))))&
(![X]:((wise(X)|patient(X))<=>(~generous(X)&patient(X))))&
((?[X]:((~happy(X)&~old(X))))=>((strong(fred)|~curious(fred))))&
(![X]:((tall(X)|~generous(X))=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((~happy(X)|~kind(X)))))&
(?[X]:((~wise(X)|~patient(X))))&
((~happy(alice)|happy(alice)))&
((~wise(susan)<~>~generous(susan)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>calm(X)))) | curious(lucy) | [] | null | 0 |
If susan is either not funny or brave then someone is both not curious and not old and vice versa. If mary is calm or not kind then mary is not creative or not patient. If someone is both wise and tall then someone is both not generous and brave and vice versa. Everyone who is old or funny is not strong. Everyone who is not brave is funny or not old and vice versa. If someone is not curious or not humble then john is both strong and happy. Everyone who is happy is not kind and vice versa. If paul is both funny and not wise then lucy is not rich or generous. Everyone who is wise is not calm or not patient. If paul is either brave or calm then paul is rich or calm. Everyone who is either tall or not happy is either not curious or not patient and vice versa. Everyone who is either not kind or rich is humble or not quiet. If fred is both funny and wise then someone is humble or wise. If lucy is either not old or wise then paul is either not brave or calm and vice versa. Everyone who is either not happy or not wise is not patient or not funny and vice versa. If john is brave or strong then mary is old or not rich and vice versa. John is not creative. Someone is not kind or not generous. Mary is funny. Someone is kind. Someone is either old or not generous. Someone is either generous or not quiet. Someone is not brave. Someone is either wise or quiet. | Lucy is not rich. | neutral | (((~funny(susan)<~>brave(susan)))<=>(?[X]:((~curious(X)&~old(X)))))&
(((calm(mary)|~kind(mary)))=>((~creative(mary)|~patient(mary))))&
((?[X]:((wise(X)&tall(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((old(X)|funny(X))=>~strong(X)))&
(![X]:(~brave(X)<=>(funny(X)|~old(X))))&
((?[X]:((~curious(X)|~humble(X))))=>((strong(john)&happy(john))))&
(![X]:(happy(X)<=>~kind(X)))&
(((funny(paul)&~wise(paul)))=>((~rich(lucy)|generous(lucy))))&
(![X]:(wise(X)=>(~calm(X)|~patient(X))))&
(((brave(paul)<~>calm(paul)))=>((rich(paul)|calm(paul))))&
(![X]:((tall(X)<~>~happy(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>rich(X))=>(humble(X)|~quiet(X))))&
(((funny(fred)&wise(fred)))=>(?[X]:((humble(X)|wise(X)))))&
(((~old(lucy)<~>wise(lucy)))<=>((~brave(paul)<~>calm(paul))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~patient(X)|~funny(X))))&
(((brave(john)|strong(john)))<=>((old(mary)|~rich(mary))))&
(~creative(john))&
(?[X]:((~kind(X)|~generous(X))))&
(funny(mary))&
(?[X]:(kind(X)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
(?[X]:(~brave(X)))&
(?[X]:((wise(X)<~>quiet(X)))) | ~rich(lucy) | [] | null | 0 |
If someone is tall or not wise then susan is either brave or not quiet. If someone is either tall or calm then fred is either not strong or not patient and vice versa. If lucy is not brave then john is both wise and calm and vice versa. Everyone who is not generous is either curious or rich and vice versa. If john is either wise or happy then john is either not funny or happy. If paul is both curious and generous then alice is either brave or not old and vice versa. If someone is tall then fred is not funny. If someone is both kind and patient then alice is either not generous or humble. If someone is patient then someone is not kind and vice versa. If fred is generous then fred is not brave. Everyone who is not brave or brave is either creative or curious. Everyone who is both brave and rich is both rich and not funny and vice versa. Everyone who is both tall and not kind is both not generous and creative and vice versa. Everyone who is either curious or generous is either tall or wise. If someone is not calm or happy then someone is brave or not curious and vice versa. Everyone who is both not calm and funny is either curious or not curious and vice versa. Paul is humble or kind. Someone is either not curious or not rich. Someone is not happy or generous. Someone is either rich or strong. Alice is rich. Someone is both strong and not kind. | Alice is not rich. | contradiction | ((?[X]:((tall(X)|~wise(X))))=>((brave(susan)<~>~quiet(susan))))&
((?[X]:((tall(X)<~>calm(X))))<=>((~strong(fred)<~>~patient(fred))))&
((~brave(lucy))<=>((wise(john)&calm(john))))&
(![X]:(~generous(X)<=>(curious(X)<~>rich(X))))&
(((wise(john)<~>happy(john)))=>((~funny(john)<~>happy(john))))&
(((curious(paul)&generous(paul)))<=>((brave(alice)<~>~old(alice))))&
((?[X]:(tall(X)))=>(~funny(fred)))&
((?[X]:((kind(X)&patient(X))))=>((~generous(alice)<~>humble(alice))))&
((?[X]:(patient(X)))<=>(?[X]:(~kind(X))))&
((generous(fred))=>(~brave(fred)))&
(![X]:((~brave(X)|brave(X))=>(creative(X)<~>curious(X))))&
(![X]:((brave(X)&rich(X))<=>(rich(X)&~funny(X))))&
(![X]:((tall(X)&~kind(X))<=>(~generous(X)&creative(X))))&
(![X]:((curious(X)<~>generous(X))=>(tall(X)<~>wise(X))))&
((?[X]:((~calm(X)|happy(X))))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((~calm(X)&funny(X))<=>(curious(X)<~>~curious(X))))&
((humble(paul)|kind(paul)))&
(?[X]:((~curious(X)<~>~rich(X))))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(rich(alice))&
(?[X]:((strong(X)&~kind(X)))) | ~rich(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 915849167132414857383854
% SZS output start Proof for 915849167132414857383854
21. rich(alice) [input p20]
23. ~rich(alice) [input hypothesis]
140. rich(alice) [cnf transformation 21]
143. ~rich(alice) [cnf transformation 23]
362. $false [subsumption resolution 143,140]
% SZS output end Proof for 915849167132414857383854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and patient is generous or not generous.
Everyone who is wise is either wise or calm.
Everyone who is both not humble and brave is not old or generous and vice versa.
If fred is not rich or not curious then someone is brave or rich.
If fred is not tall then someone is either not kind or quiet.
If someone is either patient or not happy then someone is either not rich or not curious.
Everyone who is not wise or not old is either not calm or not humble and vice versa.
If someone is both not curious and calm then susan is not tall.
Everyone who is not brave is not curious or funny and vice versa.
If someone is both patient and humble then someone is either quiet or wise.
Everyone who is rich is happy or generous and vice versa.
Everyone who is rich is both not patient and humble.
Everyone who is either not patient or not generous is not patient.
Everyone who is either rich or not calm is not old.
If someone is creative then paul is both generous and not strong.
If mary is either humble or rich then someone is not patient or not creative.
Someone is not patient or kind.
Someone is not kind.
Alice is not patient.
Mary is tall or not patient.
Someone is both not tall and quiet.
John is not brave or not curious.
Susan is not quiet or not brave. | Paul is patient. | contradiction | (![X]:((~happy(X)&patient(X))=>(generous(X)|~generous(X))))&
(![X]:(wise(X)=>(wise(X)<~>calm(X))))&
(![X]:((~humble(X)&brave(X))<=>(~old(X)|generous(X))))&
(((~rich(fred)|~curious(fred)))=>(?[X]:((brave(X)|rich(X)))))&
((~tall(fred))=>(?[X]:((~kind(X)<~>quiet(X)))))&
((?[X]:((patient(X)<~>~happy(X))))=>(?[X]:((~rich(X)<~>~curious(X)))))&
(![X]:((~wise(X)|~old(X))<=>(~calm(X)<~>~humble(X))))&
((?[X]:((~curious(X)&calm(X))))=>(~tall(susan)))&
(![X]:(~brave(X)<=>(~curious(X)|funny(X))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:(rich(X)<=>(happy(X)|generous(X))))&
(![X]:(rich(X)=>(~patient(X)&humble(X))))&
(![X]:((~patient(X)<~>~generous(X))=>~patient(X)))&
(![X]:((rich(X)<~>~calm(X))=>~old(X)))&
((?[X]:(creative(X)))=>((generous(paul)&~strong(paul))))&
(((humble(mary)<~>rich(mary)))=>(?[X]:((~patient(X)|~creative(X)))))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:(~kind(X)))&
(~patient(alice))&
((tall(mary)|~patient(mary)))&
(?[X]:((~tall(X)&quiet(X))))&
((~brave(john)|~curious(john)))&
((~quiet(susan)|~brave(susan))) | patient(paul) | [
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6412712257566572531951542
% SZS output start Proof for 6412712257566572531951542
11. ! [X0] : (rich(X0) <=> (generous(X0) | happy(X0))) [input p10]
12. ! [X0] : (rich(X0) => (humble(X0) & ~patient(X0))) [input p11]
13. ! [X0] : ((~patient(X0) <~> ~generous(X0)) => ~patient(X0)) [input p12]
24. patient(paul) [input hypothesis]
38. ! [X0] : ((humble(X0) & ~patient(X0)) | ~rich(X0)) [ennf transformation 12]
39. ! [X0] : (~patient(X0) | (~patient(X0) <=> ~generous(X0))) [ennf transformation 13]
61. ! [X0] : ((rich(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 11]
62. ! [X0] : ((rich(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | ~rich(X0))) [flattening 61]
63. ! [X0] : (~patient(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) [nnf transformation 39]
101. ~generous(X0) | rich(X0) [cnf transformation 62]
102. ~rich(X0) | ~patient(X0) [cnf transformation 38]
105. ~patient(X0) | ~patient(X0) | generous(X0) [cnf transformation 63]
116. patient(paul) [cnf transformation 24]
117. ~patient(X0) | generous(X0) [duplicate literal removal 105]
226. generous(paul) [resolution 117,116]
229. rich(paul) [resolution 226,101]
234. ~patient(paul) [resolution 229,102]
235. $false [subsumption resolution 234,116]
% SZS output end Proof for 6412712257566572531951542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and kind.
Everyone who is either creative or not creative is both patient and not curious.
If paul is both rich and not brave then mary is both not old and generous and vice versa.
Everyone who is brave is humble or calm.
If fred is both quiet and patient then someone is both creative and calm and vice versa.
Everyone who is wise or not kind is either rich or not brave and vice versa.
Everyone who is either not brave or brave is happy or not brave and vice versa.
Everyone who is calm is not tall or not generous and vice versa.
Everyone who is either brave or not humble is not creative.
If paul is both not quiet and quiet then someone is not humble and vice versa.
If mary is patient then fred is not quiet or not calm.
If someone is creative then someone is not rich and vice versa.
Everyone who is not rich or old is not happy or curious and vice versa.
If fred is not kind or not calm then fred is either rich or not calm.
Everyone who is not calm or not kind is not kind and vice versa.
Everyone who is not curious is rich or calm.
Someone is either not humble or generous.
Lucy is either not curious or generous.
Fred is both not strong and not funny.
Someone is happy or creative.
Fred is not curious or curious.
John is both not strong and not kind.
Paul is not happy or not patient. | Fred is creative. | contradiction | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&kind(X))))&
(![X]:((creative(X)<~>~creative(X))=>(patient(X)&~curious(X))))&
(((rich(paul)&~brave(paul)))<=>((~old(mary)&generous(mary))))&
(![X]:(brave(X)=>(humble(X)|calm(X))))&
(((quiet(fred)&patient(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((wise(X)|~kind(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(happy(X)|~brave(X))))&
(![X]:(calm(X)<=>(~tall(X)|~generous(X))))&
(![X]:((brave(X)<~>~humble(X))=>~creative(X)))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((patient(mary))=>((~quiet(fred)|~calm(fred))))&
((?[X]:(creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|old(X))<=>(~happy(X)|curious(X))))&
(((~kind(fred)|~calm(fred)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~kind(X))<=>~kind(X)))&
(![X]:(~curious(X)=>(rich(X)|calm(X))))&
(?[X]:((~humble(X)<~>generous(X))))&
((~curious(lucy)<~>generous(lucy)))&
((~strong(fred)&~funny(fred)))&
(?[X]:((happy(X)|creative(X))))&
((~curious(fred)|curious(fred)))&
((~strong(john)&~kind(john)))&
((~happy(paul)|~patient(paul))) | creative(fred) | [
"p1",
"p4",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 173915196980849921229249
% SZS output start Proof for 173915196980849921229249
2. ! [X0] : ((creative(X0) <~> ~creative(X0)) => (~curious(X0) & patient(X0))) [input p1]
5. (patient(fred) & quiet(fred)) <=> ? [X0] : (calm(X0) & creative(X0)) [input p4]
11. patient(mary) => (~calm(fred) | ~quiet(fred)) [input p10]
14. (~calm(fred) | ~kind(fred)) => (rich(fred) <~> ~calm(fred)) [input p13]
16. ! [X0] : (~curious(X0) => (calm(X0) | rich(X0))) [input p15]
24. creative(fred) [input hypothesis]
30. ! [X0] : ((~curious(X0) & patient(X0)) | (creative(X0) <=> ~creative(X0))) [ennf transformation 2]
34. (~calm(fred) | ~quiet(fred)) | ~patient(mary) [ennf transformation 11]
35. ~calm(fred) | ~quiet(fred) | ~patient(mary) [flattening 34]
36. (rich(fred) <~> ~calm(fred)) | (calm(fred) & kind(fred)) [ennf transformation 14]
37. ! [X0] : ((calm(X0) | rich(X0)) | curious(X0)) [ennf transformation 16]
38. ! [X0] : (calm(X0) | rich(X0) | curious(X0)) [flattening 37]
40. ! [X0] : ((~curious(X0) & patient(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 30]
43. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X0] : (calm(X0) & creative(X0)) | (~patient(fred) | ~quiet(fred))) [nnf transformation 5]
44. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X0] : (calm(X0) & creative(X0)) | ~patient(fred) | ~quiet(fred)) [flattening 43]
45. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X1] : (calm(X1) & creative(X1)) | ~patient(fred) | ~quiet(fred)) [rectify 44]
46. ? [X1] : (calm(X1) & creative(X1)) => (calm(sK0) & creative(sK0)) [choice axiom]
47. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & ((calm(sK0) & creative(sK0)) | ~patient(fred) | ~quiet(fred)) [skolemisation 45,46]
67. ((calm(fred) | ~rich(fred)) & (~calm(fred) | rich(fred))) | (calm(fred) & kind(fred)) [nnf transformation 36]
80. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
81. patient(X0) | creative(X0) | creative(X0) [cnf transformation 40]
82. ~curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
83. ~curious(X0) | creative(X0) | creative(X0) [cnf transformation 40]
91. quiet(fred) | ~calm(X0) | ~creative(X0) [cnf transformation 47]
113. ~calm(fred) | ~quiet(fred) | ~patient(mary) [cnf transformation 35]
123. calm(fred) | ~rich(fred) | calm(fred) [cnf transformation 67]
127. calm(X0) | rich(X0) | curious(X0) [cnf transformation 38]
136. creative(fred) [cnf transformation 24]
137. calm(fred) | ~rich(fred) [duplicate literal removal 123]
142. patient(X0) | ~creative(X0) [duplicate literal removal 80]
143. patient(X0) | creative(X0) [duplicate literal removal 81]
144. ~curious(X0) | ~creative(X0) [duplicate literal removal 82]
145. ~curious(X0) | creative(X0) [duplicate literal removal 83]
146. ~curious(X0) [subsumption resolution 144,145]
147. patient(X0) [subsumption resolution 142,143]
169. 5 <=> ! [X0] : (~calm(X0) | ~creative(X0)) [avatar definition]
170. ~creative(X0) | ~calm(X0) <- (5) [avatar component clause 169]
172. 6 <=> quiet(fred) [avatar definition]
175. 5 | 6 [avatar split clause 91,172,169]
197. ~calm(fred) | ~quiet(fred) [subsumption resolution 113,147]
199. 11 <=> calm(fred) [avatar definition]
201. ~calm(fred) <- (~11) [avatar component clause 199]
202. ~6 | ~11 [avatar split clause 197,199,172]
222. 16 <=> rich(fred) [avatar definition]
224. ~rich(fred) <- (~16) [avatar component clause 222]
225. ~16 | 11 [avatar split clause 137,199,222]
232. rich(X0) | calm(X0) [subsumption resolution 127,146]
261. ~calm(fred) <- (5) [resolution 170,136]
266. calm(fred) <- (~16) [resolution 232,224]
267. $false <- (~11, ~16) [subsumption resolution 266,201]
268. 11 | 16 [avatar contradiction clause 267]
269. ~11 | ~5 [avatar split clause 261,169,199]
270. $false [avatar sat refutation 175,202,225,268,269]
% SZS output end Proof for 173915196980849921229249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not patient is not calm or not brave and vice versa.
If john is not rich then someone is both rich and curious and vice versa.
If someone is patient then someone is either humble or not funny.
If susan is not old or calm then susan is old.
Everyone who is not old or generous is not brave and vice versa.
Everyone who is rich or not strong is curious or not tall and vice versa.
If lucy is both happy and quiet then mary is either not brave or not old and vice versa.
If mary is both curious and not funny then mary is brave or not funny and vice versa.
Everyone who is either not brave or not wise is either kind or not calm and vice versa.
If someone is either not creative or not generous then someone is old.
Everyone who is both brave and not calm is not kind or not wise and vice versa.
Everyone who is either brave or not happy is not tall or generous.
Everyone who is either not old or tall is both not generous and patient and vice versa.
Everyone who is both kind and brave is not patient.
If paul is strong then alice is quiet or not wise.
Everyone who is either funny or brave is either patient or happy and vice versa.
Someone is both tall and not creative.
John is funny or not creative.
Alice is not wise or patient.
John is both calm and not tall.
Someone is not wise.
Alice is not curious or wise. | Lucy is not patient. | entailment | (![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((~rich(john))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(((~old(susan)|calm(susan)))=>(old(susan)))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(((curious(mary)&~funny(mary)))<=>((brave(mary)|~funny(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((brave(X)&~calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((kind(X)&brave(X))=>~patient(X)))&
((strong(paul))=>((quiet(alice)|~wise(alice))))&
(![X]:((funny(X)<~>brave(X))<=>(patient(X)<~>happy(X))))&
(?[X]:((tall(X)&~creative(X))))&
((funny(john)|~creative(john)))&
((~wise(alice)|patient(alice)))&
((calm(john)&~tall(john)))&
(?[X]:(~wise(X)))&
((~curious(alice)|wise(alice))) | ~patient(lucy) | [
"p0",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1779524823507930116367913
% SZS output start Proof for 1779524823507930116367913
1. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~brave(X0) | ~calm(X0))) [input p0]
11. ! [X0] : ((~calm(X0) & brave(X0)) <=> (~wise(X0) | ~kind(X0))) [input p10]
14. ! [X0] : ((brave(X0) & kind(X0)) => ~patient(X0)) [input p13]
23. patient(lucy) [input hypothesis]
31. ! [X0] : (~patient(X0) | (~brave(X0) | ~kind(X0))) [ennf transformation 14]
32. ! [X0] : (~patient(X0) | ~brave(X0) | ~kind(X0)) [flattening 31]
35. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 1]
36. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | patient(X0) | ~funny(X0))) [flattening 35]
58. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0))) [flattening 58]
71. ~patient(X0) | calm(X0) [cnf transformation 36]
72. ~patient(X0) | brave(X0) [cnf transformation 36]
111. ~calm(X0) | kind(X0) [cnf transformation 59]
121. ~patient(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 32]
139. patient(lucy) [cnf transformation 23]
229. ~kind(X0) | ~patient(X0) [subsumption resolution 121,72]
268. calm(lucy) [resolution 71,139]
276. kind(lucy) [resolution 111,268]
306. ~patient(lucy) [resolution 276,229]
307. $false [subsumption resolution 306,139]
% SZS output end Proof for 1779524823507930116367913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and curious is creative and vice versa.
If mary is both generous and old then lucy is quiet or curious.
Everyone who is not rich is both rich and not brave and vice versa.
Everyone who is not happy or not patient is both creative and not strong and vice versa.
Everyone who is calm or not strong is either not brave or not rich and vice versa.
If someone is not strong or not quiet then fred is not quiet or not rich.
Everyone who is either not generous or patient is both kind and patient.
If mary is calm then someone is funny or humble.
If someone is strong then lucy is both funny and happy.
Everyone who is either not tall or not rich is not brave.
If someone is either wise or curious then someone is either not calm or not patient and vice versa.
Everyone who is old or not generous is old and vice versa.
If susan is both not happy and not quiet then susan is both brave and calm.
Everyone who is either not patient or not rich is either not brave or not happy.
Everyone who is wise is either curious or rich and vice versa.
Everyone who is not old is old or not wise and vice versa.
Someone is not funny or funny.
Someone is not happy or rich.
Mary is either not funny or not wise.
Someone is both generous and happy.
Mary is either not brave or tall. | Fred is not humble. | neutral | (![X]:((~rich(X)&curious(X))<=>creative(X)))&
(((generous(mary)&old(mary)))=>((quiet(lucy)|curious(lucy))))&
(![X]:(~rich(X)<=>(rich(X)&~brave(X))))&
(![X]:((~happy(X)|~patient(X))<=>(creative(X)&~strong(X))))&
(![X]:((calm(X)|~strong(X))<=>(~brave(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~quiet(X))))=>((~quiet(fred)|~rich(fred))))&
(![X]:((~generous(X)<~>patient(X))=>(kind(X)&patient(X))))&
((calm(mary))=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:(strong(X)))=>((funny(lucy)&happy(lucy))))&
(![X]:((~tall(X)<~>~rich(X))=>~brave(X)))&
((?[X]:((wise(X)<~>curious(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((old(X)|~generous(X))<=>old(X)))&
(((~happy(susan)&~quiet(susan)))=>((brave(susan)&calm(susan))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>~happy(X))))&
(![X]:(wise(X)<=>(curious(X)<~>rich(X))))&
(![X]:(~old(X)<=>(old(X)|~wise(X))))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((~happy(X)|rich(X))))&
((~funny(mary)<~>~wise(mary)))&
(?[X]:((generous(X)&happy(X))))&
((~brave(mary)<~>tall(mary))) | ~humble(fred) | [] | null | 0 |
Everyone who is both not calm and not strong is either brave or tall and vice versa.
Everyone who is old is both humble and not kind and vice versa.
Everyone who is old is calm or not wise and vice versa.
If lucy is tall or rich then someone is not creative.
If susan is either generous or not humble then someone is either not generous or funny and vice versa.
Everyone who is not curious or tall is either quiet or not humble.
If someone is either curious or quiet then someone is either generous or old.
If someone is generous then someone is both quiet and happy and vice versa.
If someone is both not humble and humble then someone is not old.
Everyone who is both happy and creative is both not kind and curious and vice versa.
Everyone who is either not funny or curious is both quiet and rich.
If someone is both not kind and kind then john is not tall.
Everyone who is not quiet is either happy or not funny and vice versa.
Everyone who is not humble is not funny and vice versa.
Everyone who is not patient or wise is not humble and vice versa.
Everyone who is not patient is quiet.
John is not old.
Someone is creative.
Someone is both not old and not generous.
Susan is both not calm and tall.
Someone is brave or old.
Someone is either not kind or rich.
Lucy is either kind or not humble.
Someone is either not wise or not brave. | John is not curious. | contradiction | (![X]:((~calm(X)&~strong(X))<=>(brave(X)<~>tall(X))))&
(![X]:(old(X)<=>(humble(X)&~kind(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(((tall(lucy)|rich(lucy)))=>(?[X]:(~creative(X))))&
(((generous(susan)<~>~humble(susan)))<=>(?[X]:((~generous(X)<~>funny(X)))))&
(![X]:((~curious(X)|tall(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((generous(X)<~>old(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:((~humble(X)&humble(X))))=>(?[X]:(~old(X))))&
(![X]:((happy(X)&creative(X))<=>(~kind(X)&curious(X))))&
(![X]:((~funny(X)<~>curious(X))=>(quiet(X)&rich(X))))&
((?[X]:((~kind(X)&kind(X))))=>(~tall(john)))&
(![X]:(~quiet(X)<=>(happy(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>~funny(X)))&
(![X]:((~patient(X)|wise(X))<=>~humble(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(~old(john))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)&~generous(X))))&
((~calm(susan)&tall(susan)))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~wise(X)<~>~brave(X)))) | ~curious(john) | [
"p2",
"p5",
"p10",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7921306478576486384462619
% SZS output start Proof for 7921306478576486384462619
3. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p2]
6. ! [X0] : ((tall(X0) | ~curious(X0)) => (quiet(X0) <~> ~humble(X0))) [input p5]
11. ! [X0] : ((~funny(X0) <~> curious(X0)) => (rich(X0) & quiet(X0))) [input p10]
14. ! [X0] : (~humble(X0) <=> ~funny(X0)) [input p13]
15. ! [X0] : ((wise(X0) | ~patient(X0)) <=> ~humble(X0)) [input p14]
17. ~old(john) [input p16]
25. ~curious(john) [input hypothesis]
30. ! [X0] : ((quiet(X0) <~> ~humble(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 6]
33. ! [X0] : ((rich(X0) & quiet(X0)) | (~funny(X0) <=> curious(X0))) [ennf transformation 11]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 3]
41. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 40]
48. ! [X0] : (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (~tall(X0) & curious(X0))) [nnf transformation 30]
63. ! [X0] : ((rich(X0) & quiet(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [nnf transformation 33]
65. ! [X0] : ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))) [nnf transformation 14]
66. ! [X0] : (((wise(X0) | ~patient(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [nnf transformation 15]
67. ! [X0] : ((wise(X0) | ~patient(X0) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [flattening 66]
92. wise(X0) | old(X0) [cnf transformation 41]
105. ~quiet(X0) | humble(X0) | curious(X0) [cnf transformation 48]
119. quiet(X0) | curious(X0) | funny(X0) [cnf transformation 63]
128. ~funny(X0) | humble(X0) [cnf transformation 65]
131. ~wise(X0) | ~humble(X0) [cnf transformation 67]
134. ~old(john) [cnf transformation 17]
147. ~curious(john) [cnf transformation 25]
277. ~humble(X0) | old(X0) [resolution 131,92]
329. curious(X1) | funny(X1) | humble(X1) | curious(X1) [resolution 119,105]
332. curious(X1) | funny(X1) | humble(X1) [duplicate literal removal 329]
334. curious(X1) | humble(X1) [subsumption resolution 332,128]
501. humble(john) [resolution 334,147]
630. old(john) [resolution 501,277]
634. $false [subsumption resolution 630,134]
% SZS output end Proof for 7921306478576486384462619
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or tall then someone is not calm and vice versa.
If alice is both not strong and not rich then lucy is not kind or not brave and vice versa.
Everyone who is not curious or tall is both not humble and not curious and vice versa.
If someone is both not calm and calm then john is calm or creative and vice versa.
Everyone who is not humble is both not old and wise and vice versa.
Everyone who is either not strong or not tall is both happy and not wise.
If someone is either curious or not funny then someone is creative or happy.
Everyone who is not curious or not patient is both old and not funny.
If alice is funny then someone is both not quiet and humble.
Everyone who is not funny or not kind is either not quiet or not strong and vice versa.
If someone is either kind or wise then susan is rich or kind and vice versa.
Everyone who is both generous and not brave is not wise and vice versa.
If lucy is both rich and brave then someone is either calm or not brave and vice versa.
Everyone who is funny is both old and not creative.
Everyone who is both not old and wise is humble or wise and vice versa.
If john is both old and wise then fred is both rich and not tall.
Someone is calm or not curious.
Lucy is not strong or not curious.
Someone is happy or not patient.
Someone is both not strong and not old.
Someone is curious or patient. | Susan is not humble. | entailment | ((?[X]:((generous(X)|tall(X))))<=>(?[X]:(~calm(X))))&
(((~strong(alice)&~rich(alice)))<=>((~kind(lucy)|~brave(lucy))))&
(![X]:((~curious(X)|tall(X))<=>(~humble(X)&~curious(X))))&
((?[X]:((~calm(X)&calm(X))))<=>((calm(john)|creative(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)&~wise(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~curious(X)|~patient(X))=>(old(X)&~funny(X))))&
((funny(alice))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(~quiet(X)<~>~strong(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>((rich(susan)|kind(susan))))&
(![X]:((generous(X)&~brave(X))<=>~wise(X)))&
(((rich(lucy)&brave(lucy)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(old(X)&~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(humble(X)|wise(X))))&
(((old(john)&wise(john)))=>((rich(fred)&~tall(fred))))&
(?[X]:((calm(X)|~curious(X))))&
((~strong(lucy)|~curious(lucy)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:((curious(X)|patient(X)))) | ~humble(susan) | [
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 164604811113011264788954
% SZS output start Proof for 164604811113011264788954
5. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p4]
15. ! [X0] : ((wise(X0) & ~old(X0)) <=> (wise(X0) | humble(X0))) [input p14]
22. humble(susan) [input hypothesis]
50. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 5]
51. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 50]
69. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 15]
70. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~wise(X0) | old(X0))) [flattening 69]
94. wise(X0) | humble(X0) [cnf transformation 51]
95. ~wise(X0) | ~humble(X0) | old(X0) [cnf transformation 51]
127. ~old(X0) | ~wise(X0) [cnf transformation 70]
128. wise(X0) | ~humble(X0) [cnf transformation 70]
136. humble(susan) [cnf transformation 22]
264. wise(X0) [subsumption resolution 128,94]
265. ~old(X0) [subsumption resolution 127,264]
303. ~humble(X2) | old(X2) [resolution 95,264]
305. ~humble(X2) [subsumption resolution 303,265]
309. $false [resolution 305,136]
% SZS output end Proof for 164604811113011264788954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or wise then alice is both patient and creative and vice versa. If someone is both curious and tall then someone is both rich and not rich. Everyone who is not happy is quiet or not quiet and vice versa. Everyone who is not strong or rich is both not curious and not kind and vice versa. If susan is both wise and kind then susan is not strong or curious. Everyone who is not wise or not quiet is either wise or not brave and vice versa. Everyone who is either brave or not creative is not kind. If someone is either not tall or not kind then someone is either not wise or strong and vice versa. If someone is either quiet or creative then someone is not tall. If someone is not strong then someone is both not tall and not wise and vice versa. Everyone who is either not brave or not tall is either rich or not brave and vice versa. Everyone who is not wise is either not generous or not strong. Everyone who is not funny or not old is both strong and tall. Everyone who is happy or not creative is either not tall or generous and vice versa. Everyone who is both old and not happy is not brave or not quiet and vice versa. Everyone who is not kind is either not tall or rich and vice versa. Mary is humble or not humble. Paul is kind or not humble. Someone is not humble. Someone is calm or quiet. | Susan is not kind. | contradiction | ((?[X]:((~calm(X)<~>wise(X))))<=>((patient(alice)&creative(alice))))&
((?[X]:((curious(X)&tall(X))))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:(~happy(X)<=>(quiet(X)|~quiet(X))))&
(![X]:((~strong(X)|rich(X))<=>(~curious(X)&~kind(X))))&
(((wise(susan)&kind(susan)))=>((~strong(susan)|curious(susan))))&
(![X]:((~wise(X)|~quiet(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((brave(X)<~>~creative(X))=>~kind(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:(~tall(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((~brave(X)<~>~tall(X))<=>(rich(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(~generous(X)<~>~strong(X))))&
(![X]:((~funny(X)|~old(X))=>(strong(X)&tall(X))))&
(![X]:((happy(X)|~creative(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((old(X)&~happy(X))<=>(~brave(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(~tall(X)<~>rich(X))))&
((humble(mary)|~humble(mary)))&
((kind(paul)|~humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|quiet(X)))) | ~kind(susan) | [
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2573416646680748467918994
% SZS output start Proof for 2573416646680748467918994
4. ! [X0] : ((rich(X0) | ~strong(X0)) <=> (~kind(X0) & ~curious(X0))) [input p3]
11. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p10]
16. ! [X0] : (~kind(X0) <=> (~tall(X0) <~> rich(X0))) [input p15]
21. ~kind(susan) [input hypothesis]
44. ! [X0] : (((rich(X0) | ~strong(X0)) | (kind(X0) | curious(X0))) & ((~kind(X0) & ~curious(X0)) | (~rich(X0) & strong(X0)))) [nnf transformation 4]
45. ! [X0] : ((rich(X0) | ~strong(X0) | kind(X0) | curious(X0)) & ((~kind(X0) & ~curious(X0)) | (~rich(X0) & strong(X0)))) [flattening 44]
63. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 11]
69. ! [X0] : ((~kind(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | kind(X0))) [nnf transformation 16]
88. ~kind(X0) | ~rich(X0) [cnf transformation 45]
113. ~brave(X0) | rich(X0) | ~brave(X0) | tall(X0) [cnf transformation 63]
114. brave(X0) | ~rich(X0) | ~tall(X0) | brave(X0) [cnf transformation 63]
116. ~tall(X0) | ~brave(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 63]
119. tall(X0) | brave(X0) | rich(X0) | brave(X0) [cnf transformation 63]
135. rich(X0) | ~tall(X0) | kind(X0) [cnf transformation 69]
136. ~rich(X0) | tall(X0) | kind(X0) [cnf transformation 69]
143. ~kind(susan) [cnf transformation 21]
144. ~brave(X0) | rich(X0) | tall(X0) [duplicate literal removal 113]
145. brave(X0) | ~rich(X0) | ~tall(X0) [duplicate literal removal 114]
146. ~tall(X0) | ~brave(X0) | ~rich(X0) [duplicate literal removal 116]
147. tall(X0) | brave(X0) | rich(X0) [duplicate literal removal 119]
194. 10 <=> kind(susan) [avatar definition]
196. ~kind(susan) <- (~10) [avatar component clause 194]
271. ~rich(X0) | ~tall(X0) [subsumption resolution 145,146]
272. rich(X0) | tall(X0) [subsumption resolution 144,147]
276. kind(X0) | tall(X0) [subsumption resolution 136,272]
277. kind(X0) | rich(X0) [subsumption resolution 135,276]
296. ~10 [avatar split clause 143,194]
306. tall(X0) | ~rich(X0) [resolution 276,88]
308. ~rich(X0) [subsumption resolution 306,271]
310. rich(susan) <- (~10) [resolution 277,196]
314. $false <- (~10) [subsumption resolution 310,308]
315. 10 [avatar contradiction clause 314]
320. $false [avatar sat refutation 296,315]
% SZS output end Proof for 2573416646680748467918994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is both curious and not funny.
If mary is not humble then someone is either not tall or brave.
If paul is brave then john is patient or not strong.
If paul is generous or tall then john is both not creative and not humble.
Everyone who is either not kind or not patient is not humble.
If someone is not patient or kind then susan is either not calm or not wise and vice versa.
Everyone who is either creative or not calm is either not brave or not tall.
If someone is funny then john is not patient or not quiet and vice versa.
Everyone who is not quiet is strong or not calm and vice versa.
Everyone who is calm is not humble and vice versa.
Everyone who is curious is not calm and vice versa.
Everyone who is both not calm and humble is either calm or not old and vice versa.
Everyone who is either calm or tall is either not patient or not kind and vice versa.
Everyone who is funny or quiet is not kind and vice versa.
If someone is not humble or not quiet then paul is either not calm or not strong and vice versa.
Everyone who is tall or not curious is both not patient and not quiet.
Someone is curious or creative.
Someone is rich or not brave.
Someone is tall.
Someone is creative or not generous.
Paul is either not creative or patient.
Susan is either not brave or not rich.
Someone is not curious. | Paul is not humble. | contradiction | ((?[X]:(~curious(X)))=>(?[X]:((curious(X)&~funny(X)))))&
((~humble(mary))=>(?[X]:((~tall(X)<~>brave(X)))))&
((brave(paul))=>((patient(john)|~strong(john))))&
(((generous(paul)|tall(paul)))=>((~creative(john)&~humble(john))))&
(![X]:((~kind(X)<~>~patient(X))=>~humble(X)))&
((?[X]:((~patient(X)|kind(X))))<=>((~calm(susan)<~>~wise(susan))))&
(![X]:((creative(X)<~>~calm(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:((tall(X)|~curious(X))=>(~patient(X)&~quiet(X))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:(tall(X)))&
(?[X]:((creative(X)|~generous(X))))&
((~creative(paul)<~>patient(paul)))&
((~brave(susan)<~>~rich(susan)))&
(?[X]:(~curious(X))) | ~humble(paul) | [
"p8",
"p9",
"p10",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2293823720557342819799117
% SZS output start Proof for 2293823720557342819799117
9. ! [X0] : (~quiet(X0) <=> (~calm(X0) | strong(X0))) [input p8]
10. ! [X0] : (calm(X0) <=> ~humble(X0)) [input p9]
11. ! [X0] : (curious(X0) <=> ~calm(X0)) [input p10]
15. ? [X0] : (~quiet(X0) | ~humble(X0)) <=> (~calm(paul) <~> ~strong(paul)) [input p14]
16. ! [X0] : ((~curious(X0) | tall(X0)) => (~quiet(X0) & ~patient(X0))) [input p15]
23. ? [X0] : ~curious(X0) [input p22]
24. ~humble(paul) [input hypothesis]
35. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (curious(X0) & ~tall(X0))) [ennf transformation 16]
53. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & ((~calm(X0) | strong(X0)) | quiet(X0))) [nnf transformation 9]
54. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & (~calm(X0) | strong(X0) | quiet(X0))) [flattening 53]
55. ! [X0] : ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))) [nnf transformation 10]
56. ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 11]
62. (? [X0] : (~quiet(X0) | ~humble(X0)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X0] : (quiet(X0) & humble(X0))) [nnf transformation 15]
63. (? [X0] : (~quiet(X0) | ~humble(X0)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X1] : (quiet(X1) & humble(X1))) [rectify 62]
64. ? [X0] : (~quiet(X0) | ~humble(X0)) => (~quiet(sK4) | ~humble(sK4)) [choice axiom]
65. ((~quiet(sK4) | ~humble(sK4)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X1] : (quiet(X1) & humble(X1))) [skolemisation 63,64]
74. ? [X0] : ~curious(X0) => ~curious(sK8) [choice axiom]
75. ~curious(sK8) [skolemisation 23,74]
98. ~calm(X0) | strong(X0) | quiet(X0) [cnf transformation 54]
102. calm(X0) | humble(X0) [cnf transformation 55]
103. ~calm(X0) | ~curious(X0) [cnf transformation 56]
123. ~strong(paul) | ~calm(paul) | quiet(X1) [cnf transformation 65]
131. ~quiet(X0) | curious(X0) [cnf transformation 35]
139. ~curious(sK8) [cnf transformation 75]
140. ~humble(paul) [cnf transformation 24]
144. 1 <=> ! [X1] : curious(X1) [avatar definition]
145. curious(X1) <- (1) [avatar component clause 144]
243. 22 <=> strong(paul) [avatar definition]
244. ~strong(paul) <- (~22) [avatar component clause 243]
247. 23 <=> calm(paul) [avatar definition]
248. calm(paul) <- (23) [avatar component clause 247]
249. ~calm(paul) <- (~23) [avatar component clause 247]
261. 26 <=> ! [X1] : quiet(X1) [avatar definition]
262. quiet(X1) <- (26) [avatar component clause 261]
268. 26 | ~23 | ~22 [avatar split clause 123,243,247,261]
309. humble(paul) <- (~23) [resolution 102,249]
311. $false <- (~23) [subsumption resolution 309,140]
312. 23 [avatar contradiction clause 311]
315. ~curious(paul) <- (23) [resolution 103,248]
332. strong(paul) | quiet(paul) <- (23) [resolution 98,248]
334. quiet(paul) <- (~22, 23) [subsumption resolution 332,244]
335. curious(paul) <- (~22, 23) [resolution 334,131]
340. $false <- (~22, 23) [subsumption resolution 335,315]
341. 22 | ~23 [avatar contradiction clause 340]
349. curious(X0) <- (26) [resolution 262,131]
356. 1 | ~26 [avatar split clause 349,261,144]
358. $false <- (1) [resolution 145,139]
362. ~1 [avatar contradiction clause 358]
363. $false [avatar sat refutation 268,312,341,356,362]
% SZS output end Proof for 2293823720557342819799117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both tall and not funny then someone is not calm or not kind and vice versa.
Everyone who is not patient or happy is not tall and vice versa.
If someone is not happy or rich then mary is not wise or wise and vice versa.
Everyone who is either not patient or brave is either creative or brave and vice versa.
Everyone who is old or not curious is both generous and rich and vice versa.
If someone is both kind and not patient then john is humble or calm.
Everyone who is either calm or brave is either not old or not quiet and vice versa.
If mary is not strong then someone is either brave or not calm and vice versa.
If alice is either not calm or not curious then someone is both not humble and not curious.
If mary is generous then fred is kind or calm and vice versa.
Everyone who is not quiet is both not kind and not patient.
Everyone who is generous is funny or not old.
If someone is either not humble or not kind then someone is both tall and not old and vice versa.
If john is tall or brave then someone is both quiet and not happy and vice versa.
If someone is both not tall and curious then fred is not humble.
Everyone who is either not patient or not generous is not tall.
Paul is not humble or tall.
Someone is not rich or curious.
Someone is not generous or not old.
Mary is humble.
Someone is not strong or creative.
Someone is not rich.
Someone is either not brave or not patient.
Mary is both not creative and brave. | Mary is not humble. | contradiction | (((tall(paul)&~funny(paul)))<=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((~patient(X)|happy(X))<=>~tall(X)))&
((?[X]:((~happy(X)|rich(X))))<=>((~wise(mary)|wise(mary))))&
(![X]:((~patient(X)<~>brave(X))<=>(creative(X)<~>brave(X))))&
(![X]:((old(X)|~curious(X))<=>(generous(X)&rich(X))))&
((?[X]:((kind(X)&~patient(X))))=>((humble(john)|calm(john))))&
(![X]:((calm(X)<~>brave(X))<=>(~old(X)<~>~quiet(X))))&
((~strong(mary))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(((~calm(alice)<~>~curious(alice)))=>(?[X]:((~humble(X)&~curious(X)))))&
((generous(mary))<=>((kind(fred)|calm(fred))))&
(![X]:(~quiet(X)=>(~kind(X)&~patient(X))))&
(![X]:(generous(X)=>(funny(X)|~old(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>(?[X]:((tall(X)&~old(X)))))&
(((tall(john)|brave(john)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~tall(X)&curious(X))))=>(~humble(fred)))&
(![X]:((~patient(X)<~>~generous(X))=>~tall(X)))&
((~humble(paul)|tall(paul)))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:((~generous(X)|~old(X))))&
(humble(mary))&
(?[X]:((~strong(X)|creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~brave(X)<~>~patient(X))))&
((~creative(mary)&brave(mary))) | ~humble(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9048601535810059436250779
% SZS output start Proof for 9048601535810059436250779
20. humble(mary) [input p19]
25. ~humble(mary) [input hypothesis]
147. humble(mary) [cnf transformation 20]
154. ~humble(mary) [cnf transformation 25]
362. $false [subsumption resolution 154,147]
% SZS output end Proof for 9048601535810059436250779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not brave and generous then someone is not rich or not quiet and vice versa.
If john is either creative or not brave then someone is both kind and generous.
If someone is not quiet or not strong then fred is not wise.
Everyone who is not tall is generous or strong.
Everyone who is either quiet or funny is not creative and vice versa.
Everyone who is happy or not tall is either strong or not happy.
If someone is not creative then someone is wise or not quiet and vice versa.
If someone is not quiet then someone is not curious or happy and vice versa.
Everyone who is not patient is not curious or funny and vice versa.
Everyone who is either not patient or not happy is both strong and not humble.
If someone is happy then someone is old or strong.
If fred is both not tall and not happy then someone is either not curious or curious and vice versa.
Everyone who is not old or not curious is happy or rich.
If someone is quiet or generous then fred is not old and vice versa.
Everyone who is not patient is not rich or creative.
Everyone who is not patient is brave.
Mary is not generous.
Someone is not generous.
Mary is either calm or not happy.
Susan is either old or not humble.
Someone is not tall.
Lucy is both not happy and funny.
Alice is not rich or humble.
Someone is creative. | Lucy is not patient. | entailment | (((~brave(fred)&generous(fred)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(((creative(john)<~>~brave(john)))=>(?[X]:((kind(X)&generous(X)))))&
((?[X]:((~quiet(X)|~strong(X))))=>(~wise(fred)))&
(![X]:(~tall(X)=>(generous(X)|strong(X))))&
(![X]:((quiet(X)<~>funny(X))<=>~creative(X)))&
(![X]:((happy(X)|~tall(X))=>(strong(X)<~>~happy(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~curious(X)|happy(X)))))&
(![X]:(~patient(X)<=>(~curious(X)|funny(X))))&
(![X]:((~patient(X)<~>~happy(X))=>(strong(X)&~humble(X))))&
((?[X]:(happy(X)))=>(?[X]:((old(X)|strong(X)))))&
(((~tall(fred)&~happy(fred)))<=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:((~old(X)|~curious(X))=>(happy(X)|rich(X))))&
((?[X]:((quiet(X)|generous(X))))<=>(~old(fred)))&
(![X]:(~patient(X)=>(~rich(X)|creative(X))))&
(![X]:(~patient(X)=>brave(X)))&
(~generous(mary))&
(?[X]:(~generous(X)))&
((calm(mary)<~>~happy(mary)))&
((old(susan)<~>~humble(susan)))&
(?[X]:(~tall(X)))&
((~happy(lucy)&funny(lucy)))&
((~rich(alice)|humble(alice)))&
(?[X]:(creative(X))) | ~patient(lucy) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5929949529776259201914624
% SZS output start Proof for 5929949529776259201914624
9. ! [X0] : (~patient(X0) <=> (funny(X0) | ~curious(X0))) [input p8]
22. funny(lucy) & ~happy(lucy) [input p21]
25. patient(lucy) [input hypothesis]
62. ! [X0] : ((~patient(X0) | (~funny(X0) & curious(X0))) & ((funny(X0) | ~curious(X0)) | patient(X0))) [nnf transformation 9]
63. ! [X0] : ((~patient(X0) | (~funny(X0) & curious(X0))) & (funny(X0) | ~curious(X0) | patient(X0))) [flattening 62]
111. ~patient(X0) | ~funny(X0) [cnf transformation 63]
138. funny(lucy) [cnf transformation 22]
141. patient(lucy) [cnf transformation 25]
315. ~funny(lucy) [resolution 111,141]
316. $false [subsumption resolution 315,138]
% SZS output end Proof for 5929949529776259201914624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not quiet is both not generous and kind.
Everyone who is either not funny or not wise is rich.
Everyone who is patient is either happy or not funny and vice versa.
If susan is not happy or not creative then someone is either calm or kind.
If susan is patient or curious then alice is not funny or not humble.
If someone is either not rich or not wise then lucy is not wise and vice versa.
Everyone who is not tall or happy is not old or not humble and vice versa.
Everyone who is both not curious and happy is not rich or not funny and vice versa.
Everyone who is both not wise and not curious is quiet.
Everyone who is not calm or wise is not patient or not creative.
Everyone who is tall or not rich is kind.
Everyone who is happy or not wise is both not rich and funny.
Everyone who is either not humble or tall is not strong.
If susan is both not strong and not old then someone is generous.
Everyone who is brave or funny is either not old or funny.
Everyone who is not generous or not tall is kind.
John is rich or not strong.
Someone is not brave or not old.
Someone is tall or not generous.
Mary is not happy or humble.
Fred is either not calm or not brave.
Someone is either not brave or not quiet. | Lucy is not patient. | entailment | (![X]:((~curious(X)|~quiet(X))=>(~generous(X)&kind(X))))&
(![X]:((~funny(X)<~>~wise(X))=>rich(X)))&
(![X]:(patient(X)<=>(happy(X)<~>~funny(X))))&
(((~happy(susan)|~creative(susan)))=>(?[X]:((calm(X)<~>kind(X)))))&
(((patient(susan)|curious(susan)))=>((~funny(alice)|~humble(alice))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~wise(lucy)))&
(![X]:((~tall(X)|happy(X))<=>(~old(X)|~humble(X))))&
(![X]:((~curious(X)&happy(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~wise(X)&~curious(X))=>quiet(X)))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|~creative(X))))&
(![X]:((tall(X)|~rich(X))=>kind(X)))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&funny(X))))&
(![X]:((~humble(X)<~>tall(X))=>~strong(X)))&
(((~strong(susan)&~old(susan)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|funny(X))=>(~old(X)<~>funny(X))))&
(![X]:((~generous(X)|~tall(X))=>kind(X)))&
((rich(john)|~strong(john)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((tall(X)|~generous(X))))&
((~happy(mary)|humble(mary)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((~brave(X)<~>~quiet(X)))) | ~patient(lucy) | [
"p1",
"p2",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 464917921503830599932972
% SZS output start Proof for 464917921503830599932972
2. ! [X0] : ((~funny(X0) <~> ~wise(X0)) => rich(X0)) [input p1]
3. ! [X0] : (patient(X0) <=> (happy(X0) <~> ~funny(X0))) [input p2]
6. ? [X0] : (~rich(X0) <~> ~wise(X0)) <=> ~wise(lucy) [input p5]
8. ! [X0] : ((happy(X0) & ~curious(X0)) <=> (~funny(X0) | ~rich(X0))) [input p7]
12. ! [X0] : ((~wise(X0) | happy(X0)) => (funny(X0) & ~rich(X0))) [input p11]
23. patient(lucy) [input hypothesis]
25. ! [X0] : (rich(X0) | (~funny(X0) <=> ~wise(X0))) [ennf transformation 2]
34. ! [X0] : ((funny(X0) & ~rich(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 12]
40. ! [X0] : (rich(X0) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) [nnf transformation 25]
41. ! [X0] : ((patient(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 3]
45. (? [X0] : ((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | wise(lucy)) & (~wise(lucy) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) [nnf transformation 6]
46. (? [X0] : ((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | wise(lucy)) & (~wise(lucy) | ! [X1] : ((~rich(X1) | wise(X1)) & (~wise(X1) | rich(X1)))) [rectify 45]
47. ? [X0] : ((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) => ((wise(sK1) | rich(sK1)) & (~wise(sK1) | ~rich(sK1))) [choice axiom]
48. (((wise(sK1) | rich(sK1)) & (~wise(sK1) | ~rich(sK1))) | wise(lucy)) & (~wise(lucy) | ! [X1] : ((~rich(X1) | wise(X1)) & (~wise(X1) | rich(X1)))) [skolemisation 46,47]
51. ! [X0] : (((happy(X0) & ~curious(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (~happy(X0) | curious(X0)))) [nnf transformation 8]
52. ! [X0] : (((happy(X0) & ~curious(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~happy(X0) | curious(X0))) [flattening 51]
70. ~funny(X0) | rich(X0) | wise(X0) [cnf transformation 40]
71. ~patient(X0) | happy(X0) | ~funny(X0) [cnf transformation 41]
81. ~wise(lucy) | ~wise(X1) | rich(X1) [cnf transformation 48]
93. happy(X0) | funny(X0) [cnf transformation 52]
99. ~happy(X0) | ~rich(X0) [cnf transformation 34]
100. ~rich(X0) | wise(X0) [cnf transformation 34]
101. funny(X0) | ~happy(X0) [cnf transformation 34]
120. patient(lucy) [cnf transformation 23]
161. 9 <=> wise(lucy) [avatar definition]
162. ~wise(lucy) <- (~9) [avatar component clause 161]
175. 12 <=> ! [X1] : (~rich(X1) | wise(X1)) [avatar definition]
176. ~rich(X1) | wise(X1) <- (12) [avatar component clause 175]
179. 13 <=> ! [X1] : (~wise(X1) | rich(X1)) [avatar definition]
180. ~wise(X1) | rich(X1) <- (13) [avatar component clause 179]
181. 13 | ~9 [avatar split clause 81,161,179]
182. funny(X0) [subsumption resolution 101,93]
183. 12 [avatar split clause 100,175]
269. rich(X0) | wise(X0) [resolution 70,182]
270. wise(X0) <- (12) [subsumption resolution 269,176]
271. $false <- (~9, 12) [resolution 270,162]
273. 9 | ~12 [avatar contradiction clause 271]
274. rich(X1) <- (12, 13) [subsumption resolution 180,270]
282. happy(lucy) | ~funny(lucy) [resolution 71,120]
283. happy(lucy) [subsumption resolution 282,182]
288. ~rich(lucy) [resolution 283,99]
289. $false <- (12, 13) [subsumption resolution 288,274]
290. ~12 | ~13 [avatar contradiction clause 289]
291. $false [avatar sat refutation 181,183,273,290]
% SZS output end Proof for 464917921503830599932972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not curious is both rich and funny. Everyone who is not old is either not brave or generous and vice versa. If lucy is not kind then someone is either not brave or not strong. Everyone who is both not wise and tall is humble and vice versa. If someone is rich then fred is both generous and curious. Everyone who is generous is not humble and vice versa. Everyone who is both calm and not calm is either old or patient. Everyone who is either not kind or wise is quiet or not wise and vice versa. If someone is curious or not tall then someone is both old and generous. Everyone who is curious is either strong or humble and vice versa. If someone is not quiet then someone is both generous and not quiet and vice versa. Everyone who is not tall or tall is either patient or not happy. Everyone who is either curious or happy is both brave and not brave and vice versa. Everyone who is both not happy and old is happy or quiet and vice versa. If mary is not creative then mary is either brave or tall and vice versa. Everyone who is not creative is generous. Paul is both strong and not kind. Someone is generous. Someone is not quiet. Someone is both not happy and not strong. Someone is not humble or not creative. | Mary is creative. | entailment | (![X]:((~brave(X)&~curious(X))=>(rich(X)&funny(X))))&
(![X]:(~old(X)<=>(~brave(X)<~>generous(X))))&
((~kind(lucy))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((~wise(X)&tall(X))<=>humble(X)))&
((?[X]:(rich(X)))=>((generous(fred)&curious(fred))))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((calm(X)&~calm(X))=>(old(X)<~>patient(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(quiet(X)|~wise(X))))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((old(X)&generous(X)))))&
(![X]:(curious(X)<=>(strong(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
(![X]:((~happy(X)&old(X))<=>(happy(X)|quiet(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((strong(paul)&~kind(paul)))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~humble(X)|~creative(X)))) | creative(mary) | [
"p0",
"p1",
"p4",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3716039605948109020608827
% SZS output start Proof for 3716039605948109020608827
1. ! [X0] : ((~curious(X0) & ~brave(X0)) => (funny(X0) & rich(X0))) [input p0]
2. ! [X0] : (~old(X0) <=> (~brave(X0) <~> generous(X0))) [input p1]
5. ? [X0] : rich(X0) => (curious(fred) & generous(fred)) [input p4]
9. ? [X0] : (~tall(X0) | curious(X0)) => ? [X0] : (generous(X0) & old(X0)) [input p8]
13. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~brave(X0) & brave(X0))) [input p12]
14. ! [X0] : ((old(X0) & ~happy(X0)) <=> (quiet(X0) | happy(X0))) [input p13]
15. ~creative(mary) <=> (brave(mary) <~> tall(mary)) [input p14]
22. ~creative(mary) [input hypothesis]
23. ? [X0] : (~tall(X0) | curious(X0)) => ? [X1] : (generous(X1) & old(X1)) [rectify 9]
25. ! [X0] : ((~curious(X0) & ~brave(X0)) => rich(X0)) [pure predicate removal 1]
26. ! [X0] : (rich(X0) | (curious(X0) | brave(X0))) [ennf transformation 25]
27. ! [X0] : (rich(X0) | curious(X0) | brave(X0)) [flattening 26]
29. (curious(fred) & generous(fred)) | ! [X0] : ~rich(X0) [ennf transformation 5]
32. ? [X1] : (generous(X1) & old(X1)) | ! [X0] : (tall(X0) & ~curious(X0)) [ennf transformation 23]
35. ! [X0] : ((~old(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) & (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | old(X0))) [nnf transformation 2]
45. ? [X0] : (generous(X0) & old(X0)) | ! [X1] : (tall(X1) & ~curious(X1)) [rectify 32]
46. ? [X0] : (generous(X0) & old(X0)) => (generous(sK1) & old(sK1)) [choice axiom]
47. (generous(sK1) & old(sK1)) | ! [X1] : (tall(X1) & ~curious(X1)) [skolemisation 45,46]
55. ! [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 13]
56. ! [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 55]
57. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | (~old(X0) | happy(X0)))) [nnf transformation 14]
58. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | ~old(X0) | happy(X0))) [flattening 57]
59. (~creative(mary) | ((brave(mary) | ~tall(mary)) & (tall(mary) | ~brave(mary)))) & (((~tall(mary) | ~brave(mary)) & (tall(mary) | brave(mary))) | creative(mary)) [nnf transformation 15]
68. rich(X0) | curious(X0) | brave(X0) [cnf transformation 27]
72. ~generous(X0) | ~brave(X0) | ~old(X0) [cnf transformation 35]
79. curious(fred) | ~rich(X0) [cnf transformation 29]
91. old(sK1) | tall(X1) [cnf transformation 47]
93. generous(sK1) | tall(X1) [cnf transformation 47]
105. brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 56]
107. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 56]
112. ~happy(X0) | ~happy(X0) [cnf transformation 58]
117. ~tall(mary) | ~brave(mary) | creative(mary) [cnf transformation 59]
128. ~creative(mary) [cnf transformation 22]
130. ~happy(X0) [duplicate literal removal 112]
148. 4 <=> ! [X0] : ~rich(X0) [avatar definition]
149. ~rich(X0) <- (4) [avatar component clause 148]
151. 5 <=> curious(fred) [avatar definition]
153. curious(fred) <- (5) [avatar component clause 151]
154. 4 | 5 [avatar split clause 79,151,148]
162. 7 <=> ! [X1] : tall(X1) [avatar definition]
163. tall(X1) <- (7) [avatar component clause 162]
165. 8 <=> generous(sK1) [avatar definition]
167. generous(sK1) <- (8) [avatar component clause 165]
168. 7 | 8 [avatar split clause 93,165,162]
174. 10 <=> old(sK1) [avatar definition]
176. old(sK1) <- (10) [avatar component clause 174]
177. 7 | 10 [avatar split clause 91,174,162]
203. ~curious(X0) | happy(X0) [subsumption resolution 105,107]
206. 16 <=> tall(mary) [avatar definition]
208. ~tall(mary) <- (~16) [avatar component clause 206]
210. 17 <=> brave(mary) [avatar definition]
211. ~brave(mary) <- (~17) [avatar component clause 210]
214. 18 <=> creative(mary) [avatar definition]
219. 18 | ~17 | ~16 [avatar split clause 117,206,210,214]
230. ~18 [avatar split clause 128,214]
253. curious(X0) | brave(X0) <- (4) [resolution 149,68]
313. ~brave(sK1) | ~old(sK1) <- (8) [resolution 72,167]
317. ~brave(sK1) <- (8, 10) [subsumption resolution 313,176]
369. brave(X2) | happy(X2) <- (4) [resolution 253,203]
371. brave(X2) <- (4) [subsumption resolution 369,130]
409. $false <- (4, ~17) [resolution 371,211]
411. $false <- (4, 8, 10) [resolution 371,317]
412. ~4 | ~8 | ~10 [avatar contradiction clause 411]
413. ~4 | 17 [avatar contradiction clause 409]
416. happy(fred) <- (5) [resolution 153,203]
428. $false <- (5) [subsumption resolution 416,130]
429. ~5 [avatar contradiction clause 428]
441. $false <- (7, ~16) [subsumption resolution 208,163]
442. ~7 | 16 [avatar contradiction clause 441]
443. $false [avatar sat refutation 154,168,177,219,230,412,413,429,442]
% SZS output end Proof for 3716039605948109020608827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both kind and not tall then fred is not patient and vice versa.
If fred is both kind and not funny then susan is not tall or calm and vice versa.
Everyone who is both humble and not tall is not calm.
Everyone who is not quiet is either not quiet or curious.
Everyone who is both rich and not rich is both wise and not old.
If mary is quiet or not tall then mary is either not curious or not generous.
If lucy is not kind then susan is not quiet.
If someone is both rich and humble then someone is either patient or rich and vice versa.
Everyone who is both brave and happy is either not patient or not creative.
Everyone who is brave or calm is strong.
Everyone who is either not patient or not brave is humble or not brave.
Everyone who is not kind or rich is not humble or strong.
Everyone who is both generous and not brave is both strong and brave and vice versa.
Everyone who is not old or not happy is tall or creative.
If someone is strong then someone is brave or quiet and vice versa.
Everyone who is rich is either not calm or wise.
Someone is wise or creative.
Susan is either wise or not brave.
Someone is both strong and not kind.
Someone is not happy.
Paul is calm.
Fred is generous or not strong.
Alice is both not generous and not strong. | Fred is not strong. | entailment | (((kind(mary)&~tall(mary)))<=>(~patient(fred)))&
(((kind(fred)&~funny(fred)))<=>((~tall(susan)|calm(susan))))&
(![X]:((humble(X)&~tall(X))=>~calm(X)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>curious(X))))&
(![X]:((rich(X)&~rich(X))=>(wise(X)&~old(X))))&
(((quiet(mary)|~tall(mary)))=>((~curious(mary)<~>~generous(mary))))&
((~kind(lucy))=>(~quiet(susan)))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((brave(X)&happy(X))=>(~patient(X)<~>~creative(X))))&
(![X]:((brave(X)|calm(X))=>strong(X)))&
(![X]:((~patient(X)<~>~brave(X))=>(humble(X)|~brave(X))))&
(![X]:((~kind(X)|rich(X))=>(~humble(X)|strong(X))))&
(![X]:((generous(X)&~brave(X))<=>(strong(X)&brave(X))))&
(![X]:((~old(X)|~happy(X))=>(tall(X)|creative(X))))&
((?[X]:(strong(X)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:(rich(X)=>(~calm(X)<~>wise(X))))&
(?[X]:((wise(X)|creative(X))))&
((wise(susan)<~>~brave(susan)))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:(~happy(X)))&
(calm(paul))&
((generous(fred)|~strong(fred)))&
((~generous(alice)&~strong(alice))) | ~strong(fred) | [
"p9",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6244085688511152342725567
% SZS output start Proof for 6244085688511152342725567
10. ! [X0] : ((calm(X0) | brave(X0)) => strong(X0)) [input p9]
13. ! [X0] : ((~brave(X0) & generous(X0)) <=> (brave(X0) & strong(X0))) [input p12]
22. ~strong(fred) | generous(fred) [input p21]
24. strong(fred) [input hypothesis]
36. ! [X0] : (strong(X0) | (~calm(X0) & ~brave(X0))) [ennf transformation 10]
57. ! [X0] : (((~brave(X0) & generous(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 13]
58. ! [X0] : (((~brave(X0) & generous(X0)) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | brave(X0) | ~generous(X0))) [flattening 57]
98. strong(X0) | ~brave(X0) [cnf transformation 36]
105. brave(X0) | brave(X0) | ~generous(X0) [cnf transformation 58]
107. ~brave(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 58]
122. ~strong(fred) | generous(fred) [cnf transformation 22]
125. strong(fred) [cnf transformation 24]
126. brave(X0) | ~generous(X0) [duplicate literal removal 105]
127. ~brave(X0) | ~strong(X0) [duplicate literal removal 107]
223. ~brave(X0) [subsumption resolution 127,98]
224. ~generous(X0) [subsumption resolution 126,223]
252. ~strong(fred) [subsumption resolution 122,224]
253. $false [subsumption resolution 125,252]
% SZS output end Proof for 6244085688511152342725567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is tall then someone is not old or not wise.
If someone is rich or not funny then paul is funny.
Everyone who is either not brave or not tall is both not creative and happy.
If someone is curious or not creative then someone is both not tall and strong.
If john is curious then fred is either not happy or not wise and vice versa.
Everyone who is rich or not old is both not calm and not tall and vice versa.
If alice is both creative and humble then someone is either kind or not wise.
Everyone who is calm or funny is not curious.
Everyone who is not funny is both curious and happy.
Everyone who is not curious or not generous is both not generous and rich and vice versa.
Everyone who is either rich or not kind is kind and vice versa.
If someone is either quiet or brave then someone is not brave or not tall.
Everyone who is funny is not creative or rich.
Everyone who is both not quiet and not calm is not patient or not funny.
Everyone who is either happy or not kind is funny or creative.
Everyone who is not generous is creative or tall.
Someone is not kind.
Someone is both funny and not humble.
Susan is either patient or not funny.
Someone is either not curious or not brave.
Fred is not tall or calm.
Susan is calm or not happy. | Paul is calm. | contradiction | ((tall(fred))=>(?[X]:((~old(X)|~wise(X)))))&
((?[X]:((rich(X)|~funny(X))))=>(funny(paul)))&
(![X]:((~brave(X)<~>~tall(X))=>(~creative(X)&happy(X))))&
((?[X]:((curious(X)|~creative(X))))=>(?[X]:((~tall(X)&strong(X)))))&
((curious(john))<=>((~happy(fred)<~>~wise(fred))))&
(![X]:((rich(X)|~old(X))<=>(~calm(X)&~tall(X))))&
(((creative(alice)&humble(alice)))=>(?[X]:((kind(X)<~>~wise(X)))))&
(![X]:((calm(X)|funny(X))=>~curious(X)))&
(![X]:(~funny(X)=>(curious(X)&happy(X))))&
(![X]:((~curious(X)|~generous(X))<=>(~generous(X)&rich(X))))&
(![X]:((rich(X)<~>~kind(X))<=>kind(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:(funny(X)=>(~creative(X)|rich(X))))&
(![X]:((~quiet(X)&~calm(X))=>(~patient(X)|~funny(X))))&
(![X]:((happy(X)<~>~kind(X))=>(funny(X)|creative(X))))&
(![X]:(~generous(X)=>(creative(X)|tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)&~humble(X))))&
((patient(susan)<~>~funny(susan)))&
(?[X]:((~curious(X)<~>~brave(X))))&
((~tall(fred)|calm(fred)))&
((calm(susan)|~happy(susan))) | calm(paul) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8784460441665776930351591
% SZS output start Proof for 8784460441665776930351591
6. ! [X0] : ((~old(X0) | rich(X0)) <=> (~tall(X0) & ~calm(X0))) [input p5]
11. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> kind(X0)) [input p10]
23. calm(paul) [input hypothesis]
51. ! [X0] : (((~old(X0) | rich(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (old(X0) & ~rich(X0)))) [nnf transformation 6]
52. ! [X0] : ((~old(X0) | rich(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (old(X0) & ~rich(X0)))) [flattening 51]
55. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | ~kind(X0)) & (kind(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 11]
82. ~calm(X0) | ~rich(X0) [cnf transformation 52]
97. kind(X0) | rich(X0) | kind(X0) [cnf transformation 55]
98. ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 55]
115. calm(paul) [cnf transformation 23]
116. kind(X0) | rich(X0) [duplicate literal removal 97]
117. ~kind(X0) | rich(X0) [duplicate literal removal 98]
171. rich(X0) [subsumption resolution 116,117]
223. ~rich(paul) [resolution 82,115]
224. $false [subsumption resolution 223,171]
% SZS output end Proof for 8784460441665776930351591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is wise then mary is either calm or not tall and vice versa. Everyone who is not tall is not strong or patient. Everyone who is curious or not humble is humble. If fred is both brave and rich then john is not old or tall and vice versa. Everyone who is either brave or not old is not kind. If mary is not old then paul is wise or not tall. Everyone who is not tall is not curious. If someone is not kind then someone is curious or calm. Everyone who is not humble is both generous and not brave. Everyone who is curious is not tall or happy. Everyone who is both not old and happy is either brave or not wise and vice versa. If paul is generous or not kind then someone is either not funny or not quiet and vice versa. If someone is both not creative and generous then someone is generous or not kind. Everyone who is not wise is both not old and not strong and vice versa. Everyone who is wise is both curious and not wise. Everyone who is generous or happy is either creative or funny. Lucy is either not happy or creative. Someone is not kind or not creative. Paul is not curious. Susan is not tall or not curious. Someone is not happy or not strong. Someone is brave or not patient. John is either not happy or not curious. Someone is not quiet. | Mary is not old. | entailment | ((wise(john))<=>((calm(mary)<~>~tall(mary))))&
(![X]:(~tall(X)=>(~strong(X)|patient(X))))&
(![X]:((curious(X)|~humble(X))=>humble(X)))&
(((brave(fred)&rich(fred)))<=>((~old(john)|tall(john))))&
(![X]:((brave(X)<~>~old(X))=>~kind(X)))&
((~old(mary))=>((wise(paul)|~tall(paul))))&
(![X]:(~tall(X)=>~curious(X)))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|calm(X)))))&
(![X]:(~humble(X)=>(generous(X)&~brave(X))))&
(![X]:(curious(X)=>(~tall(X)|happy(X))))&
(![X]:((~old(X)&happy(X))<=>(brave(X)<~>~wise(X))))&
(((generous(paul)|~kind(paul)))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:(~wise(X)<=>(~old(X)&~strong(X))))&
(![X]:(wise(X)=>(curious(X)&~wise(X))))&
(![X]:((generous(X)|happy(X))=>(creative(X)<~>funny(X))))&
((~happy(lucy)<~>creative(lucy)))&
(?[X]:((~kind(X)|~creative(X))))&
(~curious(paul))&
((~tall(susan)|~curious(susan)))&
(?[X]:((~happy(X)|~strong(X))))&
(?[X]:((brave(X)|~patient(X))))&
((~happy(john)<~>~curious(john)))&
(?[X]:(~quiet(X))) | ~old(mary) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5264839615680281584962931
% SZS output start Proof for 5264839615680281584962931
14. ! [X0] : (~wise(X0) <=> (~strong(X0) & ~old(X0))) [input p13]
15. ! [X0] : (wise(X0) => (~wise(X0) & curious(X0))) [input p14]
25. old(mary) [input hypothesis]
40. ! [X0] : ((~wise(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 15]
59. ! [X0] : ((~wise(X0) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | wise(X0))) [nnf transformation 14]
60. ! [X0] : ((~wise(X0) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | wise(X0))) [flattening 59]
101. ~old(X0) | wise(X0) [cnf transformation 60]
105. ~wise(X0) | ~wise(X0) [cnf transformation 40]
120. old(mary) [cnf transformation 25]
121. ~wise(X0) [duplicate literal removal 105]
160. 8 <=> old(mary) [avatar definition]
162. old(mary) <- (8) [avatar component clause 160]
265. 8 [avatar split clause 120,160]
270. wise(mary) <- (8) [resolution 101,162]
273. $false <- (8) [subsumption resolution 270,121]
274. ~8 [avatar contradiction clause 273]
275. $false [avatar sat refutation 265,274]
% SZS output end Proof for 5264839615680281584962931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not humble then someone is not tall.
Everyone who is not tall or strong is both rich and not rich and vice versa.
Everyone who is both not tall and happy is generous or not funny and vice versa.
Everyone who is both not funny and not tall is either not happy or not generous.
If susan is both rich and not strong then someone is happy.
If someone is rich then paul is both not funny and not humble.
Everyone who is both not funny and not wise is not calm or patient and vice versa.
If lucy is not strong or calm then someone is either not tall or not old and vice versa.
If alice is either happy or funny then someone is either not quiet or brave and vice versa.
Everyone who is humble is patient or not quiet.
Everyone who is both not kind and creative is not rich or not curious and vice versa.
Everyone who is not old is both funny and not quiet.
If alice is either quiet or tall then john is not quiet and vice versa.
If paul is not curious or patient then someone is either not generous or not humble and vice versa.
Someone is not rich.
Someone is either not wise or humble.
Someone is not happy or strong.
Someone is not wise.
Someone is not curious.
Someone is not old or not quiet. | Alice is rich. | contradiction | ((~humble(mary))=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|strong(X))<=>(rich(X)&~rich(X))))&
(![X]:((~tall(X)&happy(X))<=>(generous(X)|~funny(X))))&
(![X]:((~funny(X)&~tall(X))=>(~happy(X)<~>~generous(X))))&
(((rich(susan)&~strong(susan)))=>(?[X]:(happy(X))))&
((?[X]:(rich(X)))=>((~funny(paul)&~humble(paul))))&
(![X]:((~funny(X)&~wise(X))<=>(~calm(X)|patient(X))))&
(((~strong(lucy)|calm(lucy)))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((happy(alice)<~>funny(alice)))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:(humble(X)=>(patient(X)|~quiet(X))))&
(![X]:((~kind(X)&creative(X))<=>(~rich(X)|~curious(X))))&
(![X]:(~old(X)=>(funny(X)&~quiet(X))))&
(((quiet(alice)<~>tall(alice)))<=>(~quiet(john)))&
(((~curious(paul)|patient(paul)))<=>(?[X]:((~generous(X)<~>~humble(X)))))&
(?[X]:(~rich(X)))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((~happy(X)|strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~old(X)|~quiet(X)))) | rich(alice) | [
"p1",
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4513820522539315006405279
% SZS output start Proof for 4513820522539315006405279
2. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (~rich(X0) & rich(X0))) [input p1]
3. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (~funny(X0) | generous(X0))) [input p2]
6. ? [X0] : rich(X0) => (~humble(paul) & ~funny(paul)) [input p5]
21. rich(alice) [input hypothesis]
27. (~humble(paul) & ~funny(paul)) | ! [X0] : ~rich(X0) [ennf transformation 6]
33. ! [X0] : (((strong(X0) | ~tall(X0)) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 2]
34. ! [X0] : ((strong(X0) | ~tall(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | (~strong(X0) & tall(X0)))) [flattening 33]
35. ! [X0] : (((happy(X0) & ~tall(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 3]
36. ! [X0] : (((happy(X0) & ~tall(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | ~happy(X0) | tall(X0))) [flattening 35]
73. rich(X0) | tall(X0) [cnf transformation 34]
75. ~rich(X0) | tall(X0) [cnf transformation 34]
80. ~tall(X0) | funny(X0) [cnf transformation 36]
86. ~funny(paul) | ~rich(X0) [cnf transformation 27]
132. rich(alice) [cnf transformation 21]
143. tall(X0) [subsumption resolution 73,75]
144. funny(X0) [subsumption resolution 80,143]
157. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
158. ~rich(X0) <- (5) [avatar component clause 157]
164. ~rich(X0) [subsumption resolution 86,144]
165. 5 [avatar split clause 164,157]
241. $false <- (5) [resolution 158,132]
242. ~5 [avatar contradiction clause 241]
243. $false [avatar sat refutation 165,242]
% SZS output end Proof for 4513820522539315006405279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not calm is not strong or not tall.
Everyone who is both humble and not tall is not generous and vice versa.
Everyone who is not creative or not patient is both strong and tall and vice versa.
Everyone who is both strong and calm is either not strong or not tall and vice versa.
If someone is not calm or calm then someone is either curious or rich and vice versa.
Everyone who is not creative is either kind or not kind.
Everyone who is both curious and rich is both not humble and humble and vice versa.
Everyone who is both not strong and brave is patient or funny and vice versa.
Everyone who is either not funny or old is both rich and not happy.
If paul is either not quiet or patient then fred is both not rich and not wise and vice versa.
Everyone who is curious or strong is both not kind and calm and vice versa.
If someone is creative then someone is curious or patient and vice versa.
Everyone who is not calm or not humble is both wise and not tall and vice versa.
If mary is strong then someone is either not calm or creative.
If someone is either not kind or not generous then john is not brave.
Everyone who is not creative or tall is both not happy and calm and vice versa.
Someone is calm or not creative.
Someone is happy or generous.
Someone is not tall or strong.
Someone is not quiet.
Someone is both brave and calm.
Lucy is both humble and not generous.
Paul is both old and not tall. | John is not strong. | entailment | (![X]:((humble(X)<~>~calm(X))=>(~strong(X)|~tall(X))))&
(![X]:((humble(X)&~tall(X))<=>~generous(X)))&
(![X]:((~creative(X)|~patient(X))<=>(strong(X)&tall(X))))&
(![X]:((strong(X)&calm(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:(~creative(X)=>(kind(X)<~>~kind(X))))&
(![X]:((curious(X)&rich(X))<=>(~humble(X)&humble(X))))&
(![X]:((~strong(X)&brave(X))<=>(patient(X)|funny(X))))&
(![X]:((~funny(X)<~>old(X))=>(rich(X)&~happy(X))))&
(((~quiet(paul)<~>patient(paul)))<=>((~rich(fred)&~wise(fred))))&
(![X]:((curious(X)|strong(X))<=>(~kind(X)&calm(X))))&
((?[X]:(creative(X)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~calm(X)|~humble(X))<=>(wise(X)&~tall(X))))&
((strong(mary))=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((~kind(X)<~>~generous(X))))=>(~brave(john)))&
(![X]:((~creative(X)|tall(X))<=>(~happy(X)&calm(X))))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((~tall(X)|strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)&calm(X))))&
((humble(lucy)&~generous(lucy)))&
((old(paul)&~tall(paul))) | ~strong(john) | [
"p2",
"p3",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 356501178365448576573227
% SZS output start Proof for 356501178365448576573227
3. ! [X0] : ((~patient(X0) | ~creative(X0)) <=> (tall(X0) & strong(X0))) [input p2]
4. ! [X0] : ((calm(X0) & strong(X0)) <=> (~strong(X0) <~> ~tall(X0))) [input p3]
8. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (funny(X0) | patient(X0))) [input p7]
13. ! [X0] : ((~humble(X0) | ~calm(X0)) <=> (~tall(X0) & wise(X0))) [input p12]
24. strong(john) [input hypothesis]
36. ! [X0] : (((~patient(X0) | ~creative(X0)) | (~tall(X0) | ~strong(X0))) & ((tall(X0) & strong(X0)) | (patient(X0) & creative(X0)))) [nnf transformation 3]
37. ! [X0] : ((~patient(X0) | ~creative(X0) | ~tall(X0) | ~strong(X0)) & ((tall(X0) & strong(X0)) | (patient(X0) & creative(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & strong(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) & (((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~calm(X0) | ~strong(X0)))) [nnf transformation 4]
39. ! [X0] : (((calm(X0) & strong(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) & (((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ~calm(X0) | ~strong(X0))) [flattening 38]
48. ! [X0] : (((brave(X0) & ~strong(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (~brave(X0) | strong(X0)))) [nnf transformation 8]
49. ! [X0] : (((brave(X0) & ~strong(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | ~brave(X0) | strong(X0))) [flattening 48]
60. ! [X0] : (((~humble(X0) | ~calm(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (humble(X0) & calm(X0)))) [nnf transformation 13]
61. ! [X0] : ((~humble(X0) | ~calm(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | (humble(X0) & calm(X0)))) [flattening 60]
86. patient(X0) | tall(X0) [cnf transformation 37]
88. ~tall(X0) | ~strong(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 39]
90. strong(X0) | ~tall(X0) | strong(X0) [cnf transformation 39]
107. ~patient(X0) | ~strong(X0) [cnf transformation 49]
131. ~tall(X0) | calm(X0) [cnf transformation 61]
153. strong(john) [cnf transformation 24]
154. ~tall(X0) | ~strong(X0) | ~calm(X0) [duplicate literal removal 88]
155. strong(X0) | ~tall(X0) [duplicate literal removal 90]
156. ~tall(X0) | ~calm(X0) [subsumption resolution 154,155]
223. ~tall(X0) [subsumption resolution 131,156]
273. ~strong(X0) | tall(X0) [resolution 107,86]
276. ~strong(X0) [subsumption resolution 273,223]
277. $false [resolution 276,153]
% SZS output end Proof for 356501178365448576573227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or not brave then someone is humble or not calm.
Everyone who is not generous is not funny.
If someone is funny then mary is either not kind or creative and vice versa.
Everyone who is creative or kind is both not curious and quiet.
Everyone who is strong or not curious is kind and vice versa.
Everyone who is not brave or not creative is not old or quiet and vice versa.
Everyone who is old or brave is both tall and creative.
Everyone who is either not wise or quiet is not rich.
Everyone who is not brave or patient is not quiet or not kind.
Everyone who is not kind or not humble is either not happy or strong.
If someone is generous or not brave then alice is not curious or not creative.
If mary is either not old or not happy then someone is not rich or not curious.
Everyone who is brave or rich is calm or not tall.
If someone is either not quiet or curious then someone is patient and vice versa.
Everyone who is calm or wise is humble or not kind.
Susan is either happy or funny.
Someone is either brave or not calm.
Mary is patient.
Someone is either kind or patient.
Someone is rich. | Mary is not strong. | entailment | ((?[X]:((kind(X)|~brave(X))))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~generous(X)=>~funny(X)))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>creative(mary))))&
(![X]:((creative(X)|kind(X))=>(~curious(X)&quiet(X))))&
(![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:((~brave(X)|~creative(X))<=>(~old(X)|quiet(X))))&
(![X]:((old(X)|brave(X))=>(tall(X)&creative(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:((~brave(X)|patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((generous(X)|~brave(X))))=>((~curious(alice)|~creative(alice))))&
(((~old(mary)<~>~happy(mary)))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((brave(X)|rich(X))=>(calm(X)|~tall(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)|wise(X))=>(humble(X)|~kind(X))))&
((happy(susan)<~>funny(susan)))&
(?[X]:((brave(X)<~>~calm(X))))&
(patient(mary))&
(?[X]:((kind(X)<~>patient(X))))&
(?[X]:(rich(X))) | ~strong(mary) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7804331701378675283249222
% SZS output start Proof for 7804331701378675283249222
4. ! [X0] : ((kind(X0) | creative(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~brave(X0)) <=> (quiet(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((brave(X0) | old(X0)) => (creative(X0) & tall(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~brave(X0)) => (~kind(X0) | ~quiet(X0))) [input p8]
21. strong(mary) [input hypothesis]
28. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 4]
29. ! [X0] : ((creative(X0) & tall(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) | ~quiet(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 9]
32. ! [X0] : (~kind(X0) | ~quiet(X0) | (~patient(X0) & brave(X0))) [flattening 31]
43. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 43]
45. ! [X0] : (((~creative(X0) | ~brave(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (creative(X0) & brave(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~brave(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (creative(X0) & brave(X0)))) [flattening 45]
73. ~creative(X0) | quiet(X0) [cnf transformation 28]
74. ~kind(X0) | quiet(X0) [cnf transformation 28]
75. ~strong(X0) | kind(X0) [cnf transformation 44]
81. ~creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
85. creative(X0) | ~brave(X0) [cnf transformation 29]
88. ~kind(X0) | ~quiet(X0) | brave(X0) [cnf transformation 32]
110. strong(mary) [cnf transformation 21]
130. ~creative(X0) | ~brave(X0) [subsumption resolution 81,73]
132. ~brave(X0) [subsumption resolution 85,130]
134. ~kind(X0) | ~quiet(X0) [subsumption resolution 88,132]
135. ~kind(X0) [subsumption resolution 134,74]
193. kind(mary) [resolution 75,110]
194. $false [subsumption resolution 193,135]
% SZS output end Proof for 7804331701378675283249222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or tall is either humble or not happy and vice versa. If someone is either not strong or not funny then someone is wise. If lucy is not rich or not brave then john is either not generous or not funny. Everyone who is either patient or not happy is both wise and not kind. If someone is either quiet or strong then someone is either not kind or not strong. If someone is not funny or curious then someone is either not calm or not humble and vice versa. If john is both not funny and happy then alice is not patient and vice versa. Everyone who is either not humble or not curious is not curious and vice versa. Everyone who is creative or not curious is humble. If someone is both not generous and old then someone is generous or not calm. If paul is patient or not patient then someone is either tall or happy and vice versa. If someone is either not brave or happy then someone is either not quiet or happy. Everyone who is either funny or not funny is either not creative or quiet. If paul is both generous and not kind then susan is not quiet and vice versa. Everyone who is creative is either not calm or strong. Everyone who is not quiet or not tall is curious or funny and vice versa. Someone is not tall. Paul is not happy or not calm. Alice is either not wise or not quiet. Someone is not patient or humble. Someone is either not creative or strong. Someone is not quiet. Someone is not strong or happy. | John is not patient. | neutral | (![X]:((patient(X)<~>tall(X))<=>(humble(X)<~>~happy(X))))&
((?[X]:((~strong(X)<~>~funny(X))))=>(?[X]:(wise(X))))&
(((~rich(lucy)|~brave(lucy)))=>((~generous(john)<~>~funny(john))))&
(![X]:((patient(X)<~>~happy(X))=>(wise(X)&~kind(X))))&
((?[X]:((quiet(X)<~>strong(X))))=>(?[X]:((~kind(X)<~>~strong(X)))))&
((?[X]:((~funny(X)|curious(X))))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(((~funny(john)&happy(john)))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~curious(X))<=>~curious(X)))&
(![X]:((creative(X)|~curious(X))=>humble(X)))&
((?[X]:((~generous(X)&old(X))))=>(?[X]:((generous(X)|~calm(X)))))&
(((patient(paul)|~patient(paul)))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((funny(X)<~>~funny(X))=>(~creative(X)<~>quiet(X))))&
(((generous(paul)&~kind(paul)))<=>(~quiet(susan)))&
(![X]:(creative(X)=>(~calm(X)<~>strong(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(curious(X)|funny(X))))&
(?[X]:(~tall(X)))&
((~happy(paul)|~calm(paul)))&
((~wise(alice)<~>~quiet(alice)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~strong(X)|happy(X)))) | ~patient(john) | [] | null | 0 |
Subsets and Splits