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 not old or tall is humble or wise. If someone is both not brave and humble then someone is kind. If someone is both not creative and not humble then someone is both strong and not strong and vice versa. If lucy is both old and not kind then alice is old and vice versa. Everyone who is not old or patient is not wise and vice versa. Everyone who is humble is creative or not rich. Everyone who is either curious or generous is wise or patient and vice versa. If fred is either not tall or not happy then someone is not curious and vice versa. Everyone who is not quiet or rich is both not quiet and not brave and vice versa. If someone is quiet then lucy is humble or not generous and vice versa. If someone is humble then alice is both not creative and rich and vice versa. Everyone who is not generous or curious is both not calm and strong and vice versa. If someone is either old or happy then someone is both calm and patient. If susan is brave or not old then mary is brave. Everyone who is either not tall or tall is not old or funny. If someone is both quiet and brave then lucy is humble and vice versa. Someone is both patient and not brave. Fred is old or not tall. John is generous. Someone is wise. Alice is either wise or not tall. Paul is either quiet or not quiet. Mary is tall. | Alice is brave. | contradiction | (![X]:((~old(X)<~>tall(X))=>(humble(X)|wise(X))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:(kind(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((strong(X)&~strong(X)))))&
(((old(lucy)&~kind(lucy)))<=>(old(alice)))&
(![X]:((~old(X)|patient(X))<=>~wise(X)))&
(![X]:(humble(X)=>(creative(X)|~rich(X))))&
(![X]:((curious(X)<~>generous(X))<=>(wise(X)|patient(X))))&
(((~tall(fred)<~>~happy(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((~quiet(X)|rich(X))<=>(~quiet(X)&~brave(X))))&
((?[X]:(quiet(X)))<=>((humble(lucy)|~generous(lucy))))&
((?[X]:(humble(X)))<=>((~creative(alice)&rich(alice))))&
(![X]:((~generous(X)|curious(X))<=>(~calm(X)&strong(X))))&
((?[X]:((old(X)<~>happy(X))))=>(?[X]:((calm(X)&patient(X)))))&
(((brave(susan)|~old(susan)))=>(brave(mary)))&
(![X]:((~tall(X)<~>tall(X))=>(~old(X)|funny(X))))&
((?[X]:((quiet(X)&brave(X))))<=>(humble(lucy)))&
(?[X]:((patient(X)&~brave(X))))&
((old(fred)|~tall(fred)))&
(generous(john))&
(?[X]:(wise(X)))&
((wise(alice)<~>~tall(alice)))&
((quiet(paul)<~>~quiet(paul)))&
(tall(mary)) | brave(alice) | [
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8718217708423701264110838
% SZS output start Proof for 8718217708423701264110838
9. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p8]
11. ? [X0] : humble(X0) <=> (rich(alice) & ~creative(alice)) [input p10]
16. ? [X0] : (brave(X0) & quiet(X0)) <=> humble(lucy) [input p15]
24. brave(alice) [input hypothesis]
55. ! [X0] : (((rich(X0) | ~quiet(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 9]
56. ! [X0] : ((rich(X0) | ~quiet(X0) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 55]
62. (? [X0] : humble(X0) | (~rich(alice) | creative(alice))) & ((rich(alice) & ~creative(alice)) | ! [X0] : ~humble(X0)) [nnf transformation 11]
63. (? [X0] : humble(X0) | ~rich(alice) | creative(alice)) & ((rich(alice) & ~creative(alice)) | ! [X0] : ~humble(X0)) [flattening 62]
64. (? [X0] : humble(X0) | ~rich(alice) | creative(alice)) & ((rich(alice) & ~creative(alice)) | ! [X1] : ~humble(X1)) [rectify 63]
65. ? [X0] : humble(X0) => humble(sK5) [choice axiom]
66. (humble(sK5) | ~rich(alice) | creative(alice)) & ((rich(alice) & ~creative(alice)) | ! [X1] : ~humble(X1)) [skolemisation 64,65]
73. (? [X0] : (brave(X0) & quiet(X0)) | ~humble(lucy)) & (humble(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) [nnf transformation 16]
74. (? [X0] : (brave(X0) & quiet(X0)) | ~humble(lucy)) & (humble(lucy) | ! [X1] : (~brave(X1) | ~quiet(X1))) [rectify 73]
75. ? [X0] : (brave(X0) & quiet(X0)) => (brave(sK7) & quiet(sK7)) [choice axiom]
76. ((brave(sK7) & quiet(sK7)) | ~humble(lucy)) & (humble(lucy) | ! [X1] : (~brave(X1) | ~quiet(X1))) [skolemisation 74,75]
109. ~brave(X0) | quiet(X0) [cnf transformation 56]
110. ~rich(X0) | ~brave(X0) [cnf transformation 56]
116. rich(alice) | ~humble(X1) [cnf transformation 66]
129. humble(lucy) | ~brave(X1) | ~quiet(X1) [cnf transformation 76]
142. brave(alice) [cnf transformation 24]
204. 14 <=> humble(lucy) [avatar definition]
205. humble(lucy) <- (14) [avatar component clause 204]
217. 17 <=> rich(alice) [avatar definition]
218. rich(alice) <- (17) [avatar component clause 217]
226. 19 <=> ! [X1] : ~humble(X1) [avatar definition]
227. ~humble(X1) <- (19) [avatar component clause 226]
228. 19 | 17 [avatar split clause 116,217,226]
272. humble(lucy) | ~brave(X1) [subsumption resolution 129,109]
274. 29 <=> ! [X1] : ~brave(X1) [avatar definition]
275. ~brave(X1) <- (29) [avatar component clause 274]
276. 29 | 14 [avatar split clause 272,204,274]
298. ~brave(alice) <- (17) [resolution 110,218]
299. $false <- (17) [subsumption resolution 298,142]
300. ~17 [avatar contradiction clause 299]
301. $false <- (14, 19) [resolution 227,205]
304. ~14 | ~19 [avatar contradiction clause 301]
305. $false <- (29) [resolution 275,142]
308. ~29 [avatar contradiction clause 305]
309. $false [avatar sat refutation 228,276,300,304,308]
% SZS output end Proof for 8718217708423701264110838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or creative is both tall and funny and vice versa.
Everyone who is either curious or not calm is not brave.
If fred is kind or not creative then someone is kind or brave.
Everyone who is old is brave and vice versa.
Everyone who is not old or not curious is either not creative or not brave.
If someone is both not patient and not humble then mary is both happy and not quiet.
If someone is not humble then paul is both not patient and not creative and vice versa.
If someone is either not tall or generous then mary is both not brave and not happy and vice versa.
If someone is creative or not quiet then someone is both strong and not strong.
If mary is calm or not happy then paul is both not tall and old.
If mary is either not strong or kind then someone is either not quiet or not happy and vice versa.
If someone is both tall and calm then someone is either not generous or not curious and vice versa.
If someone is both calm and not rich then john is strong and vice versa.
Everyone who is either old or patient is either not patient or not calm.
If someone is not calm or happy then someone is creative or strong.
Paul is curious or not generous.
Mary is either kind or not quiet.
Someone is either not wise or not creative.
Fred is both not rich and tall.
Someone is both not humble and not generous. | Mary is humble. | neutral | (![X]:((kind(X)<~>creative(X))<=>(tall(X)&funny(X))))&
(![X]:((curious(X)<~>~calm(X))=>~brave(X)))&
(((kind(fred)|~creative(fred)))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(old(X)<=>brave(X)))&
(![X]:((~old(X)|~curious(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:((~patient(X)&~humble(X))))=>((happy(mary)&~quiet(mary))))&
((?[X]:(~humble(X)))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((~tall(X)<~>generous(X))))<=>((~brave(mary)&~happy(mary))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(((calm(mary)|~happy(mary)))=>((~tall(paul)&old(paul))))&
(((~strong(mary)<~>kind(mary)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
((?[X]:((tall(X)&calm(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((calm(X)&~rich(X))))<=>(strong(john)))&
(![X]:((old(X)<~>patient(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:((~calm(X)|happy(X))))=>(?[X]:((creative(X)|strong(X)))))&
((curious(paul)|~generous(paul)))&
((kind(mary)<~>~quiet(mary)))&
(?[X]:((~wise(X)<~>~creative(X))))&
((~rich(fred)&tall(fred)))&
(?[X]:((~humble(X)&~generous(X)))) | humble(mary) | [] | null | 0 |
If someone is curious or wise then mary is both not old and not strong.
Everyone who is both wise and not old is both tall and not strong and vice versa.
Everyone who is either not curious or not brave is both curious and not strong.
If fred is not tall or tall then alice is not old or not patient.
If someone is either not curious or tall then paul is both happy and wise and vice versa.
Everyone who is old or humble is both quiet and wise.
Everyone who is happy or not tall is both not quiet and wise and vice versa.
Everyone who is not happy is quiet and vice versa.
If susan is not humble then someone is either happy or not humble.
Everyone who is both tall and not wise is wise or not rich.
If someone is both generous and not rich then mary is not strong or not patient and vice versa.
If fred is calm or not strong then someone is not humble.
Everyone who is brave or funny is either not generous or not quiet.
Everyone who is either strong or humble is either not brave or patient and vice versa.
If fred is not rich then paul is creative.
If someone is both strong and not funny then paul is curious.
Someone is both not rich and not happy.
Someone is old or not kind.
Someone is not wise.
Susan is patient or humble.
John is both not humble and not happy.
Someone is not generous or kind.
Susan is kind or creative.
Alice is either patient or not tall. | Mary is wise. | entailment | ((?[X]:((curious(X)|wise(X))))=>((~old(mary)&~strong(mary))))&
(![X]:((wise(X)&~old(X))<=>(tall(X)&~strong(X))))&
(![X]:((~curious(X)<~>~brave(X))=>(curious(X)&~strong(X))))&
(((~tall(fred)|tall(fred)))=>((~old(alice)|~patient(alice))))&
((?[X]:((~curious(X)<~>tall(X))))<=>((happy(paul)&wise(paul))))&
(![X]:((old(X)|humble(X))=>(quiet(X)&wise(X))))&
(![X]:((happy(X)|~tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:(~happy(X)<=>quiet(X)))&
((~humble(susan))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((tall(X)&~wise(X))=>(wise(X)|~rich(X))))&
((?[X]:((generous(X)&~rich(X))))<=>((~strong(mary)|~patient(mary))))&
(((calm(fred)|~strong(fred)))=>(?[X]:(~humble(X))))&
(![X]:((brave(X)|funny(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>humble(X))<=>(~brave(X)<~>patient(X))))&
((~rich(fred))=>(creative(paul)))&
((?[X]:((strong(X)&~funny(X))))=>(curious(paul)))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:(~wise(X)))&
((patient(susan)|humble(susan)))&
((~humble(john)&~happy(john)))&
(?[X]:((~generous(X)|kind(X))))&
((kind(susan)|creative(susan)))&
((patient(alice)<~>~tall(alice))) | wise(mary) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 375658838932172663134602
% SZS output start Proof for 375658838932172663134602
1. ? [X0] : (wise(X0) | curious(X0)) => (~strong(mary) & ~old(mary)) [input p0]
2. ! [X0] : ((~old(X0) & wise(X0)) <=> (~strong(X0) & tall(X0))) [input p1]
3. ! [X0] : ((~curious(X0) <~> ~brave(X0)) => (~strong(X0) & curious(X0))) [input p2]
5. ? [X0] : (~curious(X0) <~> tall(X0)) <=> (wise(paul) & happy(paul)) [input p4]
6. ! [X0] : ((humble(X0) | old(X0)) => (wise(X0) & quiet(X0))) [input p5]
7. ! [X0] : ((~tall(X0) | happy(X0)) <=> (wise(X0) & ~quiet(X0))) [input p6]
14. ! [X0] : ((strong(X0) <~> humble(X0)) <=> (~brave(X0) <~> patient(X0))) [input p13]
24. patient(alice) <~> ~tall(alice) [input p23]
25. ~wise(mary) [input hypothesis]
29. (~strong(mary) & ~old(mary)) | ! [X0] : (~wise(X0) & ~curious(X0)) [ennf transformation 1]
30. ! [X0] : ((~strong(X0) & curious(X0)) | (~curious(X0) <=> ~brave(X0))) [ennf transformation 3]
33. ! [X0] : ((wise(X0) & quiet(X0)) | (~humble(X0) & ~old(X0))) [ennf transformation 6]
40. ! [X0] : (((~old(X0) & wise(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (old(X0) | ~wise(X0)))) [nnf transformation 2]
41. ! [X0] : (((~old(X0) & wise(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | old(X0) | ~wise(X0))) [flattening 40]
42. ! [X0] : ((~strong(X0) & curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) [nnf transformation 30]
43. (? [X0] : ((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | (~wise(paul) | ~happy(paul))) & ((wise(paul) & happy(paul)) | ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) [nnf transformation 5]
44. (? [X0] : ((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~wise(paul) | ~happy(paul)) & ((wise(paul) & happy(paul)) | ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) [flattening 43]
45. (? [X0] : ((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~wise(paul) | ~happy(paul)) & ((wise(paul) & happy(paul)) | ! [X1] : ((~curious(X1) | ~tall(X1)) & (tall(X1) | curious(X1)))) [rectify 44]
46. ? [X0] : ((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) => ((~tall(sK0) | curious(sK0)) & (tall(sK0) | ~curious(sK0))) [choice axiom]
47. (((~tall(sK0) | curious(sK0)) & (tall(sK0) | ~curious(sK0))) | ~wise(paul) | ~happy(paul)) & ((wise(paul) & happy(paul)) | ! [X1] : ((~curious(X1) | ~tall(X1)) & (tall(X1) | curious(X1)))) [skolemisation 45,46]
48. ! [X0] : (((~tall(X0) | happy(X0)) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | (tall(X0) & ~happy(X0)))) [nnf transformation 7]
49. ! [X0] : ((~tall(X0) | happy(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | (tall(X0) & ~happy(X0)))) [flattening 48]
62. ! [X0] : ((((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))))) [nnf transformation 14]
71. (tall(alice) | ~patient(alice)) & (~tall(alice) | patient(alice)) [nnf transformation 24]
75. ~strong(mary) | ~wise(X0) [cnf transformation 29]
76. ~wise(X0) | old(X0) | tall(X0) [cnf transformation 41]
78. ~tall(X0) | strong(X0) | wise(X0) [cnf transformation 41]
80. curious(X0) | ~brave(X0) | curious(X0) [cnf transformation 42]
89. wise(paul) | ~curious(X1) | ~tall(X1) [cnf transformation 47]
92. ~old(X0) | quiet(X0) [cnf transformation 33]
95. ~humble(X0) | wise(X0) [cnf transformation 33]
97. ~quiet(X0) | tall(X0) [cnf transformation 49]
99. tall(X0) | wise(X0) [cnf transformation 49]
118. ~patient(X0) | brave(X0) | humble(X0) | ~strong(X0) [cnf transformation 62]
133. ~tall(alice) | patient(alice) [cnf transformation 71]
135. ~wise(mary) [cnf transformation 25]
137. ~brave(X0) | curious(X0) [duplicate literal removal 80]
139. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
140. ~wise(X0) <- (1) [avatar component clause 139]
142. 2 <=> strong(mary) [avatar definition]
144. ~strong(mary) <- (~2) [avatar component clause 142]
145. 1 | ~2 [avatar split clause 75,142,139]
161. 6 <=> old(alice) [avatar definition]
162. old(alice) <- (6) [avatar component clause 161]
165. 7 <=> patient(alice) [avatar definition]
166. patient(alice) <- (7) [avatar component clause 165]
175. 9 <=> wise(paul) [avatar definition]
176. wise(paul) <- (9) [avatar component clause 175]
189. 12 <=> ! [X1] : (~curious(X1) | ~tall(X1)) [avatar definition]
190. ~tall(X1) | ~curious(X1) <- (12) [avatar component clause 189]
191. 12 | 9 [avatar split clause 89,175,189]
274. 30 <=> tall(alice) [avatar definition]
275. ~tall(alice) <- (~30) [avatar component clause 274]
276. tall(alice) <- (30) [avatar component clause 274]
278. 7 | ~30 [avatar split clause 133,274,165]
285. wise(alice) <- (~30) [resolution 99,275]
292. old(alice) | tall(alice) <- (~30) [resolution 76,285]
296. old(alice) <- (~30) [subsumption resolution 292,275]
297. 6 | 30 [avatar split clause 296,274,161]
310. quiet(alice) <- (6) [resolution 162,92]
318. tall(alice) <- (6) [resolution 310,97]
320. $false <- (6, ~30) [subsumption resolution 318,275]
321. ~6 | 30 [avatar contradiction clause 320]
322. ~curious(alice) <- (12, 30) [resolution 276,190]
329. strong(X0) | wise(X0) | wise(X0) [resolution 78,99]
334. strong(X0) | wise(X0) [duplicate literal removal 329]
399. brave(alice) | humble(alice) | ~strong(alice) <- (7) [resolution 118,166]
401. 43 <=> strong(alice) [avatar definition]
403. ~strong(alice) <- (~43) [avatar component clause 401]
405. 44 <=> humble(alice) [avatar definition]
407. humble(alice) <- (44) [avatar component clause 405]
409. 45 <=> brave(alice) [avatar definition]
411. brave(alice) <- (45) [avatar component clause 409]
412. ~43 | 44 | 45 | ~7 [avatar split clause 399,165,409,405,401]
499. wise(mary) <- (~2) [resolution 334,144]
503. wise(alice) <- (~43) [resolution 334,403]
504. $false <- (~2) [subsumption resolution 499,135]
505. 2 [avatar contradiction clause 504]
506. $false <- (1, 9) [resolution 140,176]
511. ~1 | ~9 [avatar contradiction clause 506]
601. $false <- (1, ~43) [resolution 503,140]
603. ~1 | 43 [avatar contradiction clause 601]
611. wise(alice) <- (44) [resolution 407,95]
613. $false <- (1, 44) [subsumption resolution 611,140]
614. ~1 | ~44 [avatar contradiction clause 613]
619. curious(alice) <- (45) [resolution 411,137]
632. $false <- (12, 30, 45) [subsumption resolution 619,322]
633. ~12 | ~30 | ~45 [avatar contradiction clause 632]
634. $false [avatar sat refutation 145,191,278,297,321,412,505,511,603,614,633]
% SZS output end Proof for 375658838932172663134602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and humble then someone is not strong or quiet and vice versa.
Everyone who is not old or not funny is brave or funny.
Everyone who is not generous or not quiet is not creative and vice versa.
Everyone who is curious or quiet is rich.
Everyone who is not happy or not tall is both curious and kind.
If someone is not tall then fred is either strong or not calm and vice versa.
If alice is creative or not strong then someone is both tall and curious and vice versa.
If someone is both creative and patient then someone is both not funny and curious.
If fred is either old or patient then someone is funny or not creative.
If paul is either tall or not curious then someone is not patient.
If alice is both not funny and not strong then someone is wise and vice versa.
Everyone who is creative is generous or not humble.
If fred is rich or not old then someone is not humble or kind and vice versa.
Everyone who is not brave is tall.
Everyone who is both kind and not patient is either tall or rich and vice versa.
If someone is both not rich and not wise then mary is funny or not curious.
John is both not calm and not generous.
Susan is both not strong and not brave.
Alice is calm.
Fred is tall.
Someone is both creative and not happy.
Someone is happy or generous.
Mary is both not tall and happy.
Someone is both wise and funny. | Fred is not calm. | neutral | ((?[X]:((kind(X)&humble(X))))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~old(X)|~funny(X))=>(brave(X)|funny(X))))&
(![X]:((~generous(X)|~quiet(X))<=>~creative(X)))&
(![X]:((curious(X)|quiet(X))=>rich(X)))&
(![X]:((~happy(X)|~tall(X))=>(curious(X)&kind(X))))&
((?[X]:(~tall(X)))<=>((strong(fred)<~>~calm(fred))))&
(((creative(alice)|~strong(alice)))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(((old(fred)<~>patient(fred)))=>(?[X]:((funny(X)|~creative(X)))))&
(((tall(paul)<~>~curious(paul)))=>(?[X]:(~patient(X))))&
(((~funny(alice)&~strong(alice)))<=>(?[X]:(wise(X))))&
(![X]:(creative(X)=>(generous(X)|~humble(X))))&
(((rich(fred)|~old(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:(~brave(X)=>tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(tall(X)<~>rich(X))))&
((?[X]:((~rich(X)&~wise(X))))=>((funny(mary)|~curious(mary))))&
((~calm(john)&~generous(john)))&
((~strong(susan)&~brave(susan)))&
(calm(alice))&
(tall(fred))&
(?[X]:((creative(X)&~happy(X))))&
(?[X]:((happy(X)|generous(X))))&
((~tall(mary)&happy(mary)))&
(?[X]:((wise(X)&funny(X)))) | ~calm(fred) | [] | null | 0 |
Everyone who is both not quiet and generous is not calm. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. If someone is either calm or curious then someone is both curious and not creative and vice versa. If someone is quiet or old then fred is not funny or not creative and vice versa. If someone is either curious or funny then someone is calm and vice versa. Fred is patient or brave. Someone is strong or not funny. Fred is both generous and funny. Alice is not funny or creative. Someone is either humble or not wise. Someone is not curious or not funny. Someone is generous. | Alice is generous. | neutral | (![X]:((~quiet(X)&generous(X))=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((quiet(X)|old(X))))<=>((~funny(fred)|~creative(fred))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
((patient(fred)|brave(fred)))&
(?[X]:((strong(X)|~funny(X))))&
((generous(fred)&funny(fred)))&
((~funny(alice)|creative(alice)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:(generous(X))) | generous(alice) | [] | null | 0 |
If someone is both strong and kind then paul is either not creative or not kind. If alice is old then mary is wise or not happy and vice versa. If someone is either not wise or humble then alice is wise. If someone is either not generous or kind then mary is either not humble or rich. Everyone who is old is funny or not funny and vice versa. If someone is not rich or kind then alice is not curious or not kind and vice versa. Everyone who is either not strong or calm is either kind or tall. Everyone who is not funny is not rich. If someone is both humble and patient then someone is not wise and vice versa. Everyone who is calm is not tall or calm and vice versa. Everyone who is generous or not generous is both not patient and curious. If someone is not patient or not funny then mary is tall and vice versa. If john is generous then someone is both not creative and not happy and vice versa. If john is both not curious and wise then someone is strong or not curious and vice versa. If fred is either not creative or not curious then someone is both patient and wise. Everyone who is humble is quiet. Someone is both not generous and not strong. Someone is either not curious or not funny. Paul is either not brave or patient. Susan is either rich or not patient. Paul is not creative. Fred is both not kind and wise. Susan is both not tall and not creative. Someone is old. | Fred is wise. | entailment | ((?[X]:((strong(X)&kind(X))))=>((~creative(paul)<~>~kind(paul))))&
((old(alice))<=>((wise(mary)|~happy(mary))))&
((?[X]:((~wise(X)<~>humble(X))))=>(wise(alice)))&
((?[X]:((~generous(X)<~>kind(X))))=>((~humble(mary)<~>rich(mary))))&
(![X]:(old(X)<=>(funny(X)|~funny(X))))&
((?[X]:((~rich(X)|kind(X))))<=>((~curious(alice)|~kind(alice))))&
(![X]:((~strong(X)<~>calm(X))=>(kind(X)<~>tall(X))))&
(![X]:(~funny(X)=>~rich(X)))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:(~wise(X))))&
(![X]:(calm(X)<=>(~tall(X)|calm(X))))&
(![X]:((generous(X)|~generous(X))=>(~patient(X)&curious(X))))&
((?[X]:((~patient(X)|~funny(X))))<=>(tall(mary)))&
((generous(john))<=>(?[X]:((~creative(X)&~happy(X)))))&
(((~curious(john)&wise(john)))<=>(?[X]:((strong(X)|~curious(X)))))&
(((~creative(fred)<~>~curious(fred)))=>(?[X]:((patient(X)&wise(X)))))&
(![X]:(humble(X)=>quiet(X)))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~brave(paul)<~>patient(paul)))&
((rich(susan)<~>~patient(susan)))&
(~creative(paul))&
((~kind(fred)&wise(fred)))&
((~tall(susan)&~creative(susan)))&
(?[X]:(old(X))) | wise(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5873344628079442713328179
% SZS output start Proof for 5873344628079442713328179
22. wise(fred) & ~kind(fred) [input p21]
25. ~wise(fred) [input hypothesis]
138. wise(fred) [cnf transformation 22]
142. ~wise(fred) [cnf transformation 25]
306. $false [subsumption resolution 142,138]
% SZS output end Proof for 5873344628079442713328179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is curious or not humble then paul is not humble or old and vice versa.
If lucy is both not curious and not rich then mary is not funny or humble.
Everyone who is not curious or rich is both strong and not tall and vice versa.
Everyone who is creative or not brave is either not funny or not brave.
Everyone who is not old is either not brave or funny.
If susan is strong then lucy is either humble or not brave and vice versa.
If someone is both not brave and not patient then alice is not old and vice versa.
Everyone who is either humble or brave is kind or not calm.
If someone is both not brave and not tall then alice is either generous or not calm and vice versa.
Everyone who is not creative or curious is both not brave and not funny.
Everyone who is calm is not humble or not quiet and vice versa.
If someone is either funny or brave then susan is either not quiet or not happy.
If lucy is wise then someone is either not curious or funny and vice versa.
If someone is either humble or not happy then someone is not tall and vice versa.
If someone is either not creative or patient then someone is either generous or not strong and vice versa.
If alice is not funny or not rich then someone is either humble or quiet and vice versa.
Lucy is either strong or brave.
Someone is either not generous or kind.
Alice is patient or not kind.
Someone is not calm or not generous.
Mary is brave or humble.
Mary is not brave or not kind.
Someone is either not happy or not curious. | Lucy is not tall. | entailment | (((curious(lucy)|~humble(lucy)))<=>((~humble(paul)|old(paul))))&
(((~curious(lucy)&~rich(lucy)))=>((~funny(mary)|humble(mary))))&
(![X]:((~curious(X)|rich(X))<=>(strong(X)&~tall(X))))&
(![X]:((creative(X)|~brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~old(X)=>(~brave(X)<~>funny(X))))&
((strong(susan))<=>((humble(lucy)<~>~brave(lucy))))&
((?[X]:((~brave(X)&~patient(X))))<=>(~old(alice)))&
(![X]:((humble(X)<~>brave(X))=>(kind(X)|~calm(X))))&
((?[X]:((~brave(X)&~tall(X))))<=>((generous(alice)<~>~calm(alice))))&
(![X]:((~creative(X)|curious(X))=>(~brave(X)&~funny(X))))&
(![X]:(calm(X)<=>(~humble(X)|~quiet(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((~quiet(susan)<~>~happy(susan))))&
((wise(lucy))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)<~>patient(X))))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(((~funny(alice)|~rich(alice)))<=>(?[X]:((humble(X)<~>quiet(X)))))&
((strong(lucy)<~>brave(lucy)))&
(?[X]:((~generous(X)<~>kind(X))))&
((patient(alice)|~kind(alice)))&
(?[X]:((~calm(X)|~generous(X))))&
((brave(mary)|humble(mary)))&
((~brave(mary)|~kind(mary)))&
(?[X]:((~happy(X)<~>~curious(X)))) | ~tall(lucy) | [
"p2",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4271277537405451057905952
% SZS output start Proof for 4271277537405451057905952
3. ! [X0] : ((rich(X0) | ~curious(X0)) <=> (~tall(X0) & strong(X0))) [input p2]
4. ! [X0] : ((~brave(X0) | creative(X0)) => (~funny(X0) <~> ~brave(X0))) [input p3]
10. ! [X0] : ((curious(X0) | ~creative(X0)) => (~funny(X0) & ~brave(X0))) [input p9]
24. tall(lucy) [input hypothesis]
29. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | (brave(X0) & ~creative(X0))) [ennf transformation 4]
33. ! [X0] : ((~funny(X0) & ~brave(X0)) | (~curious(X0) & creative(X0))) [ennf transformation 10]
37. ! [X0] : (((rich(X0) | ~curious(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~rich(X0) & curious(X0)))) [nnf transformation 3]
38. ! [X0] : ((rich(X0) | ~curious(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | (~rich(X0) & curious(X0)))) [flattening 37]
39. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | (brave(X0) & ~creative(X0))) [nnf transformation 29]
89. ~tall(X0) | curious(X0) [cnf transformation 38]
95. brave(X0) | funny(X0) | brave(X0) [cnf transformation 39]
114. ~brave(X0) | ~curious(X0) [cnf transformation 33]
116. ~funny(X0) | ~curious(X0) [cnf transformation 33]
156. tall(lucy) [cnf transformation 24]
157. brave(X0) | funny(X0) [duplicate literal removal 95]
163. 2 <=> curious(lucy) [avatar definition]
165. curious(lucy) <- (2) [avatar component clause 163]
438. curious(lucy) [resolution 89,156]
441. 2 [avatar split clause 438,163]
448. funny(X0) | ~curious(X0) [resolution 157,114]
493. ~curious(X0) [subsumption resolution 448,116]
521. $false <- (2) [resolution 493,165]
524. ~2 [avatar contradiction clause 521]
526. $false [avatar sat refutation 441,524]
% SZS output end Proof for 4271277537405451057905952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not calm is both funny and not tall.
If someone is not humble then someone is both calm and kind and vice versa.
If someone is wise or not wise then susan is either not humble or not wise.
Everyone who is brave or not wise is both not quiet and not old and vice versa.
If susan is generous then mary is not tall and vice versa.
If lucy is not tall then someone is both curious and not curious.
If someone is either not rich or strong then john is both strong and not wise and vice versa.
If lucy is either curious or not wise then someone is not generous or brave.
Everyone who is either humble or happy is not calm or not humble and vice versa.
Everyone who is curious or not kind is curious and vice versa.
Everyone who is strong is not quiet or not creative and vice versa.
Everyone who is either not brave or patient is both not old and rich.
Everyone who is either not creative or rich is tall or not brave.
Everyone who is both not wise and not patient is not funny or not calm.
Everyone who is curious is both not strong and strong.
Everyone who is both not old and not curious is not calm or not humble and vice versa.
Mary is either not calm or strong.
Someone is old or curious.
Someone is either quiet or not quiet.
Mary is strong.
John is both not wise and calm.
Someone is not kind or not rich.
Someone is not wise or not tall.
Someone is old or not funny. | Lucy is not calm. | neutral | (![X]:((humble(X)<~>~calm(X))=>(funny(X)&~tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((calm(X)&kind(X)))))&
((?[X]:((wise(X)|~wise(X))))=>((~humble(susan)<~>~wise(susan))))&
(![X]:((brave(X)|~wise(X))<=>(~quiet(X)&~old(X))))&
((generous(susan))<=>(~tall(mary)))&
((~tall(lucy))=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((~rich(X)<~>strong(X))))<=>((strong(john)&~wise(john))))&
(((curious(lucy)<~>~wise(lucy)))=>(?[X]:((~generous(X)|brave(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~calm(X)|~humble(X))))&
(![X]:((curious(X)|~kind(X))<=>curious(X)))&
(![X]:(strong(X)<=>(~quiet(X)|~creative(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~old(X)&rich(X))))&
(![X]:((~creative(X)<~>rich(X))=>(tall(X)|~brave(X))))&
(![X]:((~wise(X)&~patient(X))=>(~funny(X)|~calm(X))))&
(![X]:(curious(X)=>(~strong(X)&strong(X))))&
(![X]:((~old(X)&~curious(X))<=>(~calm(X)|~humble(X))))&
((~calm(mary)<~>strong(mary)))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(strong(mary))&
((~wise(john)&calm(john)))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((~wise(X)|~tall(X))))&
(?[X]:((old(X)|~funny(X)))) | ~calm(lucy) | [] | null | 0 |
If paul is either not kind or old then mary is not happy or not humble. If mary is both quiet and not kind then mary is wise or old and vice versa. If susan is either not brave or not happy then alice is both not wise and happy. If lucy is funny then someone is humble or calm. If someone is either quiet or not rich then someone is tall or calm and vice versa. Everyone who is both patient and brave is not strong and vice versa. Everyone who is not happy or not funny is both quiet and happy and vice versa. Everyone who is either not happy or not patient is tall or happy and vice versa. Everyone who is both wise and not curious is both not humble and quiet and vice versa. If lucy is both old and happy then alice is calm or not calm and vice versa. Everyone who is not humble or quiet is not patient or wise and vice versa. Everyone who is both not quiet and happy is not creative. If paul is not strong then someone is patient and vice versa. If someone is both not quiet and kind then someone is both not funny and wise and vice versa. If fred is both not quiet and not funny then susan is either not brave or not calm and vice versa. Everyone who is both old and brave is not quiet and vice versa. John is generous. Paul is both not creative and not funny. Someone is both not patient and not quiet. Paul is rich. Someone is not wise. Someone is not calm. Fred is both not wise and not curious. Susan is either quiet or not quiet. | Lucy is wise. | neutral | (((~kind(paul)<~>old(paul)))=>((~happy(mary)|~humble(mary))))&
(((quiet(mary)&~kind(mary)))<=>((wise(mary)|old(mary))))&
(((~brave(susan)<~>~happy(susan)))=>((~wise(alice)&happy(alice))))&
((funny(lucy))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((patient(X)&brave(X))<=>~strong(X)))&
(![X]:((~happy(X)|~funny(X))<=>(quiet(X)&happy(X))))&
(![X]:((~happy(X)<~>~patient(X))<=>(tall(X)|happy(X))))&
(![X]:((wise(X)&~curious(X))<=>(~humble(X)&quiet(X))))&
(((old(lucy)&happy(lucy)))<=>((calm(alice)|~calm(alice))))&
(![X]:((~humble(X)|quiet(X))<=>(~patient(X)|wise(X))))&
(![X]:((~quiet(X)&happy(X))=>~creative(X)))&
((~strong(paul))<=>(?[X]:(patient(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
(((~quiet(fred)&~funny(fred)))<=>((~brave(susan)<~>~calm(susan))))&
(![X]:((old(X)&brave(X))<=>~quiet(X)))&
(generous(john))&
((~creative(paul)&~funny(paul)))&
(?[X]:((~patient(X)&~quiet(X))))&
(rich(paul))&
(?[X]:(~wise(X)))&
(?[X]:(~calm(X)))&
((~wise(fred)&~curious(fred)))&
((quiet(susan)<~>~quiet(susan))) | wise(lucy) | [] | null | 0 |
Everyone who is not curious or rich is calm.
If alice is either generous or not generous then alice is both brave and not kind.
Everyone who is not tall or wise is both not rich and quiet and vice versa.
Everyone who is both not tall and not patient is either calm or quiet.
Everyone who is not quiet or not humble is humble or old.
If alice is not brave or not happy then someone is patient or not happy.
Everyone who is patient or happy is either not happy or old and vice versa.
If someone is both not patient and not quiet then someone is either not tall or rich and vice versa.
If someone is not strong or humble then someone is not rich and vice versa.
If mary is both not generous and not curious then alice is both not curious and strong.
Everyone who is both not wise and not quiet is not rich and vice versa.
Everyone who is old or not funny is not strong and vice versa.
Everyone who is both wise and curious is both brave and old and vice versa.
Everyone who is not patient is either not happy or not tall.
If mary is not generous or not quiet then someone is either not calm or kind and vice versa.
Someone is both not generous and not humble.
Someone is either not rich or not humble.
Someone is either not patient or not wise.
Lucy is both rich and not patient.
Someone is not funny.
Someone is either humble or strong. | Mary is not quiet. | neutral | (![X]:((~curious(X)|rich(X))=>calm(X)))&
(((generous(alice)<~>~generous(alice)))=>((brave(alice)&~kind(alice))))&
(![X]:((~tall(X)|wise(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~tall(X)&~patient(X))=>(calm(X)<~>quiet(X))))&
(![X]:((~quiet(X)|~humble(X))=>(humble(X)|old(X))))&
(((~brave(alice)|~happy(alice)))=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((patient(X)|happy(X))<=>(~happy(X)<~>old(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~tall(X)<~>rich(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:(~rich(X))))&
(((~generous(mary)&~curious(mary)))=>((~curious(alice)&strong(alice))))&
(![X]:((~wise(X)&~quiet(X))<=>~rich(X)))&
(![X]:((old(X)|~funny(X))<=>~strong(X)))&
(![X]:((wise(X)&curious(X))<=>(brave(X)&old(X))))&
(![X]:(~patient(X)=>(~happy(X)<~>~tall(X))))&
(((~generous(mary)|~quiet(mary)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
(?[X]:((~generous(X)&~humble(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
((rich(lucy)&~patient(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)<~>strong(X)))) | ~quiet(mary) | [] | null | 0 |
If someone is strong then someone is either not curious or wise and vice versa. Everyone who is either calm or brave is either calm or not wise and vice versa. Everyone who is not tall is not happy and vice versa. Everyone who is not creative is both not funny and strong and vice versa. Everyone who is not patient is brave or creative and vice versa. If someone is not happy or humble then lucy is both curious and not patient. If someone is not brave then someone is both not generous and not brave. Everyone who is either not curious or kind is not curious. If someone is not generous then john is both generous and tall. If lucy is either generous or kind then someone is either curious or happy. Everyone who is not patient is not wise. Everyone who is not patient or humble is not creative or rich. Everyone who is either tall or not strong is both rich and not humble. Everyone who is not wise or happy is either kind or not brave and vice versa. If someone is brave then someone is not tall and vice versa. Lucy is not generous. Someone is not creative or rich. Someone is either patient or not rich. John is both tall and quiet. | Lucy is not kind. | entailment | ((?[X]:(strong(X)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:((calm(X)<~>brave(X))<=>(calm(X)<~>~wise(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:(~creative(X)<=>(~funny(X)&strong(X))))&
(![X]:(~patient(X)<=>(brave(X)|creative(X))))&
((?[X]:((~happy(X)|humble(X))))=>((curious(lucy)&~patient(lucy))))&
((?[X]:(~brave(X)))=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((~curious(X)<~>kind(X))=>~curious(X)))&
((?[X]:(~generous(X)))=>((generous(john)&tall(john))))&
(((generous(lucy)<~>kind(lucy)))=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:(~patient(X)=>~wise(X)))&
(![X]:((~patient(X)|humble(X))=>(~creative(X)|rich(X))))&
(![X]:((tall(X)<~>~strong(X))=>(rich(X)&~humble(X))))&
(![X]:((~wise(X)|happy(X))<=>(kind(X)<~>~brave(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~tall(X))))&
(~generous(lucy))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
((tall(john)&quiet(john))) | ~kind(lucy) | [
"p2",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7661858521503565184674313
% SZS output start Proof for 7661858521503565184674313
3. ! [X0] : (~tall(X0) <=> ~happy(X0)) [input p2]
6. ? [X0] : (humble(X0) | ~happy(X0)) => (~patient(lucy) & curious(lucy)) [input p5]
8. ! [X0] : ((~curious(X0) <~> kind(X0)) => ~curious(X0)) [input p7]
14. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p13]
15. ? [X0] : brave(X0) <=> ? [X0] : ~tall(X0) [input p14]
20. kind(lucy) [input hypothesis]
23. ? [X0] : brave(X0) <=> ? [X1] : ~tall(X1) [rectify 15]
25. ? [X0] : ~happy(X0) => (~patient(lucy) & curious(lucy)) [pure predicate removal 6]
28. (~patient(lucy) & curious(lucy)) | ! [X0] : happy(X0) [ennf transformation 25]
30. ! [X0] : (~curious(X0) | (~curious(X0) <=> kind(X0))) [ennf transformation 8]
43. ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 3]
51. ! [X0] : (~curious(X0) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0)))) [nnf transformation 30]
56. ! [X0] : (((happy(X0) | ~wise(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~happy(X0) & wise(X0)))) [nnf transformation 14]
57. ! [X0] : ((happy(X0) | ~wise(X0) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~happy(X0) & wise(X0)))) [flattening 56]
58. (? [X0] : brave(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : ~brave(X0)) [nnf transformation 23]
59. (? [X0] : brave(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : ~brave(X3)) [rectify 58]
60. ? [X0] : brave(X0) => brave(sK4) [choice axiom]
61. ? [X2] : ~tall(X2) => ~tall(sK5) [choice axiom]
62. (brave(sK4) | ! [X1] : tall(X1)) & (~tall(sK5) | ! [X3] : ~brave(X3)) [skolemisation 59,61,60]
80. ~happy(X0) | tall(X0) [cnf transformation 43]
88. curious(lucy) | happy(X0) [cnf transformation 28]
93. ~curious(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 51]
107. ~kind(X0) | brave(X0) | ~happy(X0) [cnf transformation 57]
110. ~tall(sK5) | ~brave(X3) [cnf transformation 62]
117. kind(lucy) [cnf transformation 20]
118. ~kind(X0) | ~curious(X0) [duplicate literal removal 93]
151. 7 <=> ! [X0] : happy(X0) [avatar definition]
152. happy(X0) <- (7) [avatar component clause 151]
159. 9 <=> curious(lucy) [avatar definition]
162. 7 | 9 [avatar split clause 88,159,151]
190. 16 <=> kind(lucy) [avatar definition]
191. kind(lucy) <- (16) [avatar component clause 190]
213. 20 <=> ! [X1] : tall(X1) [avatar definition]
214. tall(X1) <- (20) [avatar component clause 213]
221. 22 <=> ! [X3] : ~brave(X3) [avatar definition]
222. ~brave(X3) <- (22) [avatar component clause 221]
224. 23 <=> tall(sK5) [avatar definition]
226. ~tall(sK5) <- (~23) [avatar component clause 224]
227. 22 | ~23 [avatar split clause 110,224,221]
240. 16 [avatar split clause 117,190]
249. $false <- (20, ~23) [resolution 226,214]
250. ~20 | 23 [avatar contradiction clause 249]
253. ~curious(lucy) <- (16) [resolution 118,191]
256. ~9 | ~16 [avatar split clause 253,190,159]
257. tall(X0) <- (7) [resolution 152,80]
258. 20 | ~7 [avatar split clause 257,151,213]
293. brave(lucy) | ~happy(lucy) <- (16) [resolution 107,191]
294. ~happy(lucy) <- (16, 22) [subsumption resolution 293,222]
295. $false <- (7, 16, 22) [subsumption resolution 294,152]
296. ~7 | ~16 | ~22 [avatar contradiction clause 295]
297. $false [avatar sat refutation 162,227,240,250,256,258,296]
% SZS output end Proof for 7661858521503565184674313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or calm is quiet and vice versa.
If someone is kind or not happy then someone is not kind and vice versa.
Everyone who is not humble is both old and not curious.
Everyone who is generous is both not curious and not kind.
Everyone who is tall or strong is both generous and not patient.
If john is either not creative or not tall then someone is not brave or patient and vice versa.
If someone is not brave then someone is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not calm or not brave and vice versa.
Everyone who is not calm is not old or not happy and vice versa.
Everyone who is both strong and humble is old or not brave and vice versa.
If someone is both not quiet and not curious then someone is not curious.
If mary is tall or calm then fred is either tall or not quiet and vice versa.
Susan is patient.
Someone is not wise or tall.
Fred is not wise or not creative.
Paul is not happy or not patient.
Someone is either not quiet or not calm.
Fred is either curious or not old. | Fred is brave. | entailment | (![X]:((strong(X)<~>calm(X))<=>quiet(X)))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~humble(X)=>(old(X)&~curious(X))))&
(![X]:(generous(X)=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|strong(X))=>(generous(X)&~patient(X))))&
(((~creative(john)<~>~tall(john)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
(patient(susan))&
(?[X]:((~wise(X)|tall(X))))&
((~wise(fred)|~creative(fred)))&
((~happy(paul)|~patient(paul)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((curious(fred)<~>~old(fred))) | brave(fred) | [
"p2",
"p3",
"p4",
"p7",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6457022854759576790432017
% SZS output start Proof for 6457022854759576790432017
3. ! [X0] : (~humble(X0) => (~curious(X0) & old(X0))) [input p2]
4. ! [X0] : (generous(X0) => (~kind(X0) & ~curious(X0))) [input p3]
5. ! [X0] : ((strong(X0) | tall(X0)) => (~patient(X0) & generous(X0))) [input p4]
8. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~kind(X0) | ~happy(X0))) [input p7]
11. ! [X0] : (~calm(X0) <=> (~happy(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((humble(X0) & strong(X0)) <=> (~brave(X0) | old(X0))) [input p11]
20. curious(fred) <~> ~old(fred) [input p19]
21. ~brave(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & old(X0)) | humble(X0)) [ennf transformation 3]
29. ! [X0] : ((~kind(X0) & ~curious(X0)) | ~generous(X0)) [ennf transformation 4]
30. ! [X0] : ((~patient(X0) & generous(X0)) | (~strong(X0) & ~tall(X0))) [ennf transformation 5]
46. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 8]
47. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 46]
50. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | calm(X0))) [nnf transformation 11]
51. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | calm(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 12]
53. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
62. (old(fred) | ~curious(fred)) & (~old(fred) | curious(fred)) [nnf transformation 20]
70. old(X0) | humble(X0) [cnf transformation 28]
72. ~generous(X0) | ~curious(X0) [cnf transformation 29]
73. ~generous(X0) | ~kind(X0) [cnf transformation 29]
75. ~strong(X0) | generous(X0) [cnf transformation 30]
88. ~humble(X0) | calm(X0) | kind(X0) [cnf transformation 47]
96. ~calm(X0) | old(X0) [cnf transformation 51]
100. brave(X0) | strong(X0) [cnf transformation 53]
101. humble(X0) | ~old(X0) [cnf transformation 53]
114. ~old(fred) | curious(fred) [cnf transformation 62]
116. ~brave(fred) [cnf transformation 21]
178. humble(X0) [subsumption resolution 101,70]
230. 25 <=> curious(fred) [avatar definition]
234. 26 <=> old(fred) [avatar definition]
238. 25 | ~26 [avatar split clause 114,234,230]
243. strong(fred) [resolution 100,116]
247. generous(fred) [resolution 243,75]
281. ~kind(fred) [resolution 247,73]
282. ~curious(fred) [resolution 247,72]
283. kind(X0) | calm(X0) [resolution 88,178]
321. calm(fred) [resolution 283,281]
381. old(fred) [resolution 321,96]
384. ~25 [avatar split clause 282,230]
385. 26 [avatar split clause 381,234]
386. $false [avatar sat refutation 238,384,385]
% SZS output end Proof for 6457022854759576790432017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative is curious or calm.
Everyone who is not old or wise is either strong or humble.
If someone is either not funny or happy then someone is either not generous or not kind.
Everyone who is not brave is both not funny and not calm.
If someone is both not generous and humble then john is both quiet and generous and vice versa.
Everyone who is both happy and funny is not brave and vice versa.
Everyone who is both wise and not wise is both not brave and not calm and vice versa.
If paul is either wise or curious then someone is not humble or not kind.
If someone is either not happy or not humble then someone is either not humble or not curious and vice versa.
Everyone who is not curious or not tall is kind and vice versa.
If lucy is both not happy and funny then alice is not kind and vice versa.
Everyone who is not strong is calm.
Everyone who is both rich and strong is either kind or not quiet.
Everyone who is either kind or happy is not wise.
Everyone who is both not curious and not brave is humble or not curious and vice versa.
Everyone who is strong is both brave and patient and vice versa.
Someone is quiet.
John is either not happy or not rich.
John is happy or old.
Fred is not calm.
Lucy is rich.
Mary is not rich or generous.
Someone is old or happy. | Mary is rich. | neutral | (![X]:((~patient(X)|~creative(X))=>(curious(X)|calm(X))))&
(![X]:((~old(X)|wise(X))=>(strong(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)|~curious(X))))&
(![X]:(strong(X)<=>(brave(X)&patient(X))))&
(?[X]:(quiet(X)))&
((~happy(john)<~>~rich(john)))&
((happy(john)|old(john)))&
(~calm(fred))&
(rich(lucy))&
((~rich(mary)|generous(mary)))&
(?[X]:((old(X)|happy(X)))) | rich(mary) | [] | null | 0 |
If someone is not rich then someone is happy and vice versa. If someone is not generous then someone is either wise or not tall and vice versa. If alice is either quiet or not quiet then someone is not tall. If susan is both not creative and old then alice is either humble or happy and vice versa. If mary is brave or not wise then someone is not creative. If paul is either not creative or not patient then paul is both not calm and creative and vice versa. If someone is not calm or not strong then mary is not humble and vice versa. Everyone who is not wise or not happy is patient and vice versa. Everyone who is either not generous or not tall is both wise and calm. Everyone who is both not kind and rich is not creative or not tall and vice versa. Everyone who is not creative is brave. If someone is both old and curious then alice is not happy. Everyone who is tall or not old is strong and vice versa. Everyone who is both not rich and rich is either happy or not happy. Everyone who is not kind is either old or not calm. Everyone who is generous is either not patient or not calm and vice versa. Paul is both not generous and brave. Paul is not curious. Someone is not patient or strong. Someone is both not rich and not humble. Someone is not humble or funny. Alice is creative or not humble. Susan is not quiet. | Paul is not calm. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:(happy(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(((quiet(alice)<~>~quiet(alice)))=>(?[X]:(~tall(X))))&
(((~creative(susan)&old(susan)))<=>((humble(alice)<~>happy(alice))))&
(((brave(mary)|~wise(mary)))=>(?[X]:(~creative(X))))&
(((~creative(paul)<~>~patient(paul)))<=>((~calm(paul)&creative(paul))))&
((?[X]:((~calm(X)|~strong(X))))<=>(~humble(mary)))&
(![X]:((~wise(X)|~happy(X))<=>patient(X)))&
(![X]:((~generous(X)<~>~tall(X))=>(wise(X)&calm(X))))&
(![X]:((~kind(X)&rich(X))<=>(~creative(X)|~tall(X))))&
(![X]:(~creative(X)=>brave(X)))&
((?[X]:((old(X)&curious(X))))=>(~happy(alice)))&
(![X]:((tall(X)|~old(X))<=>strong(X)))&
(![X]:((~rich(X)&rich(X))=>(happy(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(old(X)<~>~calm(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>~calm(X))))&
((~generous(paul)&brave(paul)))&
(~curious(paul))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((~rich(X)&~humble(X))))&
(?[X]:((~humble(X)|funny(X))))&
((creative(alice)|~humble(alice)))&
(~quiet(susan)) | ~calm(paul) | [] | null | 0 |
If susan is both not brave and old then fred is both not old and not patient and vice versa. If someone is not rich or kind then susan is either funny or brave and vice versa. If susan is not curious then someone is happy. If susan is calm or rich then paul is both not quiet and not curious. If alice is not creative then alice is either not rich or kind. Everyone who is either creative or not brave is not patient or curious and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is not curious is curious or not old. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Everyone who is not kind or quiet is both not creative and not kind. Someone is both not wise and not calm. Someone is either happy or curious. John is quiet. Alice is not funny. Fred is either strong or brave. | Susan is calm. | contradiction | (((~brave(susan)&old(susan)))<=>((~old(fred)&~patient(fred))))&
((?[X]:((~rich(X)|kind(X))))<=>((funny(susan)<~>brave(susan))))&
((~curious(susan))=>(?[X]:(happy(X))))&
(((calm(susan)|rich(susan)))=>((~quiet(paul)&~curious(paul))))&
((~creative(alice))=>((~rich(alice)<~>kind(alice))))&
(![X]:((creative(X)<~>~brave(X))<=>(~patient(X)|curious(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:(~curious(X)=>(curious(X)|~old(X))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(![X]:((~kind(X)|quiet(X))=>(~creative(X)&~kind(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(quiet(john))&
(~funny(alice))&
((strong(fred)<~>brave(fred))) | calm(susan) | [
"p3",
"p6",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8514219609863166860601336
% SZS output start Proof for 8514219609863166860601336
4. (rich(susan) | calm(susan)) => (~curious(paul) & ~quiet(paul)) [input p3]
7. ! [X0] : ((~old(X0) & creative(X0)) <=> (~generous(X0) & ~kind(X0))) [input p6]
11. ! [X0] : ((~curious(X0) & creative(X0)) <=> (funny(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : (~curious(X0) => (~old(X0) | curious(X0))) [input p12]
16. ! [X0] : ((quiet(X0) | ~kind(X0)) => (~kind(X0) & ~creative(X0))) [input p15]
22. calm(susan) [input hypothesis]
24. (~curious(paul) & ~quiet(paul)) | (~rich(susan) & ~calm(susan)) [ennf transformation 4]
26. ! [X0] : ((~old(X0) | curious(X0)) | curious(X0)) [ennf transformation 13]
27. ! [X0] : (~old(X0) | curious(X0) | curious(X0)) [flattening 26]
29. ! [X0] : ((~kind(X0) & ~creative(X0)) | (~quiet(X0) & kind(X0))) [ennf transformation 16]
41. ! [X0] : (((~old(X0) & creative(X0)) | (generous(X0) | kind(X0))) & ((~generous(X0) & ~kind(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 7]
42. ! [X0] : (((~old(X0) & creative(X0)) | generous(X0) | kind(X0)) & ((~generous(X0) & ~kind(X0)) | old(X0) | ~creative(X0))) [flattening 41]
49. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 11]
50. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | curious(X0) | ~creative(X0))) [flattening 49]
78. ~quiet(paul) | ~calm(susan) [cnf transformation 24]
80. ~curious(paul) | ~calm(susan) [cnf transformation 24]
90. ~creative(X0) | old(X0) | ~kind(X0) [cnf transformation 42]
107. creative(X0) | quiet(X0) [cnf transformation 50]
115. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 27]
124. ~creative(X0) | kind(X0) [cnf transformation 29]
136. calm(susan) [cnf transformation 22]
138. ~old(X0) | curious(X0) [duplicate literal removal 115]
197. 13 <=> curious(paul) [avatar definition]
199. ~curious(paul) <- (~13) [avatar component clause 197]
202. 14 <=> calm(susan) [avatar definition]
205. ~14 | ~13 [avatar split clause 80,197,202]
207. 15 <=> quiet(paul) [avatar definition]
209. ~quiet(paul) <- (~15) [avatar component clause 207]
211. ~14 | ~15 [avatar split clause 78,207,202]
307. 14 [avatar split clause 136,202]
314. quiet(X0) | kind(X0) [resolution 124,107]
360. old(X0) | ~kind(X0) | quiet(X0) [resolution 90,107]
362. quiet(X0) | old(X0) [subsumption resolution 360,314]
519. old(paul) <- (~15) [resolution 362,209]
558. curious(paul) <- (~15) [resolution 519,138]
559. $false <- (~13, ~15) [subsumption resolution 558,199]
560. 13 | 15 [avatar contradiction clause 559]
561. $false [avatar sat refutation 205,211,307,560]
% SZS output end Proof for 8514219609863166860601336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not curious and funny then someone is wise and vice versa. Everyone who is either generous or not calm is not happy. Everyone who is not calm is tall and vice versa. Everyone who is either creative or humble is generous or not strong. Everyone who is not happy or patient is not old. If susan is either rich or not patient then someone is not happy or tall and vice versa. Everyone who is creative or not curious is both not calm and generous. Everyone who is both not funny and not brave is not quiet or not curious. Everyone who is both not brave and not strong is either not patient or not quiet and vice versa. Everyone who is either generous or creative is both not quiet and brave. If john is not wise or old then john is both not old and not creative and vice versa. Everyone who is not generous or not strong is not creative or quiet and vice versa. Everyone who is both old and not strong is both not quiet and curious and vice versa. If paul is old then alice is curious and vice versa. Everyone who is not brave or strong is not brave or not curious and vice versa. If someone is kind then someone is not rich or not tall and vice versa. Paul is both generous and not curious. Someone is wise or old. Fred is not rich or calm. Someone is both strong and calm. Mary is either not tall or brave. Someone is both wise and not patient. Someone is quiet. Someone is either not patient or wise. | Susan is not strong. | neutral | (((~curious(john)&funny(john)))<=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>~calm(X))=>~happy(X)))&
(![X]:(~calm(X)<=>tall(X)))&
(![X]:((creative(X)<~>humble(X))=>(generous(X)|~strong(X))))&
(![X]:((~happy(X)|patient(X))=>~old(X)))&
(((rich(susan)<~>~patient(susan)))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((creative(X)|~curious(X))=>(~calm(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))=>(~quiet(X)|~curious(X))))&
(![X]:((~brave(X)&~strong(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:((generous(X)<~>creative(X))=>(~quiet(X)&brave(X))))&
(((~wise(john)|old(john)))<=>((~old(john)&~creative(john))))&
(![X]:((~generous(X)|~strong(X))<=>(~creative(X)|quiet(X))))&
(![X]:((old(X)&~strong(X))<=>(~quiet(X)&curious(X))))&
((old(paul))<=>(curious(alice)))&
(![X]:((~brave(X)|strong(X))<=>(~brave(X)|~curious(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)|~tall(X)))))&
((generous(paul)&~curious(paul)))&
(?[X]:((wise(X)|old(X))))&
((~rich(fred)|calm(fred)))&
(?[X]:((strong(X)&calm(X))))&
((~tall(mary)<~>brave(mary)))&
(?[X]:((wise(X)&~patient(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~patient(X)<~>wise(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is both humble and not calm is either not calm or strong.
Everyone who is not calm or rich is not wise or creative and vice versa.
If someone is both not happy and not rich then john is either not quiet or not strong.
If someone is both not strong and old then john is tall and vice versa.
If someone is tall or not generous then someone is curious and vice versa.
If alice is either brave or calm then someone is not rich and vice versa.
If someone is not generous then someone is both quiet and patient and vice versa.
Everyone who is curious or quiet is old and vice versa.
If alice is not creative then someone is quiet or not brave and vice versa.
Everyone who is both not tall and brave is both rich and quiet.
Everyone who is curious is brave and vice versa.
If lucy is both not tall and not happy then someone is either not brave or not kind and vice versa.
If alice is calm or not creative then someone is either not tall or not brave.
Everyone who is either not calm or curious is both not kind and not happy and vice versa.
Everyone who is either not patient or calm is both not generous and not kind and vice versa.
If mary is kind or not funny then john is both not rich and tall.
John is both creative and funny.
Someone is curious or not tall.
Mary is either not kind or not tall.
Someone is wise or generous.
Mary is not patient.
Alice is generous or not calm.
Someone is calm.
Lucy is both not curious and kind. | Mary is generous. | neutral | (![X]:((humble(X)&~calm(X))=>(~calm(X)<~>strong(X))))&
(![X]:((~calm(X)|rich(X))<=>(~wise(X)|creative(X))))&
((?[X]:((~happy(X)&~rich(X))))=>((~quiet(john)<~>~strong(john))))&
((?[X]:((~strong(X)&old(X))))<=>(tall(john)))&
((?[X]:((tall(X)|~generous(X))))<=>(?[X]:(curious(X))))&
(((brave(alice)<~>calm(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((curious(X)|quiet(X))<=>old(X)))&
((~creative(alice))<=>(?[X]:((quiet(X)|~brave(X)))))&
(![X]:((~tall(X)&brave(X))=>(rich(X)&quiet(X))))&
(![X]:(curious(X)<=>brave(X)))&
(((~tall(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((calm(alice)|~creative(alice)))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(![X]:((~calm(X)<~>curious(X))<=>(~kind(X)&~happy(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(~generous(X)&~kind(X))))&
(((kind(mary)|~funny(mary)))=>((~rich(john)&tall(john))))&
((creative(john)&funny(john)))&
(?[X]:((curious(X)|~tall(X))))&
((~kind(mary)<~>~tall(mary)))&
(?[X]:((wise(X)|generous(X))))&
(~patient(mary))&
((generous(alice)|~calm(alice)))&
(?[X]:(calm(X)))&
((~curious(lucy)&kind(lucy))) | generous(mary) | [] | null | 0 |
If someone is rich or humble then someone is either not rich or happy.
If fred is not strong then someone is both funny and happy and vice versa.
Everyone who is not patient or not strong is both tall and calm and vice versa.
Everyone who is not brave or not patient is wise or not humble and vice versa.
Everyone who is not calm or not curious is both humble and not calm and vice versa.
Everyone who is funny is generous or not creative and vice versa.
If someone is both not humble and not wise then someone is both not wise and happy.
Everyone who is not calm or not generous is both not old and not tall and vice versa.
If paul is not wise then someone is both not humble and humble.
Everyone who is not brave is not creative or rich and vice versa.
Everyone who is either not old or wise is either not strong or old.
If someone is either generous or patient then someone is both not kind and not brave.
Everyone who is wise or not generous is either not calm or quiet.
Everyone who is both not strong and not quiet is creative and vice versa.
Everyone who is not calm or not humble is either curious or not patient.
If someone is happy or old then someone is creative.
Lucy is not curious or not calm.
Someone is not wise.
Someone is either not rich or not creative.
Alice is both wise and not brave.
Fred is both humble and not tall.
Someone is quiet or not strong.
Someone is both not strong and generous.
Someone is both old and not quiet. | Lucy is not patient. | contradiction | ((?[X]:((rich(X)|humble(X))))=>(?[X]:((~rich(X)<~>happy(X)))))&
((~strong(fred))<=>(?[X]:((funny(X)&happy(X)))))&
(![X]:((~patient(X)|~strong(X))<=>(tall(X)&calm(X))))&
(![X]:((~brave(X)|~patient(X))<=>(wise(X)|~humble(X))))&
(![X]:((~calm(X)|~curious(X))<=>(humble(X)&~calm(X))))&
(![X]:(funny(X)<=>(generous(X)|~creative(X))))&
((?[X]:((~humble(X)&~wise(X))))=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((~calm(X)|~generous(X))<=>(~old(X)&~tall(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&humble(X)))))&
(![X]:(~brave(X)<=>(~creative(X)|rich(X))))&
(![X]:((~old(X)<~>wise(X))=>(~strong(X)<~>old(X))))&
((?[X]:((generous(X)<~>patient(X))))=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((wise(X)|~generous(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~strong(X)&~quiet(X))<=>creative(X)))&
(![X]:((~calm(X)|~humble(X))=>(curious(X)<~>~patient(X))))&
((?[X]:((happy(X)|old(X))))=>(?[X]:(creative(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((~rich(X)<~>~creative(X))))&
((wise(alice)&~brave(alice)))&
((humble(fred)&~tall(fred)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((~strong(X)&generous(X))))&
(?[X]:((old(X)&~quiet(X)))) | ~patient(lucy) | [
"p2",
"p4",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8121848205682090194935904
% SZS output start Proof for 8121848205682090194935904
3. ! [X0] : ((~strong(X0) | ~patient(X0)) <=> (calm(X0) & tall(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~calm(X0) & humble(X0))) [input p4]
15. ! [X0] : ((~humble(X0) | ~calm(X0)) => (curious(X0) <~> ~patient(X0))) [input p14]
17. ~calm(lucy) | ~curious(lucy) [input p16]
25. ~patient(lucy) [input hypothesis]
37. ! [X0] : ((curious(X0) <~> ~patient(X0)) | (humble(X0) & calm(X0))) [ennf transformation 15]
47. ! [X0] : (((~strong(X0) | ~patient(X0)) | (~calm(X0) | ~tall(X0))) & ((calm(X0) & tall(X0)) | (strong(X0) & patient(X0)))) [nnf transformation 3]
48. ! [X0] : ((~strong(X0) | ~patient(X0) | ~calm(X0) | ~tall(X0)) & ((calm(X0) & tall(X0)) | (strong(X0) & patient(X0)))) [flattening 47]
51. ! [X0] : (((~curious(X0) | ~calm(X0)) | (calm(X0) | ~humble(X0))) & ((~calm(X0) & humble(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 5]
52. ! [X0] : ((~curious(X0) | ~calm(X0) | calm(X0) | ~humble(X0)) & ((~calm(X0) & humble(X0)) | (curious(X0) & calm(X0)))) [flattening 51]
72. ! [X0] : (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (humble(X0) & calm(X0))) [nnf transformation 37]
96. calm(X0) | patient(X0) [cnf transformation 48]
106. ~calm(X0) | curious(X0) [cnf transformation 52]
136. ~patient(X0) | curious(X0) | calm(X0) [cnf transformation 72]
142. ~calm(lucy) | ~curious(lucy) [cnf transformation 17]
155. ~patient(lucy) [cnf transformation 25]
230. curious(X0) | calm(X0) [subsumption resolution 136,96]
231. curious(X0) [subsumption resolution 230,106]
244. ~calm(lucy) [subsumption resolution 142,231]
266. patient(lucy) [resolution 96,244]
267. $false [subsumption resolution 266,155]
% SZS output end Proof for 8121848205682090194935904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either kind or rich then paul is not patient. If john is either not strong or kind then someone is not calm and vice versa. If someone is either wise or tall then fred is creative or not creative. Everyone who is brave is funny or happy and vice versa. Everyone who is not funny is both creative and not happy and vice versa. Everyone who is not old or humble is either curious or not tall and vice versa. If someone is both funny and not kind then fred is both not creative and calm and vice versa. Everyone who is not curious is either curious or not humble. Everyone who is not calm is either not curious or funny. If lucy is kind then mary is either not calm or rich and vice versa. Everyone who is either not generous or creative is both strong and not quiet. If someone is old or tall then someone is not wise and vice versa. Everyone who is either not brave or not strong is both strong and not strong and vice versa. If fred is either quiet or not patient then someone is strong or wise. If fred is patient or strong then someone is brave and vice versa. If someone is creative or happy then susan is both strong and not curious. Someone is either not happy or not patient. John is not tall. Someone is either wise or happy. Fred is not brave. Alice is not calm. Someone is wise or old. Susan is rich. Someone is not wise or not calm. | Susan is not kind. | contradiction | (((kind(lucy)<~>rich(lucy)))=>(~patient(paul)))&
(((~strong(john)<~>kind(john)))<=>(?[X]:(~calm(X))))&
((?[X]:((wise(X)<~>tall(X))))=>((creative(fred)|~creative(fred))))&
(![X]:(brave(X)<=>(funny(X)|happy(X))))&
(![X]:(~funny(X)<=>(creative(X)&~happy(X))))&
(![X]:((~old(X)|humble(X))<=>(curious(X)<~>~tall(X))))&
((?[X]:((funny(X)&~kind(X))))<=>((~creative(fred)&calm(fred))))&
(![X]:(~curious(X)=>(curious(X)<~>~humble(X))))&
(![X]:(~calm(X)=>(~curious(X)<~>funny(X))))&
((kind(lucy))<=>((~calm(mary)<~>rich(mary))))&
(![X]:((~generous(X)<~>creative(X))=>(strong(X)&~quiet(X))))&
((?[X]:((old(X)|tall(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~brave(X)<~>~strong(X))<=>(strong(X)&~strong(X))))&
(((quiet(fred)<~>~patient(fred)))=>(?[X]:((strong(X)|wise(X)))))&
(((patient(fred)|strong(fred)))<=>(?[X]:(brave(X))))&
((?[X]:((creative(X)|happy(X))))=>((strong(susan)&~curious(susan))))&
(?[X]:((~happy(X)<~>~patient(X))))&
(~tall(john))&
(?[X]:((wise(X)<~>happy(X))))&
(~brave(fred))&
(~calm(alice))&
(?[X]:((wise(X)|old(X))))&
(rich(susan))&
(?[X]:((~wise(X)|~calm(X)))) | ~kind(susan) | [
"p3",
"p4",
"p6",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1591645242385451122904072
% SZS output start Proof for 1591645242385451122904072
4. ! [X0] : (brave(X0) <=> (happy(X0) | funny(X0))) [input p3]
5. ! [X0] : (~funny(X0) <=> (~happy(X0) & creative(X0))) [input p4]
7. ? [X0] : (~kind(X0) & funny(X0)) <=> (calm(fred) & ~creative(fred)) [input p6]
13. ! [X0] : ((~brave(X0) <~> ~strong(X0)) <=> (~strong(X0) & strong(X0))) [input p12]
16. ? [X0] : (happy(X0) | creative(X0)) => (~curious(susan) & strong(susan)) [input p15]
20. ~brave(fred) [input p19]
25. ~kind(susan) [input hypothesis]
34. (~curious(susan) & strong(susan)) | ! [X0] : (~happy(X0) & ~creative(X0)) [ennf transformation 16]
41. ! [X0] : ((brave(X0) | (~happy(X0) & ~funny(X0))) & ((happy(X0) | funny(X0)) | ~brave(X0))) [nnf transformation 4]
42. ! [X0] : ((brave(X0) | (~happy(X0) & ~funny(X0))) & (happy(X0) | funny(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : ((~funny(X0) | (happy(X0) | ~creative(X0))) & ((~happy(X0) & creative(X0)) | funny(X0))) [nnf transformation 5]
44. ! [X0] : ((~funny(X0) | happy(X0) | ~creative(X0)) & ((~happy(X0) & creative(X0)) | funny(X0))) [flattening 43]
47. (? [X0] : (~kind(X0) & funny(X0)) | (~calm(fred) | creative(fred))) & ((calm(fred) & ~creative(fred)) | ! [X0] : (kind(X0) | ~funny(X0))) [nnf transformation 7]
48. (? [X0] : (~kind(X0) & funny(X0)) | ~calm(fred) | creative(fred)) & ((calm(fred) & ~creative(fred)) | ! [X0] : (kind(X0) | ~funny(X0))) [flattening 47]
49. (? [X0] : (~kind(X0) & funny(X0)) | ~calm(fred) | creative(fred)) & ((calm(fred) & ~creative(fred)) | ! [X1] : (kind(X1) | ~funny(X1))) [rectify 48]
50. ? [X0] : (~kind(X0) & funny(X0)) => (~kind(sK1) & funny(sK1)) [choice axiom]
51. ((~kind(sK1) & funny(sK1)) | ~calm(fred) | creative(fred)) & ((calm(fred) & ~creative(fred)) | ! [X1] : (kind(X1) | ~funny(X1))) [skolemisation 49,50]
61. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [nnf transformation 13]
62. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [flattening 61]
89. ~brave(X0) | funny(X0) | happy(X0) [cnf transformation 42]
90. ~funny(X0) | brave(X0) [cnf transformation 42]
92. funny(X0) | creative(X0) [cnf transformation 44]
93. ~happy(X0) | funny(X0) [cnf transformation 44]
101. ~creative(fred) | kind(X1) | ~funny(X1) [cnf transformation 51]
122. ~strong(X0) | ~strong(X0) | brave(X0) [cnf transformation 62]
131. strong(susan) | ~creative(X0) [cnf transformation 34]
140. ~brave(fred) [cnf transformation 20]
145. ~kind(susan) [cnf transformation 25]
147. ~strong(X0) | brave(X0) [duplicate literal removal 122]
185. 8 <=> creative(fred) [avatar definition]
186. ~creative(fred) <- (~8) [avatar component clause 185]
203. 12 <=> ! [X1] : (kind(X1) | ~funny(X1)) [avatar definition]
204. ~funny(X1) | kind(X1) <- (12) [avatar component clause 203]
206. 12 | ~8 [avatar split clause 101,185,203]
284. 30 <=> ! [X0] : ~creative(X0) [avatar definition]
285. ~creative(X0) <- (30) [avatar component clause 284]
288. 31 <=> strong(susan) [avatar definition]
290. strong(susan) <- (31) [avatar component clause 288]
292. 30 | 31 [avatar split clause 131,288,284]
339. brave(X0) | creative(X0) [resolution 92,90]
340. brave(X0) <- (30) [subsumption resolution 339,285]
342. $false <- (30) [resolution 340,140]
343. ~30 [avatar contradiction clause 342]
348. brave(susan) <- (31) [resolution 147,290]
354. funny(susan) | happy(susan) <- (31) [resolution 89,348]
358. funny(susan) <- (31) [subsumption resolution 354,93]
434. kind(susan) <- (12, 31) [resolution 204,358]
437. $false <- (12, 31) [subsumption resolution 434,145]
438. ~12 | ~31 [avatar contradiction clause 437]
455. creative(fred) [resolution 339,140]
458. $false <- (~8) [subsumption resolution 455,186]
459. 8 [avatar contradiction clause 458]
460. $false [avatar sat refutation 206,292,343,438,459]
% SZS output end Proof for 1591645242385451122904072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not funny then paul is tall or not patient. Everyone who is either not brave or wise is both generous and not quiet and vice versa. If someone is either happy or creative then paul is both calm and not tall. If someone is not rich then john is both not quiet and not strong. Everyone who is not curious or brave is not kind or not brave. Everyone who is either humble or wise is old and vice versa. Everyone who is either rich or not happy is both not brave and quiet and vice versa. If paul is both not generous and not wise then someone is not quiet and vice versa. Everyone who is brave is funny. Everyone who is brave is both not tall and generous and vice versa. Everyone who is both strong and not generous is both not kind and not quiet. If someone is not quiet or funny then someone is calm or not quiet. Everyone who is not kind is rich and vice versa. If someone is calm or not humble then someone is either not calm or not patient and vice versa. Everyone who is either not patient or not rich is happy. If someone is either not quiet or not generous then someone is both not curious and not calm. Someone is not patient or funny. Someone is both tall and generous. Someone is both curious and not humble. John is either not calm or creative. Susan is wise. Someone is either not humble or not curious. | Mary is creative. | neutral | ((~funny(mary))=>((tall(paul)|~patient(paul))))&
(![X]:((~brave(X)<~>wise(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((calm(paul)&~tall(paul))))&
((?[X]:(~rich(X)))=>((~quiet(john)&~strong(john))))&
(![X]:((~curious(X)|brave(X))=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)<~>wise(X))<=>old(X)))&
(![X]:((rich(X)<~>~happy(X))<=>(~brave(X)&quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>funny(X)))&
(![X]:(brave(X)<=>(~tall(X)&generous(X))))&
(![X]:((strong(X)&~generous(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>happy(X)))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((curious(X)&~humble(X))))&
((~calm(john)<~>creative(john)))&
(wise(susan))&
(?[X]:((~humble(X)<~>~curious(X)))) | creative(mary) | [] | null | 0 |
Everyone who is quiet or not strong is humble or not generous.
Everyone who is not curious is either kind or not calm and vice versa.
If someone is rich then someone is either tall or rich and vice versa.
If someone is either old or not brave then john is not strong or wise and vice versa.
Everyone who is funny or not creative is patient or not tall.
If someone is old or quiet then fred is not creative or strong and vice versa.
Everyone who is both not calm and wise is wise.
Everyone who is either not generous or calm is both calm and not funny and vice versa.
If someone is rich or not tall then someone is either not tall or not curious and vice versa.
Everyone who is not kind is not brave.
Everyone who is either not rich or not patient is either rich or brave and vice versa.
If someone is not old then someone is curious.
Everyone who is quiet is not brave and vice versa.
If lucy is both not generous and not patient then lucy is brave or not quiet.
Everyone who is both wise and humble is patient.
Everyone who is humble or calm is both not quiet and not calm.
Someone is either calm or strong.
Lucy is humble or not funny.
John is either not patient or funny.
Susan is not wise.
Someone is either kind or quiet.
Someone is either quiet or patient.
Lucy is either not strong or creative. | Lucy is not kind. | contradiction | (![X]:((quiet(X)|~strong(X))=>(humble(X)|~generous(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((tall(X)<~>rich(X)))))&
((?[X]:((old(X)<~>~brave(X))))<=>((~strong(john)|wise(john))))&
(![X]:((funny(X)|~creative(X))=>(patient(X)|~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>((~creative(fred)|strong(fred))))&
(![X]:((~calm(X)&wise(X))=>wise(X)))&
(![X]:((~generous(X)<~>calm(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
(![X]:(~kind(X)=>~brave(X)))&
(![X]:((~rich(X)<~>~patient(X))<=>(rich(X)<~>brave(X))))&
((?[X]:(~old(X)))=>(?[X]:(curious(X))))&
(![X]:(quiet(X)<=>~brave(X)))&
(((~generous(lucy)&~patient(lucy)))=>((brave(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&humble(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(~quiet(X)&~calm(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((humble(lucy)|~funny(lucy)))&
((~patient(john)<~>funny(john)))&
(~wise(susan))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
((~strong(lucy)<~>creative(lucy))) | ~kind(lucy) | [
"p0",
"p7",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4588235693647544027361214
% SZS output start Proof for 4588235693647544027361214
1. ! [X0] : ((~strong(X0) | quiet(X0)) => (~generous(X0) | humble(X0))) [input p0]
8. ! [X0] : ((~generous(X0) <~> calm(X0)) <=> (~funny(X0) & calm(X0))) [input p7]
10. ! [X0] : (~kind(X0) => ~brave(X0)) [input p9]
13. ! [X0] : (quiet(X0) <=> ~brave(X0)) [input p12]
16. ! [X0] : ((calm(X0) | humble(X0)) => (~calm(X0) & ~quiet(X0))) [input p15]
24. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((~generous(X0) | humble(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 1]
29. ! [X0] : (~generous(X0) | humble(X0) | (strong(X0) & ~quiet(X0))) [flattening 28]
34. ! [X0] : (~brave(X0) | kind(X0)) [ennf transformation 10]
40. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 16]
57. ! [X0] : ((((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))))) [nnf transformation 8]
58. ! [X0] : ((((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))))) [flattening 57]
68. ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))) [nnf transformation 13]
80. ~generous(X0) | humble(X0) | ~quiet(X0) [cnf transformation 29]
103. calm(X0) | calm(X0) | generous(X0) [cnf transformation 58]
115. ~brave(X0) | kind(X0) [cnf transformation 34]
126. brave(X0) | quiet(X0) [cnf transformation 68]
129. ~humble(X0) | ~quiet(X0) [cnf transformation 40]
132. ~calm(X0) | ~calm(X0) [cnf transformation 40]
145. ~kind(lucy) [cnf transformation 24]
146. ~calm(X0) [duplicate literal removal 132]
151. calm(X0) | generous(X0) [duplicate literal removal 103]
225. 17 <=> ! [X1] : ~quiet(X1) [avatar definition]
226. ~quiet(X1) <- (17) [avatar component clause 225]
346. kind(X1) | quiet(X1) [resolution 126,115]
347. generous(X0) [resolution 151,146]
351. humble(X0) | ~quiet(X0) [resolution 80,347]
352. ~quiet(X0) [subsumption resolution 351,129]
353. 17 [avatar split clause 352,225]
362. quiet(lucy) [resolution 346,145]
365. $false <- (17) [subsumption resolution 362,226]
366. ~17 [avatar contradiction clause 365]
369. $false [avatar sat refutation 353,366]
% SZS output end Proof for 4588235693647544027361214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not creative then susan is either not tall or calm and vice versa. If alice is both generous and not strong then someone is not kind or generous. If mary is either not brave or rich then john is either kind or curious. If someone is happy or not strong then paul is calm or not calm. Everyone who is both tall and generous is not humble. Everyone who is not rich or humble is either patient or brave. Everyone who is not patient is creative and vice versa. Everyone who is creative is both not kind and not wise and vice versa. Everyone who is not strong is patient or not humble and vice versa. If alice is both generous and humble then susan is not patient. Everyone who is not tall is not happy and vice versa. Everyone who is either not happy or humble is either not generous or tall and vice versa. Everyone who is either old or not wise is either not brave or rich and vice versa. If someone is either calm or not creative then mary is either strong or not strong. Everyone who is calm or not curious is humble. Everyone who is not old or not calm is both kind and not funny. Paul is not quiet. Susan is both not patient and not wise. Someone is quiet. Susan is brave or curious. Someone is not quiet. Someone is not tall. Someone is humble. | Alice is not brave. | contradiction | ((?[X]:((~generous(X)|~creative(X))))<=>((~tall(susan)<~>calm(susan))))&
(((generous(alice)&~strong(alice)))=>(?[X]:((~kind(X)|generous(X)))))&
(((~brave(mary)<~>rich(mary)))=>((kind(john)<~>curious(john))))&
((?[X]:((happy(X)|~strong(X))))=>((calm(paul)|~calm(paul))))&
(![X]:((tall(X)&generous(X))=>~humble(X)))&
(![X]:((~rich(X)|humble(X))=>(patient(X)<~>brave(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:(creative(X)<=>(~kind(X)&~wise(X))))&
(![X]:(~strong(X)<=>(patient(X)|~humble(X))))&
(((generous(alice)&humble(alice)))=>(~patient(susan)))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((~happy(X)<~>humble(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((calm(X)<~>~creative(X))))=>((strong(mary)<~>~strong(mary))))&
(![X]:((calm(X)|~curious(X))=>humble(X)))&
(![X]:((~old(X)|~calm(X))=>(kind(X)&~funny(X))))&
(~quiet(paul))&
((~patient(susan)&~wise(susan)))&
(?[X]:(quiet(X)))&
((brave(susan)|curious(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X))) | ~brave(alice) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2254613683844873397936610
% SZS output start Proof for 2254613683844873397936610
1. ? [X0] : (~creative(X0) | ~generous(X0)) <=> (~tall(susan) <~> calm(susan)) [input p0]
5. ! [X0] : ((generous(X0) & tall(X0)) => ~humble(X0)) [input p4]
6. ! [X0] : ((humble(X0) | ~rich(X0)) => (patient(X0) <~> brave(X0))) [input p5]
7. ! [X0] : (~patient(X0) <=> creative(X0)) [input p6]
8. ! [X0] : (creative(X0) <=> (~wise(X0) & ~kind(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~humble(X0) | patient(X0))) [input p8]
11. ! [X0] : (~tall(X0) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((~happy(X0) <~> humble(X0)) <=> (~generous(X0) <~> tall(X0))) [input p11]
15. ! [X0] : ((~curious(X0) | calm(X0)) => humble(X0)) [input p14]
16. ! [X0] : ((~calm(X0) | ~old(X0)) => (~funny(X0) & kind(X0))) [input p15]
18. ~wise(susan) & ~patient(susan) [input p17]
24. ~brave(alice) [input hypothesis]
25. ! [X0] : ((~calm(X0) | ~old(X0)) => kind(X0)) [pure predicate removal 16]
31. ! [X0] : (~humble(X0) | (~generous(X0) | ~tall(X0))) [ennf transformation 5]
32. ! [X0] : (~humble(X0) | ~generous(X0) | ~tall(X0)) [flattening 31]
33. ! [X0] : ((patient(X0) <~> brave(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 6]
37. ! [X0] : (humble(X0) | (curious(X0) & ~calm(X0))) [ennf transformation 15]
38. ! [X0] : (kind(X0) | (calm(X0) & old(X0))) [ennf transformation 25]
39. (? [X0] : (~creative(X0) | ~generous(X0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X0] : (creative(X0) & generous(X0))) [nnf transformation 1]
40. (? [X0] : (~creative(X0) | ~generous(X0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X1] : (creative(X1) & generous(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~generous(X0)) => (~creative(sK0) | ~generous(sK0)) [choice axiom]
42. ((~creative(sK0) | ~generous(sK0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X1] : (creative(X1) & generous(X1))) [skolemisation 40,41]
46. ! [X0] : (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~humble(X0) & rich(X0))) [nnf transformation 33]
47. ! [X0] : ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))) [nnf transformation 7]
48. ! [X0] : ((creative(X0) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | ~creative(X0))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | ~creative(X0))) [flattening 48]
50. ! [X0] : ((~strong(X0) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | strong(X0))) [nnf transformation 9]
51. ! [X0] : ((~strong(X0) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | strong(X0))) [flattening 50]
52. ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 11]
53. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [nnf transformation 12]
67. ~calm(susan) | tall(susan) | creative(X1) [cnf transformation 42]
77. ~humble(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 32]
79. ~humble(X0) | patient(X0) | brave(X0) [cnf transformation 46]
82. patient(X0) | creative(X0) [cnf transformation 47]
83. ~patient(X0) | ~creative(X0) [cnf transformation 47]
84. ~kind(X0) | ~creative(X0) [cnf transformation 49]
87. ~humble(X0) | patient(X0) | strong(X0) [cnf transformation 51]
88. ~patient(X0) | ~strong(X0) [cnf transformation 51]
91. ~happy(X0) | tall(X0) [cnf transformation 52]
92. ~tall(X0) | happy(X0) [cnf transformation 52]
96. ~tall(X0) | generous(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 53]
98. humble(X0) | ~happy(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 53]
99. ~humble(X0) | happy(X0) | tall(X0) | generous(X0) [cnf transformation 53]
113. ~calm(X0) | humble(X0) [cnf transformation 37]
116. kind(X0) | calm(X0) [cnf transformation 38]
118. ~patient(susan) [cnf transformation 18]
125. ~brave(alice) [cnf transformation 24]
127. 1 <=> calm(susan) [avatar definition]
128. calm(susan) <- (1) [avatar component clause 127]
131. 2 <=> tall(susan) [avatar definition]
132. tall(susan) <- (2) [avatar component clause 131]
145. 5 <=> ! [X1] : creative(X1) [avatar definition]
146. creative(X1) <- (5) [avatar component clause 145]
147. 5 | 2 | ~1 [avatar split clause 67,127,131,145]
196. 16 <=> patient(susan) [avatar definition]
198. ~patient(susan) <- (~16) [avatar component clause 196]
200. ~humble(X0) | tall(X0) | generous(X0) [subsumption resolution 99,91]
201. ~happy(X0) | ~generous(X0) | ~tall(X0) [subsumption resolution 98,77]
202. ~tall(X0) | ~generous(X0) [subsumption resolution 201,92]
203. ~humble(X0) | ~happy(X0) | generous(X0) [subsumption resolution 96,200]
205. ~16 [avatar split clause 118,196]
215. creative(susan) <- (~16) [resolution 82,198]
218. ~creative(X0) | calm(X0) [resolution 116,84]
224. calm(susan) <- (~16) [resolution 218,215]
227. 1 | 16 [avatar split clause 224,196,127]
228. humble(susan) <- (1) [resolution 128,113]
229. ~generous(susan) <- (2) [resolution 132,202]
230. happy(susan) <- (2) [resolution 132,92]
291. ~happy(susan) | generous(susan) <- (1) [resolution 203,228]
292. generous(susan) <- (1, 2) [subsumption resolution 291,230]
293. $false <- (1, 2) [subsumption resolution 292,229]
294. ~1 | ~2 [avatar contradiction clause 293]
305. calm(X0) <- (5) [resolution 146,218]
387. humble(X0) <- (5) [resolution 305,113]
392. patient(X2) | strong(X2) <- (5) [resolution 387,87]
393. patient(X3) | brave(X3) <- (5) [resolution 387,79]
415. strong(X3) | ~creative(X3) <- (5) [resolution 392,83]
418. strong(X3) <- (5) [subsumption resolution 415,146]
436. brave(X2) | ~strong(X2) <- (5) [resolution 393,88]
439. brave(X2) <- (5) [subsumption resolution 436,418]
442. $false <- (5) [resolution 439,125]
443. ~5 [avatar contradiction clause 442]
444. $false [avatar sat refutation 147,205,227,294,443]
% SZS output end Proof for 2254613683844873397936610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not quiet or patient. Everyone who is not quiet or not old is quiet and vice versa. Everyone who is both not humble and not quiet is not generous and vice versa. Everyone who is either curious or not tall is both funny and tall. If someone is both tall and strong then susan is either generous or not curious and vice versa. Everyone who is both rich and happy is either curious or strong. If susan is both not calm and funny then alice is not tall or not funny and vice versa. Everyone who is both old and kind is both not patient and not rich. Everyone who is not happy is not old. If john is both not generous and rich then someone is not strong and vice versa. Everyone who is both not curious and not humble is not wise. If someone is not strong or not humble then paul is either funny or quiet. If someone is both not happy and calm then john is either not calm or happy and vice versa. Everyone who is happy or humble is either kind or curious. Everyone who is not generous is not creative or old. Everyone who is funny or not generous is either happy or old. Susan is happy or quiet. Someone is both patient and not wise. Susan is either not kind or curious. Someone is calm or patient. Someone is not creative or not strong. Someone is not funny or not humble. Lucy is either rich or tall. Someone is kind or humble. | John is quiet. | entailment | (![X]:(~humble(X)=>(~quiet(X)<~>patient(X))))&
(![X]:((~quiet(X)|~old(X))<=>quiet(X)))&
(![X]:((~humble(X)&~quiet(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~tall(X))=>(funny(X)&tall(X))))&
((?[X]:((tall(X)&strong(X))))<=>((generous(susan)<~>~curious(susan))))&
(![X]:((rich(X)&happy(X))=>(curious(X)<~>strong(X))))&
(((~calm(susan)&funny(susan)))<=>((~tall(alice)|~funny(alice))))&
(![X]:((old(X)&kind(X))=>(~patient(X)&~rich(X))))&
(![X]:(~happy(X)=>~old(X)))&
(((~generous(john)&rich(john)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&~humble(X))=>~wise(X)))&
((?[X]:((~strong(X)|~humble(X))))=>((funny(paul)<~>quiet(paul))))&
((?[X]:((~happy(X)&calm(X))))<=>((~calm(john)<~>happy(john))))&
(![X]:((happy(X)|humble(X))=>(kind(X)<~>curious(X))))&
(![X]:(~generous(X)=>(~creative(X)|old(X))))&
(![X]:((funny(X)|~generous(X))=>(happy(X)<~>old(X))))&
((happy(susan)|quiet(susan)))&
(?[X]:((patient(X)&~wise(X))))&
((~kind(susan)<~>curious(susan)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:((~funny(X)|~humble(X))))&
((rich(lucy)<~>tall(lucy)))&
(?[X]:((kind(X)|humble(X)))) | quiet(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7139459661250033768906064
% SZS output start Proof for 7139459661250033768906064
2. ! [X0] : ((~old(X0) | ~quiet(X0)) <=> quiet(X0)) [input p1]
25. ~quiet(john) [input hypothesis]
41. ! [X0] : (((~old(X0) | ~quiet(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) & quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((~old(X0) | ~quiet(X0) | ~quiet(X0)) & (quiet(X0) | (old(X0) & quiet(X0)))) [flattening 41]
77. quiet(X0) | quiet(X0) [cnf transformation 42]
133. ~quiet(john) [cnf transformation 25]
135. quiet(X0) [duplicate literal removal 77]
271. $false [subsumption resolution 133,135]
% SZS output end Proof for 7139459661250033768906064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not tall is both kind and calm. If someone is not funny or not calm then susan is both curious and kind. Everyone who is both not humble and creative is happy. Everyone who is creative or not calm is old. If susan is curious or kind then someone is not old or happy and vice versa. If paul is brave then mary is either happy or not quiet and vice versa. If someone is not old then someone is both not funny and not patient and vice versa. Everyone who is either not happy or not creative is either creative or quiet and vice versa. Everyone who is creative or old is both not calm and patient. Everyone who is both not happy and not old is not funny and vice versa. Everyone who is either not tall or happy is either patient or not curious and vice versa. If someone is not generous or not humble then lucy is not patient or not rich. If fred is either kind or not quiet then someone is either curious or rich. Everyone who is not rich or wise is either calm or not happy and vice versa. If someone is creative or not patient then paul is not patient. Someone is both funny and generous. Lucy is not creative. Mary is rich or wise. Lucy is both not strong and not happy. Mary is happy. Someone is both not creative and humble. | Lucy is funny. | contradiction | (![X]:((patient(X)|~tall(X))=>(kind(X)&calm(X))))&
((?[X]:((~funny(X)|~calm(X))))=>((curious(susan)&kind(susan))))&
(![X]:((~humble(X)&creative(X))=>happy(X)))&
(![X]:((creative(X)|~calm(X))=>old(X)))&
(((curious(susan)|kind(susan)))<=>(?[X]:((~old(X)|happy(X)))))&
((brave(paul))<=>((happy(mary)<~>~quiet(mary))))&
((?[X]:(~old(X)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((~happy(X)<~>~creative(X))<=>(creative(X)<~>quiet(X))))&
(![X]:((creative(X)|old(X))=>(~calm(X)&patient(X))))&
(![X]:((~happy(X)&~old(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>happy(X))<=>(patient(X)<~>~curious(X))))&
((?[X]:((~generous(X)|~humble(X))))=>((~patient(lucy)|~rich(lucy))))&
(((kind(fred)<~>~quiet(fred)))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((~rich(X)|wise(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:((creative(X)|~patient(X))))=>(~patient(paul)))&
(?[X]:((funny(X)&generous(X))))&
(~creative(lucy))&
((rich(mary)|wise(mary)))&
((~strong(lucy)&~happy(lucy)))&
(happy(mary))&
(?[X]:((~creative(X)&humble(X)))) | funny(lucy) | [
"p0",
"p3",
"p8",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8570190660671387925521326
% SZS output start Proof for 8570190660671387925521326
1. ! [X0] : ((~tall(X0) | patient(X0)) => (calm(X0) & kind(X0))) [input p0]
4. ! [X0] : ((~calm(X0) | creative(X0)) => old(X0)) [input p3]
9. ! [X0] : ((old(X0) | creative(X0)) => (patient(X0) & ~calm(X0))) [input p8]
10. ! [X0] : ((~old(X0) & ~happy(X0)) <=> ~funny(X0)) [input p9]
19. ~happy(lucy) & ~strong(lucy) [input p18]
22. funny(lucy) [input hypothesis]
24. ~happy(lucy) [pure predicate removal 19]
30. ! [X0] : ((calm(X0) & kind(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 1]
32. ! [X0] : (old(X0) | (calm(X0) & ~creative(X0))) [ennf transformation 4]
33. ! [X0] : ((patient(X0) & ~calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 9]
48. ! [X0] : (((~old(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | (old(X0) | happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((~old(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | old(X0) | happy(X0))) [flattening 48]
62. ~patient(X0) | calm(X0) [cnf transformation 30]
69. old(X0) | calm(X0) [cnf transformation 32]
90. ~old(X0) | ~calm(X0) [cnf transformation 33]
92. ~old(X0) | patient(X0) [cnf transformation 33]
93. ~funny(X0) | old(X0) | happy(X0) [cnf transformation 49]
119. ~happy(lucy) [cnf transformation 24]
122. funny(lucy) [cnf transformation 22]
128. 1 <=> ! [X0] : calm(X0) [avatar definition]
129. calm(X0) <- (1) [avatar component clause 128]
245. patient(X0) | calm(X0) [resolution 92,69]
246. calm(X0) [subsumption resolution 245,62]
247. 1 [avatar split clause 246,128]
259. old(lucy) | happy(lucy) [resolution 93,122]
262. old(lucy) [subsumption resolution 259,119]
274. ~calm(lucy) [resolution 262,90]
275. $false <- (1) [subsumption resolution 274,129]
276. ~1 [avatar contradiction clause 275]
277. $false [avatar sat refutation 247,276]
% SZS output end Proof for 8570190660671387925521326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and curious then someone is either not humble or rich.
If someone is both humble and not tall then someone is not funny or not tall.
Everyone who is calm is not humble or strong.
If alice is both not rich and calm then someone is strong and vice versa.
If someone is either happy or not patient then someone is not funny and vice versa.
If paul is quiet then someone is either not tall or patient.
Everyone who is not calm is both patient 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. | Mary is not funny. | contradiction | ((?[X]:((~calm(X)&curious(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
((?[X]:((humble(X)&~tall(X))))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:(calm(X)=>(~humble(X)|strong(X))))&
(((~rich(alice)&calm(alice)))<=>(?[X]:(strong(X))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(?[X]:(~funny(X))))&
((quiet(paul))=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:(~calm(X)<=>(patient(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)))) | ~funny(mary) | [
"p2",
"p4",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8379781957073752093518997
% SZS output start Proof for 8379781957073752093518997
3. ! [X0] : (calm(X0) => (strong(X0) | ~humble(X0))) [input p2]
5. ? [X0] : (happy(X0) <~> ~patient(X0)) <=> ? [X0] : ~funny(X0) [input p4]
7. ! [X0] : (~calm(X0) <=> (happy(X0) & patient(X0))) [input p6]
9. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (~rich(X0) | ~funny(X0))) [input p8]
12. ! [X0] : ((generous(X0) | ~funny(X0)) => humble(X0)) [input p11]
24. ~funny(mary) [input hypothesis]
27. ? [X0] : (happy(X0) <~> ~patient(X0)) <=> ? [X1] : ~funny(X1) [rectify 5]
30. ! [X0] : ((strong(X0) | ~humble(X0)) | ~calm(X0)) [ennf transformation 3]
31. ! [X0] : (strong(X0) | ~humble(X0) | ~calm(X0)) [flattening 30]
37. ! [X0] : (humble(X0) | (~generous(X0) & funny(X0))) [ennf transformation 12]
51. (? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ! [X1] : funny(X1)) & (? [X1] : ~funny(X1) | ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) [nnf transformation 27]
52. (? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ! [X1] : funny(X1)) & (? [X2] : ~funny(X2) | ! [X3] : ((happy(X3) | patient(X3)) & (~patient(X3) | ~happy(X3)))) [rectify 51]
53. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) => ((patient(sK3) | ~happy(sK3)) & (~patient(sK3) | happy(sK3))) [choice axiom]
54. ? [X2] : ~funny(X2) => ~funny(sK4) [choice axiom]
55. (((patient(sK3) | ~happy(sK3)) & (~patient(sK3) | happy(sK3))) | ! [X1] : funny(X1)) & (~funny(sK4) | ! [X3] : ((happy(X3) | patient(X3)) & (~patient(X3) | ~happy(X3)))) [skolemisation 52,54,53]
59. ! [X0] : ((~calm(X0) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | calm(X0))) [nnf transformation 7]
60. ! [X0] : ((~calm(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | calm(X0))) [flattening 59]
63. ! [X0] : (((~strong(X0) & ~happy(X0)) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | (strong(X0) | happy(X0)))) [nnf transformation 9]
64. ! [X0] : (((~strong(X0) & ~happy(X0)) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | strong(X0) | happy(X0))) [flattening 63]
93. ~humble(X0) | strong(X0) | ~calm(X0) [cnf transformation 31]
97. ~funny(sK4) | ~patient(X3) | ~happy(X3) [cnf transformation 55]
98. ~funny(sK4) | happy(X3) | patient(X3) [cnf transformation 55]
99. ~patient(sK3) | happy(sK3) | funny(X1) [cnf transformation 55]
100. patient(sK3) | ~happy(sK3) | funny(X1) [cnf transformation 55]
104. happy(X0) | calm(X0) [cnf transformation 60]
109. ~happy(X0) | funny(X0) [cnf transformation 64]
111. ~strong(X0) | funny(X0) [cnf transformation 64]
123. funny(X0) | humble(X0) [cnf transformation 37]
153. ~funny(mary) [cnf transformation 24]
199. 11 <=> ! [X1] : funny(X1) [avatar definition]
200. funny(X1) <- (11) [avatar component clause 199]
202. 12 <=> happy(sK3) [avatar definition]
203. happy(sK3) <- (12) [avatar component clause 202]
206. 13 <=> patient(sK3) [avatar definition]
207. ~patient(sK3) <- (~13) [avatar component clause 206]
208. patient(sK3) <- (13) [avatar component clause 206]
209. 11 | ~12 | 13 [avatar split clause 100,206,202,199]
210. 11 | 12 | ~13 [avatar split clause 99,206,202,199]
212. 14 <=> ! [X3] : (happy(X3) | patient(X3)) [avatar definition]
213. patient(X3) | happy(X3) <- (14) [avatar component clause 212]
215. 15 <=> funny(sK4) [avatar definition]
217. ~funny(sK4) <- (~15) [avatar component clause 215]
218. 14 | ~15 [avatar split clause 98,215,212]
220. 16 <=> ! [X3] : (~patient(X3) | ~happy(X3)) [avatar definition]
221. ~patient(X3) | ~happy(X3) <- (16) [avatar component clause 220]
222. 16 | ~15 [avatar split clause 97,215,220]
339. funny(X0) | calm(X0) [resolution 109,104]
342. humble(sK4) <- (~15) [resolution 123,217]
344. calm(sK4) <- (~15) [resolution 339,217]
347. strong(sK4) | ~calm(sK4) <- (~15) [resolution 93,342]
357. strong(sK4) <- (~15) [subsumption resolution 347,344]
381. funny(sK4) <- (~15) [resolution 357,111]
382. $false <- (~15) [subsumption resolution 381,217]
383. 15 [avatar contradiction clause 382]
411. happy(sK3) <- (~13, 14) [resolution 213,207]
414. 12 | 13 | ~14 [avatar split clause 411,212,206,202]
415. $false <- (11) [resolution 200,153]
418. ~11 [avatar contradiction clause 415]
425. ~happy(sK3) <- (13, 16) [resolution 221,208]
427. $false <- (12, 13, 16) [subsumption resolution 425,203]
428. ~12 | ~13 | ~16 [avatar contradiction clause 427]
429. $false [avatar sat refutation 209,210,218,222,383,414,418,428]
% SZS output end Proof for 8379781957073752093518997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or generous is either not happy or not funny and vice versa.
Everyone who is either strong or not brave is either creative or not quiet and vice versa.
Everyone who is generous or not patient is quiet.
Everyone who is calm or curious is both funny and not kind.
If susan is rich then mary is either funny or patient and vice versa.
If lucy is not patient then susan is not quiet and vice versa.
Everyone who is old or not happy is either tall or not rich.
If someone is not quiet then john is either not patient or tall.
Everyone who is either generous or not kind is calm.
If someone is tall or happy then mary is not funny.
If susan is both not calm and not quiet then fred is not funny or brave.
Everyone who is both funny and strong is not funny and vice versa.
If john is not wise or not humble then someone is either not rich or humble and vice versa.
If fred is not happy then someone is either brave or not strong and vice versa.
If someone is not patient or brave then susan is either creative or not calm.
Everyone who is not funny or not humble is patient or curious.
Alice is both not old and kind.
Someone is curious or quiet.
Someone is both not creative and not happy.
Susan is either not strong or not curious.
Alice is not old or not funny.
Someone is either brave or tall.
Lucy is wise. | John is not patient. | neutral | (![X]:((~curious(X)|generous(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:((generous(X)|~patient(X))=>quiet(X)))&
(![X]:((calm(X)|curious(X))=>(funny(X)&~kind(X))))&
((rich(susan))<=>((funny(mary)<~>patient(mary))))&
((~patient(lucy))<=>(~quiet(susan)))&
(![X]:((old(X)|~happy(X))=>(tall(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))=>((~patient(john)<~>tall(john))))&
(![X]:((generous(X)<~>~kind(X))=>calm(X)))&
((?[X]:((tall(X)|happy(X))))=>(~funny(mary)))&
(((~calm(susan)&~quiet(susan)))=>((~funny(fred)|brave(fred))))&
(![X]:((funny(X)&strong(X))<=>~funny(X)))&
(((~wise(john)|~humble(john)))<=>(?[X]:((~rich(X)<~>humble(X)))))&
((~happy(fred))<=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|brave(X))))=>((creative(susan)<~>~calm(susan))))&
(![X]:((~funny(X)|~humble(X))=>(patient(X)|curious(X))))&
((~old(alice)&kind(alice)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:((~creative(X)&~happy(X))))&
((~strong(susan)<~>~curious(susan)))&
((~old(alice)|~funny(alice)))&
(?[X]:((brave(X)<~>tall(X))))&
(wise(lucy)) | ~patient(john) | [] | null | 0 |
If someone is both not generous and not old then someone is happy or not tall and vice versa. If someone is old or not kind then someone is both not strong and curious. If someone is old or funny then mary is both not creative and creative and vice versa. Everyone who is either brave or not wise is either not happy or kind and vice versa. If john is either not happy or kind then mary is either strong or not patient. If mary is either not humble or not quiet then susan is either creative or not generous and vice versa. If someone is not calm or not generous then fred is both not creative and quiet and vice versa. If lucy is both old and humble then lucy is quiet or not kind. Everyone who is both not kind and calm is not old or rich and vice versa. If someone is both generous and not humble then fred is brave or old. Everyone who is rich is both happy and not rich and vice versa. If john is both not humble and tall then mary is humble. Everyone who is both not quiet and wise is both generous and tall. Everyone who is either strong or old is not funny. Susan is either old or not old. Someone is not rich or not humble. Fred is patient. Someone is either tall or not funny. Alice is either not patient or tall. | John is curious. | neutral | ((?[X]:((~generous(X)&~old(X))))<=>(?[X]:((happy(X)|~tall(X)))))&
((?[X]:((old(X)|~kind(X))))=>(?[X]:((~strong(X)&curious(X)))))&
((?[X]:((old(X)|funny(X))))<=>((~creative(mary)&creative(mary))))&
(![X]:((brave(X)<~>~wise(X))<=>(~happy(X)<~>kind(X))))&
(((~happy(john)<~>kind(john)))=>((strong(mary)<~>~patient(mary))))&
(((~humble(mary)<~>~quiet(mary)))<=>((creative(susan)<~>~generous(susan))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~creative(fred)&quiet(fred))))&
(((old(lucy)&humble(lucy)))=>((quiet(lucy)|~kind(lucy))))&
(![X]:((~kind(X)&calm(X))<=>(~old(X)|rich(X))))&
((?[X]:((generous(X)&~humble(X))))=>((brave(fred)|old(fred))))&
(![X]:(rich(X)<=>(happy(X)&~rich(X))))&
(((~humble(john)&tall(john)))=>(humble(mary)))&
(![X]:((~quiet(X)&wise(X))=>(generous(X)&tall(X))))&
(![X]:((strong(X)<~>old(X))=>~funny(X)))&
((old(susan)<~>~old(susan)))&
(?[X]:((~rich(X)|~humble(X))))&
(patient(fred))&
(?[X]:((tall(X)<~>~funny(X))))&
((~patient(alice)<~>tall(alice))) | curious(john) | [] | null | 0 |
Everyone who is either brave or not creative is not rich.
Everyone who is brave or not rich is not brave.
Everyone who is not old is both not kind and kind.
If someone is not wise or calm then paul is not patient.
If mary is both not strong and not calm then someone is tall or brave.
Everyone who is generous or kind is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Everyone who is not curious or calm is old.
If someone is strong or wise then mary is both funny and generous and vice versa.
Everyone who is not quiet is either old or curious and vice versa.
Everyone who is not creative or not curious is both not wise and not strong.
Everyone who is not creative or happy is either not old or happy and vice versa.
Everyone who is not old or not brave is curious.
If paul is not old or patient then john is either calm or not creative and vice versa.
If john is not creative or not rich then alice is both tall and strong.
Everyone who is either not quiet or quiet is either happy or not generous and vice versa.
Someone is either not tall or wise.
Mary is not rich.
Someone is generous or not rich.
Someone is not funny or not tall.
Someone is both not rich and not wise.
Mary is not kind or not rich.
Someone is not calm or not strong. | Paul is calm. | neutral | (![X]:((brave(X)<~>~creative(X))=>~rich(X)))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~kind(X)&kind(X))))&
((?[X]:((~wise(X)|calm(X))))=>(~patient(paul)))&
(((~strong(mary)&~calm(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((generous(X)|kind(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((?[X]:((strong(X)|wise(X))))<=>((funny(mary)&generous(mary))))&
(![X]:(~quiet(X)<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)|~curious(X))=>(~wise(X)&~strong(X))))&
(![X]:((~creative(X)|happy(X))<=>(~old(X)<~>happy(X))))&
(![X]:((~old(X)|~brave(X))=>curious(X)))&
(((~old(paul)|patient(paul)))<=>((calm(john)<~>~creative(john))))&
(((~creative(john)|~rich(john)))=>((tall(alice)&strong(alice))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(happy(X)<~>~generous(X))))&
(?[X]:((~tall(X)<~>wise(X))))&
(~rich(mary))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((~rich(X)&~wise(X))))&
((~kind(mary)|~rich(mary)))&
(?[X]:((~calm(X)|~strong(X)))) | calm(paul) | [] | null | 0 |
If someone is generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. Fred is both tall and not strong. Someone is not strong or happy. Someone is not wise or strong. Someone is curious. Someone is either generous or calm. Someone is either not happy or strong. | Fred is kind. | contradiction | ((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((tall(fred)&~strong(fred)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(?[X]:((~happy(X)<~>strong(X)))) | kind(fred) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2384310721598519959985693
% SZS output start Proof for 2384310721598519959985693
3. ! [X0] : ((patient(X0) <~> creative(X0)) => (quiet(X0) & old(X0))) [input p2]
4. ! [X0] : ((generous(X0) & ~happy(X0)) <=> ~calm(X0)) [input p3]
5. ! [X0] : (~strong(X0) <=> (old(X0) | kind(X0))) [input p4]
6. ! [X0] : ((old(X0) | kind(X0)) <=> quiet(X0)) [input p5]
7. ! [X0] : ((funny(X0) & ~humble(X0)) <=> (~generous(X0) <~> creative(X0))) [input p6]
8. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p7]
10. ! [X0] : ((~patient(X0) | wise(X0)) => ~generous(X0)) [input p9]
14. ! [X0] : (strong(X0) <=> humble(X0)) [input p13]
15. (rich(mary) & ~calm(mary)) <=> ? [X0] : ~old(X0) [input p14]
16. ! [X0] : (calm(X0) => (old(X0) <~> kind(X0))) [input p15]
23. kind(fred) [input hypothesis]
27. ! [X0] : ((quiet(X0) & old(X0)) | (patient(X0) <=> creative(X0))) [ennf transformation 3]
28. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 8]
30. ! [X0] : (~generous(X0) | (patient(X0) & ~wise(X0))) [ennf transformation 10]
32. ! [X0] : ((old(X0) <~> kind(X0)) | ~calm(X0)) [ennf transformation 16]
41. ! [X0] : ((quiet(X0) & old(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0)))) [nnf transformation 27]
42. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (~generous(X0) | happy(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | ~generous(X0) | happy(X0))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (~old(X0) & ~kind(X0))) & ((old(X0) | kind(X0)) | strong(X0))) [nnf transformation 5]
45. ! [X0] : ((~strong(X0) | (~old(X0) & ~kind(X0))) & (old(X0) | kind(X0) | strong(X0))) [flattening 44]
46. ! [X0] : (((old(X0) | kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((old(X0) | kind(X0) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [flattening 46]
48. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~funny(X0) | humble(X0)))) [nnf transformation 7]
49. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~funny(X0) | humble(X0))) [flattening 48]
56. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 14]
57. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~rich(mary) | calm(mary))) [nnf transformation 15]
58. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~rich(mary) | calm(mary)) [flattening 57]
59. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~rich(mary) | calm(mary)) [rectify 58]
60. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
61. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (~old(sK2) | ~rich(mary) | calm(mary)) [skolemisation 59,60]
62. ! [X0] : (((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | ~calm(X0)) [nnf transformation 32]
79. ~patient(X0) | creative(X0) | quiet(X0) [cnf transformation 41]
83. calm(X0) | generous(X0) [cnf transformation 43]
84. kind(X0) | old(X0) | strong(X0) [cnf transformation 45]
87. ~kind(X0) | quiet(X0) [cnf transformation 47]
88. ~old(X0) | quiet(X0) [cnf transformation 47]
93. ~creative(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 49]
97. ~quiet(X0) | ~generous(X0) [cnf transformation 28]
101. ~generous(X0) | patient(X0) [cnf transformation 30]
115. ~strong(X0) | humble(X0) [cnf transformation 56]
118. ~calm(mary) | old(X0) [cnf transformation 61]
121. ~kind(X0) | ~old(X0) | ~calm(X0) [cnf transformation 62]
130. kind(fred) [cnf transformation 23]
165. 9 <=> calm(fred) [avatar definition]
166. ~calm(fred) <- (~9) [avatar component clause 165]
178. 12 <=> quiet(fred) [avatar definition]
179. quiet(fred) <- (12) [avatar component clause 178]
204. 17 <=> ! [X0] : old(X0) [avatar definition]
205. old(X0) <- (17) [avatar component clause 204]
208. 18 <=> calm(mary) [avatar definition]
210. ~calm(mary) <- (~18) [avatar component clause 208]
211. 17 | ~18 [avatar split clause 118,208,204]
260. quiet(fred) [resolution 87,130]
261. 12 [avatar split clause 260,178]
263. ~generous(fred) <- (12) [resolution 97,179]
272. generous(mary) <- (~18) [resolution 210,83]
276. patient(mary) <- (~18) [resolution 272,101]
299. creative(mary) | quiet(mary) <- (~18) [resolution 276,79]
302. 32 <=> quiet(mary) [avatar definition]
303. ~quiet(mary) <- (~32) [avatar component clause 302]
304. quiet(mary) <- (32) [avatar component clause 302]
306. 33 <=> creative(mary) [avatar definition]
308. creative(mary) <- (33) [avatar component clause 306]
309. 32 | 33 | 18 [avatar split clause 299,208,306,302]
319. old(X0) | strong(X0) | quiet(X0) [resolution 84,87]
321. quiet(X0) | strong(X0) [subsumption resolution 319,88]
332. ~generous(mary) | ~humble(mary) <- (33) [resolution 93,308]
335. ~humble(mary) <- (~18, 33) [subsumption resolution 332,272]
350. 35 <=> old(fred) [avatar definition]
351. ~old(fred) <- (~35) [avatar component clause 350]
365. strong(mary) <- (~32) [resolution 303,321]
366. ~old(fred) | ~calm(fred) [resolution 121,130]
373. generous(fred) <- (~9) [resolution 166,83]
374. $false <- (~9, 12) [subsumption resolution 373,263]
375. 9 | ~12 [avatar contradiction clause 374]
376. ~9 | ~35 [avatar split clause 366,350,165]
395. humble(mary) <- (~32) [resolution 365,115]
396. $false <- (~18, ~32, 33) [subsumption resolution 395,335]
397. 18 | 32 | ~33 [avatar contradiction clause 396]
401. ~generous(mary) <- (32) [resolution 304,97]
402. $false <- (~18, 32) [subsumption resolution 401,272]
403. 18 | ~32 [avatar contradiction clause 402]
448. $false <- (17, ~35) [resolution 205,351]
449. ~17 | 35 [avatar contradiction clause 448]
451. $false [avatar sat refutation 211,261,309,375,376,397,403,449]
% SZS output end Proof for 2384310721598519959985693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not rich is both not brave and not generous and vice versa. Everyone who is both wise and patient is strong. If alice is curious or humble then john is tall and vice versa. If someone is either patient or rich then john is calm and vice versa. Everyone who is either not wise or not rich is not creative and vice versa. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. If someone is not creative or quiet then someone is both wise and not wise. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Mary is rich. | entailment | (![X]:((humble(X)|~rich(X))<=>(~brave(X)&~generous(X))))&
(![X]:((wise(X)&patient(X))=>strong(X)))&
(((curious(alice)|humble(alice)))<=>(tall(john)))&
((?[X]:((patient(X)<~>rich(X))))<=>(calm(john)))&
(![X]:((~wise(X)<~>~rich(X))<=>~creative(X)))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | rich(mary) | [
"p0",
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2491360723949321577638582
% SZS output start Proof for 2491360723949321577638582
1. ! [X0] : ((~rich(X0) | humble(X0)) <=> (~generous(X0) & ~brave(X0))) [input p0]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
7. ! [X0] : (~kind(X0) <=> wise(X0)) [input p6]
11. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p10]
15. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p14]
23. ~rich(mary) [input hypothesis]
24. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 11]
25. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 15]
28. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
35. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 25]
36. ! [X0] : (((~rich(X0) | humble(X0)) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((~rich(X0) | humble(X0) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [flattening 36]
45. ! [X0] : ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))) [nnf transformation 7]
50. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (brave(X0) | quiet(X0))) [nnf transformation 24]
51. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (brave(X3) | quiet(X3))) [rectify 50]
52. ? [X0] : (~brave(X0) & ~quiet(X0)) => (~brave(sK1) & ~quiet(sK1)) [choice axiom]
53. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK2) & ~wise(sK2)) [choice axiom]
54. ((~brave(sK1) & ~quiet(sK1)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK2) & ~wise(sK2)) | ! [X3] : (brave(X3) | quiet(X3))) [skolemisation 51,53,52]
59. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 35]
60. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK4) & wise(sK4)) [choice axiom]
61. (~wise(sK4) & wise(sK4)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 59,60]
71. ~brave(X0) | rich(X0) [cnf transformation 37]
90. ~kind(X0) | ~creative(X0) [cnf transformation 28]
91. kind(X0) | wise(X0) [cnf transformation 45]
103. ~wise(sK2) | brave(X3) | quiet(X3) [cnf transformation 54]
115. wise(sK4) | creative(X1) [cnf transformation 61]
116. wise(sK4) | ~quiet(X1) [cnf transformation 61]
117. ~wise(sK4) | creative(X1) [cnf transformation 61]
118. ~wise(sK4) | ~quiet(X1) [cnf transformation 61]
129. ~rich(mary) [cnf transformation 23]
197. 15 <=> ! [X3] : (brave(X3) | quiet(X3)) [avatar definition]
198. brave(X3) | quiet(X3) <- (15) [avatar component clause 197]
205. 17 <=> wise(sK2) [avatar definition]
207. ~wise(sK2) <- (~17) [avatar component clause 205]
208. 15 | ~17 [avatar split clause 103,205,197]
232. 23 <=> ! [X1] : ~quiet(X1) [avatar definition]
233. ~quiet(X1) <- (23) [avatar component clause 232]
235. 24 <=> wise(sK4) [avatar definition]
238. 23 | ~24 [avatar split clause 118,235,232]
240. 25 <=> ! [X1] : creative(X1) [avatar definition]
241. creative(X1) <- (25) [avatar component clause 240]
242. 25 | ~24 [avatar split clause 117,235,240]
243. 23 | 24 [avatar split clause 116,235,232]
244. 25 | 24 [avatar split clause 115,235,240]
273. 32 <=> rich(mary) [avatar definition]
275. ~rich(mary) <- (~32) [avatar component clause 273]
281. ~32 [avatar split clause 129,273]
293. wise(X0) | ~creative(X0) [resolution 91,90]
296. wise(X0) <- (25) [subsumption resolution 293,241]
297. $false <- (~17, 25) [resolution 296,207]
298. 17 | ~25 [avatar contradiction clause 297]
299. brave(X3) <- (15, 23) [subsumption resolution 198,233]
301. rich(X0) <- (15, 23) [resolution 299,71]
305. $false <- (15, 23, ~32) [resolution 301,275]
306. ~15 | ~23 | 32 [avatar contradiction clause 305]
308. $false [avatar sat refutation 208,238,242,243,244,281,298,306]
% SZS output end Proof for 2491360723949321577638582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 generous is not quiet and vice versa.
If paul is tall then fred is both kind and not happy and vice versa.
Everyone who is both brave and old is not tall and vice versa.
If john is not rich or not tall then paul is both wise and generous.
Everyone who is funny or calm is both not tall and wise and vice versa.
Everyone who is tall is both funny and not happy.
If lucy is not humble or not calm then lucy is not patient or not calm and vice versa.
Everyone who is either happy or not calm is both not tall and not generous.
Everyone who is either not strong or not tall is either funny or not happy.
Everyone who is brave is not quiet or not patient and vice versa.
Everyone who is both not kind and not creative is either old or patient and vice versa.
Everyone who is both not calm and wise is not old or not calm.
Everyone who is either calm or not wise is either not patient or patient.
If someone is not brave then someone is both tall and not curious and vice versa.
Mary is both not creative and quiet.
Someone is not funny or creative.
Someone is both not patient and not curious.
Fred is not creative.
Fred is both not rich and not humble.
Paul is not happy. | Lucy is not kind. | entailment | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
((tall(paul))<=>((kind(fred)&~happy(fred))))&
(![X]:((brave(X)&old(X))<=>~tall(X)))&
(((~rich(john)|~tall(john)))=>((wise(paul)&generous(paul))))&
(![X]:((funny(X)|calm(X))<=>(~tall(X)&wise(X))))&
(![X]:(tall(X)=>(funny(X)&~happy(X))))&
(((~humble(lucy)|~calm(lucy)))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((happy(X)<~>~calm(X))=>(~tall(X)&~generous(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(funny(X)<~>~happy(X))))&
(![X]:(brave(X)<=>(~quiet(X)|~patient(X))))&
(![X]:((~kind(X)&~creative(X))<=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)&wise(X))=>(~old(X)|~calm(X))))&
(![X]:((calm(X)<~>~wise(X))=>(~patient(X)<~>patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
((~creative(mary)&quiet(mary)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((~patient(X)&~curious(X))))&
(~creative(fred))&
((~rich(fred)&~humble(fred)))&
(~happy(paul)) | ~kind(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6046445409997157191990856
% SZS output start Proof for 6046445409997157191990856
1. ! [X0] : ((~patient(X0) | patient(X0)) => (tall(X0) | calm(X0))) [input p0]
2. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (wise(X0) & generous(X0))) [input p1]
3. ! [X0] : (generous(X0) <=> ~quiet(X0)) [input p2]
5. ! [X0] : ((old(X0) & brave(X0)) <=> ~tall(X0)) [input p4]
7. ! [X0] : ((calm(X0) | funny(X0)) <=> (wise(X0) & ~tall(X0))) [input p6]
8. ! [X0] : (tall(X0) => (~happy(X0) & funny(X0))) [input p7]
9. (~calm(lucy) | ~humble(lucy)) <=> (~calm(lucy) | ~patient(lucy)) [input p8]
12. ! [X0] : (brave(X0) <=> (~patient(X0) | ~quiet(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (old(X0) <~> patient(X0))) [input p12]
23. kind(lucy) [input hypothesis]
25. ! [X0] : ((tall(X0) | calm(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 1]
26. ! [X0] : (tall(X0) | calm(X0) | (patient(X0) & ~patient(X0))) [flattening 25]
28. ! [X0] : ((~happy(X0) & funny(X0)) | ~tall(X0)) [ennf transformation 8]
34. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 2]
35. ! [X0] : (((~humble(X0) & ~rich(X0)) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | humble(X0) | rich(X0))) [flattening 34]
36. ! [X0] : ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0))) [nnf transformation 3]
39. ! [X0] : (((old(X0) & brave(X0)) | tall(X0)) & (~tall(X0) | (~old(X0) | ~brave(X0)))) [nnf transformation 5]
40. ! [X0] : (((old(X0) & brave(X0)) | tall(X0)) & (~tall(X0) | ~old(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((calm(X0) | funny(X0)) | (~wise(X0) | tall(X0))) & ((wise(X0) & ~tall(X0)) | (~calm(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((calm(X0) | funny(X0) | ~wise(X0) | tall(X0)) & ((wise(X0) & ~tall(X0)) | (~calm(X0) & ~funny(X0)))) [flattening 41]
43. ((~calm(lucy) | ~humble(lucy)) | (calm(lucy) & patient(lucy))) & ((~calm(lucy) | ~patient(lucy)) | (calm(lucy) & humble(lucy))) [nnf transformation 9]
44. (~calm(lucy) | ~humble(lucy) | (calm(lucy) & patient(lucy))) & (~calm(lucy) | ~patient(lucy) | (calm(lucy) & humble(lucy))) [flattening 43]
47. ! [X0] : ((brave(X0) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | ~brave(X0))) [nnf transformation 12]
48. ! [X0] : ((brave(X0) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~brave(X0))) [flattening 47]
49. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | (creative(X0) | kind(X0)))) [nnf transformation 13]
50. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | creative(X0) | kind(X0))) [flattening 49]
61. tall(X0) | calm(X0) | ~patient(X0) [cnf transformation 26]
62. tall(X0) | calm(X0) | patient(X0) [cnf transformation 26]
66. ~wise(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 35]
68. quiet(X0) | generous(X0) [cnf transformation 36]
73. brave(X0) | tall(X0) [cnf transformation 40]
74. old(X0) | tall(X0) [cnf transformation 40]
79. ~funny(X0) | ~tall(X0) [cnf transformation 42]
82. ~calm(X0) | wise(X0) [cnf transformation 42]
84. funny(X0) | ~tall(X0) [cnf transformation 28]
86. ~calm(lucy) | ~patient(lucy) | humble(lucy) [cnf transformation 44]
98. ~brave(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 48]
103. ~old(X0) | patient(X0) | ~kind(X0) [cnf transformation 50]
124. kind(lucy) [cnf transformation 23]
125. tall(X0) | calm(X0) [subsumption resolution 61,62]
161. ~tall(X0) [subsumption resolution 84,79]
163. 8 <=> patient(lucy) [avatar definition]
165. patient(lucy) <- (8) [avatar component clause 163]
167. 9 <=> humble(lucy) [avatar definition]
168. humble(lucy) <- (9) [avatar component clause 167]
171. 10 <=> calm(lucy) [avatar definition]
173. ~calm(lucy) <- (~10) [avatar component clause 171]
175. 9 | ~8 | ~10 [avatar split clause 86,171,163,167]
202. calm(X1) [resolution 125,161]
203. $false <- (~10) [resolution 202,173]
204. wise(X0) [resolution 202,82]
205. 10 [avatar contradiction clause 203]
224. ~generous(X1) | ~humble(X1) [resolution 66,204]
235. ~quiet(X2) | ~patient(X2) | tall(X2) [resolution 98,73]
237. ~quiet(X2) | ~patient(X2) [subsumption resolution 235,161]
239. ~patient(X0) | generous(X0) [resolution 237,68]
240. patient(X0) | ~kind(X0) | tall(X0) [resolution 103,74]
241. ~kind(X0) | patient(X0) [subsumption resolution 240,161]
243. patient(lucy) [resolution 241,124]
246. 8 [avatar split clause 243,163]
254. generous(lucy) <- (8) [resolution 239,165]
255. ~humble(lucy) <- (8) [resolution 254,224]
258. $false <- (8, 9) [subsumption resolution 255,168]
259. ~8 | ~9 [avatar contradiction clause 258]
260. $false [avatar sat refutation 175,205,246,259]
% SZS output end Proof for 6046445409997157191990856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If mary is patient then lucy is funny. If lucy is both calm and generous then someone is kind or not creative. Everyone who is either not tall or not generous is patient and vice versa. Everyone who is not generous or brave is not patient or curious. If alice is both happy and not quiet then john is either not tall or not wise and vice versa. Everyone who is either brave or not curious is not funny or not generous. If susan is generous or not happy then someone is either not strong or wise and vice versa. Everyone who is both patient and creative is either not funny or rich. Everyone who is both old and not patient is either not wise or quiet. If john is not patient or curious then alice is both kind and not calm. Everyone who is both quiet and not generous is both wise and not humble. Everyone who is not old or not wise is either not tall or curious. Everyone who is generous is not tall. If someone is not creative then someone is calm and vice versa. Everyone who is quiet or tall is both calm and not tall and vice versa. If fred is both not curious and not calm then someone is either not tall or not rich. Someone is both happy and not funny. Someone is not calm or not tall. Someone is funny or tall. Someone is both humble and rich. Susan is both humble and not quiet. Susan is patient or not quiet. Someone is curious. | Lucy is not old. | neutral | ((patient(mary))=>(funny(lucy)))&
(((calm(lucy)&generous(lucy)))=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>patient(X)))&
(![X]:((~generous(X)|brave(X))=>(~patient(X)|curious(X))))&
(((happy(alice)&~quiet(alice)))<=>((~tall(john)<~>~wise(john))))&
(![X]:((brave(X)<~>~curious(X))=>(~funny(X)|~generous(X))))&
(((generous(susan)|~happy(susan)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((patient(X)&creative(X))=>(~funny(X)<~>rich(X))))&
(![X]:((old(X)&~patient(X))=>(~wise(X)<~>quiet(X))))&
(((~patient(john)|curious(john)))=>((kind(alice)&~calm(alice))))&
(![X]:((quiet(X)&~generous(X))=>(wise(X)&~humble(X))))&
(![X]:((~old(X)|~wise(X))=>(~tall(X)<~>curious(X))))&
(![X]:(generous(X)=>~tall(X)))&
((?[X]:(~creative(X)))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)|tall(X))<=>(calm(X)&~tall(X))))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~tall(X)<~>~rich(X)))))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:((humble(X)&rich(X))))&
((humble(susan)&~quiet(susan)))&
((patient(susan)|~quiet(susan)))&
(?[X]:(curious(X))) | ~old(lucy) | [] | null | 0 |
If paul is both happy and not calm then someone is happy or not old. Everyone who is either curious or kind is either kind or quiet and vice versa. Everyone who is tall is funny or generous and vice versa. Everyone who is brave is creative or not strong and vice versa. Everyone who is either kind or humble is both not kind and not creative. If john is not brave or not patient then someone is strong or humble and vice versa. If lucy is both not wise and wise then someone is not rich or not generous. If paul is not creative or not funny then someone is rich. Everyone who is not funny or humble is not strong. Everyone who is either happy or not funny is both patient and not humble. Everyone who is not brave is either rich or not quiet and vice versa. Everyone who is both kind and generous is both not generous and not strong. Everyone who is both funny and not calm is either tall or not calm. Everyone who is either not humble or old is brave. Everyone who is either patient or kind is either not curious or not tall. If mary is both not old and humble then john is not curious or quiet. John is calm or kind. Mary is not calm. Someone is both brave and strong. Paul is not old. Someone is not tall or happy. Someone is patient. Someone is generous or not kind. Mary is both old and not wise. | John is rich. | neutral | (((happy(paul)&~calm(paul)))=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((curious(X)<~>kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:(tall(X)<=>(funny(X)|generous(X))))&
(![X]:(brave(X)<=>(creative(X)|~strong(X))))&
(![X]:((kind(X)<~>humble(X))=>(~kind(X)&~creative(X))))&
(((~brave(john)|~patient(john)))<=>(?[X]:((strong(X)|humble(X)))))&
(((~wise(lucy)&wise(lucy)))=>(?[X]:((~rich(X)|~generous(X)))))&
(((~creative(paul)|~funny(paul)))=>(?[X]:(rich(X))))&
(![X]:((~funny(X)|humble(X))=>~strong(X)))&
(![X]:((happy(X)<~>~funny(X))=>(patient(X)&~humble(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:((kind(X)&generous(X))=>(~generous(X)&~strong(X))))&
(![X]:((funny(X)&~calm(X))=>(tall(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>old(X))=>brave(X)))&
(![X]:((patient(X)<~>kind(X))=>(~curious(X)<~>~tall(X))))&
(((~old(mary)&humble(mary)))=>((~curious(john)|quiet(john))))&
((calm(john)|kind(john)))&
(~calm(mary))&
(?[X]:((brave(X)&strong(X))))&
(~old(paul))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:(patient(X)))&
(?[X]:((generous(X)|~kind(X))))&
((old(mary)&~wise(mary))) | rich(john) | [] | null | 0 |
If john is happy or not kind then someone is not brave.
If someone is not wise or not kind then alice is either not tall or not generous and vice versa.
Everyone who is quiet or brave is strong or wise and vice versa.
If someone is either generous or not funny then someone is either not generous or not happy.
Everyone who is not calm is not generous or rich and vice versa.
Everyone who is not rich is both strong and not brave.
Everyone who is both not happy and not kind is happy or funny.
Everyone who is rich or not generous is both patient and not curious and vice versa.
If someone is both not patient and not wise then mary is quiet or not brave and vice versa.
Everyone who is both not old and happy is not happy or wise and vice versa.
Everyone who is either generous or happy is both not calm and not happy and vice versa.
Everyone who is either rich or creative is not happy and vice versa.
Everyone who is both quiet and patient is both calm and tall.
Everyone who is generous or happy is not tall or brave.
If someone is creative then someone is either not calm or not funny.
Everyone who is either not old or not tall is not patient or wise.
Alice is curious.
Someone is creative.
Someone is not humble or not curious.
Someone is strong or not curious.
Someone is either happy or creative.
Someone is rich or strong. | Mary is not calm. | neutral | (((happy(john)|~kind(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~wise(X)|~kind(X))))<=>((~tall(alice)<~>~generous(alice))))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)|wise(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~calm(X)<=>(~generous(X)|rich(X))))&
(![X]:(~rich(X)=>(strong(X)&~brave(X))))&
(![X]:((~happy(X)&~kind(X))=>(happy(X)|funny(X))))&
(![X]:((rich(X)|~generous(X))<=>(patient(X)&~curious(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((quiet(mary)|~brave(mary))))&
(![X]:((~old(X)&happy(X))<=>(~happy(X)|wise(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)<~>creative(X))<=>~happy(X)))&
(![X]:((quiet(X)&patient(X))=>(calm(X)&tall(X))))&
(![X]:((generous(X)|happy(X))=>(~tall(X)|brave(X))))&
((?[X]:(creative(X)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((~old(X)<~>~tall(X))=>(~patient(X)|wise(X))))&
(curious(alice))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((rich(X)|strong(X)))) | ~calm(mary) | [] | null | 0 |
Everyone who is not happy is old or patient and vice versa.
Everyone who is old or not quiet is generous and vice versa.
Everyone who is either not strong or creative is not quiet or calm.
If someone is either not strong or not happy then alice is both not tall and strong.
If someone is quiet or not kind then someone is either not happy or rich and vice versa.
Everyone who is not generous or patient is kind or funny.
If someone is both happy and not funny then fred is either not creative or curious and vice versa.
Everyone who is either not happy or not kind is patient or rich and vice versa.
If alice is quiet then alice is either not old or not rich.
Everyone who is either not wise or not funny is not kind or humble and vice versa.
Everyone who is both calm and not patient is brave.
Everyone who is both wise and curious is either not wise or patient.
Everyone who is both not happy and quiet is either not brave or not generous and vice versa.
If lucy is not wise then someone is not creative or not generous and vice versa.
Everyone who is patient is not rich and vice versa.
Everyone who is either not strong or tall is strong or not kind.
Lucy is generous or quiet.
Paul is either patient or not strong.
Someone is generous or patient.
Someone is both not brave and humble.
Fred is not quiet or brave.
Mary is kind or rich.
Susan is both wise and not brave.
Someone is both not rich and not old. | Susan is happy. | contradiction | (![X]:(~happy(X)<=>(old(X)|patient(X))))&
(![X]:((old(X)|~quiet(X))<=>generous(X)))&
(![X]:((~strong(X)<~>creative(X))=>(~quiet(X)|calm(X))))&
((?[X]:((~strong(X)<~>~happy(X))))=>((~tall(alice)&strong(alice))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:((~generous(X)|patient(X))=>(kind(X)|funny(X))))&
((?[X]:((happy(X)&~funny(X))))<=>((~creative(fred)<~>curious(fred))))&
(![X]:((~happy(X)<~>~kind(X))<=>(patient(X)|rich(X))))&
((quiet(alice))=>((~old(alice)<~>~rich(alice))))&
(![X]:((~wise(X)<~>~funny(X))<=>(~kind(X)|humble(X))))&
(![X]:((calm(X)&~patient(X))=>brave(X)))&
(![X]:((wise(X)&curious(X))=>(~wise(X)<~>patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~brave(X)<~>~generous(X))))&
((~wise(lucy))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((~strong(X)<~>tall(X))=>(strong(X)|~kind(X))))&
((generous(lucy)|quiet(lucy)))&
((patient(paul)<~>~strong(paul)))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:((~brave(X)&humble(X))))&
((~quiet(fred)|brave(fred)))&
((kind(mary)|rich(mary)))&
((wise(susan)&~brave(susan)))&
(?[X]:((~rich(X)&~old(X)))) | happy(susan) | [
"p0",
"p5",
"p7",
"p9",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5672480556912033250577899
% SZS output start Proof for 5672480556912033250577899
1. ! [X0] : (~happy(X0) <=> (patient(X0) | old(X0))) [input p0]
6. ! [X0] : ((patient(X0) | ~generous(X0)) => (funny(X0) | kind(X0))) [input p5]
8. ! [X0] : ((~happy(X0) <~> ~kind(X0)) <=> (rich(X0) | patient(X0))) [input p7]
10. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> (humble(X0) | ~kind(X0))) [input p9]
13. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p12]
15. ! [X0] : (patient(X0) <=> ~rich(X0)) [input p14]
23. ~brave(susan) & wise(susan) [input p22]
25. happy(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) | kind(X0)) | (~patient(X0) & generous(X0))) [ennf transformation 6]
31. ! [X0] : (funny(X0) | kind(X0) | (~patient(X0) & generous(X0))) [flattening 30]
39. ! [X0] : ((~happy(X0) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | happy(X0))) [nnf transformation 1]
40. ! [X0] : ((~happy(X0) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | happy(X0))) [flattening 39]
54. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [nnf transformation 8]
55. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [flattening 54]
57. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 10]
58. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [flattening 57]
60. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 13]
61. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~quiet(X0) | happy(X0))) [flattening 60]
66. ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 15]
77. ~patient(X0) | ~happy(X0) [cnf transformation 40]
93. funny(X0) | kind(X0) | generous(X0) [cnf transformation 31]
104. ~rich(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 55]
111. ~wise(X0) | ~funny(X0) | kind(X0) [cnf transformation 58]
120. ~generous(X0) | ~happy(X0) | brave(X0) [cnf transformation 61]
128. rich(X0) | patient(X0) [cnf transformation 66]
139. wise(susan) [cnf transformation 23]
140. ~brave(susan) [cnf transformation 23]
143. happy(susan) [cnf transformation 25]
339. ~happy(X0) | ~kind(X0) | patient(X0) [resolution 104,128]
340. ~kind(X0) | ~happy(X0) [subsumption resolution 339,77]
353. ~funny(susan) | kind(susan) [resolution 111,139]
355. 40 <=> kind(susan) [avatar definition]
357. kind(susan) <- (40) [avatar component clause 355]
359. 41 <=> funny(susan) [avatar definition]
361. ~funny(susan) <- (~41) [avatar component clause 359]
362. 40 | ~41 [avatar split clause 353,359,355]
363. kind(susan) | generous(susan) <- (~41) [resolution 361,93]
365. 42 <=> generous(susan) [avatar definition]
367. generous(susan) <- (42) [avatar component clause 365]
368. 42 | 40 | 41 [avatar split clause 363,359,355,365]
557. ~happy(susan) <- (40) [resolution 340,357]
560. $false <- (40) [subsumption resolution 557,143]
561. ~40 [avatar contradiction clause 560]
592. ~happy(susan) | brave(susan) <- (42) [resolution 367,120]
594. brave(susan) <- (42) [subsumption resolution 592,143]
595. $false <- (42) [subsumption resolution 594,140]
596. ~42 [avatar contradiction clause 595]
598. $false [avatar sat refutation 362,368,561,596]
% SZS output end Proof for 5672480556912033250577899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is both not brave and wise and vice versa.
If paul is not strong or curious then someone is not happy or not old and vice versa.
Everyone who is either wise or not happy is either kind or not rich and vice versa.
If someone is not generous then someone is not old and vice versa.
If someone is creative or calm then alice is either not strong or calm.
If someone is creative then mary is not wise.
If someone is patient or humble then someone is not rich or rich and vice versa.
Everyone who is not brave is strong.
If john is calm or rich then alice is both not strong and quiet and vice versa.
Everyone who is either not tall or curious is both not wise and quiet and vice versa.
Everyone who is both rich and not kind is both brave and rich.
If mary is not strong or not brave then paul is not tall or not curious and vice versa.
Everyone who is funny or kind is not curious or not funny.
If mary is either not generous or not brave then john is either not creative or not happy and vice versa.
Everyone who is not brave or patient is not generous.
If john is not rich then someone is old or not funny and vice versa.
Someone is either tall or not rich.
Alice is not humble or not brave.
Fred is not old.
Someone is either not strong or not quiet.
Susan is both kind and not curious.
Fred is not humble or kind.
Paul is both not tall and not rich.
John is both humble and not wise. | Paul is funny. | contradiction | (![X]:((happy(X)|~curious(X))<=>(~brave(X)&wise(X))))&
(((~strong(paul)|curious(paul)))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((wise(X)<~>~happy(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~old(X))))&
((?[X]:((creative(X)|calm(X))))=>((~strong(alice)<~>calm(alice))))&
((?[X]:(creative(X)))=>(~wise(mary)))&
((?[X]:((patient(X)|humble(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(((calm(john)|rich(john)))<=>((~strong(alice)&quiet(alice))))&
(![X]:((~tall(X)<~>curious(X))<=>(~wise(X)&quiet(X))))&
(![X]:((rich(X)&~kind(X))=>(brave(X)&rich(X))))&
(((~strong(mary)|~brave(mary)))<=>((~tall(paul)|~curious(paul))))&
(![X]:((funny(X)|kind(X))=>(~curious(X)|~funny(X))))&
(((~generous(mary)<~>~brave(mary)))<=>((~creative(john)<~>~happy(john))))&
(![X]:((~brave(X)|patient(X))=>~generous(X)))&
((~rich(john))<=>(?[X]:((old(X)|~funny(X)))))&
(?[X]:((tall(X)<~>~rich(X))))&
((~humble(alice)|~brave(alice)))&
(~old(fred))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((kind(susan)&~curious(susan)))&
((~humble(fred)|kind(fred)))&
((~tall(paul)&~rich(paul)))&
((humble(john)&~wise(john))) | funny(paul) | [
"p0",
"p1",
"p7",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2035873000115970397451738
% SZS output start Proof for 2035873000115970397451738
1. ! [X0] : ((~curious(X0) | happy(X0)) <=> (wise(X0) & ~brave(X0))) [input p0]
2. (curious(paul) | ~strong(paul)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p1]
8. ! [X0] : (~brave(X0) => strong(X0)) [input p7]
13. ! [X0] : ((kind(X0) | funny(X0)) => (~funny(X0) | ~curious(X0))) [input p12]
24. ~wise(john) & humble(john) [input p23]
25. funny(paul) [input hypothesis]
30. ! [X0] : (strong(X0) | brave(X0)) [ennf transformation 8]
33. ! [X0] : ((~funny(X0) | ~curious(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 13]
34. ! [X0] : (~funny(X0) | ~curious(X0) | (~kind(X0) & ~funny(X0))) [flattening 33]
36. ! [X0] : (((~curious(X0) | happy(X0)) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | (curious(X0) & ~happy(X0)))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | happy(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | (curious(X0) & ~happy(X0)))) [flattening 36]
38. ((curious(paul) | ~strong(paul)) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~curious(paul) & strong(paul))) [nnf transformation 2]
39. (curious(paul) | ~strong(paul) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~curious(paul) & strong(paul))) [flattening 38]
40. (curious(paul) | ~strong(paul) | ! [X0] : (old(X0) & happy(X0))) & (? [X1] : (~old(X1) | ~happy(X1)) | (~curious(paul) & strong(paul))) [rectify 39]
41. ? [X1] : (~old(X1) | ~happy(X1)) => (~old(sK0) | ~happy(sK0)) [choice axiom]
42. (curious(paul) | ~strong(paul) | ! [X0] : (old(X0) & happy(X0))) & ((~old(sK0) | ~happy(sK0)) | (~curious(paul) & strong(paul))) [skolemisation 40,41]
73. ~brave(X0) | curious(X0) [cnf transformation 37]
74. ~happy(X0) | wise(X0) [cnf transformation 37]
79. curious(paul) | ~strong(paul) | happy(X0) [cnf transformation 42]
100. strong(X0) | brave(X0) [cnf transformation 30]
118. ~funny(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 34]
145. ~wise(john) [cnf transformation 24]
146. funny(paul) [cnf transformation 25]
147. ~funny(X0) | ~curious(X0) [duplicate literal removal 118]
152. 2 <=> strong(paul) [avatar definition]
154. ~strong(paul) <- (~2) [avatar component clause 152]
156. 3 <=> curious(paul) [avatar definition]
158. curious(paul) <- (3) [avatar component clause 156]
161. 4 <=> ! [X0] : happy(X0) [avatar definition]
162. happy(X0) <- (4) [avatar component clause 161]
163. 4 | ~2 | 3 [avatar split clause 79,156,152,161]
343. brave(paul) <- (~2) [resolution 100,154]
347. curious(paul) <- (~2) [resolution 343,73]
349. 3 | 2 [avatar split clause 347,152,156]
357. wise(X0) <- (4) [resolution 162,74]
365. $false <- (4) [resolution 357,145]
368. ~4 [avatar contradiction clause 365]
376. ~curious(paul) [resolution 147,146]
377. $false <- (3) [subsumption resolution 376,158]
378. ~3 [avatar contradiction clause 377]
379. $false [avatar sat refutation 163,349,368,378]
% SZS output end Proof for 2035873000115970397451738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not tall then someone is both not patient and not curious.
If someone is both kind and not wise then john is not tall and vice versa.
Everyone who is either not tall or generous is either patient or not quiet and vice versa.
If someone is wise then mary is not generous or rich.
Everyone who is both creative and kind is both rich and humble and vice versa.
Everyone who is both not strong and not brave is either rich or quiet and vice versa.
Everyone who is both not generous and not tall is creative or happy.
Everyone who is brave is happy and vice versa.
Everyone who is both generous and happy is both not kind and calm and vice versa.
Everyone who is patient is both not patient and not curious.
Everyone who is not tall is not tall or not happy.
If susan is not wise or not brave then someone is either humble or calm and vice versa.
Everyone who is happy is not old.
If john is not tall or not funny then fred is strong.
If alice is humble or old then someone is both not kind and not quiet.
Everyone who is both tall and kind is either not rich or wise and vice versa.
Alice is curious or not strong.
Someone is kind.
Alice is not funny or quiet.
Alice is not calm.
Mary is either not old or happy.
John is rich or quiet.
Someone is not humble.
Someone is not curious or not creative. | Fred is not patient. | entailment | ((?[X]:((curious(X)|~tall(X))))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:((kind(X)&~wise(X))))<=>(~tall(john)))&
(![X]:((~tall(X)<~>generous(X))<=>(patient(X)<~>~quiet(X))))&
((?[X]:(wise(X)))=>((~generous(mary)|rich(mary))))&
(![X]:((creative(X)&kind(X))<=>(rich(X)&humble(X))))&
(![X]:((~strong(X)&~brave(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((~generous(X)&~tall(X))=>(creative(X)|happy(X))))&
(![X]:(brave(X)<=>happy(X)))&
(![X]:((generous(X)&happy(X))<=>(~kind(X)&calm(X))))&
(![X]:(patient(X)=>(~patient(X)&~curious(X))))&
(![X]:(~tall(X)=>(~tall(X)|~happy(X))))&
(((~wise(susan)|~brave(susan)))<=>(?[X]:((humble(X)<~>calm(X)))))&
(![X]:(happy(X)=>~old(X)))&
(((~tall(john)|~funny(john)))=>(strong(fred)))&
(((humble(alice)|old(alice)))=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((tall(X)&kind(X))<=>(~rich(X)<~>wise(X))))&
((curious(alice)|~strong(alice)))&
(?[X]:(kind(X)))&
((~funny(alice)|quiet(alice)))&
(~calm(alice))&
((~old(mary)<~>happy(mary)))&
((rich(john)|quiet(john)))&
(?[X]:(~humble(X)))&
(?[X]:((~curious(X)|~creative(X)))) | ~patient(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3399666863777445596149229
% SZS output start Proof for 3399666863777445596149229
10. ! [X0] : (patient(X0) => (~curious(X0) & ~patient(X0))) [input p9]
25. patient(fred) [input hypothesis]
32. ! [X0] : ((~curious(X0) & ~patient(X0)) | ~patient(X0)) [ennf transformation 10]
102. ~patient(X0) | ~patient(X0) [cnf transformation 32]
133. patient(fred) [cnf transformation 25]
134. ~patient(X0) [duplicate literal removal 102]
279. $false [subsumption resolution 133,134]
% SZS output end Proof for 3399666863777445596149229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either generous or not creative.
Everyone who is both happy and wise is curious or not old and vice versa.
If fred is either not strong or not quiet then john is either curious or humble.
Everyone who is curious or calm is both not kind and not quiet.
If someone is patient then someone is both brave and curious and vice versa.
If someone is either not happy or wise then someone is funny or strong.
If paul is not wise or not calm then someone is either not old or old and vice versa.
If someone is both quiet and rich then fred is both not patient and kind and vice versa.
Everyone who is not calm is not wise.
If someone is not patient then someone is generous or happy.
Everyone who is both not creative and rich is calm and vice versa.
Everyone who is both not brave and not generous is rich or curious and vice versa.
If someone is brave or not humble then someone is not humble or not calm.
Everyone who is both not wise and happy is either not wise or not humble and vice versa.
If alice is not rich then someone is old or creative and vice versa.
If someone is both kind and quiet then susan is strong or tall and vice versa.
Someone is wise.
Someone is not generous.
Someone is calm or not curious.
Mary is both not old and wise.
Someone is both happy and quiet.
Someone is either rich or not happy.
Someone is either not humble or not tall.
Someone is strong. | Mary is kind. | contradiction | (![X]:(funny(X)=>(generous(X)<~>~creative(X))))&
(![X]:((happy(X)&wise(X))<=>(curious(X)|~old(X))))&
(((~strong(fred)<~>~quiet(fred)))=>((curious(john)<~>humble(john))))&
(![X]:((curious(X)|calm(X))=>(~kind(X)&~quiet(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((funny(X)|strong(X)))))&
(((~wise(paul)|~calm(paul)))<=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((quiet(X)&rich(X))))<=>((~patient(fred)&kind(fred))))&
(![X]:(~calm(X)=>~wise(X)))&
((?[X]:(~patient(X)))=>(?[X]:((generous(X)|happy(X)))))&
(![X]:((~creative(X)&rich(X))<=>calm(X)))&
(![X]:((~brave(X)&~generous(X))<=>(rich(X)|curious(X))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)<~>~humble(X))))&
((~rich(alice))<=>(?[X]:((old(X)|creative(X)))))&
((?[X]:((kind(X)&quiet(X))))<=>((strong(susan)|tall(susan))))&
(?[X]:(wise(X)))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~old(mary)&wise(mary)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:(strong(X))) | kind(mary) | [
"p3",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7472858611536589613732416
% SZS output start Proof for 7472858611536589613732416
4. ! [X0] : ((calm(X0) | curious(X0)) => (~quiet(X0) & ~kind(X0))) [input p3]
9. ! [X0] : (~calm(X0) => ~wise(X0)) [input p8]
20. wise(mary) & ~old(mary) [input p19]
25. kind(mary) [input hypothesis]
32. ! [X0] : ((~quiet(X0) & ~kind(X0)) | (~calm(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : (~wise(X0) | calm(X0)) [ennf transformation 9]
109. ~kind(X0) | ~calm(X0) [cnf transformation 32]
127. ~wise(X0) | calm(X0) [cnf transformation 34]
157. wise(mary) [cnf transformation 20]
165. kind(mary) [cnf transformation 25]
380. ~calm(mary) [resolution 109,165]
387. calm(mary) [resolution 127,157]
388. $false [subsumption resolution 387,380]
% SZS output end Proof for 7472858611536589613732416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not happy is patient and vice versa.
Everyone who is both brave and not calm is both not old and humble.
If someone is patient or wise then fred is tall or calm.
If someone is not funny or rich then alice is both not funny and tall and vice versa.
Everyone who is not rich is both not calm and not creative.
Everyone who is not old is old or not rich.
Everyone who is either rich or not patient is not old or not quiet and vice versa.
If someone is both not humble and not generous then someone is either brave or not generous and vice versa.
Everyone who is either not curious or not patient is either calm or not creative and vice versa.
If someone is not kind then someone is funny or patient and vice versa.
Everyone who is both wise and quiet is either not quiet or calm and vice versa.
If someone is not old or curious then lucy is either not kind or old and vice versa.
Everyone who is happy is not happy.
Everyone who is not calm or not generous is either calm or not happy and vice versa.
Everyone who is not tall or not rich is not humble or tall and vice versa.
If someone is quiet or kind then fred is calm and vice versa.
Someone is curious.
John is either not creative or not quiet.
Someone is either not tall or not kind.
Someone is both humble and not kind.
Susan is either generous or rich.
Someone is not brave or brave. | Fred is not generous. | contradiction | (![X]:((strong(X)|~happy(X))<=>patient(X)))&
(![X]:((brave(X)&~calm(X))=>(~old(X)&humble(X))))&
((?[X]:((patient(X)|wise(X))))=>((tall(fred)|calm(fred))))&
((?[X]:((~funny(X)|rich(X))))<=>((~funny(alice)&tall(alice))))&
(![X]:(~rich(X)=>(~calm(X)&~creative(X))))&
(![X]:(~old(X)=>(old(X)|~rich(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~old(X)|~quiet(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~curious(X)<~>~patient(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~old(X)|curious(X))))<=>((~kind(lucy)<~>old(lucy))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((~calm(X)|~generous(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~humble(X)|tall(X))))&
((?[X]:((quiet(X)|kind(X))))<=>(calm(fred)))&
(?[X]:(curious(X)))&
((~creative(john)<~>~quiet(john)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((humble(X)&~kind(X))))&
((generous(susan)<~>rich(susan)))&
(?[X]:((~brave(X)|brave(X)))) | ~generous(fred) | [
"p0",
"p5",
"p6",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6568057262546636777923769
% SZS output start Proof for 6568057262546636777923769
1. ! [X0] : ((~happy(X0) | strong(X0)) <=> patient(X0)) [input p0]
6. ! [X0] : (~old(X0) => (~rich(X0) | old(X0))) [input p5]
7. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> (~quiet(X0) | ~old(X0))) [input p6]
12. ? [X0] : (curious(X0) | ~old(X0)) <=> (~kind(lucy) <~> old(lucy)) [input p11]
13. ! [X0] : (happy(X0) => ~happy(X0)) [input p12]
14. ! [X0] : ((~generous(X0) | ~calm(X0)) <=> (calm(X0) <~> ~happy(X0))) [input p13]
16. ? [X0] : (kind(X0) | quiet(X0)) <=> calm(fred) [input p15]
17. ? [X0] : curious(X0) [input p16]
23. ~generous(fred) [input hypothesis]
31. ! [X0] : ((~rich(X0) | old(X0)) | old(X0)) [ennf transformation 6]
32. ! [X0] : (~rich(X0) | old(X0) | old(X0)) [flattening 31]
33. ! [X0] : (~happy(X0) | ~happy(X0)) [ennf transformation 13]
34. ! [X0] : (((~happy(X0) | strong(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : ((~happy(X0) | strong(X0) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [flattening 34]
41. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 7]
42. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [flattening 41]
56. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X0] : (~curious(X0) & old(X0))) [nnf transformation 12]
57. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [rectify 56]
58. ? [X0] : (curious(X0) | ~old(X0)) => (curious(sK5) | ~old(sK5)) [choice axiom]
59. ((curious(sK5) | ~old(sK5)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [skolemisation 57,58]
60. ! [X0] : (((~generous(X0) | ~calm(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) & (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & calm(X0)))) [nnf transformation 14]
61. ! [X0] : ((~generous(X0) | ~calm(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) & (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & calm(X0)))) [flattening 60]
64. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X0] : (~kind(X0) & ~quiet(X0))) [nnf transformation 16]
65. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [rectify 64]
66. ? [X0] : (kind(X0) | quiet(X0)) => (kind(sK6) | quiet(sK6)) [choice axiom]
67. ((kind(sK6) | quiet(sK6)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [skolemisation 65,66]
68. ? [X0] : curious(X0) => curious(sK7) [choice axiom]
69. curious(sK7) [skolemisation 17,68]
80. patient(X0) | happy(X0) [cnf transformation 35]
93. ~rich(X0) | old(X0) | old(X0) [cnf transformation 32]
96. ~patient(X0) | rich(X0) | old(X0) [cnf transformation 42]
126. ~old(lucy) | kind(lucy) | ~curious(X1) [cnf transformation 59]
129. ~happy(X0) | ~happy(X0) [cnf transformation 33]
133. happy(X0) | ~calm(X0) | generous(X0) [cnf transformation 61]
141. calm(fred) | ~kind(X1) [cnf transformation 67]
143. curious(sK7) [cnf transformation 69]
153. ~generous(fred) [cnf transformation 23]
158. ~happy(X0) [duplicate literal removal 129]
161. ~rich(X0) | old(X0) [duplicate literal removal 93]
170. 3 <=> calm(fred) [avatar definition]
172. calm(fred) <- (3) [avatar component clause 170]
205. ~patient(X0) | old(X0) [subsumption resolution 96,161]
261. 23 <=> old(lucy) [avatar definition]
263. ~old(lucy) <- (~23) [avatar component clause 261]
265. 24 <=> kind(lucy) [avatar definition]
266. kind(lucy) <- (24) [avatar component clause 265]
279. 27 <=> ! [X1] : ~curious(X1) [avatar definition]
280. ~curious(X1) <- (27) [avatar component clause 279]
281. 27 | 24 | ~23 [avatar split clause 126,261,265,279]
283. 28 <=> ! [X1] : old(X1) [avatar definition]
284. old(X1) <- (28) [avatar component clause 283]
288. ~calm(X0) | generous(X0) [subsumption resolution 133,158]
299. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
300. ~kind(X1) <- (31) [avatar component clause 299]
301. 31 | 3 [avatar split clause 141,170,299]
355. old(X0) | happy(X0) [resolution 205,80]
356. old(X0) [subsumption resolution 355,158]
357. 28 [avatar split clause 356,283]
358. $false <- (~23, 28) [resolution 284,263]
361. 23 | ~28 [avatar contradiction clause 358]
362. generous(fred) <- (3) [resolution 288,172]
364. $false <- (3) [subsumption resolution 362,153]
365. ~3 [avatar contradiction clause 364]
366. $false <- (24, 31) [resolution 300,266]
367. ~24 | ~31 [avatar contradiction clause 366]
368. $false <- (27) [resolution 280,143]
371. ~27 [avatar contradiction clause 368]
372. $false [avatar sat refutation 281,301,357,361,365,367,371]
% SZS output end Proof for 6568057262546636777923769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not strong and wise then mary is creative or not patient and vice versa.
If alice is not curious then someone is wise and vice versa.
Everyone who is both brave and tall is not creative and vice versa.
If someone is either patient or not wise then someone is rich.
If someone is old then someone is either strong or not rich and vice versa.
If someone is both not kind and rich then lucy is both curious and calm and vice versa.
Everyone who is not wise is both curious and tall and vice versa.
If alice is either not quiet or curious then fred is calm and vice versa.
Everyone who is not strong or not old is not curious and vice versa.
Everyone who is not patient is not creative and vice versa.
Everyone who is either not wise or patient is either not creative or not funny and vice versa.
Everyone who is not generous is both calm and not old.
Everyone who is either funny or curious is old.
If lucy is rich or humble then someone is either not old or not strong and vice versa.
If someone is old or not tall then fred is either not generous or generous and vice versa.
Paul is either rich or not funny.
Lucy is old or not happy.
Someone is both strong and tall.
Someone is either patient or not tall.
Susan is either humble or not creative.
Someone is humble.
Alice is strong. | Lucy is not brave. | neutral | (((~strong(john)&wise(john)))<=>((creative(mary)|~patient(mary))))&
((~curious(alice))<=>(?[X]:(wise(X))))&
(![X]:((brave(X)&tall(X))<=>~creative(X)))&
((?[X]:((patient(X)<~>~wise(X))))=>(?[X]:(rich(X))))&
((?[X]:(old(X)))<=>(?[X]:((strong(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&rich(X))))<=>((curious(lucy)&calm(lucy))))&
(![X]:(~wise(X)<=>(curious(X)&tall(X))))&
(((~quiet(alice)<~>curious(alice)))<=>(calm(fred)))&
(![X]:((~strong(X)|~old(X))<=>~curious(X)))&
(![X]:(~patient(X)<=>~creative(X)))&
(![X]:((~wise(X)<~>patient(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~old(X))))&
(![X]:((funny(X)<~>curious(X))=>old(X)))&
(((rich(lucy)|humble(lucy)))<=>(?[X]:((~old(X)<~>~strong(X)))))&
((?[X]:((old(X)|~tall(X))))<=>((~generous(fred)<~>generous(fred))))&
((rich(paul)<~>~funny(paul)))&
((old(lucy)|~happy(lucy)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((patient(X)<~>~tall(X))))&
((humble(susan)<~>~creative(susan)))&
(?[X]:(humble(X)))&
(strong(alice)) | ~brave(lucy) | [] | null | 0 |
If alice is either patient or old then someone is humble or not humble. If someone is both funny and not tall then lucy is both generous and curious. Everyone who is either calm or not happy is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Everyone who is both not tall and not wise is both not brave and curious and vice versa. Everyone who is not tall is either not generous or not funny and vice versa. Everyone who is calm is funny and vice versa. Everyone who is not humble or not rich is both patient and not old. If someone is not calm then lucy is not tall or not kind and vice versa. Fred is either not tall or calm. Paul is either kind or curious. Paul is strong or not curious. | Lucy is not strong. | contradiction | (((patient(alice)<~>old(alice)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:((funny(X)&~tall(X))))=>((generous(lucy)&curious(lucy))))&
(![X]:((calm(X)<~>~happy(X))<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~brave(X)&curious(X))))&
(![X]:(~tall(X)<=>(~generous(X)<~>~funny(X))))&
(![X]:(calm(X)<=>funny(X)))&
(![X]:((~humble(X)|~rich(X))=>(patient(X)&~old(X))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)|~kind(lucy))))&
((~tall(fred)<~>calm(fred)))&
((kind(paul)<~>curious(paul)))&
((strong(paul)|~curious(paul))) | ~strong(lucy) | [
"p3",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4124199492400874434920428
% SZS output start Proof for 4124199492400874434920428
4. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p3]
11. ! [X0] : (~old(X0) <=> (strong(X0) & wise(X0))) [input p10]
15. ! [X0] : ((~rich(X0) | ~humble(X0)) => (~old(X0) & patient(X0))) [input p14]
20. ~strong(lucy) [input hypothesis]
26. ! [X0] : ((~old(X0) & patient(X0)) | (rich(X0) & humble(X0))) [ennf transformation 15]
32. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 4]
33. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 32]
48. ! [X0] : ((~old(X0) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | old(X0))) [nnf transformation 11]
49. ! [X0] : ((~old(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | old(X0))) [flattening 48]
71. ~humble(X0) | patient(X0) [cnf transformation 33]
72. ~humble(X0) | ~patient(X0) [cnf transformation 33]
98. strong(X0) | old(X0) [cnf transformation 49]
112. ~old(X0) | humble(X0) [cnf transformation 26]
122. ~strong(lucy) [cnf transformation 20]
140. ~humble(X0) [subsumption resolution 71,72]
165. ~old(X0) [subsumption resolution 112,140]
195. old(lucy) [resolution 98,122]
196. $false [subsumption resolution 195,165]
% SZS output end Proof for 4124199492400874434920428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and brave then someone is both not wise and not strong.
Everyone who is not patient or quiet is not old.
Everyone who is either not rich or creative is not humble and vice versa.
If lucy is tall then paul is both not calm and humble.
If lucy is not tall then susan is not kind and vice versa.
Everyone who is wise or not rich is either curious or generous and vice versa.
Everyone who is funny is funny or tall.
If someone is not rich then alice is either brave or not funny.
Everyone who is both not funny and patient is both not funny and not rich and vice versa.
Everyone who is both not tall and curious is not curious or creative and vice versa.
If alice is either not strong or curious then someone is either kind or wise.
Everyone who is patient or old is both quiet and not creative.
If john is both not generous and not tall then susan is both not wise and generous and vice versa.
If john is not happy or creative then someone is either not patient or brave and vice versa.
If john is old or quiet then lucy is both happy and old.
If lucy is either not patient or not generous then alice is both not old and not curious and vice versa.
Susan is creative.
Someone is quiet.
Lucy is humble or not curious.
Mary is either not generous or not happy.
Someone is both rich and tall.
Someone is both not rich and not patient.
Someone is both happy and not wise.
Alice is either not humble or generous. | Paul is calm. | neutral | ((?[X]:((quiet(X)&brave(X))))=>(?[X]:((~wise(X)&~strong(X)))))&
(![X]:((~patient(X)|quiet(X))=>~old(X)))&
(![X]:((~rich(X)<~>creative(X))<=>~humble(X)))&
((tall(lucy))=>((~calm(paul)&humble(paul))))&
((~tall(lucy))<=>(~kind(susan)))&
(![X]:((wise(X)|~rich(X))<=>(curious(X)<~>generous(X))))&
(![X]:(funny(X)=>(funny(X)|tall(X))))&
((?[X]:(~rich(X)))=>((brave(alice)<~>~funny(alice))))&
(![X]:((~funny(X)&patient(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~tall(X)&curious(X))<=>(~curious(X)|creative(X))))&
(((~strong(alice)<~>curious(alice)))=>(?[X]:((kind(X)<~>wise(X)))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~creative(X))))&
(((~generous(john)&~tall(john)))<=>((~wise(susan)&generous(susan))))&
(((~happy(john)|creative(john)))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(((old(john)|quiet(john)))=>((happy(lucy)&old(lucy))))&
(((~patient(lucy)<~>~generous(lucy)))<=>((~old(alice)&~curious(alice))))&
(creative(susan))&
(?[X]:(quiet(X)))&
((humble(lucy)|~curious(lucy)))&
((~generous(mary)<~>~happy(mary)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((happy(X)&~wise(X))))&
((~humble(alice)<~>generous(alice))) | calm(paul) | [] | null | 0 |
Everyone who is both strong and quiet is not creative or not tall. Everyone who is either not patient or old is either old or curious and vice versa. Everyone who is either not creative or brave is both not creative and strong and vice versa. Everyone who is not curious is either rich or creative. Everyone who is either funny or kind is not curious or creative. If susan is not brave then someone is not happy or not rich. If susan is strong or tall then paul is not strong or not tall and vice versa. Everyone who is both not kind and not tall is not tall. Everyone who is generous or rich is not funny and vice versa. Everyone who is either not calm or brave is either happy or not quiet and vice versa. If susan is both not tall and humble then someone is patient and vice versa. If fred is both brave and not rich then fred is patient. Everyone who is either not creative or curious is generous or quiet and vice versa. Everyone who is both not humble and not old is both happy and not curious and vice versa. If alice is not strong or curious then lucy is either kind or tall. Everyone who is old or not strong is quiet and vice versa. Fred is humble. Paul is not old or not tall. Someone is both not generous and not creative. Someone is kind. Lucy is patient. Someone is either brave or not curious. Someone is both creative and not happy. Alice is curious. | Fred is strong. | neutral | (![X]:((strong(X)&quiet(X))=>(~creative(X)|~tall(X))))&
(![X]:((~patient(X)<~>old(X))<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(~creative(X)&strong(X))))&
(![X]:(~curious(X)=>(rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>kind(X))=>(~curious(X)|creative(X))))&
((~brave(susan))=>(?[X]:((~happy(X)|~rich(X)))))&
(((strong(susan)|tall(susan)))<=>((~strong(paul)|~tall(paul))))&
(![X]:((~kind(X)&~tall(X))=>~tall(X)))&
(![X]:((generous(X)|rich(X))<=>~funny(X)))&
(![X]:((~calm(X)<~>brave(X))<=>(happy(X)<~>~quiet(X))))&
(((~tall(susan)&humble(susan)))<=>(?[X]:(patient(X))))&
(((brave(fred)&~rich(fred)))=>(patient(fred)))&
(![X]:((~creative(X)<~>curious(X))<=>(generous(X)|quiet(X))))&
(![X]:((~humble(X)&~old(X))<=>(happy(X)&~curious(X))))&
(((~strong(alice)|curious(alice)))=>((kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)|~strong(X))<=>quiet(X)))&
(humble(fred))&
((~old(paul)|~tall(paul)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:(kind(X)))&
(patient(lucy))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:((creative(X)&~happy(X))))&
(curious(alice)) | strong(fred) | [] | null | 0 |
If someone is not happy or old then someone is not rich or old and vice versa.
If someone is either rich or not calm then someone is funny or not happy and vice versa.
Everyone who is happy is not wise and vice versa.
Everyone who is either not kind or not curious is either calm or old and vice versa.
If alice is either calm or brave then someone is creative or not curious and vice versa.
Everyone who is not curious is wise or not brave.
If paul is both humble and curious then alice is wise.
Everyone who is tall is both kind and curious.
If lucy is generous or not tall then paul is both not generous and generous.
Everyone who is either curious or not strong is both not rich and calm.
Everyone who is quiet or humble is either not brave or creative and vice versa.
Everyone who is rich or not kind is not wise or not humble and vice versa.
If susan is both funny and happy then someone is both not patient and not generous.
Everyone who is both not funny and not patient is rich or happy and vice versa.
If someone is both not wise and calm then fred is not creative or creative.
Everyone who is both brave and not happy is not calm.
Someone is not funny or generous.
John is generous.
Someone is either rich or wise.
Mary is both quiet and not happy.
Someone is both not strong and not humble.
Alice is either not wise or not happy. | Fred is not funny. | neutral | ((?[X]:((~happy(X)|old(X))))<=>(?[X]:((~rich(X)|old(X)))))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:(happy(X)<=>~wise(X)))&
(![X]:((~kind(X)<~>~curious(X))<=>(calm(X)<~>old(X))))&
(((calm(alice)<~>brave(alice)))<=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:(~curious(X)=>(wise(X)|~brave(X))))&
(((humble(paul)&curious(paul)))=>(wise(alice)))&
(![X]:(tall(X)=>(kind(X)&curious(X))))&
(((generous(lucy)|~tall(lucy)))=>((~generous(paul)&generous(paul))))&
(![X]:((curious(X)<~>~strong(X))=>(~rich(X)&calm(X))))&
(![X]:((quiet(X)|humble(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((rich(X)|~kind(X))<=>(~wise(X)|~humble(X))))&
(((funny(susan)&happy(susan)))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(rich(X)|happy(X))))&
((?[X]:((~wise(X)&calm(X))))=>((~creative(fred)|creative(fred))))&
(![X]:((brave(X)&~happy(X))=>~calm(X)))&
(?[X]:((~funny(X)|generous(X))))&
(generous(john))&
(?[X]:((rich(X)<~>wise(X))))&
((quiet(mary)&~happy(mary)))&
(?[X]:((~strong(X)&~humble(X))))&
((~wise(alice)<~>~happy(alice))) | ~funny(fred) | [] | null | 0 |
Everyone who is strong is either not quiet or not rich and vice versa.
Everyone who is both not kind and not tall is either not generous or not old and vice versa.
Everyone who is either quiet or not wise is both not happy and quiet and vice versa.
If alice is either kind or not calm then someone is both not tall and not kind and vice versa.
If someone is not rich then someone is not curious and vice versa.
Everyone who is either not patient or strong is either calm or not rich.
If susan is not strong or not wise then someone is not old.
If someone is not humble or not old then mary is either not creative or wise and vice versa.
If lucy is either not creative or not old then susan is curious and vice versa.
Everyone who is either not patient or not quiet is either kind or not strong and vice versa.
Everyone who is both not funny and not generous is not patient and vice versa.
Everyone who is both kind and not generous is either calm or not kind and vice versa.
Everyone who is patient is not rich and vice versa.
Everyone who is not wise or not curious is brave or not kind and vice versa.
Everyone who is rich or humble is either humble or old and vice versa.
Everyone who is not rich or humble is funny or not curious and vice versa.
Someone is both rich and not curious.
Someone is funny.
Someone is patient or kind.
Someone is both funny and not strong.
Someone is either tall or not creative.
Mary is either rich or humble.
Someone is rich. | Mary is tall. | entailment | (![X]:(strong(X)<=>(~quiet(X)<~>~rich(X))))&
(![X]:((~kind(X)&~tall(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(~happy(X)&quiet(X))))&
(((kind(alice)<~>~calm(alice)))<=>(?[X]:((~tall(X)&~kind(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(~curious(X))))&
(![X]:((~patient(X)<~>strong(X))=>(calm(X)<~>~rich(X))))&
(((~strong(susan)|~wise(susan)))=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)|~old(X))))<=>((~creative(mary)<~>wise(mary))))&
(((~creative(lucy)<~>~old(lucy)))<=>(curious(susan)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(kind(X)<~>~strong(X))))&
(![X]:((~funny(X)&~generous(X))<=>~patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(calm(X)<~>~kind(X))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((~wise(X)|~curious(X))<=>(brave(X)|~kind(X))))&
(![X]:((rich(X)|humble(X))<=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|humble(X))<=>(funny(X)|~curious(X))))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)|kind(X))))&
(?[X]:((funny(X)&~strong(X))))&
(?[X]:((tall(X)<~>~creative(X))))&
((rich(mary)<~>humble(mary)))&
(?[X]:(rich(X))) | tall(mary) | [
"p0",
"p3",
"p5",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1701777641608649469994270
% SZS output start Proof for 1701777641608649469994270
1. ! [X0] : (strong(X0) <=> (~quiet(X0) <~> ~rich(X0))) [input p0]
4. (kind(alice) <~> ~calm(alice)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p3]
6. ! [X0] : ((~patient(X0) <~> strong(X0)) => (calm(X0) <~> ~rich(X0))) [input p5]
10. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (kind(X0) <~> ~strong(X0))) [input p9]
12. ! [X0] : ((~generous(X0) & kind(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~rich(X0)) [input p12]
24. ~tall(mary) [input hypothesis]
26. ! [X0] : ((calm(X0) <~> ~rich(X0)) | (~patient(X0) <=> strong(X0))) [ennf transformation 6]
28. ! [X0] : ((strong(X0) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | ~strong(X0))) [nnf transformation 1]
33. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & (? [X0] : (~kind(X0) & ~tall(X0)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [nnf transformation 4]
34. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [rectify 33]
35. ? [X1] : (~kind(X1) & ~tall(X1)) => (~kind(sK0) & ~tall(sK0)) [choice axiom]
36. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & ((~kind(sK0) & ~tall(sK0)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [skolemisation 34,35]
42. ! [X0] : (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) [nnf transformation 26]
50. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 10]
53. ! [X0] : (((~generous(X0) & kind(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (generous(X0) | ~kind(X0)))) [nnf transformation 12]
54. ! [X0] : (((~generous(X0) & kind(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | generous(X0) | ~kind(X0))) [flattening 53]
55. ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 13]
76. ~rich(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 28]
77. ~strong(X0) | quiet(X0) | rich(X0) [cnf transformation 28]
78. ~rich(X0) | strong(X0) | quiet(X0) [cnf transformation 28]
79. ~quiet(X0) | strong(X0) | rich(X0) [cnf transformation 28]
96. ~calm(alice) | kind(alice) | kind(X0) | tall(X0) [cnf transformation 36]
97. calm(alice) | ~kind(alice) | kind(X0) | tall(X0) [cnf transformation 36]
103. ~patient(X0) | ~calm(X0) | rich(X0) | ~strong(X0) [cnf transformation 42]
118. ~kind(X0) | strong(X0) | ~quiet(X0) | patient(X0) [cnf transformation 50]
119. ~patient(X0) | ~kind(X0) | strong(X0) | quiet(X0) [cnf transformation 50]
120. ~patient(X0) | ~quiet(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 50]
122. ~kind(X0) | patient(X0) | ~strong(X0) | quiet(X0) [cnf transformation 50]
130. kind(X0) | calm(X0) | kind(X0) [cnf transformation 54]
133. ~patient(X0) | ~rich(X0) [cnf transformation 55]
134. patient(X0) | rich(X0) [cnf transformation 55]
160. ~tall(mary) [cnf transformation 24]
164. calm(X0) | kind(X0) [duplicate literal removal 130]
168. 1 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
169. tall(X0) | kind(X0) <- (1) [avatar component clause 168]
171. 2 <=> kind(alice) [avatar definition]
172. kind(alice) <- (2) [avatar component clause 171]
173. ~kind(alice) <- (~2) [avatar component clause 171]
175. 3 <=> calm(alice) [avatar definition]
176. ~calm(alice) <- (~3) [avatar component clause 175]
177. calm(alice) <- (3) [avatar component clause 175]
178. 1 | ~2 | 3 [avatar split clause 97,175,171,168]
179. 1 | 2 | ~3 [avatar split clause 96,175,171,168]
287. 26 <=> rich(mary) [avatar definition]
288. rich(mary) <- (26) [avatar component clause 287]
289. ~rich(mary) <- (~26) [avatar component clause 287]
302. kind(alice) <- (~3) [resolution 164,176]
303. $false <- (~2, ~3) [subsumption resolution 302,173]
304. 2 | 3 [avatar contradiction clause 303]
313. ~quiet(mary) | ~strong(mary) <- (26) [resolution 76,288]
335. strong(mary) | quiet(mary) <- (26) [resolution 78,288]
510. 52 <=> patient(mary) [avatar definition]
512. patient(mary) <- (52) [avatar component clause 510]
519. 54 <=> strong(mary) [avatar definition]
521. strong(mary) <- (54) [avatar component clause 519]
529. 56 <=> quiet(mary) [avatar definition]
530. ~quiet(mary) <- (~56) [avatar component clause 529]
532. 56 | 54 | ~26 [avatar split clause 335,287,519,529]
533. ~54 | ~56 | ~26 [avatar split clause 313,287,529,519]
653. ~calm(X0) | rich(X0) | ~strong(X0) | rich(X0) [resolution 103,134]
657. ~calm(X0) | rich(X0) | ~strong(X0) [duplicate literal removal 653]
677. strong(alice) | ~quiet(alice) | patient(alice) <- (2) [resolution 118,172]
679. 79 <=> patient(alice) [avatar definition]
681. patient(alice) <- (79) [avatar component clause 679]
683. 80 <=> quiet(alice) [avatar definition]
684. quiet(alice) <- (80) [avatar component clause 683]
685. ~quiet(alice) <- (~80) [avatar component clause 683]
687. 81 <=> strong(alice) [avatar definition]
688. ~strong(alice) <- (~81) [avatar component clause 687]
690. 79 | ~80 | 81 | ~2 [avatar split clause 677,171,687,683,679]
691. ~kind(X0) | strong(X0) | quiet(X0) | rich(X0) [resolution 119,134]
695. ~kind(X0) | strong(X0) | rich(X0) [subsumption resolution 691,79]
708. ~quiet(X0) | ~strong(X0) | ~kind(X0) | rich(X0) [resolution 120,134]
712. ~kind(X0) | ~quiet(X0) | rich(X0) [subsumption resolution 708,79]
734. patient(alice) | ~strong(alice) | quiet(alice) <- (2) [resolution 122,172]
805. 90 <=> kind(mary) [avatar definition]
807. kind(mary) <- (90) [avatar component clause 805]
817. rich(alice) | ~strong(alice) <- (3) [resolution 657,177]
822. strong(alice) | rich(alice) <- (2) [resolution 695,172]
823. rich(alice) <- (2, ~81) [subsumption resolution 822,688]
904. ~quiet(mary) | rich(mary) <- (90) [resolution 807,712]
905. strong(mary) | rich(mary) <- (90) [resolution 807,695]
906. patient(mary) | ~strong(mary) | quiet(mary) <- (90) [resolution 807,122]
907. strong(mary) | ~quiet(mary) | patient(mary) <- (90) [resolution 807,118]
910. ~quiet(mary) <- (~26, 90) [subsumption resolution 904,289]
911. ~56 | 26 | ~90 [avatar split clause 910,805,287,529]
912. strong(mary) <- (~26, 90) [subsumption resolution 905,289]
913. 54 | 26 | ~90 [avatar split clause 912,805,287,519]
914. 56 | ~54 | 52 | ~90 [avatar split clause 906,805,510,519,529]
915. 52 | ~56 | 54 | ~90 [avatar split clause 907,805,519,529,510]
925. ~rich(mary) <- (52) [resolution 512,133]
927. quiet(mary) | rich(mary) <- (54) [resolution 521,77]
928. rich(mary) <- (54, ~56) [subsumption resolution 927,530]
929. $false <- (~26, 54, ~56) [subsumption resolution 928,289]
930. 26 | ~54 | 56 [avatar contradiction clause 929]
945. strong(alice) | quiet(alice) <- (2, ~81) [resolution 823,78]
948. quiet(alice) <- (2, ~81) [subsumption resolution 945,688]
949. $false <- (2, ~80, ~81) [subsumption resolution 948,685]
950. ~2 | 80 | 81 [avatar contradiction clause 949]
952. 99 <=> rich(alice) [avatar definition]
954. rich(alice) <- (99) [avatar component clause 952]
956. 80 | ~81 | 79 | ~2 [avatar split clause 734,171,679,687,683]
957. 99 | 81 | ~2 [avatar split clause 822,171,687,952]
958. ~81 | 99 | ~3 [avatar split clause 817,175,952,687]
972. ~quiet(alice) | ~strong(alice) <- (99) [resolution 954,76]
974. ~strong(alice) <- (80, 99) [subsumption resolution 972,684]
977. ~81 | ~80 | ~99 [avatar split clause 974,952,683,687]
985. ~rich(alice) <- (79) [resolution 681,133]
994. ~99 | ~79 [avatar split clause 985,679,952]
1005. kind(mary) <- (1) [resolution 169,160]
1024. ~26 | ~52 [avatar split clause 925,510,287]
1033. 90 | ~1 [avatar split clause 1005,168,805]
1039. $false [avatar sat refutation 178,179,304,532,533,690,911,913,914,915,930,950,956,957,958,977,994,1024,1033]
% SZS output end Proof for 1701777641608649469994270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and curious is either not tall or not creative and vice versa. Everyone who is either funny or happy is not creative or rich. Everyone who is either funny or not humble is either wise or calm and vice versa. If someone is not brave or not curious then someone is both wise and kind. If john is both tall and rich then lucy is either calm or tall. Everyone who is tall or generous is not kind and vice versa. Everyone who is wise or kind is either not patient or funny and vice versa. Everyone who is curious or not wise is either patient or not funny. If someone is not patient then lucy is both not strong and creative. Everyone who is not brave or not creative is wise and vice versa. Everyone who is both strong and not kind is both not funny and not kind. Everyone who is not old or not creative is both not generous and not old. If fred is either not rich or tall then someone is funny or not brave. Everyone who is either kind or not patient is not brave or funny and vice versa. If someone is either creative or curious then lucy is either not patient or not wise and vice versa. Everyone who is both not strong and curious is either strong or not quiet and vice versa. Fred is both not quiet and not brave. John is not rich or rich. Mary is both old and humble. Fred is either funny or not curious. Someone is curious. Alice is either not happy or not generous. Lucy is either brave or calm. | Mary is not wise. | contradiction | (![X]:((quiet(X)&curious(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((funny(X)<~>happy(X))=>(~creative(X)|rich(X))))&
(![X]:((funny(X)<~>~humble(X))<=>(wise(X)<~>calm(X))))&
((?[X]:((~brave(X)|~curious(X))))=>(?[X]:((wise(X)&kind(X)))))&
(((tall(john)&rich(john)))=>((calm(lucy)<~>tall(lucy))))&
(![X]:((tall(X)|generous(X))<=>~kind(X)))&
(![X]:((wise(X)|kind(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((curious(X)|~wise(X))=>(patient(X)<~>~funny(X))))&
((?[X]:(~patient(X)))=>((~strong(lucy)&creative(lucy))))&
(![X]:((~brave(X)|~creative(X))<=>wise(X)))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)&~kind(X))))&
(![X]:((~old(X)|~creative(X))=>(~generous(X)&~old(X))))&
(((~rich(fred)<~>tall(fred)))=>(?[X]:((funny(X)|~brave(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>(~brave(X)|funny(X))))&
((?[X]:((creative(X)<~>curious(X))))<=>((~patient(lucy)<~>~wise(lucy))))&
(![X]:((~strong(X)&curious(X))<=>(strong(X)<~>~quiet(X))))&
((~quiet(fred)&~brave(fred)))&
((~rich(john)|rich(john)))&
((old(mary)&humble(mary)))&
((funny(fred)<~>~curious(fred)))&
(?[X]:(curious(X)))&
((~happy(alice)<~>~generous(alice)))&
((brave(lucy)<~>calm(lucy))) | ~wise(mary) | [
"p0",
"p5",
"p6",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 28439656821851730247791
% SZS output start Proof for 28439656821851730247791
1. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p0]
6. ! [X0] : ((generous(X0) | tall(X0)) <=> ~kind(X0)) [input p5]
7. ! [X0] : ((kind(X0) | wise(X0)) <=> (~patient(X0) <~> funny(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | curious(X0)) => (patient(X0) <~> ~funny(X0))) [input p7]
10. ! [X0] : ((~creative(X0) | ~brave(X0)) <=> wise(X0)) [input p9]
14. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> (funny(X0) | ~brave(X0))) [input p13]
16. ! [X0] : ((curious(X0) & ~strong(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p15]
24. ~wise(mary) [input hypothesis]
31. ! [X0] : ((patient(X0) <~> ~funny(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 8]
37. ! [X0] : (((curious(X0) & quiet(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((curious(X0) & quiet(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 37]
45. ! [X0] : (((generous(X0) | tall(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 6]
46. ! [X0] : ((generous(X0) | tall(X0) | kind(X0)) & (~kind(X0) | (~generous(X0) & ~tall(X0)))) [flattening 45]
47. ! [X0] : (((kind(X0) | wise(X0)) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~wise(X0)))) [nnf transformation 7]
48. ! [X0] : ((kind(X0) | wise(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~wise(X0)))) [flattening 47]
49. ! [X0] : (((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | (wise(X0) & ~curious(X0))) [nnf transformation 31]
50. ! [X0] : (((~creative(X0) | ~brave(X0)) | ~wise(X0)) & (wise(X0) | (creative(X0) & brave(X0)))) [nnf transformation 10]
51. ! [X0] : ((~creative(X0) | ~brave(X0) | ~wise(X0)) & (wise(X0) | (creative(X0) & brave(X0)))) [flattening 50]
55. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (~funny(X0) & brave(X0))) & ((funny(X0) | ~brave(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 14]
56. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (~funny(X0) & brave(X0))) & (funny(X0) | ~brave(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [flattening 55]
61. ! [X0] : (((curious(X0) & ~strong(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~curious(X0) | strong(X0)))) [nnf transformation 16]
62. ! [X0] : (((curious(X0) & ~strong(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~curious(X0) | strong(X0))) [flattening 61]
70. ~creative(X0) | quiet(X0) | tall(X0) [cnf transformation 38]
72. ~creative(X0) | curious(X0) | tall(X0) [cnf transformation 38]
90. ~kind(X0) | ~tall(X0) [cnf transformation 46]
93. ~patient(X0) | funny(X0) | ~wise(X0) [cnf transformation 48]
95. ~wise(X0) | patient(X0) | ~funny(X0) [cnf transformation 48]
97. patient(X0) | wise(X0) | funny(X0) | kind(X0) [cnf transformation 48]
100. ~funny(X0) | patient(X0) | wise(X0) [cnf transformation 49]
102. funny(X0) | ~patient(X0) | wise(X0) [cnf transformation 49]
106. wise(X0) | creative(X0) [cnf transformation 51]
119. ~patient(X0) | kind(X0) | ~funny(X0) [cnf transformation 56]
130. ~quiet(X0) | strong(X0) | ~curious(X0) | strong(X0) [cnf transformation 62]
132. ~strong(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 62]
148. ~wise(mary) [cnf transformation 24]
149. ~quiet(X0) | strong(X0) | ~curious(X0) [duplicate literal removal 130]
150. ~strong(X0) | ~quiet(X0) [duplicate literal removal 132]
187. ~patient(X0) | funny(X0) [subsumption resolution 102,93]
188. ~funny(X0) | patient(X0) [subsumption resolution 100,95]
220. ~funny(X0) | kind(X0) [subsumption resolution 119,188]
252. ~curious(X0) | ~quiet(X0) [subsumption resolution 149,150]
285. creative(mary) [resolution 106,148]
290. quiet(mary) | tall(mary) [resolution 70,285]
306. 30 <=> tall(mary) [avatar definition]
308. tall(mary) <- (30) [avatar component clause 306]
310. 31 <=> quiet(mary) [avatar definition]
312. quiet(mary) <- (31) [avatar component clause 310]
313. 30 | 31 [avatar split clause 290,310,306]
317. curious(mary) | tall(mary) [resolution 72,285]
523. wise(X3) | funny(X3) | kind(X3) | funny(X3) [resolution 97,187]
524. wise(X3) | funny(X3) | kind(X3) [duplicate literal removal 523]
528. kind(X3) | wise(X3) [subsumption resolution 524,220]
533. ~tall(X2) | wise(X2) [resolution 528,90]
548. wise(mary) <- (30) [resolution 533,308]
549. $false <- (30) [subsumption resolution 548,148]
550. ~30 [avatar contradiction clause 549]
552. 57 <=> curious(mary) [avatar definition]
554. curious(mary) <- (57) [avatar component clause 552]
555. 30 | 57 [avatar split clause 317,552,306]
559. ~quiet(mary) <- (57) [resolution 554,252]
560. $false <- (31, 57) [subsumption resolution 559,312]
561. ~31 | ~57 [avatar contradiction clause 560]
562. $false [avatar sat refutation 313,550,555,561]
% SZS output end Proof for 28439656821851730247791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is rich then someone is quiet and vice versa. If someone is either not kind or not old then someone is brave or not creative and vice versa. If paul is not funny or tall then someone is both not old and not curious. Everyone who is not happy is both not happy and rich and vice versa. If alice is either not patient or humble then someone is either not humble or rich and vice versa. Everyone who is not kind or quiet is either not kind or tall. Everyone who is not calm is quiet. Everyone who is kind is not old. Everyone who is not funny is not rich or not tall. Everyone who is not rich or not happy is not calm or brave. Everyone who is creative is funny or kind. Everyone who is both not funny and tall is quiet or brave and vice versa. Everyone who is both patient and kind is either not happy or not quiet. Everyone who is creative or rich is not rich. Everyone who is generous is both calm and not creative. If someone is either not funny or not humble then susan is not patient. Alice is not generous. Someone is either funny or kind. Someone is either not strong or curious. Someone is patient or not calm. Someone is not generous. Someone is tall or not humble. Someone is both not old and not creative. | Alice is not happy. | contradiction | ((rich(mary))<=>(?[X]:(quiet(X))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(((~funny(paul)|tall(paul)))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:(~happy(X)<=>(~happy(X)&rich(X))))&
(((~patient(alice)<~>humble(alice)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(~generous(alice))&
(?[X]:((funny(X)<~>kind(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:(~generous(X)))&
(?[X]:((tall(X)|~humble(X))))&
(?[X]:((~old(X)&~creative(X)))) | ~happy(alice) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 364245603645227146813414
% SZS output start Proof for 364245603645227146813414
4. ! [X0] : (~happy(X0) <=> (rich(X0) & ~happy(X0))) [input p3]
14. ! [X0] : ((rich(X0) | creative(X0)) => ~rich(X0)) [input p13]
24. ~happy(alice) [input hypothesis]
41. ! [X0] : (~rich(X0) | (~rich(X0) & ~creative(X0))) [ennf transformation 14]
54. ! [X0] : ((~happy(X0) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | happy(X0))) [nnf transformation 4]
55. ! [X0] : ((~happy(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | happy(X0))) [flattening 54]
90. happy(X0) | rich(X0) [cnf transformation 55]
118. ~rich(X0) | ~rich(X0) [cnf transformation 41]
129. ~happy(alice) [cnf transformation 24]
130. ~rich(X0) [duplicate literal removal 118]
283. rich(alice) [resolution 90,129]
284. $false [subsumption resolution 283,130]
% SZS output end Proof for 364245603645227146813414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not calm and kind then someone is strong. Everyone who is brave or tall is both wise and brave. If someone is not tall then fred is quiet or funny. If alice is not creative then john is both not rich and creative and vice versa. Everyone who is generous is not quiet and vice versa. Everyone who is rich is both not wise and patient and vice versa. Everyone who is happy is either not wise or tall and vice versa. Everyone who is not funny or not patient is funny or not old and vice versa. Everyone who is both tall and not brave is not tall and vice versa. If someone is not strong or rich then alice is both not wise and brave and vice versa. If alice is not brave then john is either tall or not creative and vice versa. If someone is not quiet or not creative then john is brave or not creative and vice versa. If paul is either creative or not kind then someone is wise. Everyone who is not humble or not happy is either not strong or not calm. Everyone who is not calm is both not humble and generous. Everyone who is either not curious or not old is both happy and creative. John is creative or brave. Alice is either humble or tall. Someone is either rich or brave. Someone is both quiet and humble. Someone is both not funny and not humble. Paul is quiet or calm. Someone is either strong or not strong. Lucy is not wise or not generous. | John is wise. | entailment | (((~calm(fred)&kind(fred)))=>(?[X]:(strong(X))))&
(![X]:((brave(X)|tall(X))=>(wise(X)&brave(X))))&
((?[X]:(~tall(X)))=>((quiet(fred)|funny(fred))))&
((~creative(alice))<=>((~rich(john)&creative(john))))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:(rich(X)<=>(~wise(X)&patient(X))))&
(![X]:(happy(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((~funny(X)|~patient(X))<=>(funny(X)|~old(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
((?[X]:((~strong(X)|rich(X))))<=>((~wise(alice)&brave(alice))))&
((~brave(alice))<=>((tall(john)<~>~creative(john))))&
((?[X]:((~quiet(X)|~creative(X))))<=>((brave(john)|~creative(john))))&
(((creative(paul)<~>~kind(paul)))=>(?[X]:(wise(X))))&
(![X]:((~humble(X)|~happy(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(~calm(X)=>(~humble(X)&generous(X))))&
(![X]:((~curious(X)<~>~old(X))=>(happy(X)&creative(X))))&
((creative(john)|brave(john)))&
((humble(alice)<~>tall(alice)))&
(?[X]:((rich(X)<~>brave(X))))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((~funny(X)&~humble(X))))&
((quiet(paul)|calm(paul)))&
(?[X]:((strong(X)<~>~strong(X))))&
((~wise(lucy)|~generous(lucy))) | wise(john) | [
"p1",
"p3",
"p8",
"p9",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2843765730604855631852745
% SZS output start Proof for 2843765730604855631852745
2. ! [X0] : ((tall(X0) | brave(X0)) => (brave(X0) & wise(X0))) [input p1]
4. ~creative(alice) <=> (creative(john) & ~rich(john)) [input p3]
9. ! [X0] : ((~brave(X0) & tall(X0)) <=> ~tall(X0)) [input p8]
10. ? [X0] : (rich(X0) | ~strong(X0)) <=> (brave(alice) & ~wise(alice)) [input p9]
11. ~brave(alice) <=> (tall(john) <~> ~creative(john)) [input p10]
12. ? [X0] : (~creative(X0) | ~quiet(X0)) <=> (~creative(john) | brave(john)) [input p11]
17. brave(john) | creative(john) [input p16]
25. ~wise(john) [input hypothesis]
29. ! [X0] : ((brave(X0) & wise(X0)) | (~tall(X0) & ~brave(X0))) [ennf transformation 2]
39. (~creative(alice) | (~creative(john) | rich(john))) & ((creative(john) & ~rich(john)) | creative(alice)) [nnf transformation 4]
40. (~creative(alice) | ~creative(john) | rich(john)) & ((creative(john) & ~rich(john)) | creative(alice)) [flattening 39]
47. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 9]
48. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | ~tall(X0))) [flattening 47]
49. (? [X0] : (rich(X0) | ~strong(X0)) | (~brave(alice) | wise(alice))) & ((brave(alice) & ~wise(alice)) | ! [X0] : (~rich(X0) & strong(X0))) [nnf transformation 10]
50. (? [X0] : (rich(X0) | ~strong(X0)) | ~brave(alice) | wise(alice)) & ((brave(alice) & ~wise(alice)) | ! [X0] : (~rich(X0) & strong(X0))) [flattening 49]
51. (? [X0] : (rich(X0) | ~strong(X0)) | ~brave(alice) | wise(alice)) & ((brave(alice) & ~wise(alice)) | ! [X1] : (~rich(X1) & strong(X1))) [rectify 50]
52. ? [X0] : (rich(X0) | ~strong(X0)) => (rich(sK1) | ~strong(sK1)) [choice axiom]
53. ((rich(sK1) | ~strong(sK1)) | ~brave(alice) | wise(alice)) & ((brave(alice) & ~wise(alice)) | ! [X1] : (~rich(X1) & strong(X1))) [skolemisation 51,52]
54. (~brave(alice) | ((tall(john) | creative(john)) & (~creative(john) | ~tall(john)))) & (((creative(john) | ~tall(john)) & (~creative(john) | tall(john))) | brave(alice)) [nnf transformation 11]
55. (? [X0] : (~creative(X0) | ~quiet(X0)) | (creative(john) & ~brave(john))) & ((~creative(john) | brave(john)) | ! [X0] : (creative(X0) & quiet(X0))) [nnf transformation 12]
56. (? [X0] : (~creative(X0) | ~quiet(X0)) | (creative(john) & ~brave(john))) & (~creative(john) | brave(john) | ! [X0] : (creative(X0) & quiet(X0))) [flattening 55]
57. (? [X0] : (~creative(X0) | ~quiet(X0)) | (creative(john) & ~brave(john))) & (~creative(john) | brave(john) | ! [X1] : (creative(X1) & quiet(X1))) [rectify 56]
58. ? [X0] : (~creative(X0) | ~quiet(X0)) => (~creative(sK2) | ~quiet(sK2)) [choice axiom]
59. ((~creative(sK2) | ~quiet(sK2)) | (creative(john) & ~brave(john))) & (~creative(john) | brave(john) | ! [X1] : (creative(X1) & quiet(X1))) [skolemisation 57,58]
77. ~brave(X0) | wise(X0) [cnf transformation 29]
84. ~creative(alice) | ~creative(john) | rich(john) [cnf transformation 40]
97. tall(X0) | tall(X0) [cnf transformation 48]
102. brave(alice) | ~rich(X1) [cnf transformation 53]
106. ~brave(alice) | ~creative(john) | ~tall(john) [cnf transformation 54]
109. ~creative(john) | brave(john) | creative(X1) [cnf transformation 59]
124. brave(john) | creative(john) [cnf transformation 17]
137. ~wise(john) [cnf transformation 25]
139. tall(X0) [duplicate literal removal 97]
156. 4 <=> ! [X0] : tall(X0) [avatar definition]
157. tall(X0) <- (4) [avatar component clause 156]
168. 7 <=> rich(john) [avatar definition]
170. rich(john) <- (7) [avatar component clause 168]
172. 8 <=> creative(john) [avatar definition]
176. 9 <=> creative(alice) [avatar definition]
178. ~creative(alice) <- (~9) [avatar component clause 176]
179. 7 | ~8 | ~9 [avatar split clause 84,176,172,168]
182. 4 [avatar split clause 139,156]
184. 10 <=> ! [X1] : ~rich(X1) [avatar definition]
185. ~rich(X1) <- (10) [avatar component clause 184]
187. 11 <=> brave(alice) [avatar definition]
190. 10 | 11 [avatar split clause 102,187,184]
202. 14 <=> tall(john) [avatar definition]
203. ~tall(john) <- (~14) [avatar component clause 202]
206. ~14 | ~8 | ~11 [avatar split clause 106,187,172,202]
219. 17 <=> brave(john) [avatar definition]
220. brave(john) <- (17) [avatar component clause 219]
224. 18 <=> ! [X1] : creative(X1) [avatar definition]
225. creative(X1) <- (18) [avatar component clause 224]
226. 18 | 17 | ~8 [avatar split clause 109,172,219,224]
245. 8 | 17 [avatar split clause 124,219,172]
284. $false <- (4, ~14) [resolution 203,157]
285. ~4 | 14 [avatar contradiction clause 284]
291. wise(john) <- (17) [resolution 77,220]
294. $false <- (17) [subsumption resolution 291,137]
295. ~17 [avatar contradiction clause 294]
296. $false <- (7, 10) [subsumption resolution 170,185]
297. ~7 | ~10 [avatar contradiction clause 296]
298. $false <- (~9, 18) [subsumption resolution 178,225]
299. 9 | ~18 [avatar contradiction clause 298]
300. $false [avatar sat refutation 179,182,190,206,226,245,285,295,297,299]
% SZS output end Proof for 2843765730604855631852745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not humble is kind.
If someone is not creative then john is either funny or not wise and vice versa.
If someone is both not quiet and brave then fred is wise or not curious.
If someone is curious then alice is both not humble and not kind.
Everyone who is humble is creative and vice versa.
If mary is either generous or brave then someone is curious or quiet.
Everyone who is both wise and quiet is either not patient or strong and vice versa.
Everyone who is tall or not wise is tall or not curious.
If john is both strong and not strong then someone is both curious and quiet and vice versa.
Everyone who is either tall or funny is both not calm and not curious and vice versa.
Everyone who is either quiet or strong is calm or not wise.
If someone is not wise or not humble then alice is both funny and quiet.
Everyone who is not rich is either tall or creative and vice versa.
If someone is not kind or generous then alice is brave or not quiet.
If paul is not creative then lucy is brave or quiet and vice versa.
If john is curious or not curious then someone is both happy and curious and vice versa.
Someone is quiet.
Paul is old.
Someone is both not calm and not strong.
Someone is old or not funny.
Someone is brave or wise.
Paul is rich or patient. | Alice is not funny. | contradiction | (![X]:((quiet(X)<~>~humble(X))=>kind(X)))&
((?[X]:(~creative(X)))<=>((funny(john)<~>~wise(john))))&
((?[X]:((~quiet(X)&brave(X))))=>((wise(fred)|~curious(fred))))&
((?[X]:(curious(X)))=>((~humble(alice)&~kind(alice))))&
(![X]:(humble(X)<=>creative(X)))&
(((generous(mary)<~>brave(mary)))=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~patient(X)<~>strong(X))))&
(![X]:((tall(X)|~wise(X))=>(tall(X)|~curious(X))))&
(((strong(john)&~strong(john)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(calm(X)|~wise(X))))&
((?[X]:((~wise(X)|~humble(X))))=>((funny(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((~kind(X)|generous(X))))=>((brave(alice)|~quiet(alice))))&
((~creative(paul))<=>((brave(lucy)|quiet(lucy))))&
(((curious(john)|~curious(john)))<=>(?[X]:((happy(X)&curious(X)))))&
(?[X]:(quiet(X)))&
(old(paul))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul))) | ~funny(alice) | [
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 587259887424202340389427
% SZS output start Proof for 587259887424202340389427
4. ? [X0] : curious(X0) => (~kind(alice) & ~humble(alice)) [input p3]
12. ? [X0] : (~humble(X0) | ~wise(X0)) => (quiet(alice) & funny(alice)) [input p11]
16. (~curious(john) | curious(john)) <=> ? [X0] : (curious(X0) & happy(X0)) [input p15]
23. ~funny(alice) [input hypothesis]
30. (~kind(alice) & ~humble(alice)) | ! [X0] : ~curious(X0) [ennf transformation 4]
36. (quiet(alice) & funny(alice)) | ! [X0] : (humble(X0) & wise(X0)) [ennf transformation 12]
62. ((~curious(john) | curious(john)) | ! [X0] : (~curious(X0) | ~happy(X0))) & (? [X0] : (curious(X0) & happy(X0)) | (curious(john) & ~curious(john))) [nnf transformation 16]
63. (~curious(john) | curious(john) | ! [X0] : (~curious(X0) | ~happy(X0))) & (? [X0] : (curious(X0) & happy(X0)) | (curious(john) & ~curious(john))) [flattening 62]
64. (~curious(john) | curious(john) | ! [X0] : (~curious(X0) | ~happy(X0))) & (? [X1] : (curious(X1) & happy(X1)) | (curious(john) & ~curious(john))) [rectify 63]
65. ? [X1] : (curious(X1) & happy(X1)) => (curious(sK3) & happy(sK3)) [choice axiom]
66. (~curious(john) | curious(john) | ! [X0] : (~curious(X0) | ~happy(X0))) & ((curious(sK3) & happy(sK3)) | (curious(john) & ~curious(john))) [skolemisation 64,65]
80. ~humble(alice) | ~curious(X0) [cnf transformation 30]
107. funny(alice) | humble(X0) [cnf transformation 36]
119. curious(sK3) | ~curious(john) [cnf transformation 66]
120. curious(sK3) | curious(john) [cnf transformation 66]
127. ~funny(alice) [cnf transformation 23]
160. 8 <=> ! [X0] : ~curious(X0) [avatar definition]
161. ~curious(X0) <- (8) [avatar component clause 160]
168. 10 <=> humble(alice) [avatar definition]
170. ~humble(alice) <- (~10) [avatar component clause 168]
171. 8 | ~10 [avatar split clause 80,168,160]
200. 17 <=> ! [X0] : humble(X0) [avatar definition]
201. humble(X0) <- (17) [avatar component clause 200]
212. 20 <=> funny(alice) [avatar definition]
215. 17 | 20 [avatar split clause 107,212,200]
245. 27 <=> curious(john) [avatar definition]
249. 28 <=> curious(sK3) [avatar definition]
251. curious(sK3) <- (28) [avatar component clause 249]
252. 27 | 28 [avatar split clause 120,249,245]
253. ~27 | 28 [avatar split clause 119,249,245]
278. ~20 [avatar split clause 127,212]
279. $false <- (~10, 17) [subsumption resolution 170,201]
280. 10 | ~17 [avatar contradiction clause 279]
283. $false <- (8, 28) [resolution 251,161]
284. ~8 | ~28 [avatar contradiction clause 283]
285. $false [avatar sat refutation 171,215,252,253,278,280,284]
% SZS output end Proof for 587259887424202340389427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both kind and not quiet then someone is not brave or tall and vice versa.
Everyone who is both quiet and not calm is both creative and rich.
If fred is not funny or happy then someone is either not brave or not curious and vice versa.
If mary is old then someone is calm or not generous.
Everyone who is either not wise or calm is either not tall or not humble.
Everyone who is not wise or curious is either not humble or not old.
Everyone who is not old or not curious is humble or wise and vice versa.
Everyone who is creative is strong and vice versa.
Everyone who is both not wise and strong is not tall or not humble and vice versa.
Everyone who is not humble or not happy is both not funny and not curious and vice versa.
If someone is curious or not funny then fred is wise.
If john is both not patient and not curious then someone is both calm and old and vice versa.
Everyone who is not funny or not happy is both not quiet and tall.
Everyone who is generous is either creative or humble.
Everyone who is creative or curious is not humble and vice versa.
If someone is brave or not tall then someone is either creative or not brave.
Mary is either quiet or not quiet.
Alice is either not creative or funny.
Lucy is both not curious and humble.
Someone is not kind or not strong.
Someone is wise or funny.
Someone is humble.
Someone is not patient.
Someone is happy. | Alice is not humble. | contradiction | (((kind(mary)&~quiet(mary)))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((quiet(X)&~calm(X))=>(creative(X)&rich(X))))&
(((~funny(fred)|happy(fred)))<=>(?[X]:((~brave(X)<~>~curious(X)))))&
((old(mary))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(~tall(X)<~>~humble(X))))&
(![X]:((~wise(X)|curious(X))=>(~humble(X)<~>~old(X))))&
(![X]:((~old(X)|~curious(X))<=>(humble(X)|wise(X))))&
(![X]:(creative(X)<=>strong(X)))&
(![X]:((~wise(X)&strong(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~funny(X)&~curious(X))))&
((?[X]:((curious(X)|~funny(X))))=>(wise(fred)))&
(((~patient(john)&~curious(john)))<=>(?[X]:((calm(X)&old(X)))))&
(![X]:((~funny(X)|~happy(X))=>(~quiet(X)&tall(X))))&
(![X]:(generous(X)=>(creative(X)<~>humble(X))))&
(![X]:((creative(X)|curious(X))<=>~humble(X)))&
((?[X]:((brave(X)|~tall(X))))=>(?[X]:((creative(X)<~>~brave(X)))))&
((quiet(mary)<~>~quiet(mary)))&
((~creative(alice)<~>funny(alice)))&
((~curious(lucy)&humble(lucy)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:(humble(X)))&
(?[X]:(~patient(X)))&
(?[X]:(happy(X))) | ~humble(alice) | [
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 860683439666840831899057
% SZS output start Proof for 860683439666840831899057
10. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~curious(X0) & ~funny(X0))) [input p9]
15. ! [X0] : ((curious(X0) | creative(X0)) <=> ~humble(X0)) [input p14]
18. ~creative(alice) <~> funny(alice) [input p17]
25. ~humble(alice) [input hypothesis]
54. ! [X0] : (((~happy(X0) | ~humble(X0)) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 10]
55. ! [X0] : ((~happy(X0) | ~humble(X0) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | (happy(X0) & humble(X0)))) [flattening 54]
61. ! [X0] : (((curious(X0) | creative(X0)) | humble(X0)) & (~humble(X0) | (~curious(X0) & ~creative(X0)))) [nnf transformation 15]
62. ! [X0] : ((curious(X0) | creative(X0) | humble(X0)) & (~humble(X0) | (~curious(X0) & ~creative(X0)))) [flattening 61]
68. (~funny(alice) | creative(alice)) & (funny(alice) | ~creative(alice)) [nnf transformation 18]
110. ~funny(X0) | humble(X0) [cnf transformation 55]
112. ~curious(X0) | humble(X0) [cnf transformation 55]
127. curious(X0) | creative(X0) | humble(X0) [cnf transformation 62]
134. funny(alice) | ~creative(alice) [cnf transformation 68]
143. ~humble(alice) [cnf transformation 25]
234. humble(X0) | creative(X0) [subsumption resolution 127,112]
256. 25 <=> creative(alice) [avatar definition]
260. 26 <=> funny(alice) [avatar definition]
261. funny(alice) <- (26) [avatar component clause 260]
264. ~25 | 26 [avatar split clause 134,260,256]
304. creative(alice) [resolution 234,143]
308. 25 [avatar split clause 304,256]
311. humble(alice) <- (26) [resolution 261,110]
312. $false <- (26) [subsumption resolution 311,143]
313. ~26 [avatar contradiction clause 312]
314. $false [avatar sat refutation 264,308,313]
% SZS output end Proof for 860683439666840831899057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is tall or not old then lucy is both happy and not humble and vice versa. Everyone who is patient or curious is either kind or calm. Everyone who is both not wise and not brave is either not brave or not tall. If john is both humble and not patient then john is both patient and tall. If alice is not rich then someone is both not happy and not creative. If john is either humble or not rich then alice is humble or happy and vice versa. Everyone who is both not curious and generous is rich. Everyone who is patient or kind is patient or not brave. Everyone who is both old and tall is both old and not curious. If fred is creative or generous then alice is not happy. If someone is either humble or not brave then mary is both brave and patient. Everyone who is quiet is not happy. If paul is old then susan is rich or kind and vice versa. Everyone who is both not brave and not quiet is not brave or not generous. If someone is either generous or brave then lucy is either creative or not brave and vice versa. Everyone who is patient is both happy and funny and vice versa. Paul is tall or funny. Someone is both tall and not old. Susan is happy. Someone is either wise or not old. Lucy is both curious and not quiet. Someone is both not kind and not old. Someone is quiet. Mary is generous. | Alice is not brave. | neutral | (((tall(alice)|~old(alice)))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((patient(X)|curious(X))=>(kind(X)<~>calm(X))))&
(![X]:((~wise(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(((humble(john)&~patient(john)))=>((patient(john)&tall(john))))&
((~rich(alice))=>(?[X]:((~happy(X)&~creative(X)))))&
(((humble(john)<~>~rich(john)))<=>((humble(alice)|happy(alice))))&
(![X]:((~curious(X)&generous(X))=>rich(X)))&
(![X]:((patient(X)|kind(X))=>(patient(X)|~brave(X))))&
(![X]:((old(X)&tall(X))=>(old(X)&~curious(X))))&
(((creative(fred)|generous(fred)))=>(~happy(alice)))&
((?[X]:((humble(X)<~>~brave(X))))=>((brave(mary)&patient(mary))))&
(![X]:(quiet(X)=>~happy(X)))&
((old(paul))<=>((rich(susan)|kind(susan))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((creative(lucy)<~>~brave(lucy))))&
(![X]:(patient(X)<=>(happy(X)&funny(X))))&
((tall(paul)|funny(paul)))&
(?[X]:((tall(X)&~old(X))))&
(happy(susan))&
(?[X]:((wise(X)<~>~old(X))))&
((curious(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:(quiet(X)))&
(generous(mary)) | ~brave(alice) | [] | null | 0 |
Everyone who is either not curious or patient is either funny or not calm and vice versa. Everyone who is patient or not old is both curious and strong. Everyone who is both generous and rich is both not strong and rich. Everyone who is both not kind and not generous is not patient and vice versa. Everyone who is wise or not quiet is patient or wise and vice versa. Everyone who is brave or happy is both not generous and happy and vice versa. If fred is humble or not curious then someone is both not generous and tall and vice versa. If susan is curious or happy then john is either not generous or funny. If fred is either not quiet or kind then someone is not patient or not generous. Everyone who is not humble is both not humble and not old and vice versa. If fred is not funny or not creative then alice is both not curious and not tall. Everyone who is either not strong or generous is either not happy or not brave and vice versa. If someone is both not rich and not old then someone is wise or patient. If someone is patient or not kind then someone is generous or rich. If john is curious or not kind then fred is both not creative and humble and vice versa. Everyone who is rich is wise or not funny. Someone is both quiet and not brave. Mary is either not creative or not rich. Someone is either not happy or calm. John is not generous or curious. | Alice is not old. | contradiction | (![X]:((~curious(X)<~>patient(X))<=>(funny(X)<~>~calm(X))))&
(![X]:((patient(X)|~old(X))=>(curious(X)&strong(X))))&
(![X]:((generous(X)&rich(X))=>(~strong(X)&rich(X))))&
(![X]:((~kind(X)&~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:((brave(X)|happy(X))<=>(~generous(X)&happy(X))))&
(((humble(fred)|~curious(fred)))<=>(?[X]:((~generous(X)&tall(X)))))&
(((curious(susan)|happy(susan)))=>((~generous(john)<~>funny(john))))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&~old(X))))&
(((~funny(fred)|~creative(fred)))=>((~curious(alice)&~tall(alice))))&
(![X]:((~strong(X)<~>generous(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((wise(X)|patient(X)))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((curious(john)|~kind(john)))<=>((~creative(fred)&humble(fred))))&
(![X]:(rich(X)=>(wise(X)|~funny(X))))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~generous(john)|curious(john))) | ~old(alice) | [
"p1",
"p3",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 884718564244184498554765
% SZS output start Proof for 884718564244184498554765
2. ! [X0] : ((~old(X0) | patient(X0)) => (strong(X0) & curious(X0))) [input p1]
4. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> ~patient(X0)) [input p3]
11. (~creative(fred) | ~funny(fred)) => (~tall(alice) & ~curious(alice)) [input p10]
15. (~kind(john) | curious(john)) <=> (humble(fred) & ~creative(fred)) [input p14]
21. ~old(alice) [input hypothesis]
24. ! [X0] : ((strong(X0) & curious(X0)) | (old(X0) & ~patient(X0))) [ennf transformation 2]
29. (~tall(alice) & ~curious(alice)) | (creative(fred) & funny(fred)) [ennf transformation 11]
35. ! [X0] : (((~generous(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | (generous(X0) | kind(X0)))) [nnf transformation 4]
36. ! [X0] : (((~generous(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | generous(X0) | kind(X0))) [flattening 35]
59. ((~kind(john) | curious(john)) | (~humble(fred) | creative(fred))) & ((humble(fred) & ~creative(fred)) | (kind(john) & ~curious(john))) [nnf transformation 15]
60. (~kind(john) | curious(john) | ~humble(fred) | creative(fred)) & ((humble(fred) & ~creative(fred)) | (kind(john) & ~curious(john))) [flattening 59]
75. ~patient(X0) | curious(X0) [cnf transformation 24]
76. old(X0) | curious(X0) [cnf transformation 24]
82. ~kind(X0) | patient(X0) [cnf transformation 36]
108. ~curious(alice) | creative(fred) [cnf transformation 29]
122. ~creative(fred) | ~curious(john) [cnf transformation 60]
123. ~creative(fred) | kind(john) [cnf transformation 60]
135. ~old(alice) [cnf transformation 21]
197. 13 <=> creative(fred) [avatar definition]
211. 16 <=> curious(alice) [avatar definition]
214. 13 | ~16 [avatar split clause 108,211,197]
251. 24 <=> curious(john) [avatar definition]
252. ~curious(john) <- (~24) [avatar component clause 251]
255. 25 <=> kind(john) [avatar definition]
256. kind(john) <- (25) [avatar component clause 255]
261. 25 | ~13 [avatar split clause 123,197,255]
262. ~24 | ~13 [avatar split clause 122,197,251]
284. curious(alice) [resolution 76,135]
287. 16 [avatar split clause 284,211]
288. patient(john) <- (25) [resolution 82,256]
290. curious(john) <- (25) [resolution 288,75]
291. $false <- (~24, 25) [subsumption resolution 290,252]
292. 24 | ~25 [avatar contradiction clause 291]
293. $false [avatar sat refutation 214,261,262,287,292]
% SZS output end Proof for 884718564244184498554765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both brave and rich then someone is not wise or not humble.
Everyone who is both not kind and wise is both kind and old and vice versa.
Everyone who is not patient or not curious is not patient or strong and vice versa.
Everyone who is either old or happy is not quiet and vice versa.
Everyone who is both not kind and calm is strong and vice versa.
If someone is both not kind and not old then someone is both strong and happy.
If someone is either creative or not curious then someone is not strong or not generous and vice versa.
Everyone who is funny or tall is both quiet and curious and vice versa.
If fred is not wise or rich then john is both not tall and not patient and vice versa.
If fred is not brave or humble then paul is kind and vice versa.
Everyone who is either kind or curious is both rich and funny.
Everyone who is not quiet is both not quiet and not patient.
If fred is calm or kind then someone is humble.
Everyone who is wise is not happy or not calm and vice versa.
Everyone who is either rich or not patient is rich and vice versa.
If someone is either happy or curious then someone is not brave or generous.
Fred is not tall or funny.
Someone is old or not funny.
John is either not curious or not quiet.
Someone is not calm or creative.
Alice is both not old and brave.
Alice is both calm and not tall.
Someone is both rich and not funny. | Fred is not wise. | contradiction | (((brave(lucy)&rich(lucy)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~kind(X)&wise(X))<=>(kind(X)&old(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)<~>happy(X))<=>~quiet(X)))&
(![X]:((~kind(X)&calm(X))<=>strong(X)))&
((?[X]:((~kind(X)&~old(X))))=>(?[X]:((strong(X)&happy(X)))))&
((?[X]:((creative(X)<~>~curious(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((funny(X)|tall(X))<=>(quiet(X)&curious(X))))&
(((~wise(fred)|rich(fred)))<=>((~tall(john)&~patient(john))))&
(((~brave(fred)|humble(fred)))<=>(kind(paul)))&
(![X]:((kind(X)<~>curious(X))=>(rich(X)&funny(X))))&
(![X]:(~quiet(X)=>(~quiet(X)&~patient(X))))&
(((calm(fred)|kind(fred)))=>(?[X]:(humble(X))))&
(![X]:(wise(X)<=>(~happy(X)|~calm(X))))&
(![X]:((rich(X)<~>~patient(X))<=>rich(X)))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((~brave(X)|generous(X)))))&
((~tall(fred)|funny(fred)))&
(?[X]:((old(X)|~funny(X))))&
((~curious(john)<~>~quiet(john)))&
(?[X]:((~calm(X)|creative(X))))&
((~old(alice)&brave(alice)))&
((calm(alice)&~tall(alice)))&
(?[X]:((rich(X)&~funny(X)))) | ~wise(fred) | [
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7804306081344691134180210
% SZS output start Proof for 7804306081344691134180210
9. (rich(fred) | ~wise(fred)) <=> (~patient(john) & ~tall(john)) [input p8]
15. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> rich(X0)) [input p14]
24. ~wise(fred) [input hypothesis]
54. ((rich(fred) | ~wise(fred)) | (patient(john) | tall(john))) & ((~patient(john) & ~tall(john)) | (~rich(fred) & wise(fred))) [nnf transformation 9]
55. (rich(fred) | ~wise(fred) | patient(john) | tall(john)) & ((~patient(john) & ~tall(john)) | (~rich(fred) & wise(fred))) [flattening 54]
63. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ~rich(X0)) & (rich(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 15]
106. ~patient(john) | wise(fred) [cnf transformation 55]
124. rich(X0) | rich(X0) | patient(X0) [cnf transformation 63]
126. patient(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
140. ~wise(fred) [cnf transformation 24]
141. rich(X0) | patient(X0) [duplicate literal removal 124]
142. patient(X0) | ~rich(X0) [duplicate literal removal 126]
214. 17 <=> patient(john) [avatar definition]
215. ~patient(john) <- (~17) [avatar component clause 214]
218. 18 <=> wise(fred) [avatar definition]
227. 18 | ~17 [avatar split clause 106,214,218]
260. patient(X0) [subsumption resolution 141,142]
314. ~18 [avatar split clause 140,218]
315. $false <- (~17) [subsumption resolution 215,260]
316. 17 [avatar contradiction clause 315]
317. $false [avatar sat refutation 227,314,316]
% SZS output end Proof for 7804306081344691134180210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or patient then john is funny. If john is both humble and not brave then john is not brave or not curious and vice versa. If susan is not creative or not tall then mary is either patient or funny. If someone is not brave or tall then someone is either not funny or not tall and vice versa. If fred is either strong or curious then someone is brave. Everyone who is kind is funny and vice versa. Everyone who is not quiet or not humble is both not strong and not tall. Everyone who is creative or wise is curious or not generous. Everyone who is kind is patient. Everyone who is either not brave or humble is not creative and vice versa. Everyone who is not kind is either brave or patient and vice versa. Everyone who is either calm or not quiet is both curious and happy. Everyone who is wise is strong or creative. If paul is both kind and not curious then john is not quiet. Everyone who is both wise and kind is not old. Someone is either wise or not strong. John is not calm. John is quiet. Lucy is both not generous and not old. Someone is both not humble and funny. Alice is not creative. | Fred is not happy. | neutral | ((?[X]:((~curious(X)|patient(X))))=>(funny(john)))&
(((humble(john)&~brave(john)))<=>((~brave(john)|~curious(john))))&
(((~creative(susan)|~tall(susan)))=>((patient(mary)<~>funny(mary))))&
((?[X]:((~brave(X)|tall(X))))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((strong(fred)<~>curious(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)<=>funny(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)|wise(X))=>(curious(X)|~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((~brave(X)<~>humble(X))<=>~creative(X)))&
(![X]:(~kind(X)<=>(brave(X)<~>patient(X))))&
(![X]:((calm(X)<~>~quiet(X))=>(curious(X)&happy(X))))&
(![X]:(wise(X)=>(strong(X)|creative(X))))&
(((kind(paul)&~curious(paul)))=>(~quiet(john)))&
(![X]:((wise(X)&kind(X))=>~old(X)))&
(?[X]:((wise(X)<~>~strong(X))))&
(~calm(john))&
(quiet(john))&
((~generous(lucy)&~old(lucy)))&
(?[X]:((~humble(X)&funny(X))))&
(~creative(alice)) | ~happy(fred) | [] | null | 0 |
Everyone who is either not quiet or not curious is not kind or not brave and vice versa.
Everyone who is either not brave or rich is not calm or not rich.
Everyone who is either not tall or not curious is both curious and creative.
Everyone who is either not curious or generous is not old or strong and vice versa.
If someone is strong then fred is not funny and vice versa.
If someone is both rich and quiet then paul is tall and vice versa.
If someone is either not kind or not humble then someone is both not funny and funny and vice versa.
If someone is either happy or wise then lucy is tall or not happy.
Everyone who is both curious and calm is both not tall and strong.
Everyone who is not wise or wise is both humble and brave and vice versa.
If someone is not wise then lucy is either not generous or not happy and vice versa.
Everyone who is old or not old is either curious or not quiet.
Everyone who is either strong or patient is both not wise and not old and vice versa.
If alice is both not kind and not funny then lucy is either not calm or funny.
If susan is kind then fred is both not old and tall.
Everyone who is not wise is not brave and vice versa.
Alice is both not generous and old.
Mary is not funny or funny.
Someone is either not patient or not wise.
John is wise or generous.
Someone is both humble and quiet.
John is wise.
John is both strong and rich.
Susan is quiet. | Alice is humble. | entailment | (![X]:((~quiet(X)<~>~curious(X))<=>(~kind(X)|~brave(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~calm(X)|~rich(X))))&
(![X]:((~tall(X)<~>~curious(X))=>(curious(X)&creative(X))))&
(![X]:((~curious(X)<~>generous(X))<=>(~old(X)|strong(X))))&
((?[X]:(strong(X)))<=>(~funny(fred)))&
((?[X]:((rich(X)&quiet(X))))<=>(tall(paul)))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((happy(X)<~>wise(X))))=>((tall(lucy)|~happy(lucy))))&
(![X]:((curious(X)&calm(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)|wise(X))<=>(humble(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((~generous(lucy)<~>~happy(lucy))))&
(![X]:((old(X)|~old(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~wise(X)&~old(X))))&
(((~kind(alice)&~funny(alice)))=>((~calm(lucy)<~>funny(lucy))))&
((kind(susan))=>((~old(fred)&tall(fred))))&
(![X]:(~wise(X)<=>~brave(X)))&
((~generous(alice)&old(alice)))&
((~funny(mary)|funny(mary)))&
(?[X]:((~patient(X)<~>~wise(X))))&
((wise(john)|generous(john)))&
(?[X]:((humble(X)&quiet(X))))&
(wise(john))&
((strong(john)&rich(john)))&
(quiet(susan)) | humble(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 717715192846354550323948
% SZS output start Proof for 717715192846354550323948
10. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (brave(X0) & humble(X0))) [input p9]
25. ~humble(alice) [input hypothesis]
59. ! [X0] : (((wise(X0) | ~wise(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (~wise(X0) & wise(X0)))) [nnf transformation 10]
60. ! [X0] : ((wise(X0) | ~wise(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (~wise(X0) & wise(X0)))) [flattening 59]
106. humble(X0) | wise(X0) [cnf transformation 60]
107. humble(X0) | ~wise(X0) [cnf transformation 60]
143. ~humble(alice) [cnf transformation 25]
209. humble(X0) [subsumption resolution 106,107]
281. $false [subsumption resolution 143,209]
% SZS output end Proof for 717715192846354550323948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not tall is both not curious and old. If someone is not kind or quiet then someone is not patient. Everyone who is either not funny or not creative is both not happy and tall. Everyone who is not kind is not old or humble. Everyone who is not kind or generous is both kind and old. If fred is both not wise and not curious then susan is both kind and not curious. Everyone who is either happy or not rich is not generous. If someone is either not patient or brave then someone is not tall and vice versa. Everyone who is not creative or kind is not tall or patient. Everyone who is not wise or not curious is wise and vice versa. Everyone who is strong is both rich and not patient and vice versa. If susan is either rich or old then someone is either not patient or kind and vice versa. Everyone who is either strong or not creative is kind or not wise and vice versa. Everyone who is not old is not funny or not humble. Everyone who is either not old or not calm is either strong or brave and vice versa. If someone is calm then lucy is quiet or not generous and vice versa. Someone is both happy and not curious. Someone is patient. Someone is not strong or not kind. Someone is rich. John is both generous and funny. Someone is either not old or brave. Someone is not tall. | Lucy is not old. | neutral | (![X]:((calm(X)&~tall(X))=>(~curious(X)&old(X))))&
((?[X]:((~kind(X)|quiet(X))))=>(?[X]:(~patient(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~happy(X)&tall(X))))&
(![X]:(~kind(X)=>(~old(X)|humble(X))))&
(![X]:((~kind(X)|generous(X))=>(kind(X)&old(X))))&
(((~wise(fred)&~curious(fred)))=>((kind(susan)&~curious(susan))))&
(![X]:((happy(X)<~>~rich(X))=>~generous(X)))&
((?[X]:((~patient(X)<~>brave(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)|kind(X))=>(~tall(X)|patient(X))))&
(![X]:((~wise(X)|~curious(X))<=>wise(X)))&
(![X]:(strong(X)<=>(rich(X)&~patient(X))))&
(((rich(susan)<~>old(susan)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(kind(X)|~wise(X))))&
(![X]:(~old(X)=>(~funny(X)|~humble(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(strong(X)<~>brave(X))))&
((?[X]:(calm(X)))<=>((quiet(lucy)|~generous(lucy))))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:(rich(X)))&
((generous(john)&funny(john)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:(~tall(X))) | ~old(lucy) | [] | null | 0 |
If someone is both not rich and not generous then paul is patient or not rich and vice versa.
Everyone who is both patient and not kind is both not strong and curious and vice versa.
Everyone who is both happy and not humble is either not happy or not kind and vice versa.
If someone is not calm or calm then fred is both old and not creative and vice versa.
Everyone who is both not patient and funny is both curious and strong and vice versa.
Everyone who is not funny is both funny and not brave.
Everyone who is not wise is not rich or generous and vice versa.
Everyone who is both brave and not patient is happy.
Everyone who is not wise is calm.
If someone is humble or not quiet then someone is both not generous and not strong and vice versa.
Everyone who is either patient or not humble is funny or rich.
Everyone who is not wise is strong.
Everyone who is not humble is either not wise or wise.
Everyone who is both funny and old is both not strong and not generous.
If someone is both not generous and not funny then lucy is not creative.
Everyone who is either humble or not strong is both not quiet and rich and vice versa.
Lucy is both not generous and patient.
Alice is not humble or tall.
Susan is patient.
Someone is not generous.
Someone is rich or not wise.
Alice is not creative. | Lucy is strong. | neutral | ((?[X]:((~rich(X)&~generous(X))))<=>((patient(paul)|~rich(paul))))&
(![X]:((patient(X)&~kind(X))<=>(~strong(X)&curious(X))))&
(![X]:((happy(X)&~humble(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:((~calm(X)|calm(X))))<=>((old(fred)&~creative(fred))))&
(![X]:((~patient(X)&funny(X))<=>(curious(X)&strong(X))))&
(![X]:(~funny(X)=>(funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(~rich(X)|generous(X))))&
(![X]:((brave(X)&~patient(X))=>happy(X)))&
(![X]:(~wise(X)=>calm(X)))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((patient(X)<~>~humble(X))=>(funny(X)|rich(X))))&
(![X]:(~wise(X)=>strong(X)))&
(![X]:(~humble(X)=>(~wise(X)<~>wise(X))))&
(![X]:((funny(X)&old(X))=>(~strong(X)&~generous(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(~creative(lucy)))&
(![X]:((humble(X)<~>~strong(X))<=>(~quiet(X)&rich(X))))&
((~generous(lucy)&patient(lucy)))&
((~humble(alice)|tall(alice)))&
(patient(susan))&
(?[X]:(~generous(X)))&
(?[X]:((rich(X)|~wise(X))))&
(~creative(alice)) | strong(lucy) | [] | null | 0 |
Everyone who is not rich is wise or brave. If someone is both tall and funny then john is old. Everyone who is brave is either tall or strong. Everyone who is creative or not curious is both patient and quiet and vice versa. Everyone who is both strong and not brave is strong or not rich and vice versa. Everyone who is both funny and generous is either not wise or not patient and vice versa. If alice is not curious or not kind then someone is funny or quiet. If someone is not tall or rich then someone is both not rich and not wise. Everyone who is both brave and not brave is funny and vice versa. Everyone who is either old or brave is creative and vice versa. Everyone who is humble or not quiet is either not quiet or not rich and vice versa. If someone is not old then susan is happy or not creative and vice versa. Everyone who is both rich and not humble is both not humble and not brave and vice versa. If someone is either not funny or curious then lucy is not creative or not humble. Someone is humble. Someone is both not brave and strong. John is either not rich or generous. Someone is tall or curious. Mary is not funny. | Mary is quiet. | entailment | (![X]:(~rich(X)=>(wise(X)|brave(X))))&
((?[X]:((tall(X)&funny(X))))=>(old(john)))&
(![X]:(brave(X)=>(tall(X)<~>strong(X))))&
(![X]:((creative(X)|~curious(X))<=>(patient(X)&quiet(X))))&
(![X]:((strong(X)&~brave(X))<=>(strong(X)|~rich(X))))&
(![X]:((funny(X)&generous(X))<=>(~wise(X)<~>~patient(X))))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((funny(X)|quiet(X)))))&
((?[X]:((~tall(X)|rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((brave(X)&~brave(X))<=>funny(X)))&
(![X]:((old(X)<~>brave(X))<=>creative(X)))&
(![X]:((humble(X)|~quiet(X))<=>(~quiet(X)<~>~rich(X))))&
((?[X]:(~old(X)))<=>((happy(susan)|~creative(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~humble(X)&~brave(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~creative(lucy)|~humble(lucy))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)&strong(X))))&
((~rich(john)<~>generous(john)))&
(?[X]:((tall(X)|curious(X))))&
(~funny(mary)) | quiet(mary) | [
"p0",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 430945493002555913617954
% SZS output start Proof for 430945493002555913617954
1. ! [X0] : (~rich(X0) => (brave(X0) | wise(X0))) [input p0]
5. ! [X0] : ((~brave(X0) & strong(X0)) <=> (~rich(X0) | strong(X0))) [input p4]
8. ? [X0] : (rich(X0) | ~tall(X0)) => ? [X0] : (~wise(X0) & ~rich(X0)) [input p7]
11. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (~quiet(X0) <~> ~rich(X0))) [input p10]
20. ~quiet(mary) [input hypothesis]
21. ? [X0] : (rich(X0) | ~tall(X0)) => ? [X1] : (~wise(X1) & ~rich(X1)) [rectify 8]
23. ! [X0] : ((brave(X0) | wise(X0)) | rich(X0)) [ennf transformation 1]
24. ! [X0] : (brave(X0) | wise(X0) | rich(X0)) [flattening 23]
28. ? [X1] : (~wise(X1) & ~rich(X1)) | ! [X0] : (~rich(X0) & tall(X0)) [ennf transformation 21]
34. ! [X0] : (((~brave(X0) & strong(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (brave(X0) | ~strong(X0)))) [nnf transformation 5]
35. ! [X0] : (((~brave(X0) & strong(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | brave(X0) | ~strong(X0))) [flattening 34]
40. ? [X0] : (~wise(X0) & ~rich(X0)) | ! [X1] : (~rich(X1) & tall(X1)) [rectify 28]
41. ? [X0] : (~wise(X0) & ~rich(X0)) => (~wise(sK1) & ~rich(sK1)) [choice axiom]
42. (~wise(sK1) & ~rich(sK1)) | ! [X1] : (~rich(X1) & tall(X1)) [skolemisation 40,41]
46. ! [X0] : (((~quiet(X0) | humble(X0)) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | (quiet(X0) & ~humble(X0)))) [nnf transformation 11]
47. ! [X0] : ((~quiet(X0) | humble(X0) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | (quiet(X0) & ~humble(X0)))) [flattening 46]
63. brave(X0) | wise(X0) | rich(X0) [cnf transformation 24]
76. ~brave(X0) | rich(X0) [cnf transformation 35]
85. ~rich(sK1) | ~rich(X1) [cnf transformation 42]
87. ~wise(sK1) | ~rich(X1) [cnf transformation 42]
98. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 47]
117. ~quiet(mary) [cnf transformation 20]
118. quiet(X0) | rich(X0) [duplicate literal removal 98]
142. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
143. ~rich(X1) <- (6) [avatar component clause 142]
145. 7 <=> wise(sK1) [avatar definition]
147. ~wise(sK1) <- (~7) [avatar component clause 145]
148. 6 | ~7 [avatar split clause 87,145,142]
154. 9 <=> rich(sK1) [avatar definition]
156. ~rich(sK1) <- (~9) [avatar component clause 154]
157. 6 | ~9 [avatar split clause 85,154,142]
215. rich(mary) [resolution 118,117]
219. wise(X1) | rich(X1) | rich(X1) [resolution 63,76]
220. wise(X1) | rich(X1) [duplicate literal removal 219]
231. rich(sK1) <- (~7) [resolution 220,147]
232. $false <- (~7, ~9) [subsumption resolution 231,156]
233. 7 | 9 [avatar contradiction clause 232]
234. $false <- (6) [resolution 143,215]
239. ~6 [avatar contradiction clause 234]
240. $false [avatar sat refutation 148,157,233,239]
% SZS output end Proof for 430945493002555913617954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then alice is not curious or humble and vice versa.
If someone is either not tall or calm then paul is both funny and rich and vice versa.
If alice is kind then lucy is happy and vice versa.
If paul is not creative then fred is either quiet or not happy and vice versa.
Everyone who is both happy and funny is both happy and strong and vice versa.
If mary is old then someone is curious or patient.
Everyone who is strong is both tall and humble and vice versa.
If john is creative then susan is not creative.
Everyone who is both wise and happy is not old.
Everyone who is either happy or quiet is not brave.
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
John is both tall and not strong.
Someone is either not patient or not happy.
Fred is both not wise and strong.
Fred is humble.
Mary is both not patient and not kind.
Someone is either creative or old.
Susan is curious.
Someone is either calm or tall. | Fred is funny. | entailment | ((?[X]:(humble(X)))<=>((~curious(alice)|humble(alice))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((funny(paul)&rich(paul))))&
((kind(alice))<=>(happy(lucy)))&
((~creative(paul))<=>((quiet(fred)<~>~happy(fred))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
((old(mary))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(strong(X)<=>(tall(X)&humble(X))))&
((creative(john))=>(~creative(susan)))&
(![X]:((wise(X)&happy(X))=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))=>~brave(X)))&
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((~wise(fred)&strong(fred)))&
(humble(fred))&
((~patient(mary)&~kind(mary)))&
(?[X]:((creative(X)<~>old(X))))&
(curious(susan))&
(?[X]:((calm(X)<~>tall(X)))) | funny(fred) | [
"p4",
"p6",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 722562902895879656195887
% SZS output start Proof for 722562902895879656195887
5. ! [X0] : ((funny(X0) & happy(X0)) <=> (strong(X0) & happy(X0))) [input p4]
7. ! [X0] : (strong(X0) <=> (humble(X0) & tall(X0))) [input p6]
13. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p12]
14. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) & generous(X0))) [input p13]
19. strong(fred) & ~wise(fred) [input p18]
25. ~funny(fred) [input hypothesis]
44. ! [X0] : (((funny(X0) & happy(X0)) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) & happy(X0)) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | ~funny(X0) | ~happy(X0))) [flattening 44]
48. ! [X0] : ((strong(X0) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | ~strong(X0))) [nnf transformation 7]
49. ! [X0] : ((strong(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~strong(X0))) [flattening 48]
52. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 13]
53. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 53]
86. ~strong(X0) | funny(X0) | ~happy(X0) [cnf transformation 45]
89. ~strong(X0) | humble(X0) [cnf transformation 49]
102. generous(X0) | happy(X0) [cnf transformation 52]
107. funny(X0) | ~strong(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 54]
123. strong(fred) [cnf transformation 19]
132. ~funny(fred) [cnf transformation 25]
245. ~generous(X0) | ~strong(X0) | funny(X0) [subsumption resolution 107,89]
365. ~strong(X1) | funny(X1) | happy(X1) [resolution 245,102]
367. ~strong(X1) | funny(X1) [subsumption resolution 365,86]
371. funny(fred) [resolution 367,123]
373. $false [subsumption resolution 371,132]
% SZS output end Proof for 722562902895879656195887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not strong or patient then paul is both happy and not kind.
Everyone who is funny is either not rich or humble and vice versa.
Everyone who is either humble or old is not brave.
If someone is either humble or kind then susan is both not happy and kind.
Everyone who is either generous or happy is not generous and vice versa.
If lucy is not brave or not quiet then paul is both humble and not generous and vice versa.
If lucy is funny then someone is kind or not happy and vice versa.
Everyone who is either rich or not calm is old.
If john is either not humble or brave then someone is either not calm or not patient and vice versa.
If someone is both quiet and not patient then mary is both not curious and not rich.
Everyone who is both tall and not quiet is either happy or not happy.
If someone is either not quiet or not happy then someone is not humble or kind.
If someone is not humble or not tall then fred is not quiet and vice versa.
Everyone who is not kind is either funny or not old.
Everyone who is not strong is both patient and not rich.
If someone is either not humble or quiet then paul is strong or not rich and vice versa.
Someone is quiet.
Someone is not old or not funny.
Mary is either patient or happy.
Susan is funny.
Fred is tall.
Lucy is either not rich or happy.
Someone is either not brave or not quiet.
Alice is old. | Mary is not happy. | contradiction | (((~strong(lucy)<~>patient(lucy)))=>((happy(paul)&~kind(paul))))&
(![X]:(funny(X)<=>(~rich(X)<~>humble(X))))&
(![X]:((humble(X)<~>old(X))=>~brave(X)))&
((?[X]:((humble(X)<~>kind(X))))=>((~happy(susan)&kind(susan))))&
(![X]:((generous(X)<~>happy(X))<=>~generous(X)))&
(((~brave(lucy)|~quiet(lucy)))<=>((humble(paul)&~generous(paul))))&
((funny(lucy))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((rich(X)<~>~calm(X))=>old(X)))&
(((~humble(john)<~>brave(john)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))=>((~curious(mary)&~rich(mary))))&
(![X]:((tall(X)&~quiet(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))=>(?[X]:((~humble(X)|kind(X)))))&
((?[X]:((~humble(X)|~tall(X))))<=>(~quiet(fred)))&
(![X]:(~kind(X)=>(funny(X)<~>~old(X))))&
(![X]:(~strong(X)=>(patient(X)&~rich(X))))&
((?[X]:((~humble(X)<~>quiet(X))))<=>((strong(paul)|~rich(paul))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)|~funny(X))))&
((patient(mary)<~>happy(mary)))&
(funny(susan))&
(tall(fred))&
((~rich(lucy)<~>happy(lucy)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
(old(alice)) | ~happy(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4529565317387155306989448
% SZS output start Proof for 4529565317387155306989448
5. ! [X0] : ((generous(X0) <~> happy(X0)) <=> ~generous(X0)) [input p4]
25. ~happy(mary) [input hypothesis]
42. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | generous(X0)) & (~generous(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 5]
92. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 42]
94. happy(X0) | generous(X0) | generous(X0) [cnf transformation 42]
143. ~happy(mary) [cnf transformation 25]
144. ~generous(X0) | happy(X0) [duplicate literal removal 92]
145. happy(X0) | generous(X0) [duplicate literal removal 94]
184. happy(X0) [subsumption resolution 144,145]
333. $false [subsumption resolution 143,184]
% SZS output end Proof for 4529565317387155306989448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and happy is curious and vice versa. If someone is either curious or not calm then john is not humble and vice versa. If someone is either happy or not kind then paul is not wise and vice versa. If someone is both not strong and not happy then john is either not rich or wise. If someone is either not rich or not tall then mary is both curious and rich and vice versa. Everyone who is either old or not rich is either not rich or patient and vice versa. Everyone who is not rich or not humble is either not humble or strong and vice versa. Everyone who is both rich and humble is tall and vice versa. If someone is either not rich or rich then someone is not generous or not curious. If alice is generous or not funny then mary is not generous and vice versa. Everyone who is either brave or not patient is either not strong or humble. If lucy is both not calm and old then fred is strong or not humble. If someone is kind then someone is not strong. If alice is both calm and not quiet then someone is both quiet and creative. Everyone who is tall or not calm is not tall and vice versa. Paul is not curious. Someone is humble or calm. Paul is not strong or brave. Mary is either not strong or rich. Alice is patient or creative. | John is not wise. | entailment | (![X]:((~curious(X)&happy(X))<=>curious(X)))&
((?[X]:((curious(X)<~>~calm(X))))<=>(~humble(john)))&
((?[X]:((happy(X)<~>~kind(X))))<=>(~wise(paul)))&
((?[X]:((~strong(X)&~happy(X))))=>((~rich(john)<~>wise(john))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((curious(mary)&rich(mary))))&
(![X]:((old(X)<~>~rich(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~humble(X)<~>strong(X))))&
(![X]:((rich(X)&humble(X))<=>tall(X)))&
((?[X]:((~rich(X)<~>rich(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
(((generous(alice)|~funny(alice)))<=>(~generous(mary)))&
(![X]:((brave(X)<~>~patient(X))=>(~strong(X)<~>humble(X))))&
(((~calm(lucy)&old(lucy)))=>((strong(fred)|~humble(fred))))&
((?[X]:(kind(X)))=>(?[X]:(~strong(X))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((tall(X)|~calm(X))<=>~tall(X)))&
(~curious(paul))&
(?[X]:((humble(X)|calm(X))))&
((~strong(paul)|brave(paul)))&
((~strong(mary)<~>rich(mary)))&
((patient(alice)|creative(alice))) | ~wise(john) | [
"p0",
"p3",
"p4",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 169286853990830579692882
% SZS output start Proof for 169286853990830579692882
1. ! [X0] : ((happy(X0) & ~curious(X0)) <=> curious(X0)) [input p0]
4. ? [X0] : (~happy(X0) & ~strong(X0)) => (~rich(john) <~> wise(john)) [input p3]
5. ? [X0] : (~rich(X0) <~> ~tall(X0)) <=> (rich(mary) & curious(mary)) [input p4]
15. ! [X0] : ((~calm(X0) | tall(X0)) <=> ~tall(X0)) [input p14]
19. ~strong(mary) <~> rich(mary) [input p18]
21. wise(john) [input hypothesis]
27. (~rich(john) <~> wise(john)) | ! [X0] : (happy(X0) | strong(X0)) [ennf transformation 4]
33. ! [X0] : (((happy(X0) & ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((happy(X0) & ~curious(X0)) | ~curious(X0)) & (curious(X0) | ~happy(X0) | curious(X0))) [flattening 33]
43. ((~wise(john) | rich(john)) & (wise(john) | ~rich(john))) | ! [X0] : (happy(X0) | strong(X0)) [nnf transformation 27]
44. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~rich(mary) | ~curious(mary))) & ((rich(mary) & curious(mary)) | ! [X0] : ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [nnf transformation 5]
45. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ~rich(mary) | ~curious(mary)) & ((rich(mary) & curious(mary)) | ! [X0] : ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [flattening 44]
46. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ~rich(mary) | ~curious(mary)) & ((rich(mary) & curious(mary)) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [rectify 45]
47. ? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) => ((tall(sK2) | rich(sK2)) & (~tall(sK2) | ~rich(sK2))) [choice axiom]
48. (((tall(sK2) | rich(sK2)) & (~tall(sK2) | ~rich(sK2))) | ~rich(mary) | ~curious(mary)) & ((rich(mary) & curious(mary)) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [skolemisation 46,47]
64. ! [X0] : (((~calm(X0) | tall(X0)) | tall(X0)) & (~tall(X0) | (calm(X0) & ~tall(X0)))) [nnf transformation 15]
65. ! [X0] : ((~calm(X0) | tall(X0) | tall(X0)) & (~tall(X0) | (calm(X0) & ~tall(X0)))) [flattening 64]
68. (~rich(mary) | strong(mary)) & (rich(mary) | ~strong(mary)) [nnf transformation 19]
69. curious(X0) | ~happy(X0) | curious(X0) [cnf transformation 34]
70. ~curious(X0) | ~curious(X0) [cnf transformation 34]
81. ~wise(john) | rich(john) | happy(X0) | strong(X0) [cnf transformation 43]
83. curious(mary) | ~rich(X1) | tall(X1) [cnf transformation 48]
116. ~tall(X0) | ~tall(X0) [cnf transformation 65]
122. rich(mary) | ~strong(mary) [cnf transformation 68]
124. wise(john) [cnf transformation 21]
125. ~tall(X0) [duplicate literal removal 116]
135. curious(X0) | ~happy(X0) [duplicate literal removal 69]
136. ~curious(X0) [duplicate literal removal 70]
137. ~happy(X0) [subsumption resolution 135,136]
168. ~wise(john) | rich(john) | strong(X0) [subsumption resolution 81,137]
170. 7 <=> ! [X0] : strong(X0) [avatar definition]
171. strong(X0) <- (7) [avatar component clause 170]
173. 8 <=> rich(john) [avatar definition]
175. rich(john) <- (8) [avatar component clause 173]
177. 9 <=> wise(john) [avatar definition]
180. 7 | 8 | ~9 [avatar split clause 168,177,173,170]
184. 10 <=> ! [X1] : (~rich(X1) | tall(X1)) [avatar definition]
185. ~rich(X1) | tall(X1) <- (10) [avatar component clause 184]
187. 11 <=> rich(mary) [avatar definition]
189. rich(mary) <- (11) [avatar component clause 187]
195. ~rich(X1) | tall(X1) [subsumption resolution 83,136]
196. 10 [avatar split clause 195,184]
261. 26 <=> strong(mary) [avatar definition]
262. ~strong(mary) <- (~26) [avatar component clause 261]
265. ~26 | 11 [avatar split clause 122,187,261]
266. 9 [avatar split clause 124,177]
267. ~rich(X1) <- (10) [subsumption resolution 185,125]
270. $false <- (8, 10) [subsumption resolution 175,267]
271. ~8 | ~10 [avatar contradiction clause 270]
274. $false <- (7, ~26) [resolution 262,171]
275. ~7 | 26 [avatar contradiction clause 274]
276. $false <- (10, 11) [subsumption resolution 189,267]
277. ~10 | ~11 [avatar contradiction clause 276]
278. $false [avatar sat refutation 180,196,265,266,271,275,277]
% SZS output end Proof for 169286853990830579692882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or strong is not strong and vice versa.
If lucy is not rich or not calm then someone is not happy or not strong.
Everyone who is not kind or not calm is rich and vice versa.
If someone is not patient or not kind then susan is not wise.
If someone is generous or not curious then fred is both strong and curious.
Everyone who is not patient or not strong is both happy and not quiet.
Everyone who is either not rich or strong is curious or not funny and vice versa.
Everyone who is not funny is happy and vice versa.
If someone is not brave then lucy is either not brave or humble and vice versa.
Everyone who is both humble and wise is either not old or tall.
Everyone who is either not rich or kind is quiet or old.
If alice is not happy or kind then someone is patient and vice versa.
If someone is not brave or happy then someone is not brave or not curious and vice versa.
If someone is not creative then fred is both not strong and creative and vice versa.
If lucy is tall or not rich then lucy is either not generous or old and vice versa.
Everyone who is either not rich or generous is both rich and not tall.
Someone is not rich or not calm.
Someone is either not patient or not rich.
Susan is creative or old.
Paul is both not generous and calm.
Someone is both brave and funny.
Alice is strong or rich.
Lucy is either not tall or curious. | Susan is not wise. | entailment | (![X]:((quiet(X)<~>strong(X))<=>~strong(X)))&
(((~rich(lucy)|~calm(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:((~kind(X)|~calm(X))<=>rich(X)))&
((?[X]:((~patient(X)|~kind(X))))=>(~wise(susan)))&
((?[X]:((generous(X)|~curious(X))))=>((strong(fred)&curious(fred))))&
(![X]:((~patient(X)|~strong(X))=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(curious(X)|~funny(X))))&
(![X]:(~funny(X)<=>happy(X)))&
((?[X]:(~brave(X)))<=>((~brave(lucy)<~>humble(lucy))))&
(![X]:((humble(X)&wise(X))=>(~old(X)<~>tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(quiet(X)|old(X))))&
(((~happy(alice)|kind(alice)))<=>(?[X]:(patient(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))<=>((~strong(fred)&creative(fred))))&
(((tall(lucy)|~rich(lucy)))<=>((~generous(lucy)<~>old(lucy))))&
(![X]:((~rich(X)<~>generous(X))=>(rich(X)&~tall(X))))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
((creative(susan)|old(susan)))&
((~generous(paul)&calm(paul)))&
(?[X]:((brave(X)&funny(X))))&
((strong(alice)|rich(alice)))&
((~tall(lucy)<~>curious(lucy))) | ~wise(susan) | [
"p2",
"p3",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1699151012004314373185465
% SZS output start Proof for 1699151012004314373185465
3. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> rich(X0)) [input p2]
4. ? [X0] : (~kind(X0) | ~patient(X0)) => ~wise(susan) [input p3]
16. ! [X0] : ((~rich(X0) <~> generous(X0)) => (~tall(X0) & rich(X0))) [input p15]
20. calm(paul) & ~generous(paul) [input p19]
24. wise(susan) [input hypothesis]
27. ~wise(susan) | ! [X0] : (kind(X0) & patient(X0)) [ennf transformation 4]
34. ! [X0] : ((~tall(X0) & rich(X0)) | (~rich(X0) <=> generous(X0))) [ennf transformation 16]
38. ! [X0] : (((~calm(X0) | ~kind(X0)) | ~rich(X0)) & (rich(X0) | (calm(X0) & kind(X0)))) [nnf transformation 3]
39. ! [X0] : ((~calm(X0) | ~kind(X0) | ~rich(X0)) & (rich(X0) | (calm(X0) & kind(X0)))) [flattening 38]
66. ! [X0] : ((~tall(X0) & rich(X0)) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) [nnf transformation 34]
83. ~kind(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 39]
85. ~wise(susan) | kind(X0) [cnf transformation 27]
126. rich(X0) | generous(X0) | rich(X0) [cnf transformation 66]
134. ~generous(paul) [cnf transformation 20]
135. calm(paul) [cnf transformation 20]
141. wise(susan) [cnf transformation 24]
142. generous(X0) | rich(X0) [duplicate literal removal 126]
165. 5 <=> ! [X0] : kind(X0) [avatar definition]
166. kind(X0) <- (5) [avatar component clause 165]
168. 6 <=> wise(susan) [avatar definition]
171. 5 | ~6 [avatar split clause 85,168,165]
322. 6 [avatar split clause 141,168]
331. rich(paul) [resolution 142,134]
344. ~calm(X1) | ~rich(X1) <- (5) [resolution 83,166]
346. ~rich(paul) <- (5) [resolution 344,135]
348. $false <- (5) [subsumption resolution 346,331]
349. ~5 [avatar contradiction clause 348]
350. $false [avatar sat refutation 171,322,349]
% SZS output end Proof for 1699151012004314373185465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not creative is kind.
Everyone who is not humble or generous is both curious and tall and vice versa.
If someone is both not funny and not happy then john is either not kind or not strong and vice versa.
If susan is either not strong or not generous then john is not brave or curious and vice versa.
Everyone who is happy or creative is both not quiet and brave.
If mary is quiet or kind then someone is either not funny or not tall and vice versa.
If john is either patient or not happy then someone is not brave.
If someone is not brave or patient then mary is either kind or not strong and vice versa.
If lucy is calm then someone is not happy.
If paul is either kind or not curious then susan is kind and vice versa.
If john is not old then someone is not funny.
If someone is not rich then someone is both tall and patient.
Everyone who is not old or not wise is kind.
If someone is old then someone is both rich and strong and vice versa.
Everyone who is either not tall or not wise is strong.
Everyone who is curious or quiet is tall and vice versa.
Someone is calm.
Lucy is both tall and brave.
Alice is generous or funny.
Someone is not curious.
Lucy is not funny.
Someone is both not humble and calm.
John is both quiet and patient.
Susan is either quiet or not calm. | John is kind. | entailment | (![X]:((creative(X)<~>~creative(X))=>kind(X)))&
(![X]:((~humble(X)|generous(X))<=>(curious(X)&tall(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~kind(john)<~>~strong(john))))&
(((~strong(susan)<~>~generous(susan)))<=>((~brave(john)|curious(john))))&
(![X]:((happy(X)|creative(X))=>(~quiet(X)&brave(X))))&
(((quiet(mary)|kind(mary)))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((patient(john)<~>~happy(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)|patient(X))))<=>((kind(mary)<~>~strong(mary))))&
((calm(lucy))=>(?[X]:(~happy(X))))&
(((kind(paul)<~>~curious(paul)))<=>(kind(susan)))&
((~old(john))=>(?[X]:(~funny(X))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~old(X)|~wise(X))=>kind(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>strong(X)))&
(![X]:((curious(X)|quiet(X))<=>tall(X)))&
(?[X]:(calm(X)))&
((tall(lucy)&brave(lucy)))&
((generous(alice)|funny(alice)))&
(?[X]:(~curious(X)))&
(~funny(lucy))&
(?[X]:((~humble(X)&calm(X))))&
((quiet(john)&patient(john)))&
((quiet(susan)<~>~calm(susan))) | kind(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1920206502078542100315501
% SZS output start Proof for 1920206502078542100315501
1. ! [X0] : ((creative(X0) <~> ~creative(X0)) => kind(X0)) [input p0]
25. ~kind(john) [input hypothesis]
28. ! [X0] : (kind(X0) | (creative(X0) <=> ~creative(X0))) [ennf transformation 1]
36. ! [X0] : (kind(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 28]
80. kind(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 36]
81. kind(X0) | creative(X0) | creative(X0) [cnf transformation 36]
147. ~kind(john) [cnf transformation 25]
148. kind(X0) | ~creative(X0) [duplicate literal removal 80]
149. kind(X0) | creative(X0) [duplicate literal removal 81]
150. kind(X0) [subsumption resolution 148,149]
324. $false [subsumption resolution 147,150]
% SZS output end Proof for 1920206502078542100315501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and kind then fred is either not wise or not funny and vice versa.
Everyone who is brave or wise is both not curious and not happy.
Everyone who is quiet or happy is both not humble and generous and vice versa.
Everyone who is both not patient and tall is both quiet and old and vice versa.
Everyone who is either not calm or not brave is either wise or not wise and vice versa.
Everyone who is not strong or not generous is kind.
Everyone who is quiet or not patient is curious.
If someone is both not strong and not funny then someone is both patient and not rich.
If fred is not old then paul is either happy or creative.
If susan is happy then someone is both not calm and not generous and vice versa.
Everyone who is funny or not happy is both quiet and not brave.
Everyone who is both calm and curious is either creative or calm and vice versa.
Everyone who is both old and creative is not funny or not tall.
Everyone who is not funny is old.
Everyone who is either rich or curious is either calm or not funny and vice versa.
Everyone who is both patient and brave is either not curious or not patient.
Mary is not patient.
Alice is either not patient or kind.
John is both not rich and patient.
Lucy is either not tall or generous.
Someone is rich or not kind. | Paul is calm. | entailment | ((?[X]:((~patient(X)&kind(X))))<=>((~wise(fred)<~>~funny(fred))))&
(![X]:((brave(X)|wise(X))=>(~curious(X)&~happy(X))))&
(![X]:((quiet(X)|happy(X))<=>(~humble(X)&generous(X))))&
(![X]:((~patient(X)&tall(X))<=>(quiet(X)&old(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((~strong(X)|~generous(X))=>kind(X)))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
((?[X]:((~strong(X)&~funny(X))))=>(?[X]:((patient(X)&~rich(X)))))&
((~old(fred))=>((happy(paul)<~>creative(paul))))&
((happy(susan))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)|~happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))<=>(creative(X)<~>calm(X))))&
(![X]:((old(X)&creative(X))=>(~funny(X)|~tall(X))))&
(![X]:(~funny(X)=>old(X)))&
(![X]:((rich(X)<~>curious(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((patient(X)&brave(X))=>(~curious(X)<~>~patient(X))))&
(~patient(mary))&
((~patient(alice)<~>kind(alice)))&
((~rich(john)&patient(john)))&
((~tall(lucy)<~>generous(lucy)))&
(?[X]:((rich(X)|~kind(X)))) | calm(paul) | [
"p1",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6602474179245609932783867
% SZS output start Proof for 6602474179245609932783867
2. ! [X0] : ((wise(X0) | brave(X0)) => (~happy(X0) & ~curious(X0))) [input p1]
5. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p4]
11. ! [X0] : ((~happy(X0) | funny(X0)) => (~brave(X0) & quiet(X0))) [input p10]
22. ~calm(paul) [input hypothesis]
26. ! [X0] : ((~happy(X0) & ~curious(X0)) | (~wise(X0) & ~brave(X0))) [ennf transformation 2]
30. ! [X0] : ((~brave(X0) & quiet(X0)) | (happy(X0) & ~funny(X0))) [ennf transformation 11]
44. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 5]
66. ~happy(X0) | ~brave(X0) [cnf transformation 26]
83. brave(X0) | calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 44]
84. brave(X0) | calm(X0) | wise(X0) | wise(X0) [cnf transformation 44]
96. ~brave(X0) | happy(X0) [cnf transformation 30]
123. ~calm(paul) [cnf transformation 22]
129. brave(X0) | calm(X0) | ~wise(X0) [duplicate literal removal 83]
130. brave(X0) | calm(X0) | wise(X0) [duplicate literal removal 84]
156. calm(X0) | brave(X0) [subsumption resolution 129,130]
190. ~brave(X0) [subsumption resolution 96,66]
229. brave(paul) [resolution 156,123]
230. $false [subsumption resolution 229,190]
% SZS output end Proof for 6602474179245609932783867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or not tall then paul is not patient or not strong and vice versa.
If lucy is either curious or generous then someone is both not curious and not funny.
Everyone who is both happy and wise is both not quiet and quiet.
Everyone who is not wise or wise is not strong.
Everyone who is not kind or not creative is either kind or not funny.
Everyone who is not curious is both not creative and not funny.
Everyone who is both generous and rich is not happy and vice versa.
If mary is both not patient and not rich then mary is either tall or generous and vice versa.
If lucy is both curious and brave then someone is funny and vice versa.
Everyone who is both old and tall is both curious and kind and vice versa.
Everyone who is rich or kind is both not rich and strong and vice versa.
Everyone who is either not humble or tall is both funny and calm and vice versa.
If alice is both funny and kind then mary is patient and vice versa.
If alice is both not rich and brave then someone is either not brave or funny and vice versa.
If someone is either not quiet or not humble then alice is both not brave and curious.
If john is strong or calm then someone is both not generous and not curious and vice versa.
Alice is quiet.
Mary is both generous and not brave.
John is not brave.
Paul is not wise or generous.
Someone is tall or not happy. | Lucy is old. | neutral | (((old(fred)<~>~tall(fred)))<=>((~patient(paul)|~strong(paul))))&
(((curious(lucy)<~>generous(lucy)))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((happy(X)&wise(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~wise(X)|wise(X))=>~strong(X)))&
(![X]:((~kind(X)|~creative(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~curious(X)=>(~creative(X)&~funny(X))))&
(![X]:((generous(X)&rich(X))<=>~happy(X)))&
(((~patient(mary)&~rich(mary)))<=>((tall(mary)<~>generous(mary))))&
(((curious(lucy)&brave(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((old(X)&tall(X))<=>(curious(X)&kind(X))))&
(![X]:((rich(X)|kind(X))<=>(~rich(X)&strong(X))))&
(![X]:((~humble(X)<~>tall(X))<=>(funny(X)&calm(X))))&
(((funny(alice)&kind(alice)))<=>(patient(mary)))&
(((~rich(alice)&brave(alice)))<=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>((~brave(alice)&curious(alice))))&
(((strong(john)|calm(john)))<=>(?[X]:((~generous(X)&~curious(X)))))&
(quiet(alice))&
((generous(mary)&~brave(mary)))&
(~brave(john))&
((~wise(paul)|generous(paul)))&
(?[X]:((tall(X)|~happy(X)))) | old(lucy) | [] | null | 0 |
Everyone who is not calm is not funny and vice versa. If fred is both not curious and kind then alice is both not kind and not happy. If someone is funny then lucy is brave and vice versa. Everyone who is rich is both not rich and not creative and vice versa. If someone is old or not kind then someone is not strong and vice versa. Everyone who is both wise and not happy is both rich and kind. Everyone who is either not creative or quiet is calm and vice versa. If mary is not wise then mary is both not strong and not quiet. Everyone who is either not funny or not brave is funny. If someone is creative then someone is not strong or wise and vice versa. If someone is not humble or not rich then someone is not wise and vice versa. If fred is both not funny and not calm then alice is kind or old. If mary is not curious or not happy then susan is not patient or not happy and vice versa. If mary is both quiet and tall then someone is not generous and vice versa. Everyone who is both not rich and not kind is old and vice versa. Everyone who is both creative and old is both kind and tall and vice versa. Someone is either not happy or patient. Susan is both not rich and not curious. Someone is not humble. Paul is either not wise or happy. Alice is not humble or not quiet. Someone is not quiet or curious. Susan is funny or rich. | Fred is rich. | contradiction | (![X]:(~calm(X)<=>~funny(X)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>calm(X)))&
((~wise(mary))=>((~strong(mary)&~quiet(mary))))&
(![X]:((~funny(X)<~>~brave(X))=>funny(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~strong(X)|wise(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(?[X]:(~wise(X))))&
(((~funny(fred)&~calm(fred)))=>((kind(alice)|old(alice))))&
(((~curious(mary)|~happy(mary)))<=>((~patient(susan)|~happy(susan))))&
(((quiet(mary)&tall(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~kind(X))<=>old(X)))&
(![X]:((creative(X)&old(X))<=>(kind(X)&tall(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:(~humble(X)))&
((~wise(paul)<~>happy(paul)))&
((~humble(alice)|~quiet(alice)))&
(?[X]:((~quiet(X)|curious(X))))&
((funny(susan)|rich(susan))) | rich(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7622456508012569973749569
% SZS output start Proof for 7622456508012569973749569
4. ! [X0] : (rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p3]
24. rich(fred) [input hypothesis]
41. ! [X0] : ((rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [nnf transformation 4]
42. ! [X0] : ((rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [flattening 41]
85. ~rich(X0) | ~rich(X0) [cnf transformation 42]
132. rich(fred) [cnf transformation 24]
134. ~rich(X0) [duplicate literal removal 85]
313. $false [subsumption resolution 132,134]
% SZS output end Proof for 7622456508012569973749569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not creative then someone is calm or not creative.
Everyone who is strong is either happy or tall and vice versa.
If mary is not curious or not rich then lucy is either patient or not kind.
If paul is either not creative or rich then someone is either not rich or not old and vice versa.
If paul is either rich or not curious then fred is not curious or not creative.
Everyone who is not tall or brave is not quiet and vice versa.
If someone is old or quiet then fred is rich or curious and vice versa.
Everyone who is curious is either rich or humble and vice versa.
Everyone who is both brave and tall is not tall or not curious.
Everyone who is humble is either old or not patient and vice versa.
Everyone who is not wise or not funny is either not humble or not brave and vice versa.
Everyone who is both rich and not funny is either patient or funny and vice versa.
If john is either not humble or not generous then alice is tall.
If paul is both not generous and not funny then john is either creative or not brave.
Everyone who is not funny is either patient or not calm and vice versa.
Everyone who is either not wise or curious is either rich or not generous and vice versa.
Alice is creative.
Paul is strong.
Someone is not tall or kind.
Alice is humble.
Someone is kind or tall.
Someone is tall.
Someone is rich or wise.
Alice is not curious. | Lucy is patient. | neutral | ((?[X]:((~humble(X)&~creative(X))))=>(?[X]:((calm(X)|~creative(X)))))&
(![X]:(strong(X)<=>(happy(X)<~>tall(X))))&
(((~curious(mary)|~rich(mary)))=>((patient(lucy)<~>~kind(lucy))))&
(((~creative(paul)<~>rich(paul)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(((rich(paul)<~>~curious(paul)))=>((~curious(fred)|~creative(fred))))&
(![X]:((~tall(X)|brave(X))<=>~quiet(X)))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:((rich(X)&~funny(X))<=>(patient(X)<~>funny(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(![X]:(~funny(X)<=>(patient(X)<~>~calm(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(creative(alice))&
(strong(paul))&
(?[X]:((~tall(X)|kind(X))))&
(humble(alice))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:(tall(X)))&
(?[X]:((rich(X)|wise(X))))&
(~curious(alice)) | patient(lucy) | [] | null | 0 |
If paul is not wise then someone is not calm or not humble.
If someone is both not tall and not calm then someone is both not curious and not patient and vice versa.
If john is not strong or happy then someone is strong and vice versa.
If susan is not patient or not curious then someone is not kind and vice versa.
Everyone who is not old or not humble is both not wise and not quiet.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
If susan is funny or humble then susan is not humble and vice versa.
Susan is both not humble and not old.
Paul is not calm or not quiet.
Someone is both tall and calm.
John is not calm.
Mary is either funny or not kind.
Someone is not old. | Fred is creative. | contradiction | ((~wise(paul))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(john)|happy(john)))<=>(?[X]:(strong(X))))&
(((~patient(susan)|~curious(susan)))<=>(?[X]:(~kind(X))))&
(![X]:((~old(X)|~humble(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
((~humble(susan)&~old(susan)))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
(~calm(john))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X))) | creative(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2009056455392107730509673
% SZS output start Proof for 2009056455392107730509673
14. ! [X0] : (patient(X0) <=> (creative(X0) & ~patient(X0))) [input p13]
23. creative(fred) [input hypothesis]
64. ! [X0] : ((patient(X0) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 14]
65. ! [X0] : ((patient(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [flattening 64]
119. ~patient(X0) | ~patient(X0) [cnf transformation 65]
121. patient(X0) | ~creative(X0) | patient(X0) [cnf transformation 65]
137. creative(fred) [cnf transformation 23]
140. ~patient(X0) [duplicate literal removal 119]
141. ~creative(X0) | patient(X0) [duplicate literal removal 121]
270. 29 <=> creative(fred) [avatar definition]
271. creative(fred) <- (29) [avatar component clause 270]
315. 29 [avatar split clause 137,270]
324. patient(fred) <- (29) [resolution 141,271]
326. $false <- (29) [subsumption resolution 324,140]
327. ~29 [avatar contradiction clause 326]
329. $false [avatar sat refutation 315,327]
% SZS output end Proof for 2009056455392107730509673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not patient and not tall and vice versa.
If someone is both not humble and not funny then fred is either calm or strong.
If fred is both not calm and kind then someone is not strong and vice versa.
If susan is old or strong then someone is either not humble or not creative and vice versa.
Everyone who is not brave is either patient or not funny and vice versa.
Everyone who is either patient or not rich is both generous and not patient and vice versa.
If lucy is not generous or happy then john is either humble or generous and vice versa.
If someone is tall or brave then someone is creative and vice versa.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
If john is patient or old then someone is both not tall and not rich and vice versa.
If paul is strong then john is either calm or funny and vice versa.
If paul is either calm or not old then someone is quiet.
If susan is both curious and strong then someone is patient.
Susan is both quiet and not curious.
Someone is either strong or brave.
Someone is not creative.
Someone is either not brave or calm.
Lucy is either calm or not patient.
Someone is either happy or not wise.
Alice is quiet. | Susan is happy. | entailment | (![X]:(tall(X)<=>(~patient(X)&~tall(X))))&
((?[X]:((~humble(X)&~funny(X))))=>((calm(fred)<~>strong(fred))))&
(((~calm(fred)&kind(fred)))<=>(?[X]:(~strong(X))))&
(((old(susan)|strong(susan)))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:(~brave(X)<=>(patient(X)<~>~funny(X))))&
(![X]:((patient(X)<~>~rich(X))<=>(generous(X)&~patient(X))))&
(((~generous(lucy)|happy(lucy)))<=>((humble(john)<~>generous(john))))&
((?[X]:((tall(X)|brave(X))))<=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
((strong(paul))<=>((calm(john)<~>funny(john))))&
(((calm(paul)<~>~old(paul)))=>(?[X]:(quiet(X))))&
(((curious(susan)&strong(susan)))=>(?[X]:(patient(X))))&
((quiet(susan)&~curious(susan)))&
(?[X]:((strong(X)<~>brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((calm(lucy)<~>~patient(lucy)))&
(?[X]:((happy(X)<~>~wise(X))))&
(quiet(alice)) | happy(susan) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6289606264969117445473154
% SZS output start Proof for 6289606264969117445473154
1. ! [X0] : (tall(X0) <=> (~tall(X0) & ~patient(X0))) [input p0]
10. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~happy(X0) | ~kind(X0))) [input p9]
22. ~happy(susan) [input hypothesis]
32. ! [X0] : ((tall(X0) | (tall(X0) | patient(X0))) & ((~tall(X0) & ~patient(X0)) | ~tall(X0))) [nnf transformation 1]
33. ! [X0] : ((tall(X0) | tall(X0) | patient(X0)) & ((~tall(X0) & ~patient(X0)) | ~tall(X0))) [flattening 32]
58. ! [X0] : (((~old(X0) & ~patient(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (old(X0) | patient(X0)))) [nnf transformation 10]
59. ! [X0] : (((~old(X0) & ~patient(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | old(X0) | patient(X0))) [flattening 58]
79. ~tall(X0) | ~tall(X0) [cnf transformation 33]
80. tall(X0) | tall(X0) | patient(X0) [cnf transformation 33]
115. ~patient(X0) | happy(X0) [cnf transformation 59]
136. ~happy(susan) [cnf transformation 22]
139. ~tall(X0) [duplicate literal removal 79]
140. patient(X0) | tall(X0) [duplicate literal removal 80]
339. tall(X0) | happy(X0) [resolution 140,115]
343. happy(X0) [subsumption resolution 339,139]
347. $false [resolution 343,136]
% SZS output end Proof for 6289606264969117445473154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not funny is either not brave or tall and vice versa.
Everyone who is not generous or not brave is not humble.
Everyone who is not curious or not tall is either not patient or not rich.
Everyone who is tall is either curious or rich.
Everyone who is not kind or not rich is rich and vice versa.
If someone is not wise or funny then alice is both not patient and not strong and vice versa.
Everyone who is not tall or wise is either funny or kind and vice versa.
Everyone who is both not kind and wise is either tall or creative.
If john is both patient and kind then alice is not tall.
If someone is both old and not tall then susan is creative or wise and vice versa.
If alice is not generous then someone is not happy or not generous.
If paul is both not quiet and patient then someone is curious.
If susan is not happy then mary is both quiet and generous and vice versa.
If someone is wise then fred is both creative and curious and vice versa.
If someone is either funny or curious then paul is both old and not creative.
Everyone who is patient is brave and vice versa.
Mary is both quiet and not happy.
Paul is either humble or not quiet.
Fred is both not strong and not curious.
Susan is both tall and happy.
Alice is not creative or humble.
Mary is either not creative or old. | Mary is not tall. | contradiction | (![X]:((funny(X)&~funny(X))<=>(~brave(X)<~>tall(X))))&
(![X]:((~generous(X)|~brave(X))=>~humble(X)))&
(![X]:((~curious(X)|~tall(X))=>(~patient(X)<~>~rich(X))))&
(![X]:(tall(X)=>(curious(X)<~>rich(X))))&
(![X]:((~kind(X)|~rich(X))<=>rich(X)))&
((?[X]:((~wise(X)|funny(X))))<=>((~patient(alice)&~strong(alice))))&
(![X]:((~tall(X)|wise(X))<=>(funny(X)<~>kind(X))))&
(![X]:((~kind(X)&wise(X))=>(tall(X)<~>creative(X))))&
(((patient(john)&kind(john)))=>(~tall(alice)))&
((?[X]:((old(X)&~tall(X))))<=>((creative(susan)|wise(susan))))&
((~generous(alice))=>(?[X]:((~happy(X)|~generous(X)))))&
(((~quiet(paul)&patient(paul)))=>(?[X]:(curious(X))))&
((~happy(susan))<=>((quiet(mary)&generous(mary))))&
((?[X]:(wise(X)))<=>((creative(fred)&curious(fred))))&
((?[X]:((funny(X)<~>curious(X))))=>((old(paul)&~creative(paul))))&
(![X]:(patient(X)<=>brave(X)))&
((quiet(mary)&~happy(mary)))&
((humble(paul)<~>~quiet(paul)))&
((~strong(fred)&~curious(fred)))&
((tall(susan)&happy(susan)))&
((~creative(alice)|humble(alice)))&
((~creative(mary)<~>old(mary))) | ~tall(mary) | [
"p0",
"p2",
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 467376268670537603846019
% SZS output start Proof for 467376268670537603846019
1. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~brave(X0) <~> tall(X0))) [input p0]
3. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~patient(X0) <~> ~rich(X0))) [input p2]
5. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> rich(X0)) [input p4]
16. ! [X0] : (patient(X0) <=> brave(X0)) [input p15]
23. ~tall(mary) [input hypothesis]
25. ! [X0] : ((~patient(X0) <~> ~rich(X0)) | (tall(X0) & curious(X0))) [ennf transformation 3]
35. ! [X0] : (((~funny(X0) & funny(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0)))) & (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | (funny(X0) | ~funny(X0)))) [nnf transformation 1]
36. ! [X0] : (((~funny(X0) & funny(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0)))) & (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | funny(X0) | ~funny(X0))) [flattening 35]
37. ! [X0] : (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (tall(X0) & curious(X0))) [nnf transformation 25]
39. ! [X0] : (((~rich(X0) | ~kind(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) & kind(X0)))) [nnf transformation 5]
40. ! [X0] : ((~rich(X0) | ~kind(X0) | ~rich(X0)) & (rich(X0) | (rich(X0) & kind(X0)))) [flattening 39]
66. ! [X0] : ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))) [nnf transformation 16]
71. funny(X0) | tall(X0) | brave(X0) [cnf transformation 36]
73. ~funny(X0) | tall(X0) | brave(X0) [cnf transformation 36]
78. ~rich(X0) | ~patient(X0) | tall(X0) [cnf transformation 37]
84. rich(X0) | rich(X0) [cnf transformation 40]
118. ~brave(X0) | patient(X0) [cnf transformation 66]
130. ~tall(mary) [cnf transformation 23]
131. rich(X0) [duplicate literal removal 84]
134. tall(X0) | brave(X0) [subsumption resolution 71,73]
307. brave(mary) [resolution 134,130]
315. patient(mary) [resolution 307,118]
322. ~patient(X0) | tall(X0) [resolution 78,131]
332. tall(mary) [resolution 322,315]
333. $false [subsumption resolution 332,130]
% SZS output end Proof for 467376268670537603846019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or humble is not funny and vice versa.
Everyone who is not funny is strong.
If fred is either not old or strong then someone is both not calm and calm.
Everyone who is either not brave or not kind is both not old and not rich and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Everyone who is either happy or not quiet is either wise or happy and vice versa.
If susan is both not humble and not rich then fred is not brave and vice versa.
If mary is not rich or not wise then someone is brave or happy.
Everyone who is either tall or humble is either strong or not creative and vice versa.
Someone is either not tall or tall.
Someone is not generous or not kind.
Fred is both not calm and not kind.
Someone is both not strong and not kind.
Paul is calm or not strong.
Paul is either strong or not happy.
Susan is not happy.
Someone is either not curious or wise. | Mary is tall. | contradiction | (![X]:((~creative(X)<~>humble(X))<=>~funny(X)))&
(![X]:(~funny(X)=>strong(X)))&
(((~old(fred)<~>strong(fred)))=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(strong(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((~calm(fred)&~kind(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(paul)|~strong(paul)))&
((strong(paul)<~>~happy(paul)))&
(~happy(susan))&
(?[X]:((~curious(X)<~>wise(X)))) | tall(mary) | [
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 182837694759129737366017
% SZS output start Proof for 182837694759129737366017
5. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p5]
25. tall(mary) [input hypothesis]
45. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 5]
46. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 45]
47. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
48. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 47]
94. ~quiet(X0) | ~tall(X0) [cnf transformation 46]
98. curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 48]
100. ~tall(X0) | ~curious(X0) | ~curious(X0) | quiet(X0) [cnf transformation 48]
151. tall(mary) [cnf transformation 25]
156. curious(X0) | ~tall(X0) [duplicate literal removal 98]
157. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 100]
174. ~tall(X0) | ~curious(X0) [subsumption resolution 157,94]
175. ~tall(X0) [subsumption resolution 156,174]
304. $false [subsumption resolution 151,175]
% SZS output end Proof for 182837694759129737366017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not rich is both humble and patient. If paul is not creative or not calm then mary is quiet or curious and vice versa. If mary is not funny or not kind then paul is either wise or strong. Everyone who is both funny and not kind is not calm or not old. If someone is wise or curious then someone is both brave and not old and vice versa. Everyone who is strong or not funny is both not humble and not quiet and vice versa. Everyone who is both not kind and tall is both calm and not wise. Everyone who is not patient or not funny is both patient and not rich and vice versa. Everyone who is brave is creative or patient and vice versa. If fred is tall then someone is not funny or not calm and vice versa. Everyone who is either not strong or happy is not tall or calm. If fred is old or not brave then john is not strong or curious and vice versa. If susan is either not kind or tall then someone is not brave or patient. Everyone who is not quiet or humble is strong. If alice is both not humble and old then someone is not funny and vice versa. Everyone who is both not patient and strong is both generous and not strong. Someone is not rich or old. Fred is either old or generous. Someone is both not happy and not curious. Someone is rich. Susan is kind. Susan is generous or not curious. | John is old. | neutral | (![X]:((~curious(X)&~rich(X))=>(humble(X)&patient(X))))&
(((~creative(paul)|~calm(paul)))<=>((quiet(mary)|curious(mary))))&
(((~funny(mary)|~kind(mary)))=>((wise(paul)<~>strong(paul))))&
(![X]:((funny(X)&~kind(X))=>(~calm(X)|~old(X))))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(((old(fred)|~brave(fred)))<=>((~strong(john)|curious(john))))&
(((~kind(susan)<~>tall(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(((~humble(alice)&old(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&strong(X))=>(generous(X)&~strong(X))))&
(?[X]:((~rich(X)|old(X))))&
((old(fred)<~>generous(fred)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(rich(X)))&
(kind(susan))&
((generous(susan)|~curious(susan))) | old(john) | [] | null | 0 |
If john is either not happy or not quiet then someone is not creative.
If someone is both creative and not happy then lucy is tall and vice versa.
Everyone who is creative is not tall and vice versa.
Everyone who is not wise or humble is not kind.
If alice is both wise and not patient then someone is not rich and vice versa.
If alice is either wise or calm then lucy is both not calm and patient.
Everyone who is both rich and calm is not tall and vice versa.
Everyone who is either creative or curious is either generous or wise.
Everyone who is either generous or not patient is not generous.
If someone is brave or not brave then susan is both not wise and strong.
Everyone who is either humble or rich is both quiet and not quiet and vice versa.
If someone is either wise or humble then susan is creative and vice versa.
If fred is tall then alice is not humble and vice versa.
If john is not strong then someone is either not calm or patient and vice versa.
If someone is both calm and not old then mary is not kind and vice versa.
If susan is both quiet and not happy then mary is either creative or not generous and vice versa.
Someone is both generous and quiet.
Someone is either calm or not humble.
Mary is both brave and humble.
John is not funny or tall.
John is not strong.
Fred is not funny or not calm.
Paul is either not rich or tall.
Susan is not tall or not curious. | Paul is not calm. | entailment | (((~happy(john)<~>~quiet(john)))=>(?[X]:(~creative(X))))&
((?[X]:((creative(X)&~happy(X))))<=>(tall(lucy)))&
(![X]:(creative(X)<=>~tall(X)))&
(![X]:((~wise(X)|humble(X))=>~kind(X)))&
(((wise(alice)&~patient(alice)))<=>(?[X]:(~rich(X))))&
(((wise(alice)<~>calm(alice)))=>((~calm(lucy)&patient(lucy))))&
(![X]:((rich(X)&calm(X))<=>~tall(X)))&
(![X]:((creative(X)<~>curious(X))=>(generous(X)<~>wise(X))))&
(![X]:((generous(X)<~>~patient(X))=>~generous(X)))&
((?[X]:((brave(X)|~brave(X))))=>((~wise(susan)&strong(susan))))&
(![X]:((humble(X)<~>rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(creative(susan)))&
((tall(fred))<=>(~humble(alice)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(~kind(mary)))&
(((quiet(susan)&~happy(susan)))<=>((creative(mary)<~>~generous(mary))))&
(?[X]:((generous(X)&quiet(X))))&
(?[X]:((calm(X)<~>~humble(X))))&
((brave(mary)&humble(mary)))&
((~funny(john)|tall(john)))&
(~strong(john))&
((~funny(fred)|~calm(fred)))&
((~rich(paul)<~>tall(paul)))&
((~tall(susan)|~curious(susan))) | ~calm(paul) | [
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3173910873370406853384134
% SZS output start Proof for 3173910873370406853384134
7. ! [X0] : ((calm(X0) & rich(X0)) <=> ~tall(X0)) [input p6]
23. ~rich(paul) <~> tall(paul) [input p22]
25. calm(paul) [input hypothesis]
48. ! [X0] : (((calm(X0) & rich(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) | ~rich(X0)))) [nnf transformation 7]
49. ! [X0] : (((calm(X0) & rich(X0)) | tall(X0)) & (~tall(X0) | ~calm(X0) | ~rich(X0))) [flattening 48]
74. (~tall(paul) | rich(paul)) & (tall(paul) | ~rich(paul)) [nnf transformation 23]
91. ~calm(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 49]
92. rich(X0) | tall(X0) [cnf transformation 49]
136. tall(paul) | ~rich(paul) [cnf transformation 74]
137. ~tall(paul) | rich(paul) [cnf transformation 74]
139. calm(paul) [cnf transformation 25]
332. rich(paul) [subsumption resolution 137,92]
333. tall(paul) [subsumption resolution 136,332]
361. ~tall(paul) | ~rich(paul) [resolution 91,139]
364. ~rich(paul) [subsumption resolution 361,333]
365. $false [subsumption resolution 364,332]
% SZS output end Proof for 3173910873370406853384134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not funny and not happy then someone is not old. If lucy is not calm or not kind then someone is both not generous and not old and vice versa. If someone is both funny and not strong then someone is quiet or curious. Everyone who is wise or kind is both not generous and old. Everyone who is wise is not wise or patient. If someone is not generous then susan is either not generous or old and vice versa. If someone is both not strong and not curious then mary is generous or not calm and vice versa. Everyone who is not generous or humble is both quiet and not kind. If someone is both strong and curious then alice is not humble or humble. If someone is quiet then someone is funny and vice versa. Everyone who is either creative or not kind is either happy or not humble. Everyone who is not tall or old is either quiet or kind. Everyone who is either not happy or tall is both old and creative and vice versa. If susan is both wise and brave then lucy is old or happy and vice versa. Everyone who is brave or quiet is not creative and vice versa. If paul is kind or not wise then fred is brave and vice versa. Alice is either happy or not quiet. Susan is either not old or not rich. Fred is both generous and rich. Someone is either generous or not strong. Fred is either wise or funny. Someone is either curious or not happy. | Susan is quiet. | entailment | (((~funny(mary)&~happy(mary)))=>(?[X]:(~old(X))))&
(((~calm(lucy)|~kind(lucy)))<=>(?[X]:((~generous(X)&~old(X)))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((wise(X)|kind(X))=>(~generous(X)&old(X))))&
(![X]:(wise(X)=>(~wise(X)|patient(X))))&
((?[X]:(~generous(X)))<=>((~generous(susan)<~>old(susan))))&
((?[X]:((~strong(X)&~curious(X))))<=>((generous(mary)|~calm(mary))))&
(![X]:((~generous(X)|humble(X))=>(quiet(X)&~kind(X))))&
((?[X]:((strong(X)&curious(X))))=>((~humble(alice)|humble(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)<~>~kind(X))=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(((kind(paul)|~wise(paul)))<=>(brave(fred)))&
((happy(alice)<~>~quiet(alice)))&
((~old(susan)<~>~rich(susan)))&
((generous(fred)&rich(fred)))&
(?[X]:((generous(X)<~>~strong(X))))&
((wise(fred)<~>funny(fred)))&
(?[X]:((curious(X)<~>~happy(X)))) | quiet(susan) | [
"p1",
"p3",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1106074985982130582994479
% SZS output start Proof for 1106074985982130582994479
2. (~kind(lucy) | ~calm(lucy)) <=> ? [X0] : (~old(X0) & ~generous(X0)) [input p1]
4. ! [X0] : ((kind(X0) | wise(X0)) => (old(X0) & ~generous(X0))) [input p3]
6. ? [X0] : ~generous(X0) <=> (~generous(susan) <~> old(susan)) [input p5]
8. ! [X0] : ((humble(X0) | ~generous(X0)) => (~kind(X0) & quiet(X0))) [input p7]
12. ! [X0] : ((old(X0) | ~tall(X0)) => (quiet(X0) <~> kind(X0))) [input p11]
23. ~quiet(susan) [input hypothesis]
30. ! [X0] : ((old(X0) & ~generous(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 4]
31. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 8]
35. ! [X0] : ((quiet(X0) <~> kind(X0)) | (~old(X0) & tall(X0))) [ennf transformation 12]
38. ((~kind(lucy) | ~calm(lucy)) | ! [X0] : (old(X0) | generous(X0))) & (? [X0] : (~old(X0) & ~generous(X0)) | (kind(lucy) & calm(lucy))) [nnf transformation 2]
39. (~kind(lucy) | ~calm(lucy) | ! [X0] : (old(X0) | generous(X0))) & (? [X0] : (~old(X0) & ~generous(X0)) | (kind(lucy) & calm(lucy))) [flattening 38]
40. (~kind(lucy) | ~calm(lucy) | ! [X0] : (old(X0) | generous(X0))) & (? [X1] : (~old(X1) & ~generous(X1)) | (kind(lucy) & calm(lucy))) [rectify 39]
41. ? [X1] : (~old(X1) & ~generous(X1)) => (~old(sK1) & ~generous(sK1)) [choice axiom]
42. (~kind(lucy) | ~calm(lucy) | ! [X0] : (old(X0) | generous(X0))) & ((~old(sK1) & ~generous(sK1)) | (kind(lucy) & calm(lucy))) [skolemisation 40,41]
46. (? [X0] : ~generous(X0) | ((~generous(susan) | ~old(susan)) & (old(susan) | generous(susan)))) & (((~old(susan) | generous(susan)) & (old(susan) | ~generous(susan))) | ! [X0] : generous(X0)) [nnf transformation 6]
47. (? [X0] : ~generous(X0) | ((~generous(susan) | ~old(susan)) & (old(susan) | generous(susan)))) & (((~old(susan) | generous(susan)) & (old(susan) | ~generous(susan))) | ! [X1] : generous(X1)) [rectify 46]
48. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
49. (~generous(sK3) | ((~generous(susan) | ~old(susan)) & (old(susan) | generous(susan)))) & (((~old(susan) | generous(susan)) & (old(susan) | ~generous(susan))) | ! [X1] : generous(X1)) [skolemisation 47,48]
61. ! [X0] : (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (~old(X0) & tall(X0))) [nnf transformation 35]
81. ~generous(sK1) | kind(lucy) [cnf transformation 42]
87. ~generous(X0) | ~kind(X0) [cnf transformation 30]
90. old(susan) | ~generous(susan) | generous(X1) [cnf transformation 49]
99. quiet(X0) | generous(X0) [cnf transformation 31]
101. ~kind(X0) | generous(X0) [cnf transformation 31]
111. kind(X0) | quiet(X0) | ~old(X0) [cnf transformation 61]
143. ~quiet(susan) [cnf transformation 23]
165. 6 <=> kind(lucy) [avatar definition]
166. kind(lucy) <- (6) [avatar component clause 165]
176. 8 <=> generous(sK1) [avatar definition]
178. ~generous(sK1) <- (~8) [avatar component clause 176]
179. 6 | ~8 [avatar split clause 81,176,165]
194. 12 <=> old(susan) [avatar definition]
195. old(susan) <- (12) [avatar component clause 194]
198. 13 <=> generous(susan) [avatar definition]
208. 15 <=> ! [X1] : generous(X1) [avatar definition]
209. generous(X1) <- (15) [avatar component clause 208]
211. 15 | ~13 | 12 [avatar split clause 90,194,198,208]
236. ~kind(X0) [subsumption resolution 101,87]
255. ~old(X0) | quiet(X0) [subsumption resolution 111,236]
344. generous(susan) [resolution 99,143]
350. quiet(susan) <- (12) [resolution 255,195]
351. $false <- (12) [subsumption resolution 350,143]
352. ~12 [avatar contradiction clause 351]
353. 13 [avatar split clause 344,198]
355. $false <- (~8, 15) [resolution 209,178]
360. 8 | ~15 [avatar contradiction clause 355]
361. $false <- (6) [subsumption resolution 166,236]
362. ~6 [avatar contradiction clause 361]
363. $false [avatar sat refutation 179,211,352,353,360,362]
% SZS output end Proof for 1106074985982130582994479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and not wise is patient or not rich and vice versa. Everyone who is both curious and not calm is both not brave and brave and vice versa. If someone is either not generous or not wise then someone is either tall or brave and vice versa. Everyone who is curious is both not strong and not funny. If fred is not strong or happy then john is happy or not kind and vice versa. Everyone who is funny or generous is curious or rich. If someone is wise then mary is both kind and strong. If fred is either not patient or happy then alice is either brave or quiet. Everyone who is curious is funny. Everyone who is not calm or not brave is both not patient and humble and vice versa. If someone is funny then someone is either not humble or old and vice versa. If someone is strong or wise then fred is both not funny and not patient and vice versa. Everyone who is not funny or strong is either calm or not curious. If someone is happy then someone is both happy and old and vice versa. If susan is either rich or not wise then alice is not funny or not brave and vice versa. If alice is kind then someone is either calm or rich. Someone is not kind or not generous. Susan is both humble and not quiet. Someone is not humble or kind. Someone is rich. Someone is both generous and not calm. Someone is either not quiet or not wise. Someone is not creative or curious. Mary is not wise. | Alice is curious. | contradiction | (![X]:((~tall(X)&~wise(X))<=>(patient(X)|~rich(X))))&
(![X]:((curious(X)&~calm(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(curious(X)=>(~strong(X)&~funny(X))))&
(((~strong(fred)|happy(fred)))<=>((happy(john)|~kind(john))))&
(![X]:((funny(X)|generous(X))=>(curious(X)|rich(X))))&
((?[X]:(wise(X)))=>((kind(mary)&strong(mary))))&
(((~patient(fred)<~>happy(fred)))=>((brave(alice)<~>quiet(alice))))&
(![X]:(curious(X)=>funny(X)))&
(![X]:((~calm(X)|~brave(X))<=>(~patient(X)&humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~humble(X)<~>old(X)))))&
((?[X]:((strong(X)|wise(X))))<=>((~funny(fred)&~patient(fred))))&
(![X]:((~funny(X)|strong(X))=>(calm(X)<~>~curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((happy(X)&old(X)))))&
(((rich(susan)<~>~wise(susan)))<=>((~funny(alice)|~brave(alice))))&
((kind(alice))=>(?[X]:((calm(X)<~>rich(X)))))&
(?[X]:((~kind(X)|~generous(X))))&
((humble(susan)&~quiet(susan)))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(rich(X)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((~creative(X)|curious(X))))&
(~wise(mary)) | curious(alice) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5378596456782217642959490
% SZS output start Proof for 5378596456782217642959490
4. ! [X0] : (curious(X0) => (~funny(X0) & ~strong(X0))) [input p3]
9. ! [X0] : (curious(X0) => funny(X0)) [input p8]
25. curious(alice) [input hypothesis]
30. ! [X0] : ((~funny(X0) & ~strong(X0)) | ~curious(X0)) [ennf transformation 4]
35. ! [X0] : (funny(X0) | ~curious(X0)) [ennf transformation 9]
102. ~funny(X0) | ~curious(X0) [cnf transformation 30]
115. funny(X0) | ~curious(X0) [cnf transformation 35]
155. curious(alice) [cnf transformation 25]
243. ~curious(X0) [subsumption resolution 115,102]
372. $false [subsumption resolution 155,243]
% SZS output end Proof for 5378596456782217642959490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not kind then paul is not wise or strong and vice versa.
If john is rich or not calm then someone is either strong or kind and vice versa.
If fred is not creative then paul is either not tall or not calm and vice versa.
If someone is creative or not humble then fred is both kind and rich and vice versa.
If someone is old or generous then someone is not happy or generous.
Everyone who is both not curious and curious is not quiet or creative.
If someone is both patient and not kind then someone is either not tall or not funny.
If someone is patient or not generous then susan is either not rich or not strong and vice versa.
Everyone who is quiet is both not old and rich.
If lucy is both not calm and generous then someone is both happy and not humble.
Everyone who is not quiet is both tall and not humble.
Everyone who is both not humble and happy is both patient and humble.
If fred is both not old and not patient then someone is not funny and vice versa.
If someone is not calm or not happy then fred is not patient or funny and vice versa.
If alice is both strong and not strong then someone is both calm and not generous.
Everyone who is both humble and creative is rich and vice versa.
Lucy is not humble.
Fred is curious or not old.
Someone is both creative and calm.
Paul is rich or not patient.
Someone is rich or not rich.
Lucy is happy or not calm.
Someone is not curious or quiet. | Lucy is quiet. | contradiction | ((?[X]:((~quiet(X)&~kind(X))))<=>((~wise(paul)|strong(paul))))&
(((rich(john)|~calm(john)))<=>(?[X]:((strong(X)<~>kind(X)))))&
((~creative(fred))<=>((~tall(paul)<~>~calm(paul))))&
((?[X]:((creative(X)|~humble(X))))<=>((kind(fred)&rich(fred))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((~curious(X)&curious(X))=>(~quiet(X)|creative(X))))&
((?[X]:((patient(X)&~kind(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:((patient(X)|~generous(X))))<=>((~rich(susan)<~>~strong(susan))))&
(![X]:(quiet(X)=>(~old(X)&rich(X))))&
(((~calm(lucy)&generous(lucy)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:(~quiet(X)=>(tall(X)&~humble(X))))&
(![X]:((~humble(X)&happy(X))=>(patient(X)&humble(X))))&
(((~old(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~patient(fred)|funny(fred))))&
(((strong(alice)&~strong(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((humble(X)&creative(X))<=>rich(X)))&
(~humble(lucy))&
((curious(fred)|~old(fred)))&
(?[X]:((creative(X)&calm(X))))&
((rich(paul)|~patient(paul)))&
(?[X]:((rich(X)|~rich(X))))&
((happy(lucy)|~calm(lucy)))&
(?[X]:((~curious(X)|quiet(X)))) | quiet(lucy) | [
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 213640968107070304640961
% SZS output start Proof for 213640968107070304640961
9. ! [X0] : (quiet(X0) => (rich(X0) & ~old(X0))) [input p8]
16. ! [X0] : ((creative(X0) & humble(X0)) <=> rich(X0)) [input p15]
17. ~humble(lucy) [input p16]
24. quiet(lucy) [input hypothesis]
31. ! [X0] : ((rich(X0) & ~old(X0)) | ~quiet(X0)) [ennf transformation 9]
80. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | (~creative(X0) | ~humble(X0)))) [nnf transformation 16]
81. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | ~creative(X0) | ~humble(X0))) [flattening 80]
120. ~quiet(X0) | rich(X0) [cnf transformation 31]
137. ~rich(X0) | humble(X0) [cnf transformation 81]
139. ~humble(lucy) [cnf transformation 17]
147. quiet(lucy) [cnf transformation 24]
387. rich(lucy) [resolution 120,147]
392. humble(lucy) [resolution 137,387]
393. $false [subsumption resolution 392,139]
% SZS output end Proof for 213640968107070304640961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both happy and not strong is either happy or brave.
If paul is calm or curious then paul is either not patient or not curious and vice versa.
If john is either not calm or kind then someone is both quiet and not patient.
If john is both not curious and not quiet then someone is not patient.
Everyone who is both strong and not rich is both tall and not strong and vice versa.
If someone is either happy or not quiet then someone is both not humble and not kind and vice versa.
If someone is calm or creative then someone is quiet or funny.
If mary is not creative or not quiet then john is not wise and vice versa.
If susan is not kind or tall then someone is not generous or happy and vice versa.
Everyone who is kind or happy is not tall or curious and vice versa.
Everyone who is either not calm or old is not wise.
Everyone who is creative or wise is wise or not humble.
If someone is happy then someone is either not quiet or not strong and vice versa.
If someone is wise or not strong then someone is either creative or brave.
Everyone who is kind or rich is not curious or not calm.
Everyone who is not old or not kind is both kind and not curious.
John is not generous.
Paul is funny or not generous.
Someone is happy.
Someone is quiet or patient.
Mary is quiet or not happy.
Someone is calm or funny.
Someone is both creative and happy.
Paul is not curious. | John is not wise. | neutral | (![X]:((happy(X)&~strong(X))=>(happy(X)<~>brave(X))))&
(((calm(paul)|curious(paul)))<=>((~patient(paul)<~>~curious(paul))))&
(((~calm(john)<~>kind(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(((~curious(john)&~quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)&~rich(X))<=>(tall(X)&~strong(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>(?[X]:((~humble(X)&~kind(X)))))&
((?[X]:((calm(X)|creative(X))))=>(?[X]:((quiet(X)|funny(X)))))&
(((~creative(mary)|~quiet(mary)))<=>(~wise(john)))&
(((~kind(susan)|tall(susan)))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((kind(X)|happy(X))<=>(~tall(X)|curious(X))))&
(![X]:((~calm(X)<~>old(X))=>~wise(X)))&
(![X]:((creative(X)|wise(X))=>(wise(X)|~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((kind(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((~old(X)|~kind(X))=>(kind(X)&~curious(X))))&
(~generous(john))&
((funny(paul)|~generous(paul)))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)|patient(X))))&
((quiet(mary)|~happy(mary)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((creative(X)&happy(X))))&
(~curious(paul)) | ~wise(john) | [] | null | 0 |
Everyone who is both rich and funny is rich or happy. If john is both generous and strong then someone is not old and vice versa. Everyone who is either not happy or not strong is brave and vice versa. Everyone who is old or creative is either not wise or generous and vice versa. Everyone who is wise is happy or not old. Everyone who is either not patient or quiet is calm. Everyone who is kind or old is both not tall and not funny and vice versa. Everyone who is patient or tall is either wise or not patient and vice versa. Everyone who is not generous is humble or kind and vice versa. Everyone who is both not curious and not patient is either not generous or not strong and vice versa. If fred is either generous or not funny then someone is both calm and not funny and vice versa. If susan is both not rich and not brave then someone is both brave and rich and vice versa. Everyone who is quiet is not curious. If someone is either not strong or rich then fred is both old and wise. If lucy is both not quiet and not happy then someone is either not brave or rich and vice versa. Everyone who is both wise and not brave is both not humble and quiet. Someone is either not curious or calm. Mary is both generous and old. Mary is not creative. Someone is rich or not tall. Alice is either brave or not strong. Someone is either calm or not calm. Alice is both not humble and not curious. | John is humble. | contradiction | (![X]:((rich(X)&funny(X))=>(rich(X)|happy(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>brave(X)))&
(![X]:((old(X)|creative(X))<=>(~wise(X)<~>generous(X))))&
(![X]:(wise(X)=>(happy(X)|~old(X))))&
(![X]:((~patient(X)<~>quiet(X))=>calm(X)))&
(![X]:((kind(X)|old(X))<=>(~tall(X)&~funny(X))))&
(![X]:((patient(X)|tall(X))<=>(wise(X)<~>~patient(X))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~generous(X)<~>~strong(X))))&
(((generous(fred)<~>~funny(fred)))<=>(?[X]:((calm(X)&~funny(X)))))&
(((~rich(susan)&~brave(susan)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~strong(X)<~>rich(X))))=>((old(fred)&wise(fred))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:((wise(X)&~brave(X))=>(~humble(X)&quiet(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
((generous(mary)&old(mary)))&
(~creative(mary))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~humble(alice)&~curious(alice))) | humble(john) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8441592591759729386863726
% SZS output start Proof for 8441592591759729386863726
2. (strong(john) & generous(john)) <=> ? [X0] : ~old(X0) [input p1]
4. ! [X0] : ((creative(X0) | old(X0)) <=> (~wise(X0) <~> generous(X0))) [input p3]
7. ! [X0] : ((old(X0) | kind(X0)) <=> (~funny(X0) & ~tall(X0))) [input p6]
8. ! [X0] : ((tall(X0) | patient(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (kind(X0) | humble(X0))) [input p8]
24. humble(john) [input hypothesis]
34. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~strong(john) | ~generous(john))) [nnf transformation 2]
35. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~strong(john) | ~generous(john)) [flattening 34]
36. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~strong(john) | ~generous(john)) [rectify 35]
37. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
38. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (~old(sK0) | ~strong(john) | ~generous(john)) [skolemisation 36,37]
40. ! [X0] : (((creative(X0) | old(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [nnf transformation 4]
41. ! [X0] : ((creative(X0) | old(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [flattening 40]
43. ! [X0] : (((old(X0) | kind(X0)) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : ((old(X0) | kind(X0) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [flattening 43]
45. ! [X0] : (((tall(X0) | patient(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [nnf transformation 8]
46. ! [X0] : ((tall(X0) | patient(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [flattening 45]
47. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & ((kind(X0) | humble(X0)) | generous(X0))) [nnf transformation 9]
48. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & (kind(X0) | humble(X0) | generous(X0))) [flattening 47]
77. generous(john) | old(X0) [cnf transformation 38]
83. ~wise(X0) | generous(X0) | ~old(X0) [cnf transformation 41]
93. ~tall(X0) | ~old(X0) [cnf transformation 44]
97. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 46]
102. tall(X0) | patient(X0) | wise(X0) | patient(X0) [cnf transformation 46]
104. ~humble(X0) | ~generous(X0) [cnf transformation 48]
147. humble(john) [cnf transformation 24]
148. ~patient(X0) | wise(X0) [duplicate literal removal 97]
149. tall(X0) | patient(X0) | wise(X0) [duplicate literal removal 102]
151. 1 <=> ! [X0] : old(X0) [avatar definition]
152. old(X0) <- (1) [avatar component clause 151]
159. 3 <=> generous(john) [avatar definition]
160. ~generous(john) <- (~3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 77,159,151]
289. ~generous(john) [resolution 104,147]
292. ~3 [avatar split clause 289,159]
431. patient(X2) | wise(X2) | ~old(X2) [resolution 149,93]
436. patient(X2) | wise(X2) <- (1) [subsumption resolution 431,152]
437. wise(X2) <- (1) [subsumption resolution 436,148]
474. generous(X3) | ~old(X3) <- (1) [resolution 437,83]
480. generous(X3) <- (1) [subsumption resolution 474,152]
555. $false <- (1, ~3) [resolution 480,160]
558. ~1 | 3 [avatar contradiction clause 555]
559. $false [avatar sat refutation 162,292,558]
% SZS output end Proof for 8441592591759729386863726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not brave then someone is quiet or brave.
Everyone who is either tall or not wise is generous or patient and vice versa.
If someone is both old and not calm then lucy is not tall or curious and vice versa.
Everyone who is not quiet is patient or brave and vice versa.
If someone is either happy or not strong then someone is creative or humble.
Everyone who is either not quiet or old is not kind or funny and vice versa.
If paul is generous then someone is patient or strong.
If fred is not patient or creative then someone is either not curious or happy and vice versa.
Everyone who is not patient is brave and vice versa.
If alice is either not quiet or rich then mary is tall or patient.
Everyone who is both not rich and brave is either not old or not wise.
Everyone who is either not wise or not curious is either not kind or funny and vice versa.
Everyone who is either quiet or not rich is funny and vice versa.
Everyone who is not quiet or not rich is either not kind or creative.
Everyone who is generous or curious is both wise and not generous.
Everyone who is brave or not quiet is both humble and not funny and vice versa.
Someone is old or not humble.
Someone is both not kind and humble.
Someone is not strong or not kind.
Paul is both not strong and kind.
Someone is both happy and not patient. | Mary is not generous. | entailment | ((?[X]:((~creative(X)&~brave(X))))=>(?[X]:((quiet(X)|brave(X)))))&
(![X]:((tall(X)<~>~wise(X))<=>(generous(X)|patient(X))))&
((?[X]:((old(X)&~calm(X))))<=>((~tall(lucy)|curious(lucy))))&
(![X]:(~quiet(X)<=>(patient(X)|brave(X))))&
((?[X]:((happy(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((~quiet(X)<~>old(X))<=>(~kind(X)|funny(X))))&
((generous(paul))=>(?[X]:((patient(X)|strong(X)))))&
(((~patient(fred)|creative(fred)))<=>(?[X]:((~curious(X)<~>happy(X)))))&
(![X]:(~patient(X)<=>brave(X)))&
(((~quiet(alice)<~>rich(alice)))=>((tall(mary)|patient(mary))))&
(![X]:((~rich(X)&brave(X))=>(~old(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~kind(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>funny(X)))&
(![X]:((~quiet(X)|~rich(X))=>(~kind(X)<~>creative(X))))&
(![X]:((generous(X)|curious(X))=>(wise(X)&~generous(X))))&
(![X]:((brave(X)|~quiet(X))<=>(humble(X)&~funny(X))))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~strong(X)|~kind(X))))&
((~strong(paul)&kind(paul)))&
(?[X]:((happy(X)&~patient(X)))) | ~generous(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1813488289289307049133730
% SZS output start Proof for 1813488289289307049133730
15. ! [X0] : ((curious(X0) | generous(X0)) => (~generous(X0) & wise(X0))) [input p14]
22. generous(mary) [input hypothesis]
33. ! [X0] : ((~generous(X0) & wise(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 15]
129. ~generous(X0) | ~generous(X0) [cnf transformation 33]
144. generous(mary) [cnf transformation 22]
145. ~generous(X0) [duplicate literal removal 129]
276. $false [subsumption resolution 144,145]
% SZS output end Proof for 1813488289289307049133730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and not humble is both calm and not brave.
Everyone who is rich is both tall and curious.
Everyone who is not rich is not creative.
Everyone who is not calm or calm is patient.
If someone is tall or not humble then someone is either not quiet or not happy and vice versa.
Everyone who is both not calm and kind is both not generous and humble.
If someone is both quiet and not generous then someone is not rich.
If paul is not happy then someone is quiet and vice versa.
Everyone who is not rich is both generous and rich and vice versa.
Everyone who is not rich is both creative and not old and vice versa.
Everyone who is strong or kind is either not curious or patient and vice versa.
If lucy is both not quiet and wise then someone is either not tall or not calm and vice versa.
Everyone who is patient or not calm is not kind.
If mary is not rich then mary is not happy or not patient and vice versa.
Everyone who is both quiet and not rich is both not funny and rich.
Lucy is either kind or happy.
Lucy is rich or not tall.
Paul is either old or not brave.
Someone is either tall or wise.
Lucy is not old. | Mary is not quiet. | entailment | (![X]:((~brave(X)&~humble(X))=>(calm(X)&~brave(X))))&
(![X]:(rich(X)=>(tall(X)&curious(X))))&
(![X]:(~rich(X)=>~creative(X)))&
(![X]:((~calm(X)|calm(X))=>patient(X)))&
((?[X]:((tall(X)|~humble(X))))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:((~calm(X)&kind(X))=>(~generous(X)&humble(X))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:(~rich(X))))&
((~happy(paul))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>(generous(X)&rich(X))))&
(![X]:(~rich(X)<=>(creative(X)&~old(X))))&
(![X]:((strong(X)|kind(X))<=>(~curious(X)<~>patient(X))))&
(((~quiet(lucy)&wise(lucy)))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((patient(X)|~calm(X))=>~kind(X)))&
((~rich(mary))<=>((~happy(mary)|~patient(mary))))&
(![X]:((quiet(X)&~rich(X))=>(~funny(X)&rich(X))))&
((kind(lucy)<~>happy(lucy)))&
((rich(lucy)|~tall(lucy)))&
((old(paul)<~>~brave(paul)))&
(?[X]:((tall(X)<~>wise(X))))&
(~old(lucy)) | ~quiet(mary) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6562381365206605636300515
% SZS output start Proof for 6562381365206605636300515
7. ? [X0] : (~generous(X0) & quiet(X0)) => ? [X0] : ~rich(X0) [input p6]
9. ! [X0] : (~rich(X0) <=> (rich(X0) & generous(X0))) [input p8]
21. quiet(mary) [input hypothesis]
23. ? [X0] : (~generous(X0) & quiet(X0)) => ? [X1] : ~rich(X1) [rectify 7]
32. ? [X1] : ~rich(X1) | ! [X0] : (generous(X0) | ~quiet(X0)) [ennf transformation 23]
41. ? [X0] : ~rich(X0) | ! [X1] : (generous(X1) | ~quiet(X1)) [rectify 32]
42. ? [X0] : ~rich(X0) => ~rich(sK2) [choice axiom]
43. ~rich(sK2) | ! [X1] : (generous(X1) | ~quiet(X1)) [skolemisation 41,42]
48. ! [X0] : ((~rich(X0) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | rich(X0))) [nnf transformation 9]
49. ! [X0] : ((~rich(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | rich(X0))) [flattening 48]
81. ~rich(sK2) | generous(X1) | ~quiet(X1) [cnf transformation 43]
85. rich(X0) | rich(X0) [cnf transformation 49]
86. ~rich(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 49]
116. quiet(mary) [cnf transformation 21]
118. rich(X0) [duplicate literal removal 85]
119. ~generous(X0) | ~rich(X0) [duplicate literal removal 86]
156. 9 <=> ! [X1] : (generous(X1) | ~quiet(X1)) [avatar definition]
157. ~quiet(X1) | generous(X1) <- (9) [avatar component clause 156]
159. 10 <=> rich(sK2) [avatar definition]
161. ~rich(sK2) <- (~10) [avatar component clause 159]
162. 9 | ~10 [avatar split clause 81,159,156]
231. $false <- (~10) [subsumption resolution 161,118]
232. 10 [avatar contradiction clause 231]
239. generous(mary) <- (9) [resolution 157,116]
241. ~rich(mary) <- (9) [resolution 239,119]
242. $false <- (9) [subsumption resolution 241,118]
243. ~9 [avatar contradiction clause 242]
244. $false [avatar sat refutation 162,232,243]
% SZS output end Proof for 6562381365206605636300515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and tall then someone is funny or creative and vice versa.
If someone is creative then someone is either happy or kind and vice versa.
If susan is either strong or not humble then mary is not funny or not generous.
Everyone who is both generous and not funny is both creative and not happy.
Everyone who is funny or rich is either not old or generous.
Everyone who is happy or not brave is not happy or not kind.
Everyone who is either humble or brave is either calm or not wise and vice versa.
If mary is not funny then someone is not rich or not strong and vice versa.
Everyone who is quiet or generous is both not wise and generous.
Everyone who is funny or not quiet is either wise or not old and vice versa.
If someone is generous or not tall then lucy is not quiet.
Everyone who is not brave is both not funny and not generous and vice versa.
Everyone who is creative is both not curious and curious and vice versa.
If someone is tall then fred is both old and not happy.
If someone is generous or funny then someone is either funny or not funny and vice versa.
If someone is either rich or curious then someone is not curious and vice versa.
Someone is either not curious or not humble.
Someone is not wise.
Susan is both not curious and not brave.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old. | Mary is not generous. | entailment | ((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((funny(X)|creative(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(((strong(susan)<~>~humble(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((generous(X)&~funny(X))=>(creative(X)&~happy(X))))&
(![X]:((funny(X)|rich(X))=>(~old(X)<~>generous(X))))&
(![X]:((happy(X)|~brave(X))=>(~happy(X)|~kind(X))))&
(![X]:((humble(X)<~>brave(X))<=>(calm(X)<~>~wise(X))))&
((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X)))) | ~generous(mary) | [
"p3",
"p7",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 737619293046222359514811
% SZS output start Proof for 737619293046222359514811
4. ! [X0] : ((~funny(X0) & generous(X0)) => (~happy(X0) & creative(X0))) [input p3]
8. ~funny(mary) <=> ? [X0] : (~strong(X0) | ~rich(X0)) [input p7]
13. ! [X0] : (creative(X0) <=> (curious(X0) & ~curious(X0))) [input p12]
20. ? [X0] : ~strong(X0) [input p19]
24. generous(mary) [input hypothesis]
32. ! [X0] : ((~happy(X0) & creative(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & creative(X0)) | funny(X0) | ~generous(X0)) [flattening 32]
53. (~funny(mary) | ! [X0] : (strong(X0) & rich(X0))) & (? [X0] : (~strong(X0) | ~rich(X0)) | funny(mary)) [nnf transformation 8]
54. (~funny(mary) | ! [X0] : (strong(X0) & rich(X0))) & (? [X1] : (~strong(X1) | ~rich(X1)) | funny(mary)) [rectify 53]
55. ? [X1] : (~strong(X1) | ~rich(X1)) => (~strong(sK4) | ~rich(sK4)) [choice axiom]
56. (~funny(mary) | ! [X0] : (strong(X0) & rich(X0))) & ((~strong(sK4) | ~rich(sK4)) | funny(mary)) [skolemisation 54,55]
61. ! [X0] : ((creative(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [nnf transformation 13]
62. ! [X0] : ((creative(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [flattening 61]
78. ? [X0] : ~strong(X0) => ~strong(sK11) [choice axiom]
79. ~strong(sK11) [skolemisation 20,78]
95. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 33]
113. ~funny(mary) | strong(X0) [cnf transformation 56]
129. ~curious(X0) | ~creative(X0) [cnf transformation 62]
130. ~creative(X0) | curious(X0) [cnf transformation 62]
149. ~strong(sK11) [cnf transformation 79]
152. generous(mary) [cnf transformation 24]
157. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
158. ~creative(X1) <- (1) [avatar component clause 157]
217. 15 <=> funny(mary) [avatar definition]
221. 16 <=> generous(mary) [avatar definition]
222. generous(mary) <- (16) [avatar component clause 221]
227. 17 <=> ! [X0] : strong(X0) [avatar definition]
228. strong(X0) <- (17) [avatar component clause 227]
229. 17 | ~15 [avatar split clause 113,217,227]
257. ~creative(X0) [subsumption resolution 129,130]
258. 1 [avatar split clause 257,157]
338. 16 [avatar split clause 152,221]
353. funny(mary) | creative(mary) <- (16) [resolution 95,222]
363. funny(mary) <- (1, 16) [subsumption resolution 353,158]
364. 15 | ~1 | ~16 [avatar split clause 363,221,157,217]
370. $false <- (17) [resolution 228,149]
371. ~17 [avatar contradiction clause 370]
372. $false [avatar sat refutation 229,258,338,364,371]
% SZS output end Proof for 737619293046222359514811
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not quiet is either not brave or kind.
If mary is either wise or not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Everyone who is either not wise or not calm is either not curious or wise.
Everyone who is tall is both strong and not happy.
Everyone who is not humble or old is not rich and vice versa.
Everyone who is both strong and not rich is either not generous or creative and vice versa.
Everyone who is either not brave or patient is both rich and not kind and vice versa.
If someone is either humble or rich then lucy is quiet or not funny.
If someone is either kind or not kind then alice is quiet or not happy.
Everyone who is kind is either not quiet or happy.
If alice is quiet then john is either not old or not generous and vice versa.
Everyone who is not generous is quiet or wise and vice versa.
If lucy is either not kind or not happy then someone is not wise.
Everyone who is both not generous and not strong is calm or kind and vice versa.
Everyone who is not rich is either generous or quiet and vice versa.
Someone is either brave or not strong.
Susan is both not funny and not kind.
Susan is not old.
Someone is either not generous or generous.
Someone is either happy or humble.
Fred is either tall or not old.
Someone is wise or not brave.
Paul is either not happy or not tall. | John is not curious. | neutral | (![X]:((~tall(X)|~quiet(X))=>(~brave(X)<~>kind(X))))&
(((wise(mary)<~>~old(mary)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(![X]:((~wise(X)<~>~calm(X))=>(~curious(X)<~>wise(X))))&
(![X]:(tall(X)=>(strong(X)&~happy(X))))&
(![X]:((~humble(X)|old(X))<=>~rich(X)))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(rich(X)&~kind(X))))&
((?[X]:((humble(X)<~>rich(X))))=>((quiet(lucy)|~funny(lucy))))&
((?[X]:((kind(X)<~>~kind(X))))=>((quiet(alice)|~happy(alice))))&
(![X]:(kind(X)=>(~quiet(X)<~>happy(X))))&
((quiet(alice))<=>((~old(john)<~>~generous(john))))&
(![X]:(~generous(X)<=>(quiet(X)|wise(X))))&
(((~kind(lucy)<~>~happy(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>(calm(X)|kind(X))))&
(![X]:(~rich(X)<=>(generous(X)<~>quiet(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
((~funny(susan)&~kind(susan)))&
(~old(susan))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((tall(fred)<~>~old(fred)))&
(?[X]:((wise(X)|~brave(X))))&
((~happy(paul)<~>~tall(paul))) | ~curious(john) | [] | null | 0 |
Everyone who is funny is not humble or wise and vice versa.
Everyone who is creative or kind is both quiet and strong and vice versa.
Everyone who is both old and not humble is not wise and vice versa.
If someone is both creative and not kind then paul is old or brave and vice versa.
If fred is both not rich and old then paul is both old and funny.
Everyone who is both not patient and strong is both quiet and not wise.
If fred is curious or not strong then lucy is both rich and not creative and vice versa.
Everyone who is both not wise and curious is either not quiet or not creative and vice versa.
Everyone who is either not funny or not calm is both rich and not creative.
If john is both not creative and patient then john is not strong and vice versa.
Everyone who is not generous is wise and vice versa.
Everyone who is not generous is either generous or funny.
If paul is humble then mary is quiet or curious and vice versa.
If fred is not strong or not humble then someone is quiet or not generous and vice versa.
If paul is patient then someone is not humble or happy.
Everyone who is either not creative or not generous is quiet or curious.
Lucy is both not brave and funny.
Someone is both not brave and not creative.
Susan is not creative.
Someone is not old or funny.
John is both rich and patient.
Someone is both generous and quiet.
Susan is either humble or not wise.
John is not calm. | Susan is not wise. | neutral | (![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(![X]:((creative(X)|kind(X))<=>(quiet(X)&strong(X))))&
(![X]:((old(X)&~humble(X))<=>~wise(X)))&
((?[X]:((creative(X)&~kind(X))))<=>((old(paul)|brave(paul))))&
(((~rich(fred)&old(fred)))=>((old(paul)&funny(paul))))&
(![X]:((~patient(X)&strong(X))=>(quiet(X)&~wise(X))))&
(((curious(fred)|~strong(fred)))<=>((rich(lucy)&~creative(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(rich(X)&~creative(X))))&
(((~creative(john)&patient(john)))<=>(~strong(john)))&
(![X]:(~generous(X)<=>wise(X)))&
(![X]:(~generous(X)=>(generous(X)<~>funny(X))))&
((humble(paul))<=>((quiet(mary)|curious(mary))))&
(((~strong(fred)|~humble(fred)))<=>(?[X]:((quiet(X)|~generous(X)))))&
((patient(paul))=>(?[X]:((~humble(X)|happy(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(quiet(X)|curious(X))))&
((~brave(lucy)&funny(lucy)))&
(?[X]:((~brave(X)&~creative(X))))&
(~creative(susan))&
(?[X]:((~old(X)|funny(X))))&
((rich(john)&patient(john)))&
(?[X]:((generous(X)&quiet(X))))&
((humble(susan)<~>~wise(susan)))&
(~calm(john)) | ~wise(susan) | [] | null | 0 |
Everyone who is both funny and old is not strong or not happy and vice versa.
Everyone who is calm or kind is both tall and not rich and vice versa.
If susan is both not wise and not happy then someone is not strong.
If fred is curious or kind then someone is both not old and not funny.
Everyone who is both not old and happy is rich.
If susan is either creative or calm then lucy is both creative and wise and vice versa.
Everyone who is not strong or happy is both creative and not wise and vice versa.
Everyone who is kind is not generous or creative.
If someone is both not strong and kind then someone is kind and vice versa.
If someone is both generous and not generous then someone is kind or not calm.
If someone is strong or old then fred is humble.
Everyone who is generous or not wise is either happy or not wise.
Everyone who is not patient is quiet or not curious.
Everyone who is either not kind or old is both not brave and not old and vice versa.
Everyone who is brave or not curious is both not wise and not brave and vice versa.
Everyone who is both not creative and not humble is not rich and vice versa.
Alice is not creative.
Someone is not generous.
Susan is both old and not tall.
John is calm.
Someone is not creative or generous.
Someone is both quiet and not creative. | Alice is curious. | neutral | (![X]:((funny(X)&old(X))<=>(~strong(X)|~happy(X))))&
(![X]:((calm(X)|kind(X))<=>(tall(X)&~rich(X))))&
(((~wise(susan)&~happy(susan)))=>(?[X]:(~strong(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((~old(X)&happy(X))=>rich(X)))&
(((creative(susan)<~>calm(susan)))<=>((creative(lucy)&wise(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(creative(X)&~wise(X))))&
(![X]:(kind(X)=>(~generous(X)|creative(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~generous(X))))=>(?[X]:((kind(X)|~calm(X)))))&
((?[X]:((strong(X)|old(X))))=>(humble(fred)))&
(![X]:((generous(X)|~wise(X))=>(happy(X)<~>~wise(X))))&
(![X]:(~patient(X)=>(quiet(X)|~curious(X))))&
(![X]:((~kind(X)<~>old(X))<=>(~brave(X)&~old(X))))&
(![X]:((brave(X)|~curious(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~creative(X)&~humble(X))<=>~rich(X)))&
(~creative(alice))&
(?[X]:(~generous(X)))&
((old(susan)&~tall(susan)))&
(calm(john))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:((quiet(X)&~creative(X)))) | curious(alice) | [] | null | 0 |
If someone is not rich then someone is patient or quiet.
If someone is both old and rich then someone is both curious and brave.
If paul is either not wise or tall then someone is both not creative and patient.
Everyone who is not quiet or strong is not strong.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
If john is either wise or kind then someone is rich or not kind and vice versa.
Everyone who is either not wise or curious is not brave and vice versa.
If someone is both kind and brave then lucy is not brave and vice versa.
Everyone who is either not old or curious is not kind or brave.
Fred is not funny or not tall.
Someone is either not curious or strong.
John is both not old and humble.
Lucy is both calm and not quiet.
Someone is both not patient and curious.
Someone is not funny or not creative.
Someone is either not patient or humble.
Paul is either not curious or curious. | Fred is strong. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((patient(X)|quiet(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((curious(X)&brave(X)))))&
(((~wise(paul)<~>tall(paul)))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~quiet(X)|strong(X))=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
(((wise(john)<~>kind(john)))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>~brave(X)))&
((?[X]:((kind(X)&brave(X))))<=>(~brave(lucy)))&
(![X]:((~old(X)<~>curious(X))=>(~kind(X)|brave(X))))&
((~funny(fred)|~tall(fred)))&
(?[X]:((~curious(X)<~>strong(X))))&
((~old(john)&humble(john)))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((~patient(X)&curious(X))))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:((~patient(X)<~>humble(X))))&
((~curious(paul)<~>curious(paul))) | strong(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 173344581501113216132274
% SZS output start Proof for 173344581501113216132274
4. ! [X0] : ((strong(X0) | ~quiet(X0)) => ~strong(X0)) [input p3]
25. strong(fred) [input hypothesis]
34. ! [X0] : (~strong(X0) | (~strong(X0) & quiet(X0))) [ennf transformation 4]
89. ~strong(X0) | ~strong(X0) [cnf transformation 34]
146. strong(fred) [cnf transformation 25]
149. ~strong(X0) [duplicate literal removal 89]
283. $false [subsumption resolution 146,149]
% SZS output end Proof for 173344581501113216132274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not rich and brave is either not patient or brave.
Everyone who is not kind is both generous and kind.
Everyone who is either humble or not patient is either not generous or curious and vice versa.
Everyone who is not humble or brave is both not tall and not funny.
If someone is both brave and tall then someone is either not creative or not old and vice versa.
Everyone who is quiet is patient and vice versa.
If someone is old then someone is not kind.
If fred is both old and creative then john is both happy and not patient and vice versa.
Everyone who is either not generous or not calm is kind.
If alice is not quiet then someone is either generous or quiet.
If alice is strong then alice is either brave or quiet.
If someone is happy then someone is not old and vice versa.
If susan is quiet then mary is both not humble and not happy.
If someone is humble or brave then someone is not kind and vice versa.
Everyone who is not tall or quiet is both not quiet and not rich and vice versa.
Someone is not patient.
John is both not creative and not tall.
Someone is both wise and not funny.
Someone is brave or not calm.
Mary is either not tall or wise. | Alice is not curious. | neutral | (![X]:((~rich(X)&brave(X))=>(~patient(X)<~>brave(X))))&
(![X]:(~kind(X)=>(generous(X)&kind(X))))&
(![X]:((humble(X)<~>~patient(X))<=>(~generous(X)<~>curious(X))))&
(![X]:((~humble(X)|brave(X))=>(~tall(X)&~funny(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~creative(X)<~>~old(X)))))&
(![X]:(quiet(X)<=>patient(X)))&
((?[X]:(old(X)))=>(?[X]:(~kind(X))))&
(((old(fred)&creative(fred)))<=>((happy(john)&~patient(john))))&
(![X]:((~generous(X)<~>~calm(X))=>kind(X)))&
((~quiet(alice))=>(?[X]:((generous(X)<~>quiet(X)))))&
((strong(alice))=>((brave(alice)<~>quiet(alice))))&
((?[X]:(happy(X)))<=>(?[X]:(~old(X))))&
((quiet(susan))=>((~humble(mary)&~happy(mary))))&
((?[X]:((humble(X)|brave(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)|quiet(X))<=>(~quiet(X)&~rich(X))))&
(?[X]:(~patient(X)))&
((~creative(john)&~tall(john)))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:((brave(X)|~calm(X))))&
((~tall(mary)<~>wise(mary))) | ~curious(alice) | [] | null | 0 |
Everyone who is not old or brave is both not brave and not old and vice versa. If someone is humble or happy then mary is either tall or not creative. Everyone who is not brave or kind is not funny and vice versa. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Someone is either not calm or generous. Susan is either not wise or rich. Someone is either not calm or funny. Someone is not tall. | Lucy is strong. | neutral | (![X]:((~old(X)|brave(X))<=>(~brave(X)&~old(X))))&
((?[X]:((humble(X)|happy(X))))=>((tall(mary)<~>~creative(mary))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(~tall(X))) | strong(lucy) | [] | null | 0 |
Everyone who is both kind and quiet is either wise or old and vice versa. If someone is quiet then alice is both creative and not old and vice versa. Everyone who is either brave or not patient is old or wise. Everyone who is patient is not strong or not brave and vice versa. Everyone who is both wise and happy is not old or kind and vice versa. Everyone who is either not old or not curious is not wise or not funny and vice versa. If someone is either not strong or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. If alice is calm or rich then fred is not humble or curious and vice versa. Everyone who is generous or not happy is both tall and wise and vice versa. Everyone who is both not rich and creative is creative or funny. Someone is both not patient and happy. Susan is happy. Someone is not calm or not curious. | Alice is not quiet. | entailment | (![X]:((kind(X)&quiet(X))<=>(wise(X)<~>old(X))))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
(![X]:((~rich(X)&creative(X))=>(creative(X)|funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(happy(susan))&
(?[X]:((~calm(X)|~curious(X)))) | ~quiet(alice) | [
"p0",
"p1",
"p4",
"p7",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 752940990271761238563350
% SZS output start Proof for 752940990271761238563350
1. ! [X0] : ((quiet(X0) & kind(X0)) <=> (wise(X0) <~> old(X0))) [input p0]
2. ? [X0] : quiet(X0) <=> (~old(alice) & creative(alice)) [input p1]
5. ! [X0] : ((happy(X0) & wise(X0)) <=> (kind(X0) | ~old(X0))) [input p4]
8. ! [X0] : ((~funny(X0) <~> ~generous(X0)) => (brave(X0) & funny(X0))) [input p7]
10. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (~funny(X0) & kind(X0))) [input p9]
12. ! [X0] : ((funny(X0) | rich(X0)) <=> (old(X0) | ~quiet(X0))) [input p11]
15. ! [X0] : ((~happy(X0) | generous(X0)) <=> (wise(X0) & tall(X0))) [input p14]
20. quiet(alice) [input hypothesis]
23. ! [X0] : ((brave(X0) & funny(X0)) | (~funny(X0) <=> ~generous(X0))) [ennf transformation 8]
26. ! [X0] : (((quiet(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 1]
27. ! [X0] : (((quiet(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ~quiet(X0) | ~kind(X0))) [flattening 26]
28. (? [X0] : quiet(X0) | (old(alice) | ~creative(alice))) & ((~old(alice) & creative(alice)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
29. (? [X0] : quiet(X0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X0] : ~quiet(X0)) [flattening 28]
30. (? [X0] : quiet(X0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X1] : ~quiet(X1)) [rectify 29]
31. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
32. (quiet(sK0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X1] : ~quiet(X1)) [skolemisation 30,31]
36. ! [X0] : (((happy(X0) & wise(X0)) | (~kind(X0) & old(X0))) & ((kind(X0) | ~old(X0)) | (~happy(X0) | ~wise(X0)))) [nnf transformation 5]
37. ! [X0] : (((happy(X0) & wise(X0)) | (~kind(X0) & old(X0))) & (kind(X0) | ~old(X0) | ~happy(X0) | ~wise(X0))) [flattening 36]
45. ! [X0] : ((brave(X0) & funny(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) [nnf transformation 23]
51. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 51]
57. ! [X0] : (((funny(X0) | rich(X0)) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | (~funny(X0) & ~rich(X0)))) [nnf transformation 12]
58. ! [X0] : ((funny(X0) | rich(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | (~funny(X0) & ~rich(X0)))) [flattening 57]
63. ! [X0] : (((~happy(X0) | generous(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 15]
64. ! [X0] : ((~happy(X0) | generous(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (happy(X0) & ~generous(X0)))) [flattening 63]
71. ~wise(X0) | old(X0) | kind(X0) [cnf transformation 27]
76. ~old(alice) | ~quiet(X1) [cnf transformation 32]
84. old(X0) | wise(X0) [cnf transformation 37]
87. ~kind(X0) | happy(X0) [cnf transformation 37]
100. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 45]
112. tall(X0) | ~happy(X0) | funny(X0) | ~kind(X0) [cnf transformation 52]
119. ~funny(X0) | ~quiet(X0) | old(X0) [cnf transformation 58]
136. ~tall(X0) | generous(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 64]
142. quiet(alice) [cnf transformation 20]
143. ~generous(X0) | funny(X0) [duplicate literal removal 100]
149. 2 <=> old(alice) [avatar definition]
150. ~old(alice) <- (~2) [avatar component clause 149]
158. 4 <=> ! [X1] : ~quiet(X1) [avatar definition]
159. ~quiet(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 [avatar split clause 76,149,158]
179. 8 <=> kind(alice) [avatar definition]
181. kind(alice) <- (8) [avatar component clause 179]
209. ~kind(X0) | funny(X0) | tall(X0) [subsumption resolution 112,87]
262. $false <- (4) [resolution 159,142]
263. ~4 [avatar contradiction clause 262]
266. wise(alice) <- (~2) [resolution 84,150]
267. old(alice) | kind(alice) <- (~2) [resolution 71,266]
268. kind(alice) <- (~2) [subsumption resolution 267,150]
271. 8 | 2 [avatar split clause 268,149,179]
272. happy(alice) <- (8) [resolution 181,87]
432. funny(alice) | tall(alice) <- (8) [resolution 209,181]
436. 37 <=> tall(alice) [avatar definition]
438. tall(alice) <- (37) [avatar component clause 436]
440. 38 <=> funny(alice) [avatar definition]
441. ~funny(alice) <- (~38) [avatar component clause 440]
442. funny(alice) <- (38) [avatar component clause 440]
443. 37 | 38 | ~8 [avatar split clause 432,179,440,436]
552. generous(alice) | ~wise(alice) | ~happy(alice) <- (37) [resolution 136,438]
555. generous(alice) | ~happy(alice) <- (~2, 37) [subsumption resolution 552,266]
556. generous(alice) <- (~2, 8, 37) [subsumption resolution 555,272]
576. funny(alice) <- (~2, 8, 37) [resolution 556,143]
580. $false <- (~2, 8, 37, ~38) [subsumption resolution 576,441]
581. 2 | ~8 | ~37 | 38 [avatar contradiction clause 580]
585. ~quiet(alice) | old(alice) <- (38) [resolution 442,119]
589. old(alice) <- (38) [subsumption resolution 585,142]
590. $false <- (~2, 38) [subsumption resolution 589,150]
591. 2 | ~38 [avatar contradiction clause 590]
601. $false [avatar sat refutation 160,263,271,443,581,591]
% SZS output end Proof for 752940990271761238563350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not patient and quiet.
If susan is strong then fred is not quiet.
If someone is both not brave and not patient then someone is not generous.
If alice is either not creative or old then susan is humble and vice versa.
Everyone who is not calm is both not funny and brave.
If someone is either not generous or creative then mary is both old and quiet.
Everyone who is both not kind and funny is either not happy or not rich.
Everyone who is both kind and old is not strong.
Everyone who is both not funny and not generous is either happy or not creative and vice versa.
Everyone who is both patient and humble is both not strong and not kind.
If susan is either funny or not humble then someone is wise.
If paul is both not patient and not funny then someone is either not old or humble.
Everyone who is either not funny or not humble is not humble.
Everyone who is not quiet or funny is not patient and vice versa.
Everyone who is tall is either not kind or quiet.
If mary is not old then someone is either not humble or not generous and vice versa.
John is funny.
Someone is both tall and kind.
Someone is generous or wise.
Someone is not curious.
Mary is tall or old.
Alice is not rich or calm.
Mary is either rich or tall.
Someone is not wise. | Alice is calm. | neutral | (![X]:(~wise(X)=>(~patient(X)&quiet(X))))&
((strong(susan))=>(~quiet(fred)))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:(~generous(X))))&
(((~creative(alice)<~>old(alice)))<=>(humble(susan)))&
(![X]:(~calm(X)=>(~funny(X)&brave(X))))&
((?[X]:((~generous(X)<~>creative(X))))=>((old(mary)&quiet(mary))))&
(![X]:((~kind(X)&funny(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((kind(X)&old(X))=>~strong(X)))&
(![X]:((~funny(X)&~generous(X))<=>(happy(X)<~>~creative(X))))&
(![X]:((patient(X)&humble(X))=>(~strong(X)&~kind(X))))&
(((funny(susan)<~>~humble(susan)))=>(?[X]:(wise(X))))&
(((~patient(paul)&~funny(paul)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~funny(X)<~>~humble(X))=>~humble(X)))&
(![X]:((~quiet(X)|funny(X))<=>~patient(X)))&
(![X]:(tall(X)=>(~kind(X)<~>quiet(X))))&
((~old(mary))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
(funny(john))&
(?[X]:((tall(X)&kind(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:(~curious(X)))&
((tall(mary)|old(mary)))&
((~rich(alice)|calm(alice)))&
((rich(mary)<~>tall(mary)))&
(?[X]:(~wise(X))) | calm(alice) | [] | null | 0 |
Everyone who is not kind is both not rich and generous and vice versa.
Everyone who is not rich is not curious or happy.
If someone is funny then mary is both calm and not curious and vice versa.
If someone is calm or tall then lucy is not patient or happy and vice versa.
Everyone who is either patient or happy is both strong and not rich.
Everyone who is curious is either humble or quiet.
Everyone who is quiet or strong is both not wise and not curious and vice versa.
If lucy is calm or wise then lucy is both happy and not tall.
Everyone who is not strong is either brave or not strong.
If someone is both creative and wise then mary is calm or wise and vice versa.
If susan is quiet then someone is funny and vice versa.
Everyone who is calm is either calm or strong.
Everyone who is not rich or curious is both kind and not patient and vice versa.
If someone is wise then susan is tall.
Everyone who is creative or humble is wise and vice versa.
Everyone who is not curious is both wise and old.
Someone is not funny.
Fred is not old or rich.
Someone is either not happy or not rich.
John is curious or not calm.
Someone is not quiet. | Mary is not wise. | contradiction | (![X]:(~kind(X)<=>(~rich(X)&generous(X))))&
(![X]:(~rich(X)=>(~curious(X)|happy(X))))&
((?[X]:(funny(X)))<=>((calm(mary)&~curious(mary))))&
((?[X]:((calm(X)|tall(X))))<=>((~patient(lucy)|happy(lucy))))&
(![X]:((patient(X)<~>happy(X))=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(humble(X)<~>quiet(X))))&
(![X]:((quiet(X)|strong(X))<=>(~wise(X)&~curious(X))))&
(((calm(lucy)|wise(lucy)))=>((happy(lucy)&~tall(lucy))))&
(![X]:(~strong(X)=>(brave(X)<~>~strong(X))))&
((?[X]:((creative(X)&wise(X))))<=>((calm(mary)|wise(mary))))&
((quiet(susan))<=>(?[X]:(funny(X))))&
(![X]:(calm(X)=>(calm(X)<~>strong(X))))&
(![X]:((~rich(X)|curious(X))<=>(kind(X)&~patient(X))))&
((?[X]:(wise(X)))=>(tall(susan)))&
(![X]:((creative(X)|humble(X))<=>wise(X)))&
(![X]:(~curious(X)=>(wise(X)&old(X))))&
(?[X]:(~funny(X)))&
((~old(fred)|rich(fred)))&
(?[X]:((~happy(X)<~>~rich(X))))&
((curious(john)|~calm(john)))&
(?[X]:(~quiet(X))) | ~wise(mary) | [
"p5",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2414884851484409995409004
% SZS output start Proof for 2414884851484409995409004
6. ! [X0] : (curious(X0) => (humble(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : ((strong(X0) | quiet(X0)) <=> (~curious(X0) & ~wise(X0))) [input p6]
15. ! [X0] : ((humble(X0) | creative(X0)) <=> wise(X0)) [input p14]
16. ! [X0] : (~curious(X0) => (old(X0) & wise(X0))) [input p15]
22. ~wise(mary) [input hypothesis]
26. ! [X0] : ((humble(X0) <~> quiet(X0)) | ~curious(X0)) [ennf transformation 6]
31. ! [X0] : ((old(X0) & wise(X0)) | curious(X0)) [ennf transformation 16]
45. ! [X0] : (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ~curious(X0)) [nnf transformation 26]
46. ! [X0] : (((strong(X0) | quiet(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (~strong(X0) & ~quiet(X0)))) [nnf transformation 7]
47. ! [X0] : ((strong(X0) | quiet(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | (~strong(X0) & ~quiet(X0)))) [flattening 46]
61. ! [X0] : (((humble(X0) | creative(X0)) | ~wise(X0)) & (wise(X0) | (~humble(X0) & ~creative(X0)))) [nnf transformation 15]
62. ! [X0] : ((humble(X0) | creative(X0) | ~wise(X0)) & (wise(X0) | (~humble(X0) & ~creative(X0)))) [flattening 61]
85. ~curious(X0) | humble(X0) | quiet(X0) [cnf transformation 45]
87. ~wise(X0) | ~quiet(X0) [cnf transformation 47]
89. ~quiet(X0) | ~curious(X0) [cnf transformation 47]
114. ~humble(X0) | wise(X0) [cnf transformation 62]
116. wise(X0) | curious(X0) [cnf transformation 31]
124. ~wise(mary) [cnf transformation 22]
132. 2 <=> curious(mary) [avatar definition]
134. curious(mary) <- (2) [avatar component clause 132]
188. 14 <=> wise(mary) [avatar definition]
190. ~wise(mary) <- (~14) [avatar component clause 188]
255. ~14 [avatar split clause 124,188]
257. curious(X1) | ~quiet(X1) [resolution 116,87]
260. ~quiet(X1) [subsumption resolution 257,89]
279. curious(mary) <- (~14) [resolution 190,116]
280. 2 | 14 [avatar split clause 279,188,132]
310. humble(mary) | quiet(mary) <- (2) [resolution 85,134]
313. humble(mary) <- (2) [subsumption resolution 310,260]
316. wise(mary) <- (2) [resolution 313,114]
317. $false <- (2, ~14) [subsumption resolution 316,190]
318. ~2 | 14 [avatar contradiction clause 317]
319. $false [avatar sat refutation 255,280,318]
% SZS output end Proof for 2414884851484409995409004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then alice is not tall or not wise and vice versa.
Everyone who is not brave or not old is not rich or not old and vice versa.
If someone is not humble then fred is not creative or not brave and vice versa.
Everyone who is not kind is both rich and calm.
Everyone who is both not rich and not happy is both rich and not old and vice versa.
If john is patient or quiet then someone is both old and not calm and vice versa.
If paul is both not funny and not tall then someone is strong or kind.
If someone is both creative and quiet then john is both not rich and old.
If mary is not calm or tall then someone is brave or not creative and vice versa.
Everyone who is not tall or not rich is not generous or not old.
If someone is both brave and not strong then paul is both brave and not calm and vice versa.
If someone is either not tall or not brave then susan is not brave and vice versa.
Everyone who is quiet or wise is either curious or rich and vice versa.
If someone is rich then lucy is funny or not humble.
Everyone who is not brave is tall and vice versa.
Everyone who is either not curious or creative is both humble and not generous and vice versa.
Someone is wise.
Alice is curious.
Fred is either wise or generous.
Alice is either strong or generous.
Alice is tall.
Paul is either not brave or not happy.
Mary is either quiet or not rich.
Mary is kind. | Susan is brave. | contradiction | ((?[X]:(humble(X)))<=>((~tall(alice)|~wise(alice))))&
(![X]:((~brave(X)|~old(X))<=>(~rich(X)|~old(X))))&
((?[X]:(~humble(X)))<=>((~creative(fred)|~brave(fred))))&
(![X]:(~kind(X)=>(rich(X)&calm(X))))&
(![X]:((~rich(X)&~happy(X))<=>(rich(X)&~old(X))))&
(((patient(john)|quiet(john)))<=>(?[X]:((old(X)&~calm(X)))))&
(((~funny(paul)&~tall(paul)))=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((creative(X)&quiet(X))))=>((~rich(john)&old(john))))&
(((~calm(mary)|tall(mary)))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((~tall(X)|~rich(X))=>(~generous(X)|~old(X))))&
((?[X]:((brave(X)&~strong(X))))<=>((brave(paul)&~calm(paul))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(~brave(susan)))&
(![X]:((quiet(X)|wise(X))<=>(curious(X)<~>rich(X))))&
((?[X]:(rich(X)))=>((funny(lucy)|~humble(lucy))))&
(![X]:(~brave(X)<=>tall(X)))&
(![X]:((~curious(X)<~>creative(X))<=>(humble(X)&~generous(X))))&
(?[X]:(wise(X)))&
(curious(alice))&
((wise(fred)<~>generous(fred)))&
((strong(alice)<~>generous(alice)))&
(tall(alice))&
((~brave(paul)<~>~happy(paul)))&
((quiet(mary)<~>~rich(mary)))&
(kind(mary)) | brave(susan) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8235365300556906497215327
% SZS output start Proof for 8235365300556906497215327
12. ? [X0] : (~tall(X0) <~> ~brave(X0)) <=> ~brave(susan) [input p11]
15. ! [X0] : (~brave(X0) <=> tall(X0)) [input p14]
25. brave(susan) [input hypothesis]
62. (? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | brave(susan)) & (~brave(susan) | ! [X0] : ((~tall(X0) | brave(X0)) & (~brave(X0) | tall(X0)))) [nnf transformation 12]
63. (? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | brave(susan)) & (~brave(susan) | ! [X1] : ((~tall(X1) | brave(X1)) & (~brave(X1) | tall(X1)))) [rectify 62]
64. ? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) => ((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) [choice axiom]
65. (((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) | brave(susan)) & (~brave(susan) | ! [X1] : ((~tall(X1) | brave(X1)) & (~brave(X1) | tall(X1)))) [skolemisation 63,64]
68. ! [X0] : ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))) [nnf transformation 15]
108. ~brave(susan) | ~brave(X1) | tall(X1) [cnf transformation 65]
109. ~brave(susan) | ~tall(X1) | brave(X1) [cnf transformation 65]
118. brave(X0) | tall(X0) [cnf transformation 68]
119. ~brave(X0) | ~tall(X0) [cnf transformation 68]
137. brave(susan) [cnf transformation 25]
263. 28 <=> brave(susan) [avatar definition]
277. 31 <=> ! [X1] : (~tall(X1) | brave(X1)) [avatar definition]
278. ~tall(X1) | brave(X1) <- (31) [avatar component clause 277]
279. 31 | ~28 [avatar split clause 109,263,277]
281. 32 <=> ! [X1] : (~brave(X1) | tall(X1)) [avatar definition]
282. ~brave(X1) | tall(X1) <- (32) [avatar component clause 281]
283. 32 | ~28 [avatar split clause 108,263,281]
321. 28 [avatar split clause 137,263]
322. tall(X1) <- (32) [subsumption resolution 282,118]
323. brave(X1) <- (31, 32) [subsumption resolution 278,322]
325. ~tall(X1) <- (31, 32) [resolution 119,323]
326. $false <- (31, 32) [subsumption resolution 325,322]
327. ~31 | ~32 [avatar contradiction clause 326]
328. $false [avatar sat refutation 279,283,321,327]
% SZS output end Proof for 8235365300556906497215327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is either not quiet or not humble and vice versa. If someone is both curious and not generous then someone is both quiet and rich and vice versa. Everyone who is both not funny and wise is funny and vice versa. Everyone who is not rich is wise. If someone is both not curious and quiet then alice is not quiet or brave. If alice is either not generous or not brave then mary is not wise. Everyone who is not kind or not old is wise or rich. If fred is both not calm and strong then mary is calm and vice versa. Everyone who is either funny or happy is not quiet or not funny. If someone is either not brave or quiet then paul is either tall or not wise and vice versa. Everyone who is both wise and kind is both not humble and wise. Everyone who is happy is either wise or old and vice versa. If alice is not strong or creative then someone is creative and vice versa. Everyone who is not creative or not curious is not calm and vice versa. If someone is not wise or not brave then someone is not wise or old and vice versa. Everyone who is not kind is both quiet and tall. Someone is not rich or not curious. Someone is both not creative and tall. John is either quiet or rich. Someone is either not calm or not strong. Someone is not humble or not happy. Mary is strong. Someone is both brave and not curious. Mary is either calm or creative. | Fred is generous. | neutral | (![X]:((strong(X)<~>~rich(X))<=>(~quiet(X)<~>~humble(X))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:((~funny(X)&wise(X))<=>funny(X)))&
(![X]:(~rich(X)=>wise(X)))&
((?[X]:((~curious(X)&quiet(X))))=>((~quiet(alice)|brave(alice))))&
(((~generous(alice)<~>~brave(alice)))=>(~wise(mary)))&
(![X]:((~kind(X)|~old(X))=>(wise(X)|rich(X))))&
(((~calm(fred)&strong(fred)))<=>(calm(mary)))&
(![X]:((funny(X)<~>happy(X))=>(~quiet(X)|~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((tall(paul)<~>~wise(paul))))&
(![X]:((wise(X)&kind(X))=>(~humble(X)&wise(X))))&
(![X]:(happy(X)<=>(wise(X)<~>old(X))))&
(((~strong(alice)|creative(alice)))<=>(?[X]:(creative(X))))&
(![X]:((~creative(X)|~curious(X))<=>~calm(X)))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((~wise(X)|old(X)))))&
(![X]:(~kind(X)=>(quiet(X)&tall(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((~creative(X)&tall(X))))&
((quiet(john)<~>rich(john)))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((~humble(X)|~happy(X))))&
(strong(mary))&
(?[X]:((brave(X)&~curious(X))))&
((calm(mary)<~>creative(mary))) | generous(fred) | [] | null | 0 |
If someone is happy then alice is patient and vice versa.
If alice is both not happy and creative then lucy is both curious and not kind and vice versa.
Everyone who is not old is tall.
Everyone who is both not old and not happy is creative or humble and vice versa.
Everyone who is either happy or not funny is not tall or humble and vice versa.
Everyone who is either not creative or tall is not humble.
Everyone who is curious or brave is both humble and quiet and vice versa.
Everyone who is both not brave and not rich is not brave.
Everyone who is not brave or wise is either tall or funny.
Everyone who is either funny or not curious is generous.
If someone is patient or quiet then susan is both funny and not quiet.
Everyone who is kind is either not generous or not kind and vice versa.
Everyone who is not strong is both humble and not brave and vice versa.
Everyone who is rich or calm is not funny.
Everyone who is either wise or quiet is either quiet or funny and vice versa.
If someone is generous then lucy is either calm or not creative.
Someone is not generous.
Lucy is either tall or not brave.
Someone is curious.
Susan is not generous.
Lucy is either not brave or not calm.
Someone is both not funny and not generous.
Mary is patient or brave. | Susan is humble. | contradiction | ((?[X]:(happy(X)))<=>(patient(alice)))&
(((~happy(alice)&creative(alice)))<=>((curious(lucy)&~kind(lucy))))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((~old(X)&~happy(X))<=>(creative(X)|humble(X))))&
(![X]:((happy(X)<~>~funny(X))<=>(~tall(X)|humble(X))))&
(![X]:((~creative(X)<~>tall(X))=>~humble(X)))&
(![X]:((curious(X)|brave(X))<=>(humble(X)&quiet(X))))&
(![X]:((~brave(X)&~rich(X))=>~brave(X)))&
(![X]:((~brave(X)|wise(X))=>(tall(X)<~>funny(X))))&
(![X]:((funny(X)<~>~curious(X))=>generous(X)))&
((?[X]:((patient(X)|quiet(X))))=>((funny(susan)&~quiet(susan))))&
(![X]:(kind(X)<=>(~generous(X)<~>~kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~brave(X))))&
(![X]:((rich(X)|calm(X))=>~funny(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(quiet(X)<~>funny(X))))&
((?[X]:(generous(X)))=>((calm(lucy)<~>~creative(lucy))))&
(?[X]:(~generous(X)))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:(curious(X)))&
(~generous(susan))&
((~brave(lucy)<~>~calm(lucy)))&
(?[X]:((~funny(X)&~generous(X))))&
((patient(mary)|brave(mary))) | humble(susan) | [
"p3",
"p4",
"p6",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4710153535064105153576951
% SZS output start Proof for 4710153535064105153576951
4. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (humble(X0) | creative(X0))) [input p3]
5. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (humble(X0) | ~tall(X0))) [input p4]
7. ! [X0] : ((brave(X0) | curious(X0)) <=> (quiet(X0) & humble(X0))) [input p6]
11. ? [X0] : (quiet(X0) | patient(X0)) => (~quiet(susan) & funny(susan)) [input p10]
19. ? [X0] : curious(X0) [input p18]
24. humble(susan) [input hypothesis]
31. (~quiet(susan) & funny(susan)) | ! [X0] : (~quiet(X0) & ~patient(X0)) [ennf transformation 11]
40. ! [X0] : (((~happy(X0) & ~old(X0)) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | (happy(X0) | old(X0)))) [nnf transformation 4]
41. ! [X0] : (((~happy(X0) & ~old(X0)) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | happy(X0) | old(X0))) [flattening 40]
42. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (~humble(X0) & tall(X0))) & ((humble(X0) | ~tall(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 5]
43. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (~humble(X0) & tall(X0))) & (humble(X0) | ~tall(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [flattening 42]
45. ! [X0] : (((brave(X0) | curious(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 7]
46. ! [X0] : ((brave(X0) | curious(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 45]
55. ? [X0] : curious(X0) => curious(sK2) [choice axiom]
56. curious(sK2) [skolemisation 19,55]
71. ~humble(X0) | ~happy(X0) [cnf transformation 41]
75. ~funny(X0) | happy(X0) | ~humble(X0) [cnf transformation 43]
82. ~curious(X0) | quiet(X0) [cnf transformation 46]
93. funny(susan) | ~quiet(X0) [cnf transformation 31]
115. curious(sK2) [cnf transformation 56]
122. humble(susan) [cnf transformation 24]
162. ~funny(X0) | ~humble(X0) [subsumption resolution 75,71]
165. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
166. ~quiet(X0) <- (8) [avatar component clause 165]
177. 11 <=> funny(susan) [avatar definition]
179. funny(susan) <- (11) [avatar component clause 177]
180. 8 | 11 [avatar split clause 93,177,165]
218. quiet(sK2) [resolution 82,115]
219. $false <- (8) [subsumption resolution 218,166]
220. ~8 [avatar contradiction clause 219]
224. ~humble(susan) <- (11) [resolution 162,179]
225. $false <- (11) [subsumption resolution 224,122]
226. ~11 [avatar contradiction clause 225]
227. $false [avatar sat refutation 180,220,226]
% SZS output end Proof for 4710153535064105153576951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not patient then someone is either not rich or not kind. Everyone who is both humble and not funny is wise or not calm and vice versa. Everyone who is either not generous or not curious is patient and vice versa. Everyone who is either not generous or curious is not brave and vice versa. If someone is kind then paul is creative and vice versa. Everyone who is both wise and brave is either funny or not patient and vice versa. If someone is either not quiet or not generous then someone is either generous or quiet. Everyone who is both kind and not curious is humble or calm and vice versa. Everyone who is brave is kind or not generous. If someone is funny or not creative then susan is not generous and vice versa. Everyone who is both rich and patient is either not funny or kind. If susan is happy or not rich then someone is brave or humble. If alice is humble then john is not old. If lucy is rich or calm then someone is curious and vice versa. Everyone who is either not calm or old is either not creative or not calm and vice versa. If someone is not wise then someone is not patient and vice versa. Someone is brave. Someone is either generous or calm. Mary is strong. John is either creative or not funny. Mary is not calm. Susan is tall. Someone is not quiet or humble. Someone is tall. | Susan is not wise. | entailment | ((?[X]:((~rich(X)&~patient(X))))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((humble(X)&~funny(X))<=>(wise(X)|~calm(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~generous(X)<~>curious(X))<=>~brave(X)))&
((?[X]:(kind(X)))<=>(creative(paul)))&
(![X]:((wise(X)&brave(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((kind(X)&~curious(X))<=>(humble(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)|~generous(X))))&
((?[X]:((funny(X)|~creative(X))))<=>(~generous(susan)))&
(![X]:((rich(X)&patient(X))=>(~funny(X)<~>kind(X))))&
(((happy(susan)|~rich(susan)))=>(?[X]:((brave(X)|humble(X)))))&
((humble(alice))=>(~old(john)))&
(((rich(lucy)|calm(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((~calm(X)<~>old(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(strong(mary))&
((creative(john)<~>~funny(john)))&
(~calm(mary))&
(tall(susan))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:(tall(X))) | ~wise(susan) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p9",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2237657849350931732212562
% SZS output start Proof for 2237657849350931732212562
2. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~calm(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> patient(X0)) [input p2]
4. ! [X0] : ((~generous(X0) <~> curious(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : ((brave(X0) & wise(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p5]
8. ! [X0] : ((~curious(X0) & kind(X0)) <=> (calm(X0) | humble(X0))) [input p7]
10. ? [X0] : (~creative(X0) | funny(X0)) <=> ~generous(susan) [input p9]
14. (calm(lucy) | rich(lucy)) <=> ? [X0] : curious(X0) [input p13]
16. ? [X0] : ~wise(X0) <=> ? [X0] : ~patient(X0) [input p15]
17. ? [X0] : brave(X0) [input p16]
25. wise(susan) [input hypothesis]
28. ? [X0] : ~wise(X0) <=> ? [X1] : ~patient(X1) [rectify 16]
45. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 2]
46. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | funny(X0) | ~humble(X0))) [flattening 45]
47. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 3]
48. ! [X0] : ((((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | brave(X0)) & (~brave(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0))))) [nnf transformation 4]
53. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~brave(X0) | ~wise(X0)))) [nnf transformation 6]
54. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~brave(X0) | ~wise(X0))) [flattening 53]
59. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | (curious(X0) | ~kind(X0)))) [nnf transformation 8]
60. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | curious(X0) | ~kind(X0))) [flattening 59]
61. (? [X0] : (~creative(X0) | funny(X0)) | generous(susan)) & (~generous(susan) | ! [X0] : (creative(X0) & ~funny(X0))) [nnf transformation 10]
62. (? [X0] : (~creative(X0) | funny(X0)) | generous(susan)) & (~generous(susan) | ! [X1] : (creative(X1) & ~funny(X1))) [rectify 61]
63. ? [X0] : (~creative(X0) | funny(X0)) => (~creative(sK3) | funny(sK3)) [choice axiom]
64. ((~creative(sK3) | funny(sK3)) | generous(susan)) & (~generous(susan) | ! [X1] : (creative(X1) & ~funny(X1))) [skolemisation 62,63]
68. ((calm(lucy) | rich(lucy)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [nnf transformation 14]
69. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [flattening 68]
70. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | (~calm(lucy) & ~rich(lucy))) [rectify 69]
71. ? [X1] : curious(X1) => curious(sK5) [choice axiom]
72. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (curious(sK5) | (~calm(lucy) & ~rich(lucy))) [skolemisation 70,71]
74. (? [X0] : ~wise(X0) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : wise(X0)) [nnf transformation 28]
75. (? [X0] : ~wise(X0) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : wise(X3)) [rectify 74]
76. ? [X0] : ~wise(X0) => ~wise(sK6) [choice axiom]
77. ? [X2] : ~patient(X2) => ~patient(sK7) [choice axiom]
78. (~wise(sK6) | ! [X1] : patient(X1)) & (~patient(sK7) | ! [X3] : wise(X3)) [skolemisation 75,77,76]
79. ? [X0] : brave(X0) => brave(sK8) [choice axiom]
80. brave(sK8) [skolemisation 17,79]
91. calm(X0) | humble(X0) [cnf transformation 46]
92. ~wise(X0) | ~funny(X0) [cnf transformation 46]
95. ~generous(X0) | patient(X0) | curious(X0) [cnf transformation 47]
97. ~patient(X0) | generous(X0) | curious(X0) [cnf transformation 47]
98. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 48]
104. ~patient(X0) | funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 54]
109. brave(X0) | funny(X0) | patient(X0) [cnf transformation 54]
117. ~curious(X0) | ~humble(X0) [cnf transformation 60]
118. ~curious(X0) | ~calm(X0) [cnf transformation 60]
120. ~generous(susan) | ~funny(X1) [cnf transformation 64]
127. curious(sK5) | ~rich(lucy) [cnf transformation 72]
128. curious(sK5) | ~calm(lucy) [cnf transformation 72]
129. calm(lucy) | rich(lucy) | ~curious(X0) [cnf transformation 72]
138. ~patient(sK7) | wise(X3) [cnf transformation 78]
140. brave(sK8) [cnf transformation 80]
147. wise(susan) [cnf transformation 25]
179. ~brave(X0) | ~patient(X0) | ~wise(X0) [subsumption resolution 104,92]
199. 11 <=> generous(susan) [avatar definition]
216. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
217. ~funny(X1) <- (15) [avatar component clause 216]
218. 15 | ~11 [avatar split clause 120,199,216]
243. 21 <=> ! [X0] : ~curious(X0) [avatar definition]
244. ~curious(X0) <- (21) [avatar component clause 243]
246. 22 <=> rich(lucy) [avatar definition]
250. 23 <=> calm(lucy) [avatar definition]
253. 21 | 22 | 23 [avatar split clause 129,250,246,243]
255. 24 <=> curious(sK5) [avatar definition]
257. curious(sK5) <- (24) [avatar component clause 255]
258. ~23 | 24 [avatar split clause 128,255,250]
259. ~22 | 24 [avatar split clause 127,255,246]
263. 25 <=> ! [X1] : patient(X1) [avatar definition]
264. patient(X1) <- (25) [avatar component clause 263]
271. 27 <=> ! [X3] : wise(X3) [avatar definition]
272. wise(X3) <- (27) [avatar component clause 271]
274. 28 <=> patient(sK7) [avatar definition]
276. ~patient(sK7) <- (~28) [avatar component clause 274]
277. 27 | ~28 [avatar split clause 138,274,271]
311. ~funny(susan) [resolution 92,147]
336. curious(sK8) | generous(sK8) [resolution 98,140]
365. $false <- (25, ~28) [resolution 264,276]
367. ~25 | 28 [avatar contradiction clause 365]
403. 41 <=> curious(sK8) [avatar definition]
404. curious(sK8) <- (41) [avatar component clause 403]
405. ~curious(sK8) <- (~41) [avatar component clause 403]
407. 42 <=> generous(sK8) [avatar definition]
408. generous(sK8) <- (42) [avatar component clause 407]
415. ~calm(sK5) <- (24) [resolution 257,118]
416. ~humble(sK5) <- (24) [resolution 257,117]
438. 42 | 41 [avatar split clause 336,403,407]
443. funny(X1) | patient(X1) | curious(X1) | generous(X1) [resolution 109,98]
446. patient(X1) | curious(X1) | generous(X1) <- (15) [subsumption resolution 443,217]
447. curious(X1) | generous(X1) <- (15) [subsumption resolution 446,97]
463. patient(sK8) | curious(sK8) <- (42) [resolution 408,95]
464. patient(sK8) <- (~41, 42) [subsumption resolution 463,405]
465. ~patient(sK8) | ~wise(sK8) [resolution 179,140]
467. ~wise(sK8) <- (~41, 42) [subsumption resolution 465,464]
468. humble(sK5) <- (24) [resolution 415,91]
469. $false <- (24) [subsumption resolution 468,416]
470. ~24 [avatar contradiction clause 469]
508. generous(X5) <- (15, 21) [resolution 447,244]
515. patient(X1) | curious(X1) <- (15, 21) [resolution 508,95]
525. patient(X1) <- (15, 21) [subsumption resolution 515,244]
526. 25 | ~15 | ~21 [avatar split clause 525,243,216,263]
531. generous(X1) | patient(X1) | funny(X1) <- (21) [subsumption resolution 443,244]
587. patient(X1) | funny(X1) | patient(X1) | curious(X1) <- (21) [resolution 531,95]
592. patient(X1) | funny(X1) | curious(X1) <- (21) [duplicate literal removal 587]
593. funny(X1) | patient(X1) <- (21) [subsumption resolution 592,244]
614. patient(susan) <- (21) [resolution 593,311]
635. generous(susan) | curious(susan) <- (21) [resolution 614,97]
641. generous(susan) <- (21) [subsumption resolution 635,244]
642. 11 | ~21 [avatar split clause 641,243,199]
670. $false <- (27, ~41, 42) [resolution 272,467]
671. ~27 | 41 | ~42 [avatar contradiction clause 670]
681. $false <- (21, 41) [subsumption resolution 404,244]
682. ~21 | ~41 [avatar contradiction clause 681]
683. $false [avatar sat refutation 218,253,258,259,277,367,438,470,526,642,671,682]
% SZS output end Proof for 2237657849350931732212562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and not creative then alice is not humble.
Everyone who is both not kind and humble is not funny or not generous.
If someone is not tall or generous then someone is both kind and not old and vice versa.
Everyone who is both brave and kind is not humble or strong and vice versa.
Everyone who is both rich and not kind is either not happy or not calm and vice versa.
Everyone who is tall is curious and vice versa.
If someone is both wise and not funny then someone is humble or rich.
If john is either quiet or old then someone is rich and vice versa.
Everyone who is both rich and not tall is both not generous and patient.
If mary is both not old and wise then someone is happy and vice versa.
Everyone who is both not old and not generous is either not rich or not kind and vice versa.
If fred is funny then alice is both not rich and not generous.
Everyone who is humble or not creative is both happy and rich.
Everyone who is both not strong and funny is either not calm or patient.
If someone is either not funny or not curious then someone is quiet or not curious.
Everyone who is strong or rich is both generous and not wise and vice versa.
Someone is wise or patient.
Someone is quiet.
Someone is either happy or rich.
Lucy is curious or wise.
Alice is both quiet and not rich.
Mary is both brave and curious.
Fred is not wise.
Someone is either not humble or not curious. | Alice is not humble. | entailment | (((~wise(mary)&~creative(mary)))=>(~humble(alice)))&
(![X]:((~kind(X)&humble(X))=>(~funny(X)|~generous(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((brave(X)&kind(X))<=>(~humble(X)|strong(X))))&
(![X]:((rich(X)&~kind(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:(tall(X)<=>curious(X)))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((humble(X)|rich(X)))))&
(((quiet(john)<~>old(john)))<=>(?[X]:(rich(X))))&
(![X]:((rich(X)&~tall(X))=>(~generous(X)&patient(X))))&
(((~old(mary)&wise(mary)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)&~generous(X))<=>(~rich(X)<~>~kind(X))))&
((funny(fred))=>((~rich(alice)&~generous(alice))))&
(![X]:((humble(X)|~creative(X))=>(happy(X)&rich(X))))&
(![X]:((~strong(X)&funny(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((~funny(X)<~>~curious(X))))=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:((strong(X)|rich(X))<=>(generous(X)&~wise(X))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)<~>rich(X))))&
((curious(lucy)|wise(lucy)))&
((quiet(alice)&~rich(alice)))&
((brave(mary)&curious(mary)))&
(~wise(fred))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~humble(alice) | [
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5945531016625761897423563
% SZS output start Proof for 5945531016625761897423563
13. ! [X0] : ((~creative(X0) | humble(X0)) => (rich(X0) & happy(X0))) [input p12]
21. ~rich(alice) & quiet(alice) [input p20]
25. humble(alice) [input hypothesis]
30. ! [X0] : (humble(X0) => (rich(X0) & happy(X0))) [pure predicate removal 13]
37. ! [X0] : ((rich(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 30]
120. ~humble(X0) | rich(X0) [cnf transformation 37]
136. ~rich(alice) [cnf transformation 21]
142. humble(alice) [cnf transformation 25]
232. 21 <=> rich(alice) [avatar definition]
234. ~rich(alice) <- (~21) [avatar component clause 232]
280. ~21 [avatar split clause 136,232]
300. rich(alice) [resolution 120,142]
302. $false <- (~21) [subsumption resolution 300,234]
303. 21 [avatar contradiction clause 302]
306. $false [avatar sat refutation 280,303]
% SZS output end Proof for 5945531016625761897423563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not funny is humble or not rich.
Everyone who is both not happy and old is both not brave and brave and vice versa.
If someone is not humble then lucy is both humble and not generous.
If someone is both rich and calm then someone is not brave and vice versa.
If someone is both not brave and not wise then susan is not strong or not rich.
Everyone who is either rich or not strong is both not generous and not kind and vice versa.
Everyone who is calm or not curious is not humble.
Everyone who is funny is both kind and not wise and vice versa.
If susan is either not quiet or happy then alice is not funny.
If john is either not patient or not happy then susan is either humble or old and vice versa.
Everyone who is brave or not strong is either not brave or funny.
If susan is either patient or not humble then someone is curious or wise.
If paul is tall then someone is both not kind and not wise and vice versa.
If paul is not patient or not happy then john is old or generous.
Everyone who is rich is wise and vice versa.
Someone is both not creative and old.
Alice is both not creative and not patient.
Someone is not curious.
Alice is not creative or generous.
Susan is creative.
Mary is happy. | Lucy is wise. | contradiction | (![X]:((calm(X)&~funny(X))=>(humble(X)|~rich(X))))&
(![X]:((~happy(X)&old(X))<=>(~brave(X)&brave(X))))&
((?[X]:(~humble(X)))=>((humble(lucy)&~generous(lucy))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)&~wise(X))))=>((~strong(susan)|~rich(susan))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~kind(X))))&
(![X]:((calm(X)|~curious(X))=>~humble(X)))&
(![X]:(funny(X)<=>(kind(X)&~wise(X))))&
(((~quiet(susan)<~>happy(susan)))=>(~funny(alice)))&
(((~patient(john)<~>~happy(john)))<=>((humble(susan)<~>old(susan))))&
(![X]:((brave(X)|~strong(X))=>(~brave(X)<~>funny(X))))&
(((patient(susan)<~>~humble(susan)))=>(?[X]:((curious(X)|wise(X)))))&
((tall(paul))<=>(?[X]:((~kind(X)&~wise(X)))))&
(((~patient(paul)|~happy(paul)))=>((old(john)|generous(john))))&
(![X]:(rich(X)<=>wise(X)))&
(?[X]:((~creative(X)&old(X))))&
((~creative(alice)&~patient(alice)))&
(?[X]:(~curious(X)))&
((~creative(alice)|generous(alice)))&
(creative(susan))&
(happy(mary)) | wise(lucy) | [
"p0",
"p3",
"p6",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2897014713172194218314325
% SZS output start Proof for 2897014713172194218314325
1. ! [X0] : ((~funny(X0) & calm(X0)) => (~rich(X0) | humble(X0))) [input p0]
4. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X0] : ~brave(X0) [input p3]
7. ! [X0] : ((~curious(X0) | calm(X0)) => ~humble(X0)) [input p6]
8. ! [X0] : (funny(X0) <=> (~wise(X0) & kind(X0))) [input p7]
11. ! [X0] : ((~strong(X0) | brave(X0)) => (~brave(X0) <~> funny(X0))) [input p10]
15. ! [X0] : (rich(X0) <=> wise(X0)) [input p14]
22. wise(lucy) [input hypothesis]
23. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X1] : ~brave(X1) [rectify 4]
24. ! [X0] : ((~rich(X0) | humble(X0)) | (funny(X0) | ~calm(X0))) [ennf transformation 1]
25. ! [X0] : (~rich(X0) | humble(X0) | funny(X0) | ~calm(X0)) [flattening 24]
29. ! [X0] : (~humble(X0) | (curious(X0) & ~calm(X0))) [ennf transformation 7]
31. ! [X0] : ((~brave(X0) <~> funny(X0)) | (strong(X0) & ~brave(X0))) [ennf transformation 11]
37. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (~calm(X0) | ~rich(X0))) [nnf transformation 23]
38. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (~calm(X3) | ~rich(X3))) [rectify 37]
39. ? [X0] : (calm(X0) & rich(X0)) => (calm(sK0) & rich(sK0)) [choice axiom]
40. ? [X2] : ~brave(X2) => ~brave(sK1) [choice axiom]
41. ((calm(sK0) & rich(sK0)) | ! [X1] : brave(X1)) & (~brave(sK1) | ! [X3] : (~calm(X3) | ~rich(X3))) [skolemisation 38,40,39]
44. ! [X0] : ((funny(X0) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [nnf transformation 8]
45. ! [X0] : ((funny(X0) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [flattening 44]
48. ! [X0] : (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (strong(X0) & ~brave(X0))) [nnf transformation 31]
56. ! [X0] : ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0))) [nnf transformation 15]
61. ~rich(X0) | humble(X0) | funny(X0) | ~calm(X0) [cnf transformation 25]
69. rich(sK0) | brave(X1) [cnf transformation 41]
70. calm(sK0) | brave(X1) [cnf transformation 41]
78. ~humble(X0) | ~calm(X0) [cnf transformation 29]
81. ~wise(X0) | ~funny(X0) [cnf transformation 45]
93. funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 48]
104. ~rich(X0) | wise(X0) [cnf transformation 56]
114. wise(lucy) [cnf transformation 22]
115. ~brave(X0) | funny(X0) [duplicate literal removal 93]
131. 4 <=> ! [X1] : brave(X1) [avatar definition]
132. brave(X1) <- (4) [avatar component clause 131]
134. 5 <=> calm(sK0) [avatar definition]
136. calm(sK0) <- (5) [avatar component clause 134]
137. 4 | 5 [avatar split clause 70,134,131]
139. 6 <=> rich(sK0) [avatar definition]
141. rich(sK0) <- (6) [avatar component clause 139]
142. 4 | 6 [avatar split clause 69,139,131]
257. ~funny(lucy) [resolution 81,114]
260. funny(X0) <- (4) [resolution 115,132]
263. $false <- (4) [resolution 260,257]
264. ~4 [avatar contradiction clause 263]
266. wise(sK0) <- (6) [resolution 141,104]
269. ~funny(sK0) <- (6) [resolution 266,81]
295. humble(sK0) | funny(sK0) | ~calm(sK0) <- (6) [resolution 61,141]
298. humble(sK0) | ~calm(sK0) <- (6) [subsumption resolution 295,269]
299. humble(sK0) <- (5, 6) [subsumption resolution 298,136]
302. ~calm(sK0) <- (5, 6) [resolution 299,78]
303. $false <- (5, 6) [subsumption resolution 302,136]
304. ~5 | ~6 [avatar contradiction clause 303]
305. $false [avatar sat refutation 137,142,264,304]
% SZS output end Proof for 2897014713172194218314325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or rich is rich or quiet and vice versa. If alice is either not creative or humble then someone is either humble or old and vice versa. Everyone who is generous or not quiet is either happy or strong and vice versa. Everyone who is either not funny or not humble is strong or generous. Everyone who is not happy or not kind is either tall or not happy and vice versa. If someone is either not calm or not rich then lucy is both quiet and calm and vice versa. Everyone who is either not tall or funny is happy and vice versa. Everyone who is not strong or not kind is brave and vice versa. If someone is either funny or happy then fred is not funny or not generous and vice versa. If someone is not quiet or patient then mary is either tall or generous. Everyone who is either old or generous is not calm and vice versa. If alice is calm then someone is calm. Everyone who is both not quiet and calm is old or tall. Everyone who is both brave and not calm is both wise and calm and vice versa. Everyone who is both not kind and not brave is not old or not kind and vice versa. Everyone who is quiet or not strong is strong or funny. Someone is both kind and wise. John is not generous or not wise. Lucy is generous. Mary is both quiet and not funny. Fred is not happy or not funny. Someone is calm. Lucy is wise or curious. Mary is either not generous or generous. | Mary is not generous. | entailment | (![X]:((tall(X)|rich(X))<=>(rich(X)|quiet(X))))&
(((~creative(alice)<~>humble(alice)))<=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(happy(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(strong(X)|generous(X))))&
(![X]:((~happy(X)|~kind(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((quiet(lucy)&calm(lucy))))&
(![X]:((~tall(X)<~>funny(X))<=>happy(X)))&
(![X]:((~strong(X)|~kind(X))<=>brave(X)))&
((?[X]:((funny(X)<~>happy(X))))<=>((~funny(fred)|~generous(fred))))&
((?[X]:((~quiet(X)|patient(X))))=>((tall(mary)<~>generous(mary))))&
(![X]:((old(X)<~>generous(X))<=>~calm(X)))&
((calm(alice))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)&calm(X))=>(old(X)|tall(X))))&
(![X]:((brave(X)&~calm(X))<=>(wise(X)&calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)|~strong(X))=>(strong(X)|funny(X))))&
(?[X]:((kind(X)&wise(X))))&
((~generous(john)|~wise(john)))&
(generous(lucy))&
((quiet(mary)&~funny(mary)))&
((~happy(fred)|~funny(fred)))&
(?[X]:(calm(X)))&
((wise(lucy)|curious(lucy)))&
((~generous(mary)<~>generous(mary))) | ~generous(mary) | [
"p2",
"p4",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8704674071354114023125390
% SZS output start Proof for 8704674071354114023125390
3. ! [X0] : ((~quiet(X0) | generous(X0)) <=> (happy(X0) <~> strong(X0))) [input p2]
5. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (tall(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> happy(X0)) [input p6]
16. ! [X0] : ((~strong(X0) | quiet(X0)) => (funny(X0) | strong(X0))) [input p15]
20. ~funny(mary) & quiet(mary) [input p19]
25. generous(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) | strong(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 16]
35. ! [X0] : (funny(X0) | strong(X0) | (strong(X0) & ~quiet(X0))) [flattening 34]
42. ! [X0] : (((~quiet(X0) | generous(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [nnf transformation 3]
43. ! [X0] : ((~quiet(X0) | generous(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [flattening 42]
45. ! [X0] : (((~kind(X0) | ~happy(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (kind(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((~kind(X0) | ~happy(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (kind(X0) & happy(X0)))) [flattening 45]
52. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 7]
87. ~strong(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 43]
95. happy(X0) | ~tall(X0) | happy(X0) [cnf transformation 46]
105. happy(X0) | funny(X0) | tall(X0) [cnf transformation 52]
107. funny(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 52]
136. funny(X0) | strong(X0) | strong(X0) [cnf transformation 35]
142. ~funny(mary) [cnf transformation 20]
147. generous(mary) [cnf transformation 25]
148. funny(X0) | strong(X0) [duplicate literal removal 136]
151. ~tall(X0) | happy(X0) [duplicate literal removal 95]
211. ~tall(X0) | funny(X0) [subsumption resolution 107,151]
212. funny(X0) | happy(X0) [subsumption resolution 105,211]
249. 21 <=> generous(mary) [avatar definition]
250. generous(mary) <- (21) [avatar component clause 249]
279. 21 [avatar split clause 147,249]
285. strong(mary) [resolution 148,142]
291. happy(mary) [resolution 212,142]
322. ~happy(mary) | ~generous(mary) [resolution 87,285]
327. ~generous(mary) [subsumption resolution 322,291]
328. $false <- (21) [subsumption resolution 327,250]
329. ~21 [avatar contradiction clause 328]
330. $false [avatar sat refutation 279,329]
% SZS output end Proof for 8704674071354114023125390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not humble or not kind then paul is either not patient or curious. Everyone who is calm or wise is either quiet or brave and vice versa. Everyone who is patient or not happy is either not happy or not kind. If someone is either not strong or old then susan is both not calm and not curious. If someone is not quiet then alice is both not happy and not wise and vice versa. Everyone who is both not calm and not creative is tall. If someone is tall or not old then someone is both brave and not generous and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is both generous and not quiet is either not strong or not humble and vice versa. If fred is either not patient or not strong then susan is either strong or not quiet and vice versa. Everyone who is creative is both calm and strong and vice versa. Everyone who is both not quiet and not creative is rich or not happy and vice versa. Everyone who is both brave and not strong is either not tall or not creative and vice versa. If someone is both kind and brave then someone is not curious or not humble and vice versa. If fred is both not patient and generous then someone is curious. If someone is both not generous and not creative then someone is not patient or humble. John is both curious and not wise. John is not happy. Someone is wise or not patient. Someone is not brave. Someone is not curious or not patient. Susan is not happy. Mary is rich or not tall. | John is not tall. | contradiction | (((~humble(mary)|~kind(mary)))=>((~patient(paul)<~>curious(paul))))&
(![X]:((calm(X)|wise(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((patient(X)|~happy(X))=>(~happy(X)<~>~kind(X))))&
((?[X]:((~strong(X)<~>old(X))))=>((~calm(susan)&~curious(susan))))&
((?[X]:(~quiet(X)))<=>((~happy(alice)&~wise(alice))))&
(![X]:((~calm(X)&~creative(X))=>tall(X)))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((generous(X)&~quiet(X))<=>(~strong(X)<~>~humble(X))))&
(((~patient(fred)<~>~strong(fred)))<=>((strong(susan)<~>~quiet(susan))))&
(![X]:(creative(X)<=>(calm(X)&strong(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(rich(X)|~happy(X))))&
(![X]:((brave(X)&~strong(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~patient(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~patient(X)|humble(X)))))&
((curious(john)&~wise(john)))&
(~happy(john))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~curious(X)|~patient(X))))&
(~happy(susan))&
((rich(mary)|~tall(mary))) | ~tall(john) | [
"p1",
"p5",
"p10",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7855820017800311913379764
% SZS output start Proof for 7855820017800311913379764
2. ! [X0] : ((wise(X0) | calm(X0)) <=> (quiet(X0) <~> brave(X0))) [input p1]
6. ! [X0] : ((~creative(X0) & ~calm(X0)) => tall(X0)) [input p5]
11. ! [X0] : (creative(X0) <=> (strong(X0) & calm(X0))) [input p10]
12. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~happy(X0) | rich(X0))) [input p11]
13. ! [X0] : ((~strong(X0) & brave(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p12]
18. ~happy(john) [input p17]
24. ~tall(john) [input hypothesis]
31. ! [X0] : (tall(X0) | (creative(X0) | calm(X0))) [ennf transformation 6]
32. ! [X0] : (tall(X0) | creative(X0) | calm(X0)) [flattening 31]
37. ! [X0] : (((wise(X0) | calm(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~wise(X0) & ~calm(X0)))) [nnf transformation 2]
38. ! [X0] : ((wise(X0) | calm(X0) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~wise(X0) & ~calm(X0)))) [flattening 37]
55. ! [X0] : ((creative(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | ~creative(X0))) [nnf transformation 11]
56. ! [X0] : ((creative(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | ~creative(X0))) [flattening 55]
57. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | creative(X0) | quiet(X0))) [flattening 57]
59. ! [X0] : (((~strong(X0) & brave(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (strong(X0) | ~brave(X0)))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & brave(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | strong(X0) | ~brave(X0))) [flattening 59]
81. ~calm(X0) | quiet(X0) | brave(X0) [cnf transformation 38]
98. tall(X0) | creative(X0) | calm(X0) [cnf transformation 32]
120. ~creative(X0) | calm(X0) [cnf transformation 56]
121. ~creative(X0) | strong(X0) [cnf transformation 56]
122. ~strong(X0) | creative(X0) | ~calm(X0) [cnf transformation 56]
125. ~quiet(X0) | happy(X0) [cnf transformation 58]
127. ~creative(X0) | happy(X0) [cnf transformation 58]
129. creative(X0) | tall(X0) | strong(X0) | ~brave(X0) [cnf transformation 60]
132. ~strong(X0) | ~creative(X0) | tall(X0) [cnf transformation 60]
133. ~tall(X0) | ~strong(X0) | creative(X0) [cnf transformation 60]
143. ~happy(john) [cnf transformation 18]
149. ~tall(john) [cnf transformation 24]
261. ~creative(X0) | tall(X0) [subsumption resolution 132,121]
262. ~brave(X0) | strong(X0) | tall(X0) [subsumption resolution 129,261]
374. creative(john) | calm(john) [resolution 98,149]
377. calm(john) [subsumption resolution 374,120]
379. quiet(john) | brave(john) [resolution 377,81]
381. 45 <=> brave(john) [avatar definition]
383. brave(john) <- (45) [avatar component clause 381]
385. 46 <=> quiet(john) [avatar definition]
387. quiet(john) <- (46) [avatar component clause 385]
388. 45 | 46 [avatar split clause 379,385,381]
472. ~strong(X0) | creative(X0) | creative(X0) | calm(X0) [resolution 133,98]
473. ~strong(X0) | creative(X0) | calm(X0) [duplicate literal removal 472]
577. ~strong(X0) | creative(X0) [subsumption resolution 473,122]
667. happy(john) <- (46) [resolution 387,125]
669. 70 <=> strong(john) [avatar definition]
671. strong(john) <- (70) [avatar component clause 669]
677. $false <- (46) [subsumption resolution 667,143]
678. ~46 [avatar contradiction clause 677]
682. strong(john) | tall(john) <- (45) [resolution 383,262]
685. strong(john) <- (45) [subsumption resolution 682,149]
686. 70 | ~45 [avatar split clause 685,381,669]
724. creative(john) <- (70) [resolution 671,577]
808. happy(john) <- (70) [resolution 724,127]
813. $false <- (70) [subsumption resolution 808,143]
814. ~70 [avatar contradiction clause 813]
815. $false [avatar sat refutation 388,678,686,814]
% SZS output end Proof for 7855820017800311913379764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not kind is humble or old.
Everyone who is patient or not old is funny.
Everyone who is either not patient or old is both not calm and not creative.
Everyone who is either patient or not brave is both calm and not happy and vice versa.
If someone is happy then someone is either not kind or brave.
Everyone who is not wise is both not quiet and not wise and vice versa.
Everyone who is kind or not happy is not strong or curious and vice versa.
Everyone who is not funny or not tall is either happy or old.
If alice is either kind or tall then someone is both not generous and creative and vice versa.
If alice is not tall then someone is both brave and not funny and vice versa.
If someone is both old and not curious then someone is both happy and quiet.
If someone is both not kind and wise then mary is not quiet and vice versa.
Everyone who is not rich is creative.
If fred is both not brave and rich then someone is funny or not calm and vice versa.
If alice is not tall or funny then someone is not rich or calm and vice versa.
Everyone who is both not kind and not calm is not patient or humble and vice versa.
Fred is either not brave or not old.
Susan is not creative or not rich.
Someone is either not tall or not patient.
Someone is not calm or patient.
John is calm or not curious.
Someone is either kind or patient.
Alice is creative.
Someone is either not brave or not strong. | Fred is not patient. | contradiction | (![X]:((wise(X)|~kind(X))=>(humble(X)|old(X))))&
(![X]:((patient(X)|~old(X))=>funny(X)))&
(![X]:((~patient(X)<~>old(X))=>(~calm(X)&~creative(X))))&
(![X]:((patient(X)<~>~brave(X))<=>(calm(X)&~happy(X))))&
((?[X]:(happy(X)))=>(?[X]:((~kind(X)<~>brave(X)))))&
(![X]:(~wise(X)<=>(~quiet(X)&~wise(X))))&
(![X]:((kind(X)|~happy(X))<=>(~strong(X)|curious(X))))&
(![X]:((~funny(X)|~tall(X))=>(happy(X)<~>old(X))))&
(((kind(alice)<~>tall(alice)))<=>(?[X]:((~generous(X)&creative(X)))))&
((~tall(alice))<=>(?[X]:((brave(X)&~funny(X)))))&
((?[X]:((old(X)&~curious(X))))=>(?[X]:((happy(X)&quiet(X)))))&
((?[X]:((~kind(X)&wise(X))))<=>(~quiet(mary)))&
(![X]:(~rich(X)=>creative(X)))&
(((~brave(fred)&rich(fred)))<=>(?[X]:((funny(X)|~calm(X)))))&
(((~tall(alice)|funny(alice)))<=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((~kind(X)&~calm(X))<=>(~patient(X)|humble(X))))&
((~brave(fred)<~>~old(fred)))&
((~creative(susan)|~rich(susan)))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:((~calm(X)|patient(X))))&
((calm(john)|~curious(john)))&
(?[X]:((kind(X)<~>patient(X))))&
(creative(alice))&
(?[X]:((~brave(X)<~>~strong(X)))) | ~patient(fred) | [
"p1",
"p3",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8737761541288206278831041
% SZS output start Proof for 8737761541288206278831041
2. ! [X0] : ((~old(X0) | patient(X0)) => funny(X0)) [input p1]
4. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> (~happy(X0) & calm(X0))) [input p3]
14. (rich(fred) & ~brave(fred)) <=> ? [X0] : (~calm(X0) | funny(X0)) [input p13]
16. ! [X0] : ((~calm(X0) & ~kind(X0)) <=> (humble(X0) | ~patient(X0))) [input p15]
22. ? [X0] : (kind(X0) <~> patient(X0)) [input p21]
25. ~patient(fred) [input hypothesis]
30. ! [X0] : (funny(X0) | (old(X0) & ~patient(X0))) [ennf transformation 2]
37. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (happy(X0) | ~calm(X0))) & ((~happy(X0) & calm(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 4]
38. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | happy(X0) | ~calm(X0)) & ((~happy(X0) & calm(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [flattening 37]
63. ((rich(fred) & ~brave(fred)) | ! [X0] : (calm(X0) & ~funny(X0))) & (? [X0] : (~calm(X0) | funny(X0)) | (~rich(fred) | brave(fred))) [nnf transformation 14]
64. ((rich(fred) & ~brave(fred)) | ! [X0] : (calm(X0) & ~funny(X0))) & (? [X0] : (~calm(X0) | funny(X0)) | ~rich(fred) | brave(fred)) [flattening 63]
65. ((rich(fred) & ~brave(fred)) | ! [X0] : (calm(X0) & ~funny(X0))) & (? [X1] : (~calm(X1) | funny(X1)) | ~rich(fred) | brave(fred)) [rectify 64]
66. ? [X1] : (~calm(X1) | funny(X1)) => (~calm(sK5) | funny(sK5)) [choice axiom]
67. ((rich(fred) & ~brave(fred)) | ! [X0] : (calm(X0) & ~funny(X0))) & ((~calm(sK5) | funny(sK5)) | ~rich(fred) | brave(fred)) [skolemisation 65,66]
73. ! [X0] : (((~calm(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (calm(X0) | kind(X0)))) [nnf transformation 16]
74. ! [X0] : (((~calm(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | calm(X0) | kind(X0))) [flattening 73]
81. ? [X0] : ((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) [nnf transformation 22]
82. ? [X0] : ((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) => ((~patient(sK9) | ~kind(sK9)) & (patient(sK9) | kind(sK9))) [choice axiom]
83. (~patient(sK9) | ~kind(sK9)) & (patient(sK9) | kind(sK9)) [skolemisation 81,82]
89. ~patient(X0) | funny(X0) [cnf transformation 30]
96. brave(X0) | patient(X0) | calm(X0) [cnf transformation 38]
130. ~brave(fred) | ~funny(X0) [cnf transformation 67]
139. ~kind(X0) | patient(X0) [cnf transformation 74]
141. ~calm(X0) | patient(X0) [cnf transformation 74]
150. patient(sK9) | kind(sK9) [cnf transformation 83]
151. ~patient(sK9) | ~kind(sK9) [cnf transformation 83]
155. ~patient(fred) [cnf transformation 25]
249. 21 <=> ! [X0] : ~funny(X0) [avatar definition]
250. ~funny(X0) <- (21) [avatar component clause 249]
253. 22 <=> brave(fred) [avatar definition]
255. ~brave(fred) <- (~22) [avatar component clause 253]
257. 21 | ~22 [avatar split clause 130,253,249]
323. ~kind(sK9) [subsumption resolution 151,139]
324. patient(sK9) [subsumption resolution 150,323]
335. funny(sK9) [resolution 89,324]
336. $false <- (21) [subsumption resolution 335,250]
337. ~21 [avatar contradiction clause 336]
442. patient(fred) | calm(fred) <- (~22) [resolution 96,255]
448. calm(fred) <- (~22) [subsumption resolution 442,155]
473. patient(fred) <- (~22) [resolution 448,141]
474. $false <- (~22) [subsumption resolution 473,155]
475. 22 [avatar contradiction clause 474]
476. $false [avatar sat refutation 257,337,475]
% SZS output end Proof for 8737761541288206278831041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or kind then lucy is patient or not curious and vice versa. If someone is both not brave and curious then susan is calm and vice versa. If someone is both not creative and old then someone is either curious or not brave and vice versa. If john is either not rich or generous then someone is either creative or quiet and vice versa. If lucy is either not old or happy then someone is either not wise or tall and vice versa. If alice is not happy then someone is both happy and not brave and vice versa. Everyone who is not tall or calm is either not strong or not rich and vice versa. If mary is both not brave and not calm then mary is either brave or curious and vice versa. If someone is not curious then someone is not brave or not tall. Everyone who is quiet or not curious is strong and vice versa. Everyone who is both not curious and not wise is both not humble and not rich and vice versa. Everyone who is old or not strong is not old. Everyone who is either not curious or tall is either humble or not brave. If someone is not calm then john is not quiet or not tall. Everyone who is not curious or old is either not funny or not generous and vice versa. If someone is not old or not brave then someone is patient and vice versa. Someone is either not tall or calm. Susan is both funny and not strong. Alice is calm. Someone is either not generous or not tall. Someone is not brave. Someone is creative or wise. Susan is both not happy and not old. Someone is creative or quiet. | John is not old. | entailment | ((?[X]:((wise(X)|kind(X))))<=>((patient(lucy)|~curious(lucy))))&
((?[X]:((~brave(X)&curious(X))))<=>(calm(susan)))&
((?[X]:((~creative(X)&old(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(((~rich(john)<~>generous(john)))<=>(?[X]:((creative(X)<~>quiet(X)))))&
(((~old(lucy)<~>happy(lucy)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~happy(alice))<=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((~tall(X)|calm(X))<=>(~strong(X)<~>~rich(X))))&
(((~brave(mary)&~calm(mary)))<=>((brave(mary)<~>curious(mary))))&
((?[X]:(~curious(X)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((quiet(X)|~curious(X))<=>strong(X)))&
(![X]:((~curious(X)&~wise(X))<=>(~humble(X)&~rich(X))))&
(![X]:((old(X)|~strong(X))=>~old(X)))&
(![X]:((~curious(X)<~>tall(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(~calm(X)))=>((~quiet(john)|~tall(john))))&
(![X]:((~curious(X)|old(X))<=>(~funny(X)<~>~generous(X))))&
((?[X]:((~old(X)|~brave(X))))<=>(?[X]:(patient(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
((funny(susan)&~strong(susan)))&
(calm(alice))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|wise(X))))&
((~happy(susan)&~old(susan)))&
(?[X]:((creative(X)|quiet(X)))) | ~old(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2173710750417560860757699
% SZS output start Proof for 2173710750417560860757699
12. ! [X0] : ((~strong(X0) | old(X0)) => ~old(X0)) [input p11]
25. old(john) [input hypothesis]
30. ! [X0] : (~old(X0) | (strong(X0) & ~old(X0))) [ennf transformation 12]
143. ~old(X0) | ~old(X0) [cnf transformation 30]
171. old(john) [cnf transformation 25]
172. ~old(X0) [duplicate literal removal 143]
418. $false [subsumption resolution 171,172]
% SZS output end Proof for 2173710750417560860757699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits