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 not rich or not old is old or wise and vice versa.
Everyone who is generous or not creative is either not brave or wise.
If mary is not tall or not creative then paul is wise or not funny and vice versa.
Everyone who is either curious or humble is both rich and not rich.
Everyone who is both wise and not calm is either not patient or not old and vice versa.
If someone is not curious then someone is kind.
If someone is either not calm or not tall then mary is quiet.
Everyone who is creative is both patient and not strong and vice versa.
Everyone who is either not quiet or not humble is both not curious and creative and vice versa.
Everyone who is not humble is both happy and not quiet.
Everyone who is either not kind or strong is either calm or not creative and vice versa.
Everyone who is wise is both not creative and generous.
Everyone who is not quiet or not wise is either not curious or curious and vice versa.
If someone is both generous and not strong then fred is quiet.
Everyone who is not old or not patient is both not old and not calm and vice versa.
Everyone who is humble or not brave is both not patient and not generous.
Lucy is generous.
Someone is not old or quiet.
Susan is patient or kind.
Mary is either funny or creative.
Susan is either kind or creative. | Lucy is wise. | entailment | (![X]:((~rich(X)|~old(X))<=>(old(X)|wise(X))))&
(![X]:((generous(X)|~creative(X))=>(~brave(X)<~>wise(X))))&
(((~tall(mary)|~creative(mary)))<=>((wise(paul)|~funny(paul))))&
(![X]:((curious(X)<~>humble(X))=>(rich(X)&~rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>~old(X))))&
((?[X]:(~curious(X)))=>(?[X]:(kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(quiet(mary)))&
(![X]:(creative(X)<=>(patient(X)&~strong(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~quiet(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(calm(X)<~>~creative(X))))&
(![X]:(wise(X)=>(~creative(X)&generous(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((generous(X)&~strong(X))))=>(quiet(fred)))&
(![X]:((~old(X)|~patient(X))<=>(~old(X)&~calm(X))))&
(![X]:((humble(X)|~brave(X))=>(~patient(X)&~generous(X))))&
(generous(lucy))&
(?[X]:((~old(X)|quiet(X))))&
((patient(susan)|kind(susan)))&
((funny(mary)<~>creative(mary)))&
((kind(susan)<~>creative(susan))) | wise(lucy) | [
"p1",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6915367063019726363786625
% SZS output start Proof for 6915367063019726363786625
2. ! [X0] : ((~creative(X0) | generous(X0)) => (~brave(X0) <~> wise(X0))) [input p1]
16. ! [X0] : ((~brave(X0) | humble(X0)) => (~generous(X0) & ~patient(X0))) [input p15]
17. generous(lucy) [input p16]
22. ~wise(lucy) [input hypothesis]
25. ! [X0] : ((~brave(X0) <~> wise(X0)) | (creative(X0) & ~generous(X0))) [ennf transformation 2]
32. ! [X0] : ((~generous(X0) & ~patient(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 16]
35. ! [X0] : (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (creative(X0) & ~generous(X0))) [nnf transformation 25]
62. ~brave(X0) | wise(X0) | ~generous(X0) [cnf transformation 35]
118. ~generous(X0) | brave(X0) [cnf transformation 32]
119. generous(lucy) [cnf transformation 17]
126. ~wise(lucy) [cnf transformation 22]
227. brave(lucy) [resolution 118,119]
253. wise(lucy) | ~generous(lucy) [resolution 62,227]
254. ~generous(lucy) [subsumption resolution 253,126]
255. $false [subsumption resolution 254,119]
% SZS output end Proof for 6915367063019726363786625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is both calm and patient and vice versa. Everyone who is both generous and not funny is both strong and not tall. If someone is rich or creative then someone is both quiet and curious. If someone is not patient or patient then john is old or calm. Everyone who is either tall or not generous is either patient or wise and vice versa. If someone is not creative then paul is either not calm or quiet. If someone is not funny then mary is strong and vice versa. Everyone who is both not generous and not funny is both not curious and not brave and vice versa. Everyone who is either tall or strong is calm and vice versa. Everyone who is either happy or not calm is curious. If susan is either happy or old then paul is not old and vice versa. Everyone who is both not creative and not quiet is brave or rich and vice versa. If someone is rich then paul is happy and vice versa. Everyone who is both not happy and not funny is not funny or not kind and vice versa. If paul is both not kind and not rich then someone is curious or brave and vice versa. If someone is not humble then someone is humble and vice versa. Someone is quiet or not brave. Someone is either not wise or not patient. Someone is not wise. Someone is calm or quiet. Lucy is strong or not generous. Lucy is not strong. Someone is not generous or calm. Someone is either not strong or not brave. | Paul is calm. | entailment | ((?[X]:((~humble(X)&kind(X))))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:((generous(X)&~funny(X))=>(strong(X)&~tall(X))))&
((?[X]:((rich(X)|creative(X))))=>(?[X]:((quiet(X)&curious(X)))))&
((?[X]:((~patient(X)|patient(X))))=>((old(john)|calm(john))))&
(![X]:((tall(X)<~>~generous(X))<=>(patient(X)<~>wise(X))))&
((?[X]:(~creative(X)))=>((~calm(paul)<~>quiet(paul))))&
((?[X]:(~funny(X)))<=>(strong(mary)))&
(![X]:((~generous(X)&~funny(X))<=>(~curious(X)&~brave(X))))&
(![X]:((tall(X)<~>strong(X))<=>calm(X)))&
(![X]:((happy(X)<~>~calm(X))=>curious(X)))&
(((happy(susan)<~>old(susan)))<=>(~old(paul)))&
(![X]:((~creative(X)&~quiet(X))<=>(brave(X)|rich(X))))&
((?[X]:(rich(X)))<=>(happy(paul)))&
(![X]:((~happy(X)&~funny(X))<=>(~funny(X)|~kind(X))))&
(((~kind(paul)&~rich(paul)))<=>(?[X]:((curious(X)|brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(humble(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:(~wise(X)))&
(?[X]:((calm(X)|quiet(X))))&
((strong(lucy)|~generous(lucy)))&
(~strong(lucy))&
(?[X]:((~generous(X)|calm(X))))&
(?[X]:((~strong(X)<~>~brave(X)))) | calm(paul) | [
"p1",
"p2",
"p7",
"p8",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2946179568131753608202375
% SZS output start Proof for 2946179568131753608202375
2. ! [X0] : ((~funny(X0) & generous(X0)) => (~tall(X0) & strong(X0))) [input p1]
3. ? [X0] : (creative(X0) | rich(X0)) => ? [X0] : (curious(X0) & quiet(X0)) [input p2]
8. ! [X0] : ((~funny(X0) & ~generous(X0)) <=> (~brave(X0) & ~curious(X0))) [input p7]
9. ! [X0] : ((tall(X0) <~> strong(X0)) <=> calm(X0)) [input p8]
10. ! [X0] : ((happy(X0) <~> ~calm(X0)) => curious(X0)) [input p9]
13. ? [X0] : rich(X0) <=> happy(paul) [input p12]
14. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> (~kind(X0) | ~funny(X0))) [input p13]
15. (~rich(paul) & ~kind(paul)) <=> ? [X0] : (brave(X0) | curious(X0)) [input p14]
25. ~calm(paul) [input hypothesis]
27. ? [X0] : (creative(X0) | rich(X0)) => ? [X1] : (curious(X1) & quiet(X1)) [rectify 3]
29. ! [X0] : ((~tall(X0) & strong(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 2]
30. ! [X0] : ((~tall(X0) & strong(X0)) | funny(X0) | ~generous(X0)) [flattening 29]
31. ? [X1] : (curious(X1) & quiet(X1)) | ! [X0] : (~creative(X0) & ~rich(X0)) [ennf transformation 27]
35. ! [X0] : (curious(X0) | (happy(X0) <=> ~calm(X0))) [ennf transformation 10]
41. ? [X0] : (curious(X0) & quiet(X0)) | ! [X1] : (~creative(X1) & ~rich(X1)) [rectify 31]
42. ? [X0] : (curious(X0) & quiet(X0)) => (curious(sK2) & quiet(sK2)) [choice axiom]
43. (curious(sK2) & quiet(sK2)) | ! [X1] : (~creative(X1) & ~rich(X1)) [skolemisation 41,42]
50. ! [X0] : (((~funny(X0) & ~generous(X0)) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | (funny(X0) | generous(X0)))) [nnf transformation 8]
51. ! [X0] : (((~funny(X0) & ~generous(X0)) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | funny(X0) | generous(X0))) [flattening 50]
52. ! [X0] : ((((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | ~calm(X0)) & (calm(X0) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))))) [nnf transformation 9]
53. ! [X0] : (curious(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 35]
57. (? [X0] : rich(X0) | ~happy(paul)) & (happy(paul) | ! [X0] : ~rich(X0)) [nnf transformation 13]
58. (? [X0] : rich(X0) | ~happy(paul)) & (happy(paul) | ! [X1] : ~rich(X1)) [rectify 57]
59. ? [X0] : rich(X0) => rich(sK4) [choice axiom]
60. (rich(sK4) | ~happy(paul)) & (happy(paul) | ! [X1] : ~rich(X1)) [skolemisation 58,59]
61. ! [X0] : (((~funny(X0) & ~happy(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (funny(X0) | happy(X0)))) [nnf transformation 14]
62. ! [X0] : (((~funny(X0) & ~happy(X0)) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | funny(X0) | happy(X0))) [flattening 61]
63. ((~rich(paul) & ~kind(paul)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X0] : (brave(X0) | curious(X0)) | (rich(paul) | kind(paul))) [nnf transformation 15]
64. ((~rich(paul) & ~kind(paul)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X0] : (brave(X0) | curious(X0)) | rich(paul) | kind(paul)) [flattening 63]
65. ((~rich(paul) & ~kind(paul)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X1] : (brave(X1) | curious(X1)) | rich(paul) | kind(paul)) [rectify 64]
66. ? [X1] : (brave(X1) | curious(X1)) => (brave(sK5) | curious(sK5)) [choice axiom]
67. ((~rich(paul) & ~kind(paul)) | ! [X0] : (~brave(X0) & ~curious(X0))) & ((brave(sK5) | curious(sK5)) | rich(paul) | kind(paul)) [skolemisation 65,66]
91. ~generous(X0) | funny(X0) | strong(X0) [cnf transformation 30]
92. ~tall(X0) | funny(X0) | ~generous(X0) [cnf transformation 30]
95. curious(sK2) | ~rich(X1) [cnf transformation 43]
111. ~curious(X0) | funny(X0) | generous(X0) [cnf transformation 51]
116. ~strong(X0) | tall(X0) | calm(X0) [cnf transformation 52]
120. happy(X0) | curious(X0) | calm(X0) [cnf transformation 53]
131. rich(sK4) | ~happy(paul) [cnf transformation 60]
133. ~happy(X0) | funny(X0) [cnf transformation 62]
136. ~funny(X0) | kind(X0) [cnf transformation 62]
138. ~kind(paul) | ~curious(X0) [cnf transformation 67]
154. ~calm(paul) [cnf transformation 25]
185. 8 <=> curious(sK2) [avatar definition]
187. curious(sK2) <- (8) [avatar component clause 185]
190. 9 <=> ! [X1] : ~rich(X1) [avatar definition]
191. ~rich(X1) <- (9) [avatar component clause 190]
192. 9 | 8 [avatar split clause 95,185,190]
219. 16 <=> calm(paul) [avatar definition]
220. ~calm(paul) <- (~16) [avatar component clause 219]
258. 24 <=> happy(paul) [avatar definition]
260. ~happy(paul) <- (~24) [avatar component clause 258]
262. 25 <=> rich(sK4) [avatar definition]
264. rich(sK4) <- (25) [avatar component clause 262]
265. ~24 | 25 [avatar split clause 131,262,258]
276. 28 <=> ! [X0] : ~curious(X0) [avatar definition]
277. ~curious(X0) <- (28) [avatar component clause 276]
280. 29 <=> kind(paul) [avatar definition]
282. ~kind(paul) <- (~29) [avatar component clause 280]
284. 28 | ~29 [avatar split clause 138,280,276]
359. ~16 [avatar split clause 154,219]
366. $false <- (8, 28) [subsumption resolution 187,277]
367. ~8 | ~28 [avatar contradiction clause 366]
368. $false <- (9, 25) [resolution 264,191]
369. ~9 | ~25 [avatar contradiction clause 368]
422. curious(paul) | calm(paul) <- (~24) [resolution 120,260]
425. curious(X2) | calm(X2) | funny(X2) [resolution 120,133]
428. calm(paul) <- (~24, 28) [subsumption resolution 422,277]
429. $false <- (~16, ~24, 28) [subsumption resolution 428,220]
430. 16 | 24 | ~28 [avatar contradiction clause 429]
456. 58 <=> generous(paul) [avatar definition]
458. generous(paul) <- (58) [avatar component clause 456]
460. 59 <=> funny(paul) [avatar definition]
461. ~funny(paul) <- (~59) [avatar component clause 460]
462. funny(paul) <- (59) [avatar component clause 460]
596. funny(paul) | strong(paul) <- (58) [resolution 458,91]
606. 78 <=> tall(paul) [avatar definition]
608. tall(paul) <- (78) [avatar component clause 606]
611. 79 <=> strong(paul) [avatar definition]
613. strong(paul) <- (79) [avatar component clause 611]
614. 79 | 59 | ~58 [avatar split clause 596,456,460,611]
615. calm(X0) | funny(X0) | funny(X0) | generous(X0) [resolution 425,111]
617. funny(X0) | calm(X0) | generous(X0) [duplicate literal removal 615]
624. kind(paul) <- (59) [resolution 462,136]
625. $false <- (~29, 59) [subsumption resolution 624,282]
626. 29 | ~59 [avatar contradiction clause 625]
678. tall(paul) | calm(paul) <- (79) [resolution 613,116]
679. tall(paul) <- (~16, 79) [subsumption resolution 678,220]
680. 78 | 16 | ~79 [avatar split clause 679,611,219,606]
684. calm(paul) | generous(paul) <- (~59) [resolution 617,461]
699. funny(paul) | ~generous(paul) <- (78) [resolution 608,92]
703. ~generous(paul) <- (~59, 78) [subsumption resolution 699,461]
704. $false <- (58, ~59, 78) [subsumption resolution 703,458]
705. ~58 | 59 | ~78 [avatar contradiction clause 704]
727. generous(paul) <- (~16, ~59) [subsumption resolution 684,220]
728. 58 | 16 | 59 [avatar split clause 727,460,219,456]
729. $false [avatar sat refutation 192,265,284,359,367,369,430,614,626,680,705,728]
% SZS output end Proof for 2946179568131753608202375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both not strong and not creative and vice versa.
If alice is not wise then susan is brave or not old and vice versa.
Everyone who is both not strong and not rich is either not tall or funny and vice versa.
If susan is not calm then alice is either not calm or not funny and vice versa.
Everyone who is tall or brave is not wise and vice versa.
If someone is not calm then someone is not tall or not rich.
If alice is either wise or not brave then someone is both generous and not wise and vice versa.
If someone is calm then someone is calm or not funny and vice versa.
Everyone who is patient is tall or not old and vice versa.
Everyone who is generous is both rich and not quiet and vice versa.
Everyone who is not funny is either not old or patient and vice versa.
If someone is not tall then someone is not brave or not generous and vice versa.
Everyone who is either curious or not quiet is both not patient and not rich.
If fred is either generous or not patient then fred is not brave.
Everyone who is old is both creative and not funny and vice versa.
Everyone who is both not quiet and not curious is wise or not funny and vice versa.
Mary is either calm or patient.
Someone is brave.
John is either not funny or tall.
Susan is not curious.
Someone is tall. | Alice is not old. | entailment | (![X]:(calm(X)<=>(~strong(X)&~creative(X))))&
((~wise(alice))<=>((brave(susan)|~old(susan))))&
(![X]:((~strong(X)&~rich(X))<=>(~tall(X)<~>funny(X))))&
((~calm(susan))<=>((~calm(alice)<~>~funny(alice))))&
(![X]:((tall(X)|brave(X))<=>~wise(X)))&
((?[X]:(~calm(X)))=>(?[X]:((~tall(X)|~rich(X)))))&
(((wise(alice)<~>~brave(alice)))<=>(?[X]:((generous(X)&~wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:(brave(X)))&
((~funny(john)<~>tall(john)))&
(~curious(susan))&
(?[X]:(tall(X))) | ~old(alice) | [
"p8",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 872188552466033956537918
% SZS output start Proof for 872188552466033956537918
9. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p8]
11. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p10]
13. ! [X0] : ((curious(X0) <~> ~quiet(X0)) => (~rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p14]
16. ! [X0] : ((~curious(X0) & ~quiet(X0)) <=> (~funny(X0) | wise(X0))) [input p15]
22. old(alice) [input hypothesis]
27. ! [X0] : ((~rich(X0) & ~patient(X0)) | (curious(X0) <=> ~quiet(X0))) [ennf transformation 13]
50. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 50]
54. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 11]
60. ! [X0] : ((~rich(X0) & ~patient(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) [nnf transformation 27]
62. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 15]
63. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 62]
64. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | (curious(X0) | quiet(X0)))) [nnf transformation 16]
65. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | curious(X0) | quiet(X0))) [flattening 64]
103. patient(X0) | old(X0) [cnf transformation 51]
107. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 54]
108. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 54]
115. ~patient(X0) | curious(X0) | quiet(X0) [cnf transformation 60]
121. ~funny(X0) | ~old(X0) [cnf transformation 63]
125. ~quiet(X0) | funny(X0) [cnf transformation 65]
127. ~curious(X0) | funny(X0) [cnf transformation 65]
135. old(alice) [cnf transformation 22]
152. 4 <=> funny(alice) [avatar definition]
153. ~funny(alice) <- (~4) [avatar component clause 152]
154. funny(alice) <- (4) [avatar component clause 152]
201. 14 <=> ! [X1] : funny(X1) [avatar definition]
202. funny(X1) <- (14) [avatar component clause 201]
221. funny(X0) | old(X0) [subsumption resolution 108,103]
222. patient(X0) | funny(X0) [subsumption resolution 107,221]
288. ~old(alice) <- (4) [resolution 121,154]
289. $false <- (4) [subsumption resolution 288,135]
290. ~4 [avatar contradiction clause 289]
373. curious(X0) | quiet(X0) | funny(X0) [resolution 115,222]
379. quiet(X0) | funny(X0) [subsumption resolution 373,127]
380. funny(X0) [subsumption resolution 379,125]
381. 14 [avatar split clause 380,201]
423. $false <- (~4, 14) [resolution 202,153]
426. 4 | ~14 [avatar contradiction clause 423]
427. $false [avatar sat refutation 290,381,426]
% SZS output end Proof for 872188552466033956537918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is not calm and vice versa.
Everyone who is both creative and strong is not happy or not kind.
Everyone who is creative or strong is not generous and vice versa.
If someone is strong then someone is not quiet.
Everyone who is both patient and not patient is brave and vice versa.
Everyone who is funny is not patient or not wise.
If paul is both not creative and not wise then someone is both tall and humble and vice versa.
If mary is not kind then fred is either not strong or not curious.
Everyone who is not strong or strong is either brave or happy and vice versa.
Everyone who is generous or not strong is both not brave and patient.
If someone is either not calm or not funny then fred is both not funny and not creative and vice versa.
Everyone who is humble is not curious or humble.
If lucy is not funny or not humble then paul is both not patient and not wise.
Everyone who is either not rich or calm is not old or kind.
Everyone who is either not tall or quiet is not wise.
If lucy is either not humble or strong then someone is funny or curious and vice versa.
Alice is both not brave and not wise.
Paul is both rich and generous.
Lucy is either happy or not quiet.
Someone is both not patient and not funny.
Someone is not brave.
Mary is both not tall and not generous.
Someone is either creative or happy.
Someone is rich or wise. | Fred is not funny. | entailment | (![X]:(~happy(X)<=>~calm(X)))&
(![X]:((creative(X)&strong(X))=>(~happy(X)|~kind(X))))&
(![X]:((creative(X)|strong(X))<=>~generous(X)))&
((?[X]:(strong(X)))=>(?[X]:(~quiet(X))))&
(![X]:((patient(X)&~patient(X))<=>brave(X)))&
(![X]:(funny(X)=>(~patient(X)|~wise(X))))&
(((~creative(paul)&~wise(paul)))<=>(?[X]:((tall(X)&humble(X)))))&
((~kind(mary))=>((~strong(fred)<~>~curious(fred))))&
(![X]:((~strong(X)|strong(X))<=>(brave(X)<~>happy(X))))&
(![X]:((generous(X)|~strong(X))=>(~brave(X)&patient(X))))&
((?[X]:((~calm(X)<~>~funny(X))))<=>((~funny(fred)&~creative(fred))))&
(![X]:(humble(X)=>(~curious(X)|humble(X))))&
(((~funny(lucy)|~humble(lucy)))=>((~patient(paul)&~wise(paul))))&
(![X]:((~rich(X)<~>calm(X))=>(~old(X)|kind(X))))&
(![X]:((~tall(X)<~>quiet(X))=>~wise(X)))&
(((~humble(lucy)<~>strong(lucy)))<=>(?[X]:((funny(X)|curious(X)))))&
((~brave(alice)&~wise(alice)))&
((rich(paul)&generous(paul)))&
((happy(lucy)<~>~quiet(lucy)))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(~brave(X)))&
((~tall(mary)&~generous(mary)))&
(?[X]:((creative(X)<~>happy(X))))&
(?[X]:((rich(X)|wise(X)))) | ~funny(fred) | [
"p0",
"p4",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7807187279019465964831692
% SZS output start Proof for 7807187279019465964831692
1. ! [X0] : (~happy(X0) <=> ~calm(X0)) [input p0]
5. ! [X0] : ((~patient(X0) & patient(X0)) <=> brave(X0)) [input p4]
9. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (brave(X0) <~> happy(X0))) [input p8]
11. ? [X0] : (~calm(X0) <~> ~funny(X0)) <=> (~creative(fred) & ~funny(fred)) [input p10]
20. ? [X0] : (~funny(X0) & ~patient(X0)) [input p19]
25. funny(fred) [input hypothesis]
41. ! [X0] : ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))) [nnf transformation 1]
47. ! [X0] : (((~patient(X0) & patient(X0)) | ~brave(X0)) & (brave(X0) | (patient(X0) | ~patient(X0)))) [nnf transformation 5]
48. ! [X0] : (((~patient(X0) & patient(X0)) | ~brave(X0)) & (brave(X0) | patient(X0) | ~patient(X0))) [flattening 47]
55. ! [X0] : (((strong(X0) | ~strong(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (~strong(X0) & strong(X0)))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~strong(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (~strong(X0) & strong(X0)))) [flattening 55]
57. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (creative(fred) | funny(fred))) & ((~creative(fred) & ~funny(fred)) | ! [X0] : ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) [nnf transformation 11]
58. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X0] : ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) [flattening 57]
59. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X1] : ((~calm(X1) | funny(X1)) & (~funny(X1) | calm(X1)))) [rectify 58]
60. ? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) => ((funny(sK2) | calm(sK2)) & (~funny(sK2) | ~calm(sK2))) [choice axiom]
61. (((funny(sK2) | calm(sK2)) & (~funny(sK2) | ~calm(sK2))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X1] : ((~calm(X1) | funny(X1)) & (~funny(X1) | calm(X1)))) [skolemisation 59,60]
68. ? [X0] : (~funny(X0) & ~patient(X0)) => (~funny(sK4) & ~patient(sK4)) [choice axiom]
69. ~funny(sK4) & ~patient(sK4) [skolemisation 20,68]
76. ~happy(X0) | calm(X0) [cnf transformation 41]
83. patient(X0) | ~brave(X0) [cnf transformation 48]
84. ~brave(X0) | ~patient(X0) [cnf transformation 48]
92. happy(X0) | brave(X0) | strong(X0) [cnf transformation 56]
93. happy(X0) | brave(X0) | ~strong(X0) [cnf transformation 56]
103. ~funny(fred) | ~calm(X1) | funny(X1) [cnf transformation 61]
127. ~funny(sK4) [cnf transformation 69]
133. funny(fred) [cnf transformation 25]
142. ~brave(X0) [subsumption resolution 83,84]
180. ~strong(X0) | happy(X0) [subsumption resolution 93,142]
181. happy(X0) | strong(X0) [subsumption resolution 92,142]
182. happy(X0) [subsumption resolution 181,180]
184. 11 <=> funny(fred) [avatar definition]
202. 15 <=> ! [X1] : (~calm(X1) | funny(X1)) [avatar definition]
203. ~calm(X1) | funny(X1) <- (15) [avatar component clause 202]
209. 15 | ~11 [avatar split clause 103,184,202]
253. 11 [avatar split clause 133,184]
259. calm(X0) [resolution 76,182]
277. funny(X0) <- (15) [resolution 203,259]
278. $false <- (15) [resolution 277,127]
279. ~15 [avatar contradiction clause 278]
280. $false [avatar sat refutation 209,253,279]
% SZS output end Proof for 7807187279019465964831692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either happy or rich and vice versa.
Everyone who is wise is quiet or not curious.
Everyone who is either not wise or tall is both not patient and creative.
Everyone who is both patient and funny is both not old and not patient and vice versa.
Everyone who is not generous is kind or not wise and vice versa.
If someone is not happy then someone is either happy or funny.
Everyone who is not patient or not strong is either kind or rich.
If someone is not generous then john is not rich or rich and vice versa.
Everyone who is either old or not old is either humble or curious.
Everyone who is either not brave or not creative is not curious or happy and vice versa.
Everyone who is not creative is both not curious and not tall and vice versa.
Everyone who is both kind and quiet is either wise or not wise and vice versa.
Everyone who is rich or not curious is not funny or curious and vice versa.
If susan is both wise and not old then someone is both quiet and brave.
Everyone who is creative or not quiet is both not calm and not wise and vice versa.
Everyone who is calm or humble is either not quiet or happy.
Someone is calm or quiet.
Someone is not curious or tall.
Susan is generous or not generous.
Someone is kind or not rich. | John is generous. | contradiction | (![X]:(~generous(X)<=>(happy(X)<~>rich(X))))&
(![X]:(wise(X)=>(quiet(X)|~curious(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~patient(X)&creative(X))))&
(![X]:((patient(X)&funny(X))<=>(~old(X)&~patient(X))))&
(![X]:(~generous(X)<=>(kind(X)|~wise(X))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)<~>funny(X)))))&
(![X]:((~patient(X)|~strong(X))=>(kind(X)<~>rich(X))))&
((?[X]:(~generous(X)))<=>((~rich(john)|rich(john))))&
(![X]:((old(X)<~>~old(X))=>(humble(X)<~>curious(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~curious(X)|happy(X))))&
(![X]:(~creative(X)<=>(~curious(X)&~tall(X))))&
(![X]:((kind(X)&quiet(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((rich(X)|~curious(X))<=>(~funny(X)|curious(X))))&
(((wise(susan)&~old(susan)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:((calm(X)|humble(X))=>(~quiet(X)<~>happy(X))))&
(?[X]:((calm(X)|quiet(X))))&
(?[X]:((~curious(X)|tall(X))))&
((generous(susan)|~generous(susan)))&
(?[X]:((kind(X)|~rich(X)))) | generous(john) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 52130303226644615736187
% SZS output start Proof for 52130303226644615736187
5. ! [X0] : (~generous(X0) <=> (~wise(X0) | kind(X0))) [input p4]
12. ! [X0] : ((quiet(X0) & kind(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p11]
21. generous(john) [input hypothesis]
37. ! [X0] : ((~generous(X0) | (wise(X0) & ~kind(X0))) & ((~wise(X0) | kind(X0)) | generous(X0))) [nnf transformation 5]
38. ! [X0] : ((~generous(X0) | (wise(X0) & ~kind(X0))) & (~wise(X0) | kind(X0) | generous(X0))) [flattening 37]
54. ! [X0] : (((quiet(X0) & kind(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 12]
55. ! [X0] : (((quiet(X0) & kind(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~quiet(X0) | ~kind(X0))) [flattening 54]
83. ~kind(X0) | ~generous(X0) [cnf transformation 38]
107. kind(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 55]
108. kind(X0) | wise(X0) | wise(X0) [cnf transformation 55]
130. generous(john) [cnf transformation 21]
133. kind(X0) | ~wise(X0) [duplicate literal removal 107]
134. kind(X0) | wise(X0) [duplicate literal removal 108]
169. kind(X0) [subsumption resolution 133,134]
195. ~generous(X0) [resolution 83,169]
197. $false [resolution 195,130]
% SZS output end Proof for 52130303226644615736187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or curious then mary is curious and vice versa.
Everyone who is happy is either strong or calm.
Everyone who is both not strong and curious is either patient or not wise and vice versa.
Everyone who is old is both not patient and brave and vice versa.
Everyone who is strong is either not strong or not humble.
If mary is not happy or not funny then alice is either humble or wise.
Everyone who is funny is not creative.
Everyone who is strong or rich is either rich or humble.
If susan is both patient and not patient then susan is not calm or not generous and vice versa.
Everyone who is not happy or quiet is either not curious or not brave.
If paul is brave or not strong then someone is quiet or happy.
Everyone who is both strong and not old is funny and vice versa.
Everyone who is both not happy and strong is either not humble or humble.
Everyone who is not rich is strong or not brave.
Everyone who is kind is not funny and vice versa.
If fred is quiet then alice is both not funny and creative and vice versa.
Someone is patient.
Someone is not creative or not wise.
Fred is happy or not calm.
Fred is not strong or wise.
Alice is either not rich or not tall.
Someone is not tall or funny.
Susan is wise.
Someone is humble. | Alice is rich. | neutral | ((?[X]:((~rich(X)<~>curious(X))))<=>(curious(mary)))&
(![X]:(happy(X)=>(strong(X)<~>calm(X))))&
(![X]:((~strong(X)&curious(X))<=>(patient(X)<~>~wise(X))))&
(![X]:(old(X)<=>(~patient(X)&brave(X))))&
(![X]:(strong(X)=>(~strong(X)<~>~humble(X))))&
(((~happy(mary)|~funny(mary)))=>((humble(alice)<~>wise(alice))))&
(![X]:(funny(X)=>~creative(X)))&
(![X]:((strong(X)|rich(X))=>(rich(X)<~>humble(X))))&
(((patient(susan)&~patient(susan)))<=>((~calm(susan)|~generous(susan))))&
(![X]:((~happy(X)|quiet(X))=>(~curious(X)<~>~brave(X))))&
(((brave(paul)|~strong(paul)))=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((strong(X)&~old(X))<=>funny(X)))&
(![X]:((~happy(X)&strong(X))=>(~humble(X)<~>humble(X))))&
(![X]:(~rich(X)=>(strong(X)|~brave(X))))&
(![X]:(kind(X)<=>~funny(X)))&
((quiet(fred))<=>((~funny(alice)&creative(alice))))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)|~wise(X))))&
((happy(fred)|~calm(fred)))&
((~strong(fred)|wise(fred)))&
((~rich(alice)<~>~tall(alice)))&
(?[X]:((~tall(X)|funny(X))))&
(wise(susan))&
(?[X]:(humble(X))) | rich(alice) | [] | null | 0 |
Everyone who is not curious is both not brave and not wise. Everyone who is either not old or quiet is kind and vice versa. Everyone who is both not calm and calm is either not rich or not patient. Everyone who is both not quiet and not rich is both generous and curious. If someone is both kind and not old then someone is tall or creative. Everyone who is either creative or tall is either funny or not happy. If lucy is both not generous and not creative then alice is both not wise and tall and vice versa. If someone is both not old and not funny then someone is not funny and vice versa. Everyone who is both not patient and generous is curious and vice versa. If susan is humble then someone is either not generous or not curious. If someone is brave or funny then someone is both not old and not happy and vice versa. Everyone who is either not creative or rich is both not calm and patient. If someone is either not generous or not curious then someone is not creative and vice versa. Everyone who is both not brave and not kind is strong. If someone is both quiet and happy then lucy is both humble and not quiet. Someone is not rich. Mary is not tall or not happy. Someone is not creative or not old. Fred is either not humble or old. Lucy is both not brave and generous. Lucy is either happy or calm. Fred is not humble or wise. John is quiet. | Lucy is tall. | neutral | (![X]:(~curious(X)=>(~brave(X)&~wise(X))))&
(![X]:((~old(X)<~>quiet(X))<=>kind(X)))&
(![X]:((~calm(X)&calm(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~rich(X))=>(generous(X)&curious(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((creative(X)<~>tall(X))=>(funny(X)<~>~happy(X))))&
(((~generous(lucy)&~creative(lucy)))<=>((~wise(alice)&tall(alice))))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&generous(X))<=>curious(X)))&
((humble(susan))=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((brave(X)|funny(X))))<=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~calm(X)&patient(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~brave(X)&~kind(X))=>strong(X)))&
((?[X]:((quiet(X)&happy(X))))=>((humble(lucy)&~quiet(lucy))))&
(?[X]:(~rich(X)))&
((~tall(mary)|~happy(mary)))&
(?[X]:((~creative(X)|~old(X))))&
((~humble(fred)<~>old(fred)))&
((~brave(lucy)&generous(lucy)))&
((happy(lucy)<~>calm(lucy)))&
((~humble(fred)|wise(fred)))&
(quiet(john)) | tall(lucy) | [] | null | 0 |
Everyone who is both old and not strong is not funny or strong and vice versa. Everyone who is both not old and wise is strong. Everyone who is both tall and humble is either not curious or not brave and vice versa. Everyone who is not happy or tall is not humble or not wise and vice versa. Everyone who is both not tall and not calm is old and vice versa. If paul is either not curious or not humble then john is not brave or quiet. Everyone who is both not rich and not kind is both funny and kind and vice versa. Everyone who is generous is either not strong or happy and vice versa. Everyone who is patient is both curious and funny. Everyone who is both not calm and old is quiet and vice versa. Everyone who is either not funny or wise is humble and vice versa. If someone is not funny then someone is funny or old and vice versa. If fred is either not humble or patient then someone is not brave or humble and vice versa. If someone is both happy and not humble then lucy is not wise or not rich and vice versa. If someone is either quiet or not patient then alice is not tall and vice versa. Everyone who is not calm is brave or not rich and vice versa. Lucy is not calm or not patient. Someone is either calm or patient. Alice is either old or wise. Lucy is both funny and rich. John is both wise and not funny. Mary is either old or not old. Paul is not kind or wise. Fred is not curious or generous. | John is quiet. | entailment | (![X]:((old(X)&~strong(X))<=>(~funny(X)|strong(X))))&
(![X]:((~old(X)&wise(X))=>strong(X)))&
(![X]:((tall(X)&humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((~happy(X)|tall(X))<=>(~humble(X)|~wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>old(X)))&
(((~curious(paul)<~>~humble(paul)))=>((~brave(john)|quiet(john))))&
(![X]:((~rich(X)&~kind(X))<=>(funny(X)&kind(X))))&
(![X]:(generous(X)<=>(~strong(X)<~>happy(X))))&
(![X]:(patient(X)=>(curious(X)&funny(X))))&
(![X]:((~calm(X)&old(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>wise(X))<=>humble(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)|old(X)))))&
(((~humble(fred)<~>patient(fred)))<=>(?[X]:((~brave(X)|humble(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>((~wise(lucy)|~rich(lucy))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(~tall(alice)))&
(![X]:(~calm(X)<=>(brave(X)|~rich(X))))&
((~calm(lucy)|~patient(lucy)))&
(?[X]:((calm(X)<~>patient(X))))&
((old(alice)<~>wise(alice)))&
((funny(lucy)&rich(lucy)))&
((wise(john)&~funny(john)))&
((old(mary)<~>~old(mary)))&
((~kind(paul)|wise(paul)))&
((~curious(fred)|generous(fred))) | quiet(john) | [
"p0",
"p4",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8045423119473926503443121
% SZS output start Proof for 8045423119473926503443121
1. ! [X0] : ((~strong(X0) & old(X0)) <=> (strong(X0) | ~funny(X0))) [input p0]
5. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> old(X0)) [input p4]
10. ! [X0] : ((old(X0) & ~calm(X0)) <=> quiet(X0)) [input p9]
21. ~funny(john) & wise(john) [input p20]
25. ~quiet(john) [input hypothesis]
34. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 1]
35. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | strong(X0) | ~old(X0))) [flattening 34]
40. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | (calm(X0) | tall(X0)))) [nnf transformation 5]
41. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | calm(X0) | tall(X0))) [flattening 40]
46. ! [X0] : (((old(X0) & ~calm(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) | calm(X0)))) [nnf transformation 10]
47. ! [X0] : (((old(X0) & ~calm(X0)) | ~quiet(X0)) & (quiet(X0) | ~old(X0) | calm(X0))) [flattening 46]
75. funny(X0) | old(X0) [cnf transformation 35]
92. ~calm(X0) | ~old(X0) [cnf transformation 41]
103. quiet(X0) | ~old(X0) | calm(X0) [cnf transformation 47]
139. ~funny(john) [cnf transformation 21]
144. ~quiet(john) [cnf transformation 25]
164. 4 <=> quiet(john) [avatar definition]
165. ~quiet(john) <- (~4) [avatar component clause 164]
170. ~old(X0) | quiet(X0) [subsumption resolution 103,92]
297. ~4 [avatar split clause 144,164]
298. old(john) [resolution 75,139]
309. quiet(john) [resolution 170,298]
311. $false <- (~4) [subsumption resolution 309,165]
312. 4 [avatar contradiction clause 311]
313. $false [avatar sat refutation 297,312]
% SZS output end Proof for 8045423119473926503443121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and happy is both not calm and patient and vice versa.
If fred is either creative or patient then fred is both not patient and kind.
If someone is both strong and not strong then paul is kind or not generous.
Everyone who is not humble is not curious or tall.
Everyone who is not old is brave or not kind.
Everyone who is either quiet or not creative is both strong and tall.
Everyone who is both not curious and not humble is either happy or brave.
Everyone who is not strong or wise is either tall or quiet.
If someone is either kind or not funny then someone is wise.
Everyone who is either not kind or rich is both rich and old and vice versa.
If fred is both not humble and curious then someone is both curious and patient and vice versa.
Everyone who is not quiet or patient is happy or creative.
Everyone who is kind or brave is either old or not humble and vice versa.
If someone is tall or kind then someone is not generous or old.
Everyone who is either not patient or tall is both brave and not happy.
If someone is either funny or not creative then someone is either old or not patient.
Mary is not patient or not brave.
Someone is not quiet.
Lucy is both not wise and not quiet.
Mary is both not brave and not tall.
Someone is both happy and not strong.
Mary is not creative.
Paul is both wise and not patient.
Someone is humble or kind. | Mary is not happy. | contradiction | (![X]:((old(X)&happy(X))<=>(~calm(X)&patient(X))))&
(((creative(fred)<~>patient(fred)))=>((~patient(fred)&kind(fred))))&
((?[X]:((strong(X)&~strong(X))))=>((kind(paul)|~generous(paul))))&
(![X]:(~humble(X)=>(~curious(X)|tall(X))))&
(![X]:(~old(X)=>(brave(X)|~kind(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(strong(X)&tall(X))))&
(![X]:((~curious(X)&~humble(X))=>(happy(X)<~>brave(X))))&
(![X]:((~strong(X)|wise(X))=>(tall(X)<~>quiet(X))))&
((?[X]:((kind(X)<~>~funny(X))))=>(?[X]:(wise(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(rich(X)&old(X))))&
(((~humble(fred)&curious(fred)))<=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((~quiet(X)|patient(X))=>(happy(X)|creative(X))))&
(![X]:((kind(X)|brave(X))<=>(old(X)<~>~humble(X))))&
((?[X]:((tall(X)|kind(X))))=>(?[X]:((~generous(X)|old(X)))))&
(![X]:((~patient(X)<~>tall(X))=>(brave(X)&~happy(X))))&
((?[X]:((funny(X)<~>~creative(X))))=>(?[X]:((old(X)<~>~patient(X)))))&
((~patient(mary)|~brave(mary)))&
(?[X]:(~quiet(X)))&
((~wise(lucy)&~quiet(lucy)))&
((~brave(mary)&~tall(mary)))&
(?[X]:((happy(X)&~strong(X))))&
(~creative(mary))&
((wise(paul)&~patient(paul)))&
(?[X]:((humble(X)|kind(X)))) | ~happy(mary) | [
"p11",
"p14",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1966619260307923773561577
% SZS output start Proof for 1966619260307923773561577
12. ! [X0] : ((patient(X0) | ~quiet(X0)) => (creative(X0) | happy(X0))) [input p11]
15. ! [X0] : ((~patient(X0) <~> tall(X0)) => (~happy(X0) & brave(X0))) [input p14]
20. ~tall(mary) & ~brave(mary) [input p19]
22. ~creative(mary) [input p21]
25. ~happy(mary) [input hypothesis]
41. ! [X0] : ((creative(X0) | happy(X0)) | (~patient(X0) & quiet(X0))) [ennf transformation 12]
42. ! [X0] : (creative(X0) | happy(X0) | (~patient(X0) & quiet(X0))) [flattening 41]
43. ! [X0] : ((~happy(X0) & brave(X0)) | (~patient(X0) <=> tall(X0))) [ennf transformation 15]
64. ! [X0] : ((~happy(X0) & brave(X0)) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 43]
108. ~patient(X0) | happy(X0) | creative(X0) [cnf transformation 42]
115. brave(X0) | tall(X0) | patient(X0) [cnf transformation 64]
127. ~brave(mary) [cnf transformation 20]
128. ~tall(mary) [cnf transformation 20]
131. ~creative(mary) [cnf transformation 22]
135. ~happy(mary) [cnf transformation 25]
209. 16 <=> patient(mary) [avatar definition]
210. patient(mary) <- (16) [avatar component clause 209]
213. 17 <=> brave(mary) [avatar definition]
215. ~brave(mary) <- (~17) [avatar component clause 213]
217. ~17 [avatar split clause 127,213]
342. tall(mary) | patient(mary) <- (~17) [resolution 115,215]
345. patient(mary) <- (~17) [subsumption resolution 342,128]
346. 16 | 17 [avatar split clause 345,213,209]
347. happy(mary) | creative(mary) <- (16) [resolution 210,108]
350. creative(mary) <- (16) [subsumption resolution 347,135]
351. $false <- (16) [subsumption resolution 350,131]
352. ~16 [avatar contradiction clause 351]
354. $false [avatar sat refutation 217,346,352]
% SZS output end Proof for 1966619260307923773561577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If susan is strong then fred is not humble.
Everyone who is generous or not quiet is humble or curious and vice versa.
Everyone who is either old or not humble is not quiet or not kind and vice versa.
Everyone who is happy or rich is either wise or patient.
If fred is brave or not quiet then someone is calm.
If someone is either strong or not calm then mary is both curious and not quiet.
Everyone who is brave or wise is not rich.
If someone is wise or curious then someone is both not rich and tall.
Everyone who is either creative or not kind is both not funny and quiet and vice versa.
Everyone who is either humble or not quiet is both not happy and not calm.
If someone is tall or not strong then someone is either not happy or creative and vice versa.
If someone is not calm or tall then someone is calm and vice versa.
Everyone who is strong is both curious and not curious and vice versa.
Everyone who is both quiet and patient is humble or calm.
Everyone who is both not funny and old is not happy.
Everyone who is calm is curious and vice versa.
Alice is either not wise or generous.
Someone is both not creative and wise.
Someone is either curious or rich.
John is both brave and not rich.
Someone is both not rich and quiet.
Susan is both happy and kind.
Someone is not humble.
Fred is not tall. | Mary is not strong. | entailment | ((strong(susan))=>(~humble(fred)))&
(![X]:((generous(X)|~quiet(X))<=>(humble(X)|curious(X))))&
(![X]:((old(X)<~>~humble(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((happy(X)|rich(X))=>(wise(X)<~>patient(X))))&
(((brave(fred)|~quiet(fred)))=>(?[X]:(calm(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((curious(mary)&~quiet(mary))))&
(![X]:((brave(X)|wise(X))=>~rich(X)))&
((?[X]:((wise(X)|curious(X))))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((creative(X)<~>~kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((humble(X)<~>~quiet(X))=>(~happy(X)&~calm(X))))&
((?[X]:((tall(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(curious(X)&~curious(X))))&
(![X]:((quiet(X)&patient(X))=>(humble(X)|calm(X))))&
(![X]:((~funny(X)&old(X))=>~happy(X)))&
(![X]:(calm(X)<=>curious(X)))&
((~wise(alice)<~>generous(alice)))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((curious(X)<~>rich(X))))&
((brave(john)&~rich(john)))&
(?[X]:((~rich(X)&quiet(X))))&
((happy(susan)&kind(susan)))&
(?[X]:(~humble(X)))&
(~tall(fred)) | ~strong(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7823405689705920698339574
% SZS output start Proof for 7823405689705920698339574
13. ! [X0] : (strong(X0) <=> (~curious(X0) & curious(X0))) [input p12]
25. strong(mary) [input hypothesis]
64. ! [X0] : ((strong(X0) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | ~strong(X0))) [nnf transformation 13]
65. ! [X0] : ((strong(X0) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | ~strong(X0))) [flattening 64]
123. curious(X0) | ~strong(X0) [cnf transformation 65]
124. ~curious(X0) | ~strong(X0) [cnf transformation 65]
144. strong(mary) [cnf transformation 25]
259. ~strong(X0) [subsumption resolution 123,124]
280. $false [subsumption resolution 144,259]
% SZS output end Proof for 7823405689705920698339574
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not calm is old or not calm.
Everyone who is not creative is either not happy or strong and vice versa.
If paul is patient or not patient then john is wise or creative.
Everyone who is either creative or not old is not patient and vice versa.
If lucy is generous or not calm then mary is either not rich or not strong.
If mary is both not calm and calm then someone is not funny or happy and vice versa.
If fred is tall then someone is both not brave and not rich.
Everyone who is not tall or humble is both calm and strong.
If someone is either not calm or not old then someone is either rich or not humble and vice versa.
Everyone who is not funny is not patient and vice versa.
Everyone who is either curious or happy is both not wise and not quiet.
If someone is either not quiet or tall then lucy is not curious.
Everyone who is strong or calm is not funny and vice versa.
Everyone who is not calm or not happy is not calm or kind.
Everyone who is both kind and not happy is curious.
Someone is not creative or not happy.
Someone is both not kind and not strong.
Paul is either not rich or curious.
Alice is not rich or funny.
Lucy is both not curious and not happy. | Alice is not funny. | contradiction | (![X]:((calm(X)<~>~calm(X))=>(old(X)|~calm(X))))&
(![X]:(~creative(X)<=>(~happy(X)<~>strong(X))))&
(((patient(paul)|~patient(paul)))=>((wise(john)|creative(john))))&
(![X]:((creative(X)<~>~old(X))<=>~patient(X)))&
(((generous(lucy)|~calm(lucy)))=>((~rich(mary)<~>~strong(mary))))&
(((~calm(mary)&calm(mary)))<=>(?[X]:((~funny(X)|happy(X)))))&
((tall(fred))=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((~tall(X)|humble(X))=>(calm(X)&strong(X))))&
((?[X]:((~calm(X)<~>~old(X))))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:(~funny(X)<=>~patient(X)))&
(![X]:((curious(X)<~>happy(X))=>(~wise(X)&~quiet(X))))&
((?[X]:((~quiet(X)<~>tall(X))))=>(~curious(lucy)))&
(![X]:((strong(X)|calm(X))<=>~funny(X)))&
(![X]:((~calm(X)|~happy(X))=>(~calm(X)|kind(X))))&
(![X]:((kind(X)&~happy(X))=>curious(X)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)&~strong(X))))&
((~rich(paul)<~>curious(paul)))&
((~rich(alice)|funny(alice)))&
((~curious(lucy)&~happy(lucy))) | ~funny(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7499992006185853415886360
% SZS output start Proof for 7499992006185853415886360
6. (calm(mary) & ~calm(mary)) <=> ? [X0] : (happy(X0) | ~funny(X0)) [input p5]
21. ~funny(alice) [input hypothesis]
42. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X0] : (happy(X0) | ~funny(X0)) | (~calm(mary) | calm(mary))) [nnf transformation 6]
43. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X0] : (happy(X0) | ~funny(X0)) | ~calm(mary) | calm(mary)) [flattening 42]
44. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X1] : (happy(X1) | ~funny(X1)) | ~calm(mary) | calm(mary)) [rectify 43]
45. ? [X1] : (happy(X1) | ~funny(X1)) => (happy(sK0) | ~funny(sK0)) [choice axiom]
46. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & ((happy(sK0) | ~funny(sK0)) | ~calm(mary) | calm(mary)) [skolemisation 44,45]
79. ~calm(mary) | funny(X0) [cnf transformation 46]
81. calm(mary) | funny(X0) [cnf transformation 46]
118. ~funny(alice) [cnf transformation 21]
153. 8 <=> calm(mary) [avatar definition]
158. 9 <=> ! [X0] : funny(X0) [avatar definition]
159. funny(X0) <- (9) [avatar component clause 158]
160. 9 | 8 [avatar split clause 81,153,158]
162. 9 | ~8 [avatar split clause 79,153,158]
243. 27 <=> funny(alice) [avatar definition]
244. ~funny(alice) <- (~27) [avatar component clause 243]
248. ~27 [avatar split clause 118,243]
249. $false <- (9, ~27) [resolution 244,159]
250. ~9 | 27 [avatar contradiction clause 249]
251. $false [avatar sat refutation 160,162,248,250]
% SZS output end Proof for 7499992006185853415886360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not happy and not old then john is funny or patient and vice versa.
If someone is either generous or not old then someone is not generous and vice versa.
Everyone who is either not generous or quiet is not wise or not kind and vice versa.
Everyone who is not funny is both not tall and brave.
Everyone who is both strong and not generous is calm or not old and vice versa.
Everyone who is brave or not rich is generous or old.
If john is both not tall and brave then alice is not kind or old and vice versa.
Everyone who is not curious is either patient or creative and vice versa.
Everyone who is not calm or kind is both not humble and creative and vice versa.
If john is either not funny or curious then john is either creative or generous and vice versa.
Everyone who is not patient or not creative is humble and vice versa.
If susan is either not curious or curious then alice is not rich.
If someone is both happy and not strong then someone is quiet and vice versa.
Everyone who is patient or creative is tall or not brave.
If someone is either happy or kind then alice is not curious or creative and vice versa.
Fred is both tall and funny.
Fred is either not funny or calm.
Alice is both brave and curious.
Someone is quiet or not humble.
Someone is not humble.
Mary is not kind or not patient.
John is curious or old.
Paul is either not strong or kind. | Susan is not funny. | neutral | (((~happy(lucy)&~old(lucy)))<=>((funny(john)|patient(john))))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~wise(X)|~kind(X))))&
(![X]:(~funny(X)=>(~tall(X)&brave(X))))&
(![X]:((strong(X)&~generous(X))<=>(calm(X)|~old(X))))&
(![X]:((brave(X)|~rich(X))=>(generous(X)|old(X))))&
(((~tall(john)&brave(john)))<=>((~kind(alice)|old(alice))))&
(![X]:(~curious(X)<=>(patient(X)<~>creative(X))))&
(![X]:((~calm(X)|kind(X))<=>(~humble(X)&creative(X))))&
(((~funny(john)<~>curious(john)))<=>((creative(john)<~>generous(john))))&
(![X]:((~patient(X)|~creative(X))<=>humble(X)))&
(((~curious(susan)<~>curious(susan)))=>(~rich(alice)))&
((?[X]:((happy(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)|creative(X))=>(tall(X)|~brave(X))))&
((?[X]:((happy(X)<~>kind(X))))<=>((~curious(alice)|creative(alice))))&
((tall(fred)&funny(fred)))&
((~funny(fred)<~>calm(fred)))&
((brave(alice)&curious(alice)))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:(~humble(X)))&
((~kind(mary)|~patient(mary)))&
((curious(john)|old(john)))&
((~strong(paul)<~>kind(paul))) | ~funny(susan) | [] | null | 0 |
Everyone who is both quiet and not tall is either happy or not creative.
Everyone who is both not calm and happy is rich.
Everyone who is both rich and kind is generous or not old and vice versa.
If susan is either humble or not curious then someone is both not quiet and quiet and vice versa.
If someone is both not funny and not wise then someone is either not generous or not happy and vice versa.
Everyone who is not curious is either humble or not strong.
If someone is not humble or not quiet then alice is both not brave and not happy and vice versa.
If mary is either not old or wise then mary is creative or calm and vice versa.
If someone is not happy or not strong then someone is not patient or tall.
Everyone who is both old and not calm is either not brave or not quiet and vice versa.
If someone is quiet then alice is both not patient and not happy and vice versa.
Everyone who is either not brave or not happy is humble.
If someone is both old and quiet then paul is funny.
Everyone who is not creative or brave is either not curious or quiet.
Everyone who is both not rich and not happy is creative or rich and vice versa.
If someone is not old or old then paul is both not funny and not generous and vice versa.
Someone is not kind or curious.
Alice is both not generous and not kind.
Someone is either not creative or humble.
Alice is not funny.
Someone is not tall or happy.
Someone is both not funny and strong.
John is either patient or not strong. | Mary is not quiet. | entailment | (![X]:((quiet(X)&~tall(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(![X]:((rich(X)&kind(X))<=>(generous(X)|~old(X))))&
(((humble(susan)<~>~curious(susan)))<=>(?[X]:((~quiet(X)&quiet(X)))))&
((?[X]:((~funny(X)&~wise(X))))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~curious(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~brave(alice)&~happy(alice))))&
(((~old(mary)<~>wise(mary)))<=>((creative(mary)|calm(mary))))&
((?[X]:((~happy(X)|~strong(X))))=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((old(X)&~calm(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))<=>((~patient(alice)&~happy(alice))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
((?[X]:((old(X)&quiet(X))))=>(funny(paul)))&
(![X]:((~creative(X)|brave(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~rich(X)&~happy(X))<=>(creative(X)|rich(X))))&
((?[X]:((~old(X)|old(X))))<=>((~funny(paul)&~generous(paul))))&
(?[X]:((~kind(X)|curious(X))))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~creative(X)<~>humble(X))))&
(~funny(alice))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~funny(X)&strong(X))))&
((patient(john)<~>~strong(john))) | ~quiet(mary) | [
"p2",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3889035042201278270570743
% SZS output start Proof for 3889035042201278270570743
3. ! [X0] : ((kind(X0) & rich(X0)) <=> (~old(X0) | generous(X0))) [input p2]
13. ? [X0] : (quiet(X0) & old(X0)) => funny(paul) [input p12]
15. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (rich(X0) | creative(X0))) [input p14]
16. ? [X0] : (old(X0) | ~old(X0)) <=> (~generous(paul) & ~funny(paul)) [input p15]
24. quiet(mary) [input hypothesis]
34. funny(paul) | ! [X0] : (~quiet(X0) | ~old(X0)) [ennf transformation 13]
37. ! [X0] : (((kind(X0) & rich(X0)) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | (~kind(X0) | ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : (((kind(X0) & rich(X0)) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~kind(X0) | ~rich(X0))) [flattening 37]
68. ! [X0] : (((~happy(X0) & ~rich(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (happy(X0) | rich(X0)))) [nnf transformation 15]
69. ! [X0] : (((~happy(X0) & ~rich(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | happy(X0) | rich(X0))) [flattening 68]
70. (? [X0] : (old(X0) | ~old(X0)) | (generous(paul) | funny(paul))) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (~old(X0) & old(X0))) [nnf transformation 16]
71. (? [X0] : (old(X0) | ~old(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (~old(X0) & old(X0))) [flattening 70]
72. (? [X0] : (old(X0) | ~old(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (~old(X1) & old(X1))) [rectify 71]
73. ? [X0] : (old(X0) | ~old(X0)) => (old(sK6) | ~old(sK6)) [choice axiom]
74. ((old(sK6) | ~old(sK6)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (~old(X1) & old(X1))) [skolemisation 72,73]
90. old(X0) | rich(X0) [cnf transformation 38]
131. funny(paul) | ~quiet(X0) | ~old(X0) [cnf transformation 34]
138. ~rich(X0) | ~rich(X0) [cnf transformation 69]
141. ~funny(paul) | old(X1) [cnf transformation 74]
142. ~funny(paul) | ~old(X1) [cnf transformation 74]
157. quiet(mary) [cnf transformation 24]
159. ~rich(X0) [duplicate literal removal 138]
239. 18 <=> old(mary) [avatar definition]
240. ~old(mary) <- (~18) [avatar component clause 239]
241. old(mary) <- (18) [avatar component clause 239]
287. 28 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
288. ~old(X0) | ~quiet(X0) <- (28) [avatar component clause 287]
290. 29 <=> funny(paul) [avatar definition]
293. 28 | 29 [avatar split clause 131,290,287]
296. 30 <=> ! [X1] : ~old(X1) [avatar definition]
297. ~old(X1) <- (30) [avatar component clause 296]
304. 32 <=> ! [X1] : old(X1) [avatar definition]
305. old(X1) <- (32) [avatar component clause 304]
307. 30 | ~29 [avatar split clause 142,290,296]
308. 32 | ~29 [avatar split clause 141,290,304]
347. rich(mary) <- (~18) [resolution 90,240]
348. $false <- (~18) [subsumption resolution 347,159]
349. 18 [avatar contradiction clause 348]
356. ~quiet(mary) <- (18, 28) [resolution 288,241]
359. $false <- (18, 28) [subsumption resolution 356,157]
360. ~18 | ~28 [avatar contradiction clause 359]
361. $false <- (30, 32) [subsumption resolution 297,305]
362. ~30 | ~32 [avatar contradiction clause 361]
363. $false [avatar sat refutation 293,307,308,349,360,362]
% SZS output end Proof for 3889035042201278270570743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either old or quiet then paul is both not strong and not wise and vice versa. Everyone who is either happy or not calm is kind and vice versa. Everyone who is either quiet or not quiet is both kind and not tall and vice versa. If someone is rich then fred is quiet. If susan is both curious and quiet then john is funny and vice versa. Everyone who is either quiet or not rich is strong and vice versa. Everyone who is quiet is either not happy or not quiet and vice versa. Everyone who is either not wise or not kind is either wise or generous and vice versa. If someone is both not old and not tall then someone is either not curious or quiet and vice versa. Everyone who is tall is either not patient or not strong and vice versa. Everyone who is not tall is not humble and vice versa. If john is both not kind and calm then someone is either brave or generous and vice versa. Everyone who is kind is not kind or not funny. Everyone who is either not brave or tall is not strong or humble and vice versa. Everyone who is either rich or curious is both wise and not calm. Someone is either not tall or happy. Mary is not wise. Someone is not quiet. Paul is either rich or not creative. Mary is not tall or strong. Susan is either strong or tall. Someone is not old. | Paul is not generous. | contradiction | (((old(mary)<~>quiet(mary)))<=>((~strong(paul)&~wise(paul))))&
(![X]:((happy(X)<~>~calm(X))<=>kind(X)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(kind(X)&~tall(X))))&
((?[X]:(rich(X)))=>(quiet(fred)))&
(((curious(susan)&quiet(susan)))<=>(funny(john)))&
(![X]:((quiet(X)<~>~rich(X))<=>strong(X)))&
(![X]:(quiet(X)<=>(~happy(X)<~>~quiet(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(wise(X)<~>generous(X))))&
((?[X]:((~old(X)&~tall(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:(tall(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(((~kind(john)&calm(john)))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(kind(X)=>(~kind(X)|~funny(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(~strong(X)|humble(X))))&
(![X]:((rich(X)<~>curious(X))=>(wise(X)&~calm(X))))&
(?[X]:((~tall(X)<~>happy(X))))&
(~wise(mary))&
(?[X]:(~quiet(X)))&
((rich(paul)<~>~creative(paul)))&
((~tall(mary)|strong(mary)))&
((strong(susan)<~>tall(susan)))&
(?[X]:(~old(X))) | ~generous(paul) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2432554688704872650701266
% SZS output start Proof for 2432554688704872650701266
3. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) <=> (~tall(X0) & kind(X0))) [input p2]
8. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (wise(X0) <~> generous(X0))) [input p7]
23. ~generous(paul) [input hypothesis]
32. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [nnf transformation 3]
33. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [flattening 32]
38. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 8]
73. kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 33]
74. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 33]
91. generous(X0) | wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 38]
95. ~kind(X0) | ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 38]
138. ~generous(paul) [cnf transformation 23]
140. generous(X0) | wise(X0) | ~kind(X0) [duplicate literal removal 91]
142. ~kind(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 95]
146. kind(X0) | ~quiet(X0) [duplicate literal removal 73]
147. kind(X0) | quiet(X0) [duplicate literal removal 74]
173. kind(X0) [subsumption resolution 146,147]
198. ~wise(X0) | generous(X0) [subsumption resolution 142,173]
199. generous(X0) | wise(X0) [subsumption resolution 140,173]
200. generous(X0) [subsumption resolution 199,198]
258. $false [subsumption resolution 138,200]
% SZS output end Proof for 2432554688704872650701266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not brave is not tall and vice versa.
Everyone who is either brave or old is generous or not funny and vice versa.
Everyone who is either not quiet or not kind is either not strong or not patient and vice versa.
If someone is both not kind and generous then someone is either not funny or wise and vice versa.
Everyone who is both not humble and not funny is both creative and patient and vice versa.
If someone is both rich and not curious then lucy is not kind or not generous.
Everyone who is both not humble and not tall is both humble and not rich.
Everyone who is both strong and not creative is either not rich or patient and vice versa.
If someone is not funny then susan is not calm.
If someone is both not kind and old then someone is either rich or not kind and vice versa.
Everyone who is not old is both not creative and generous and vice versa.
Everyone who is not rich is brave or creative.
If fred is both calm and not wise then someone is calm and vice versa.
If someone is creative then someone is either not tall or humble and vice versa.
Everyone who is both rich and not curious is happy or not calm and vice versa.
Everyone who is not generous is either creative or calm.
Alice is generous or not humble.
Lucy is both not quiet and not patient.
Susan is either wise or brave.
Lucy is rich or not calm.
Someone is either not kind or not curious.
Someone is quiet.
Someone is both happy and not humble.
Someone is not calm or not tall. | Lucy is brave. | neutral | (![X]:((~patient(X)<~>~brave(X))<=>~tall(X)))&
(![X]:((brave(X)<~>old(X))<=>(generous(X)|~funny(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~strong(X)<~>~patient(X))))&
((?[X]:((~kind(X)&generous(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(![X]:((~humble(X)&~funny(X))<=>(creative(X)&patient(X))))&
((?[X]:((rich(X)&~curious(X))))=>((~kind(lucy)|~generous(lucy))))&
(![X]:((~humble(X)&~tall(X))=>(humble(X)&~rich(X))))&
(![X]:((strong(X)&~creative(X))<=>(~rich(X)<~>patient(X))))&
((?[X]:(~funny(X)))=>(~calm(susan)))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:((rich(X)<~>~kind(X)))))&
(![X]:(~old(X)<=>(~creative(X)&generous(X))))&
(![X]:(~rich(X)=>(brave(X)|creative(X))))&
(((calm(fred)&~wise(fred)))<=>(?[X]:(calm(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((rich(X)&~curious(X))<=>(happy(X)|~calm(X))))&
(![X]:(~generous(X)=>(creative(X)<~>calm(X))))&
((generous(alice)|~humble(alice)))&
((~quiet(lucy)&~patient(lucy)))&
((wise(susan)<~>brave(susan)))&
((rich(lucy)|~calm(lucy)))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:((~calm(X)|~tall(X)))) | brave(lucy) | [] | null | 0 |
If someone is not old or funny then john is either calm or not old.
If someone is both generous and not wise then someone is both generous and not calm.
If someone is not rich or not brave then someone is curious.
Everyone who is brave is both humble and not old.
Everyone who is rich or not strong is both not generous and rich and vice versa.
If someone is either not brave or humble then someone is not happy.
Everyone who is not creative or generous is both not calm and calm.
Everyone who is both not kind and not funny is either humble or not happy and vice versa.
Everyone who is either brave or not calm is either kind or not brave.
Everyone who is not funny or not old is patient.
If someone is not wise or generous then someone is humble and vice versa.
If someone is not strong then someone is both tall and curious and vice versa.
If someone is either not creative or old then alice is either funny or not generous and vice versa.
Everyone who is either not funny or not quiet is both curious and not happy and vice versa.
Everyone who is not creative is kind or not curious.
If john is either tall or brave then someone is happy or not happy and vice versa.
Susan is both not quiet and not calm.
Alice is generous or funny.
Someone is not creative or strong.
Someone is tall.
Someone is either old or not curious.
John is either strong or not brave.
Someone is either not creative or funny. | John is not patient. | contradiction | ((?[X]:((~old(X)|funny(X))))=>((calm(john)<~>~old(john))))&
((?[X]:((generous(X)&~wise(X))))=>(?[X]:((generous(X)&~calm(X)))))&
((?[X]:((~rich(X)|~brave(X))))=>(?[X]:(curious(X))))&
(![X]:(brave(X)=>(humble(X)&~old(X))))&
(![X]:((rich(X)|~strong(X))<=>(~generous(X)&rich(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:(~happy(X))))&
(![X]:((~creative(X)|generous(X))=>(~calm(X)&calm(X))))&
(![X]:((~kind(X)&~funny(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~calm(X))=>(kind(X)<~>~brave(X))))&
(![X]:((~funny(X)|~old(X))=>patient(X)))&
((?[X]:((~wise(X)|generous(X))))<=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:((~creative(X)<~>old(X))))<=>((funny(alice)<~>~generous(alice))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(curious(X)&~happy(X))))&
(![X]:(~creative(X)=>(kind(X)|~curious(X))))&
(((tall(john)<~>brave(john)))<=>(?[X]:((happy(X)|~happy(X)))))&
((~quiet(susan)&~calm(susan)))&
((generous(alice)|funny(alice)))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((old(X)<~>~curious(X))))&
((strong(john)<~>~brave(john)))&
(?[X]:((~creative(X)<~>funny(X)))) | ~patient(john) | [
"p6",
"p9",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4698726804991778239744333
% SZS output start Proof for 4698726804991778239744333
7. ! [X0] : ((generous(X0) | ~creative(X0)) => (calm(X0) & ~calm(X0))) [input p6]
10. ! [X0] : ((~old(X0) | ~funny(X0)) => patient(X0)) [input p9]
13. ? [X0] : (~creative(X0) <~> old(X0)) <=> (funny(alice) <~> ~generous(alice)) [input p12]
18. funny(alice) | generous(alice) [input p17]
24. ~patient(john) [input hypothesis]
35. ! [X0] : ((calm(X0) & ~calm(X0)) | (~generous(X0) & creative(X0))) [ennf transformation 7]
37. ! [X0] : (patient(X0) | (old(X0) & funny(X0))) [ennf transformation 10]
66. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ((funny(alice) | generous(alice)) & (~generous(alice) | ~funny(alice)))) & (((generous(alice) | ~funny(alice)) & (~generous(alice) | funny(alice))) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 13]
67. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ((funny(alice) | generous(alice)) & (~generous(alice) | ~funny(alice)))) & (((generous(alice) | ~funny(alice)) & (~generous(alice) | funny(alice))) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [rectify 66]
68. ? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) => ((~old(sK7) | creative(sK7)) & (old(sK7) | ~creative(sK7))) [choice axiom]
69. (((~old(sK7) | creative(sK7)) & (old(sK7) | ~creative(sK7))) | ((funny(alice) | generous(alice)) & (~generous(alice) | ~funny(alice)))) & (((generous(alice) | ~funny(alice)) & (~generous(alice) | funny(alice))) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [skolemisation 67,68]
104. ~calm(X0) | creative(X0) [cnf transformation 35]
105. ~calm(X0) | ~generous(X0) [cnf transformation 35]
106. creative(X0) | calm(X0) [cnf transformation 35]
107. ~generous(X0) | calm(X0) [cnf transformation 35]
119. patient(X0) | old(X0) [cnf transformation 37]
129. generous(alice) | ~funny(alice) | ~creative(X1) | ~old(X1) [cnf transformation 69]
149. funny(alice) | generous(alice) [cnf transformation 18]
158. ~patient(john) [cnf transformation 24]
218. ~generous(X0) [subsumption resolution 105,107]
219. creative(X0) [subsumption resolution 104,106]
261. 23 <=> funny(alice) [avatar definition]
269. ~funny(alice) | ~creative(X1) | ~old(X1) [subsumption resolution 129,218]
270. ~funny(alice) | ~old(X1) [subsumption resolution 269,219]
272. 25 <=> ! [X1] : ~old(X1) [avatar definition]
273. ~old(X1) <- (25) [avatar component clause 272]
274. 25 | ~23 [avatar split clause 270,261,272]
293. funny(alice) [subsumption resolution 149,218]
294. 23 [avatar split clause 293,261]
322. old(john) [resolution 119,158]
323. $false <- (25) [subsumption resolution 322,273]
324. ~25 [avatar contradiction clause 323]
325. $false [avatar sat refutation 274,294,324]
% SZS output end Proof for 4698726804991778239744333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both creative and not happy then alice is both humble and wise.
Everyone who is not calm or not generous is not rich and vice versa.
If john is not wise then someone is either kind or generous.
Everyone who is strong or not quiet is creative or calm.
If someone is funny then someone is not brave and vice versa.
Everyone who is both not strong and brave is either calm or not tall and vice versa.
Everyone who is not kind is both strong and not rich.
Everyone who is wise or tall is not old or happy.
Everyone who is calm is not kind or not strong.
Everyone who is either not happy or not generous is not happy or brave and vice versa.
If susan is not old or kind then lucy is calm or not creative.
Everyone who is calm is both not humble and curious and vice versa.
If john is both generous and tall then susan is either wise or not strong and vice versa.
If john is not funny or not old then someone is not old or not happy.
If lucy is funny then paul is generous or not humble and vice versa.
If fred is not curious then mary is rich.
Fred is either not curious or tall.
Alice is brave or not calm.
Someone is either happy or not rich.
Someone is both brave and not calm.
Mary is both not old and wise.
Mary is strong.
Someone is strong or calm.
Someone is old or not old. | John is not funny. | neutral | (((creative(mary)&~happy(mary)))=>((humble(alice)&wise(alice))))&
(![X]:((~calm(X)|~generous(X))<=>~rich(X)))&
((~wise(john))=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((strong(X)|~quiet(X))=>(creative(X)|calm(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(calm(X)<~>~tall(X))))&
(![X]:(~kind(X)=>(strong(X)&~rich(X))))&
(![X]:((wise(X)|tall(X))=>(~old(X)|happy(X))))&
(![X]:(calm(X)=>(~kind(X)|~strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(~happy(X)|brave(X))))&
(((~old(susan)|kind(susan)))=>((calm(lucy)|~creative(lucy))))&
(![X]:(calm(X)<=>(~humble(X)&curious(X))))&
(((generous(john)&tall(john)))<=>((wise(susan)<~>~strong(susan))))&
(((~funny(john)|~old(john)))=>(?[X]:((~old(X)|~happy(X)))))&
((funny(lucy))<=>((generous(paul)|~humble(paul))))&
((~curious(fred))=>(rich(mary)))&
((~curious(fred)<~>tall(fred)))&
((brave(alice)|~calm(alice)))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:((brave(X)&~calm(X))))&
((~old(mary)&wise(mary)))&
(strong(mary))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((old(X)|~old(X)))) | ~funny(john) | [] | null | 0 |
If fred is either not generous or tall then susan is both not tall and not patient and vice versa.
If susan is not happy or not curious then someone is kind or not curious.
Everyone who is both not wise and not tall is strong.
Everyone who is either calm or not calm is both not wise and rich.
Everyone who is not wise or curious is happy and vice versa.
Everyone who is not old or not funny is not generous and vice versa.
Everyone who is curious or wise is humble or not funny.
Everyone who is brave or wise is not rich and vice versa.
Everyone who is either not old or not curious is strong or not strong and vice versa.
Everyone who is both funny and humble is creative or funny and vice versa.
Everyone who is strong or not humble is either rich or not strong.
Everyone who is both calm and quiet is not brave and vice versa.
If alice is both happy and strong then fred is both not quiet and quiet.
Everyone who is not kind or not creative is not rich.
Everyone who is both curious and not generous is either strong or not quiet and vice versa.
Paul is curious.
Paul is either rich or not quiet.
Someone is kind.
Alice is either calm or not tall.
Mary is creative.
Someone is not rich or generous. | Mary is not quiet. | contradiction | (((~generous(fred)<~>tall(fred)))<=>((~tall(susan)&~patient(susan))))&
(((~happy(susan)|~curious(susan)))=>(?[X]:((kind(X)|~curious(X)))))&
(![X]:((~wise(X)&~tall(X))=>strong(X)))&
(![X]:((calm(X)<~>~calm(X))=>(~wise(X)&rich(X))))&
(![X]:((~wise(X)|curious(X))<=>happy(X)))&
(![X]:((~old(X)|~funny(X))<=>~generous(X)))&
(![X]:((curious(X)|wise(X))=>(humble(X)|~funny(X))))&
(![X]:((brave(X)|wise(X))<=>~rich(X)))&
(![X]:((~old(X)<~>~curious(X))<=>(strong(X)|~strong(X))))&
(![X]:((funny(X)&humble(X))<=>(creative(X)|funny(X))))&
(![X]:((strong(X)|~humble(X))=>(rich(X)<~>~strong(X))))&
(![X]:((calm(X)&quiet(X))<=>~brave(X)))&
(((happy(alice)&strong(alice)))=>((~quiet(fred)&quiet(fred))))&
(![X]:((~kind(X)|~creative(X))=>~rich(X)))&
(![X]:((curious(X)&~generous(X))<=>(strong(X)<~>~quiet(X))))&
(curious(paul))&
((rich(paul)<~>~quiet(paul)))&
(?[X]:(kind(X)))&
((calm(alice)<~>~tall(alice)))&
(creative(mary))&
(?[X]:((~rich(X)|generous(X)))) | ~quiet(mary) | [
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 868157980917577476280271
% SZS output start Proof for 868157980917577476280271
4. ! [X0] : ((calm(X0) <~> ~calm(X0)) => (rich(X0) & ~wise(X0))) [input p3]
8. ! [X0] : ((wise(X0) | brave(X0)) <=> ~rich(X0)) [input p7]
12. ! [X0] : ((quiet(X0) & calm(X0)) <=> ~brave(X0)) [input p11]
22. ~quiet(mary) [input hypothesis]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | (calm(X0) <=> ~calm(X0))) [ennf transformation 4]
39. ! [X0] : ((rich(X0) & ~wise(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) [nnf transformation 29]
42. ! [X0] : (((wise(X0) | brave(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~brave(X0)))) [nnf transformation 8]
43. ! [X0] : ((wise(X0) | brave(X0) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~brave(X0)))) [flattening 42]
49. ! [X0] : (((quiet(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | (~quiet(X0) | ~calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((quiet(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | ~quiet(X0) | ~calm(X0))) [flattening 49]
66. rich(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 39]
67. rich(X0) | calm(X0) | calm(X0) [cnf transformation 39]
75. ~rich(X0) | ~brave(X0) [cnf transformation 43]
95. quiet(X0) | brave(X0) [cnf transformation 50]
112. ~quiet(mary) [cnf transformation 22]
116. rich(X0) | ~calm(X0) [duplicate literal removal 66]
117. rich(X0) | calm(X0) [duplicate literal removal 67]
140. rich(X0) [subsumption resolution 116,117]
143. ~brave(X0) [subsumption resolution 75,140]
147. quiet(X0) [subsumption resolution 95,143]
157. $false [subsumption resolution 112,147]
% SZS output end Proof for 868157980917577476280271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both calm and not kind then lucy is brave or kind. Everyone who is humble or generous is either happy or not quiet. If someone is either not humble or rich then someone is brave. Everyone who is not humble or not brave is not tall or not patient and vice versa. If susan is both quiet and not kind then alice is not rich or not creative. Everyone who is both not happy and happy is funny or curious and vice versa. If someone is tall or not patient then someone is both not kind and not strong. Everyone who is both rich and patient is calm and vice versa. Everyone who is both not generous and not humble is creative and vice versa. Everyone who is not happy or not funny is both wise and happy. Everyone who is quiet or not quiet is both not old and creative and vice versa. Everyone who is quiet or calm is wise and vice versa. If someone is either kind or not calm then someone is either not quiet or not rich. If alice is not creative or creative then lucy is both brave and creative. If someone is both old and not quiet then someone is funny and vice versa. John is brave. Mary is either calm or not brave. Someone is not wise or not rich. Someone is calm or not strong. Someone is either strong or not creative. | Alice is funny. | contradiction | (((calm(susan)&~kind(susan)))=>((brave(lucy)|kind(lucy))))&
(![X]:((humble(X)|generous(X))=>(happy(X)<~>~quiet(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(?[X]:(brave(X))))&
(![X]:((~humble(X)|~brave(X))<=>(~tall(X)|~patient(X))))&
(((quiet(susan)&~kind(susan)))=>((~rich(alice)|~creative(alice))))&
(![X]:((~happy(X)&happy(X))<=>(funny(X)|curious(X))))&
((?[X]:((tall(X)|~patient(X))))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((rich(X)&patient(X))<=>calm(X)))&
(![X]:((~generous(X)&~humble(X))<=>creative(X)))&
(![X]:((~happy(X)|~funny(X))=>(wise(X)&happy(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~old(X)&creative(X))))&
(![X]:((quiet(X)|calm(X))<=>wise(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(((~creative(alice)|creative(alice)))=>((brave(lucy)&creative(lucy))))&
((?[X]:((old(X)&~quiet(X))))<=>(?[X]:(funny(X))))&
(brave(john))&
((calm(mary)<~>~brave(mary)))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((strong(X)<~>~creative(X)))) | funny(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3464840191726736984206497
% SZS output start Proof for 3464840191726736984206497
6. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (curious(X0) | funny(X0))) [input p5]
21. funny(alice) [input hypothesis]
43. ! [X0] : (((happy(X0) & ~happy(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 6]
44. ! [X0] : (((happy(X0) & ~happy(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | ~happy(X0) | happy(X0))) [flattening 43]
86. ~happy(X0) | ~funny(X0) [cnf transformation 44]
88. happy(X0) | ~funny(X0) [cnf transformation 44]
130. funny(alice) [cnf transformation 21]
175. ~funny(X0) [subsumption resolution 86,88]
240. $false [subsumption resolution 130,175]
% SZS output end Proof for 3464840191726736984206497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not funny is not old and vice versa.
If someone is wise then someone is both not patient and not quiet.
If lucy is both quiet and rich then paul is tall and vice versa.
Everyone who is either wise or not curious is not brave or not quiet and vice versa.
Everyone who is not generous is wise or not strong.
Everyone who is wise is not humble and vice versa.
If someone is kind or curious then lucy is curious or not funny and vice versa.
Everyone who is not calm is both not quiet and not tall.
Everyone who is both not quiet and not generous is happy or tall.
Everyone who is calm or not patient is either old or curious.
If mary is wise or happy then susan is funny and vice versa.
If someone is funny then john is either not humble or old and vice versa.
If lucy is either not humble or humble then alice is happy.
Everyone who is not patient or not kind is both not tall and not curious and vice versa.
If susan is not tall then alice is not humble or patient.
Everyone who is either not rich or not creative is not quiet or quiet and vice versa.
John is either calm or not humble.
Paul is not wise.
John is either not generous or not tall.
Paul is not curious.
Alice is not curious or not funny.
Someone is both strong and old.
Someone is either not brave or generous.
Someone is either calm or not humble. | John is not humble. | neutral | (![X]:((curious(X)|~funny(X))<=>~old(X)))&
((?[X]:(wise(X)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(((quiet(lucy)&rich(lucy)))<=>(tall(paul)))&
(![X]:((wise(X)<~>~curious(X))<=>(~brave(X)|~quiet(X))))&
(![X]:(~generous(X)=>(wise(X)|~strong(X))))&
(![X]:(wise(X)<=>~humble(X)))&
((?[X]:((kind(X)|curious(X))))<=>((curious(lucy)|~funny(lucy))))&
(![X]:(~calm(X)=>(~quiet(X)&~tall(X))))&
(![X]:((~quiet(X)&~generous(X))=>(happy(X)|tall(X))))&
(![X]:((calm(X)|~patient(X))=>(old(X)<~>curious(X))))&
(((wise(mary)|happy(mary)))<=>(funny(susan)))&
((?[X]:(funny(X)))<=>((~humble(john)<~>old(john))))&
(((~humble(lucy)<~>humble(lucy)))=>(happy(alice)))&
(![X]:((~patient(X)|~kind(X))<=>(~tall(X)&~curious(X))))&
((~tall(susan))=>((~humble(alice)|patient(alice))))&
(![X]:((~rich(X)<~>~creative(X))<=>(~quiet(X)|quiet(X))))&
((calm(john)<~>~humble(john)))&
(~wise(paul))&
((~generous(john)<~>~tall(john)))&
(~curious(paul))&
((~curious(alice)|~funny(alice)))&
(?[X]:((strong(X)&old(X))))&
(?[X]:((~brave(X)<~>generous(X))))&
(?[X]:((calm(X)<~>~humble(X)))) | ~humble(john) | [] | null | 0 |
Everyone who is strong is humble or not strong and vice versa.
If someone is not wise then paul is not rich or not humble and vice versa.
Everyone who is either not curious or generous is both not brave and kind.
If paul is funny then paul is not tall or happy and vice versa.
Everyone who is not old or not happy is both calm and not old and vice versa.
Everyone who is wise or brave is not strong or happy and vice versa.
If someone is either not creative or not strong then fred is not calm.
If susan is not quiet or funny then susan is both wise and not tall.
If someone is either not humble or not tall then mary is rich and vice versa.
Everyone who is both strong and not generous is wise and vice versa.
If someone is funny then mary is happy or not rich and vice versa.
If mary is both strong and not kind then someone is wise.
If someone is either creative or humble then fred is not rich.
If alice is both not happy and kind then alice is either brave or not tall and vice versa.
Everyone who is patient is wise or not rich.
Everyone who is both not kind and not old is not kind or not happy.
Someone is quiet.
Mary is strong.
Paul is either curious or tall.
Lucy is not rich.
Fred is either rich or not tall.
Fred is not creative.
Fred is not patient. | Fred is not calm. | entailment | (![X]:(strong(X)<=>(humble(X)|~strong(X))))&
((?[X]:(~wise(X)))<=>((~rich(paul)|~humble(paul))))&
(![X]:((~curious(X)<~>generous(X))=>(~brave(X)&kind(X))))&
((funny(paul))<=>((~tall(paul)|happy(paul))))&
(![X]:((~old(X)|~happy(X))<=>(calm(X)&~old(X))))&
(![X]:((wise(X)|brave(X))<=>(~strong(X)|happy(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(~calm(fred)))&
(((~quiet(susan)|funny(susan)))=>((wise(susan)&~tall(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(rich(mary)))&
(![X]:((strong(X)&~generous(X))<=>wise(X)))&
((?[X]:(funny(X)))<=>((happy(mary)|~rich(mary))))&
(((strong(mary)&~kind(mary)))=>(?[X]:(wise(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(~rich(fred)))&
(((~happy(alice)&kind(alice)))<=>((brave(alice)<~>~tall(alice))))&
(![X]:(patient(X)=>(wise(X)|~rich(X))))&
(![X]:((~kind(X)&~old(X))=>(~kind(X)|~happy(X))))&
(?[X]:(quiet(X)))&
(strong(mary))&
((curious(paul)<~>tall(paul)))&
(~rich(lucy))&
((rich(fred)<~>~tall(fred)))&
(~creative(fred))&
(~patient(fred)) | ~calm(fred) | [
"p0",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4494543909074676086677324
% SZS output start Proof for 4494543909074676086677324
1. ! [X0] : (strong(X0) <=> (~strong(X0) | humble(X0))) [input p0]
7. ? [X0] : (~creative(X0) <~> ~strong(X0)) => ~calm(fred) [input p6]
22. ~creative(fred) [input p21]
24. calm(fred) [input hypothesis]
30. ~calm(fred) | ! [X0] : (~creative(X0) <=> ~strong(X0)) [ennf transformation 7]
37. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~strong(X0))) [flattening 37]
51. ~calm(fred) | ! [X0] : ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))) [nnf transformation 30]
72. strong(X0) | strong(X0) [cnf transformation 38]
92. ~calm(fred) | ~strong(X0) | creative(X0) [cnf transformation 51]
122. ~creative(fred) [cnf transformation 22]
123. calm(fred) [cnf transformation 24]
125. strong(X0) [duplicate literal removal 72]
158. ~calm(fred) | creative(X0) [subsumption resolution 92,125]
160. 7 <=> ! [X0] : creative(X0) [avatar definition]
161. creative(X0) <- (7) [avatar component clause 160]
163. 8 <=> calm(fred) [avatar definition]
166. 7 | ~8 [avatar split clause 158,163,160]
262. 8 [avatar split clause 123,163]
263. $false <- (7) [resolution 161,122]
264. ~7 [avatar contradiction clause 263]
265. $false [avatar sat refutation 166,262,264]
% SZS output end Proof for 4494543909074676086677324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is not old or tall and vice versa. If lucy is both calm and not creative then someone is both funny and old. If mary is both not rich and creative then susan is not happy or not creative and vice versa. If fred is curious or wise then someone is both happy and old. If someone is strong then someone is both not patient and patient. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. If mary is not generous or brave then alice is rich or calm. Mary is happy or not creative. Someone is calm. Fred is strong or not generous. Someone is either humble or not curious. | Lucy is humble. | contradiction | (![X]:((brave(X)|~strong(X))<=>(~old(X)|tall(X))))&
(((calm(lucy)&~creative(lucy)))=>(?[X]:((funny(X)&old(X)))))&
(((~rich(mary)&creative(mary)))<=>((~happy(susan)|~creative(susan))))&
(((curious(fred)|wise(fred)))=>(?[X]:((happy(X)&old(X)))))&
((?[X]:(strong(X)))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(((~generous(mary)|brave(mary)))=>((rich(alice)|calm(alice))))&
((happy(mary)|~creative(mary)))&
(?[X]:(calm(X)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X)))) | humble(lucy) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4448834287217124797677163
% SZS output start Proof for 4448834287217124797677163
5. ? [X0] : strong(X0) => ? [X0] : (patient(X0) & ~patient(X0)) [input p4]
14. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p13]
20. humble(lucy) [input hypothesis]
21. ? [X0] : strong(X0) => ? [X1] : (patient(X1) & ~patient(X1)) [rectify 5]
25. ? [X1] : (patient(X1) & ~patient(X1)) | ! [X0] : ~strong(X0) [ennf transformation 21]
32. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 14]
43. ? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : ~strong(X1) [rectify 25]
44. ? [X0] : (patient(X0) & ~patient(X0)) => (patient(sK2) & ~patient(sK2)) [choice axiom]
45. (patient(sK2) & ~patient(sK2)) | ! [X1] : ~strong(X1) [skolemisation 43,44]
80. ~patient(sK2) | ~strong(X1) [cnf transformation 45]
81. patient(sK2) | ~strong(X1) [cnf transformation 45]
108. ~humble(X0) | strong(X0) [cnf transformation 32]
116. humble(lucy) [cnf transformation 20]
177. 13 <=> ! [X1] : ~strong(X1) [avatar definition]
178. ~strong(X1) <- (13) [avatar component clause 177]
180. 14 <=> patient(sK2) [avatar definition]
183. 13 | 14 [avatar split clause 81,180,177]
184. 13 | ~14 [avatar split clause 80,180,177]
292. strong(lucy) [resolution 108,116]
293. $false <- (13) [subsumption resolution 292,178]
294. ~13 [avatar contradiction clause 293]
295. $false [avatar sat refutation 183,184,294]
% SZS output end Proof for 4448834287217124797677163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not old and not calm.
Everyone who is both strong and brave is not strong and vice versa.
If alice is both not creative and rich then someone is both tall and humble and vice versa.
Everyone who is not strong is not generous and vice versa.
If fred is creative or not kind then someone is not creative or creative and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If someone is strong then john is either generous or happy.
If someone is either generous or not brave then mary is either calm or not quiet.
Everyone who is either kind or wise is both not curious and calm and vice versa.
Everyone who is either not strong or quiet is both wise and not patient.
Everyone who is not happy or patient is not wise and vice versa.
Everyone who is either not creative or not patient is either not happy or not old and vice versa.
Everyone who is patient or not creative is both rich and not humble.
Everyone who is funny is either not rich or not wise and vice versa.
Someone is both not tall and happy.
Someone is not strong or strong.
Someone is humble.
Someone is patient or not quiet.
Mary is either brave or creative.
Someone is either not quiet or calm. | John is quiet. | contradiction | (![X]:(~happy(X)=>(~old(X)&~calm(X))))&
(![X]:((strong(X)&brave(X))<=>~strong(X)))&
(((~creative(alice)&rich(alice)))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:(~strong(X)<=>~generous(X)))&
(((creative(fred)|~kind(fred)))<=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(strong(X)))=>((generous(john)<~>happy(john))))&
((?[X]:((generous(X)<~>~brave(X))))=>((calm(mary)<~>~quiet(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(wise(X)&~patient(X))))&
(![X]:((~happy(X)|patient(X))<=>~wise(X)))&
(![X]:((~creative(X)<~>~patient(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:(funny(X)<=>(~rich(X)<~>~wise(X))))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|~quiet(X))))&
((brave(mary)<~>creative(mary)))&
(?[X]:((~quiet(X)<~>calm(X)))) | quiet(john) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3665389527054741091620294
% SZS output start Proof for 3665389527054741091620294
2. ! [X0] : ((brave(X0) & strong(X0)) <=> ~strong(X0)) [input p1]
4. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p3]
7. ? [X0] : strong(X0) => (generous(john) <~> happy(john)) [input p6]
10. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~patient(X0) & wise(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~happy(X0)) <=> ~wise(X0)) [input p10]
21. quiet(john) [input hypothesis]
23. (generous(john) <~> happy(john)) | ! [X0] : ~strong(X0) [ennf transformation 7]
25. ! [X0] : ((~patient(X0) & wise(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 10]
27. ! [X0] : (((brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~brave(X0) | ~strong(X0)))) [nnf transformation 2]
28. ! [X0] : (((brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | ~brave(X0) | ~strong(X0))) [flattening 27]
34. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 4]
42. ((~happy(john) | ~generous(john)) & (happy(john) | generous(john))) | ! [X0] : ~strong(X0) [nnf transformation 23]
46. ! [X0] : ((~patient(X0) & wise(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 25]
47. ! [X0] : (((patient(X0) | ~happy(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & happy(X0)))) [nnf transformation 11]
48. ! [X0] : ((patient(X0) | ~happy(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & happy(X0)))) [flattening 47]
65. strong(X0) | strong(X0) [cnf transformation 28]
72. ~strong(X0) | generous(X0) [cnf transformation 34]
81. ~happy(john) | ~generous(john) | ~strong(X0) [cnf transformation 42]
93. wise(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 46]
96. ~wise(X0) | happy(X0) [cnf transformation 48]
120. quiet(john) [cnf transformation 21]
122. strong(X0) [duplicate literal removal 65]
147. generous(X0) [subsumption resolution 72,122]
165. ~happy(john) | ~strong(X0) [subsumption resolution 81,147]
166. ~happy(john) [subsumption resolution 165,122]
168. ~quiet(X0) | wise(X0) [subsumption resolution 93,122]
192. wise(john) [resolution 168,120]
195. happy(john) [resolution 192,96]
196. $false [subsumption resolution 195,166]
% SZS output end Proof for 3665389527054741091620294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not happy then paul is curious or not kind.
If mary is both wise and calm then someone is not kind or not rich and vice versa.
If fred is brave then fred is either not kind or not patient and vice versa.
If mary is both old and not wise then mary is both kind and not happy and vice versa.
If someone is both funny and not happy then someone is creative.
Everyone who is both calm and not funny is not funny or not curious and vice versa.
If susan is either not tall or strong then someone is brave or not happy and vice versa.
If someone is either generous or not strong then someone is either wise or not tall and vice versa.
Everyone who is generous or not strong is both calm and not funny and vice versa.
Everyone who is either not strong or not kind is both curious and not strong and vice versa.
If someone is quiet or curious then john is both not patient and strong and vice versa.
If mary is not old then john is patient.
If alice is both not generous and kind then fred is curious or not creative.
If someone is both happy and wise then john is both patient and generous.
If someone is not patient then someone is both tall and not old.
Everyone who is both patient and funny is both not tall and not wise.
John is either not wise or kind.
Someone is not kind.
Fred is calm or not patient.
Fred is calm.
Someone is both brave and old.
Mary is both rich and not creative.
John is not kind or not strong. | Mary is quiet. | contradiction | ((?[X]:((~quiet(X)&~happy(X))))=>((curious(paul)|~kind(paul))))&
(((wise(mary)&calm(mary)))<=>(?[X]:((~kind(X)|~rich(X)))))&
((brave(fred))<=>((~kind(fred)<~>~patient(fred))))&
(((old(mary)&~wise(mary)))<=>((kind(mary)&~happy(mary))))&
((?[X]:((funny(X)&~happy(X))))=>(?[X]:(creative(X))))&
(![X]:((calm(X)&~funny(X))<=>(~funny(X)|~curious(X))))&
(((~tall(susan)<~>strong(susan)))<=>(?[X]:((brave(X)|~happy(X)))))&
((?[X]:((generous(X)<~>~strong(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((generous(X)|~strong(X))<=>(calm(X)&~funny(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(curious(X)&~strong(X))))&
((?[X]:((quiet(X)|curious(X))))<=>((~patient(john)&strong(john))))&
((~old(mary))=>(patient(john)))&
(((~generous(alice)&kind(alice)))=>((curious(fred)|~creative(fred))))&
((?[X]:((happy(X)&wise(X))))=>((patient(john)&generous(john))))&
((?[X]:(~patient(X)))=>(?[X]:((tall(X)&~old(X)))))&
(![X]:((patient(X)&funny(X))=>(~tall(X)&~wise(X))))&
((~wise(john)<~>kind(john)))&
(?[X]:(~kind(X)))&
((calm(fred)|~patient(fred)))&
(calm(fred))&
(?[X]:((brave(X)&old(X))))&
((rich(mary)&~creative(mary)))&
((~kind(john)|~strong(john))) | quiet(mary) | [
"p9",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1562225544092325096220611
% SZS output start Proof for 1562225544092325096220611
10. ! [X0] : ((~strong(X0) <~> ~kind(X0)) <=> (~strong(X0) & curious(X0))) [input p9]
11. ? [X0] : (curious(X0) | quiet(X0)) <=> (strong(john) & ~patient(john)) [input p10]
23. ~strong(john) | ~kind(john) [input p22]
24. quiet(mary) [input hypothesis]
62. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [nnf transformation 10]
63. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [flattening 62]
64. (? [X0] : (curious(X0) | quiet(X0)) | (~strong(john) | patient(john))) & ((strong(john) & ~patient(john)) | ! [X0] : (~curious(X0) & ~quiet(X0))) [nnf transformation 11]
65. (? [X0] : (curious(X0) | quiet(X0)) | ~strong(john) | patient(john)) & ((strong(john) & ~patient(john)) | ! [X0] : (~curious(X0) & ~quiet(X0))) [flattening 64]
66. (? [X0] : (curious(X0) | quiet(X0)) | ~strong(john) | patient(john)) & ((strong(john) & ~patient(john)) | ! [X1] : (~curious(X1) & ~quiet(X1))) [rectify 65]
67. ? [X0] : (curious(X0) | quiet(X0)) => (curious(sK5) | quiet(sK5)) [choice axiom]
68. ((curious(sK5) | quiet(sK5)) | ~strong(john) | patient(john)) & ((strong(john) & ~patient(john)) | ! [X1] : (~curious(X1) & ~quiet(X1))) [skolemisation 66,67]
119. ~strong(X0) | ~strong(X0) | kind(X0) [cnf transformation 63]
124. strong(john) | ~quiet(X1) [cnf transformation 68]
144. ~strong(john) | ~kind(john) [cnf transformation 23]
145. quiet(mary) [cnf transformation 24]
146. ~strong(X0) | kind(X0) [duplicate literal removal 119]
297. 33 <=> strong(john) [avatar definition]
314. 37 <=> ! [X1] : ~quiet(X1) [avatar definition]
315. ~quiet(X1) <- (37) [avatar component clause 314]
316. 37 | 33 [avatar split clause 124,297,314]
375. ~strong(john) [subsumption resolution 144,146]
376. ~33 [avatar split clause 375,297]
379. $false <- (37) [resolution 315,145]
380. ~37 [avatar contradiction clause 379]
381. $false [avatar sat refutation 316,376,380]
% SZS output end Proof for 1562225544092325096220611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or not curious then someone is either not humble or not happy. If someone is funny then alice is creative. If paul is not kind then alice is both not brave and not calm. If someone is creative or funny then someone is both not brave and rich and vice versa. Everyone who is either not tall or creative is both tall and patient. If someone is brave or not wise then someone is patient or happy. If alice is either not generous or not brave then susan is curious or not generous and vice versa. Everyone who is curious or not funny is both generous and curious. If someone is either quiet or humble then someone is either tall or strong. Everyone who is both not happy and not patient is wise. If someone is strong then someone is generous or not calm and vice versa. Everyone who is not calm is creative and vice versa. Everyone who is kind or generous is calm or not rich. Everyone who is both not quiet and rich is both not brave and quiet. Everyone who is happy or not strong is happy and vice versa. Everyone who is either patient or not tall is not curious and vice versa. Someone is curious. Someone is not generous or not creative. Mary is either rich or not quiet. Someone is not patient. Susan is quiet. Susan is not funny. Someone is both patient and happy. Alice is happy or curious. | Alice is brave. | neutral | ((?[X]:((funny(X)<~>~curious(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
((?[X]:(funny(X)))=>(creative(alice)))&
((~kind(paul))=>((~brave(alice)&~calm(alice))))&
((?[X]:((creative(X)|funny(X))))<=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((~tall(X)<~>creative(X))=>(tall(X)&patient(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((patient(X)|happy(X)))))&
(((~generous(alice)<~>~brave(alice)))<=>((curious(susan)|~generous(susan))))&
(![X]:((curious(X)|~funny(X))=>(generous(X)&curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((~happy(X)&~patient(X))=>wise(X)))&
((?[X]:(strong(X)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
(![X]:((kind(X)|generous(X))=>(calm(X)|~rich(X))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&quiet(X))))&
(![X]:((happy(X)|~strong(X))<=>happy(X)))&
(![X]:((patient(X)<~>~tall(X))<=>~curious(X)))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|~creative(X))))&
((rich(mary)<~>~quiet(mary)))&
(?[X]:(~patient(X)))&
(quiet(susan))&
(~funny(susan))&
(?[X]:((patient(X)&happy(X))))&
((happy(alice)|curious(alice))) | brave(alice) | [] | null | 0 |
Everyone who is not calm or not strong is not strong or tall and vice versa.
If john is not rich then someone is quiet or old and vice versa.
If lucy is not strong or not wise then mary is either not happy or creative.
Everyone who is not tall is wise and vice versa.
Everyone who is not brave is both not rich and not patient.
If alice is not creative or tall then fred is either creative or patient and vice versa.
If mary is humble or not brave then someone is both not kind and not wise.
If susan is either happy or old then susan is either not funny or not creative and vice versa.
If paul is curious then someone is generous or not happy and vice versa.
Everyone who is not happy is not creative and vice versa.
If someone is wise then someone is not brave and vice versa.
If someone is both not kind and not funny then susan is either old or generous and vice versa.
If lucy is both not humble and not quiet then susan is both not strong and not patient.
If paul is either not wise or not tall then john is not curious and vice versa.
Everyone who is both not brave and calm is generous or not brave and vice versa.
Everyone who is not humble or not calm is either humble or not patient and vice versa.
Someone is either old or not calm.
Someone is both strong and calm.
Someone is brave or not humble.
Paul is not kind or tall.
Lucy is not strong or not humble.
Mary is both not humble and not wise.
Paul is both patient and not calm.
Someone is either curious or happy. | Lucy is not rich. | neutral | (![X]:((~calm(X)|~strong(X))<=>(~strong(X)|tall(X))))&
((~rich(john))<=>(?[X]:((quiet(X)|old(X)))))&
(((~strong(lucy)|~wise(lucy)))=>((~happy(mary)<~>creative(mary))))&
(![X]:(~tall(X)<=>wise(X)))&
(![X]:(~brave(X)=>(~rich(X)&~patient(X))))&
(((~creative(alice)|tall(alice)))<=>((creative(fred)<~>patient(fred))))&
(((humble(mary)|~brave(mary)))=>(?[X]:((~kind(X)&~wise(X)))))&
(((happy(susan)<~>old(susan)))<=>((~funny(susan)<~>~creative(susan))))&
((curious(paul))<=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~happy(X)<=>~creative(X)))&
((?[X]:(wise(X)))<=>(?[X]:(~brave(X))))&
((?[X]:((~kind(X)&~funny(X))))<=>((old(susan)<~>generous(susan))))&
(((~humble(lucy)&~quiet(lucy)))=>((~strong(susan)&~patient(susan))))&
(((~wise(paul)<~>~tall(paul)))<=>(~curious(john)))&
(![X]:((~brave(X)&calm(X))<=>(generous(X)|~brave(X))))&
(![X]:((~humble(X)|~calm(X))<=>(humble(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((brave(X)|~humble(X))))&
((~kind(paul)|tall(paul)))&
((~strong(lucy)|~humble(lucy)))&
((~humble(mary)&~wise(mary)))&
((patient(paul)&~calm(paul)))&
(?[X]:((curious(X)<~>happy(X)))) | ~rich(lucy) | [] | null | 0 |
Everyone who is funny is either creative or patient.
If someone is both kind and humble then someone is not brave or rich.
If alice is tall or rich then fred is either rich or not calm.
Everyone who is old or tall is both tall and not strong and vice versa.
Everyone who is not tall is either curious or happy and vice versa.
Everyone who is both not curious and tall is kind or rich and vice versa.
If someone is quiet then lucy is calm or not calm.
If someone is both not quiet and not curious then susan is rich or not generous and vice versa.
Everyone who is wise or not strong is humble.
If fred is both tall and brave then someone is not quiet.
If someone is both not strong and strong then john is happy.
If susan is both not creative and patient then lucy is not creative or not strong and vice versa.
Everyone who is both happy and wise is kind and vice versa.
If someone is not happy then someone is either not generous or creative and vice versa.
If mary is brave or not funny then someone is kind.
If alice is either not happy or not tall then paul is either not patient or quiet and vice versa.
Someone is not brave or not tall.
Someone is both not brave and humble.
John is either wise or not funny.
Fred is curious.
Someone is not humble.
Paul is creative.
Someone is either not old or not funny.
Susan is either old or not strong. | Mary is not brave. | entailment | (![X]:(funny(X)=>(creative(X)<~>patient(X))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(((tall(alice)|rich(alice)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&~strong(X))))&
(![X]:(~tall(X)<=>(curious(X)<~>happy(X))))&
(![X]:((~curious(X)&tall(X))<=>(kind(X)|rich(X))))&
((?[X]:(quiet(X)))=>((calm(lucy)|~calm(lucy))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((rich(susan)|~generous(susan))))&
(![X]:((wise(X)|~strong(X))=>humble(X)))&
(((tall(fred)&brave(fred)))=>(?[X]:(~quiet(X))))&
((?[X]:((~strong(X)&strong(X))))=>(happy(john)))&
(((~creative(susan)&patient(susan)))<=>((~creative(lucy)|~strong(lucy))))&
(![X]:((happy(X)&wise(X))<=>kind(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((~generous(X)<~>creative(X)))))&
(((brave(mary)|~funny(mary)))=>(?[X]:(kind(X))))&
(((~happy(alice)<~>~tall(alice)))<=>((~patient(paul)<~>quiet(paul))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~brave(X)&humble(X))))&
((wise(john)<~>~funny(john)))&
(curious(fred))&
(?[X]:(~humble(X)))&
(creative(paul))&
(?[X]:((~old(X)<~>~funny(X))))&
((old(susan)<~>~strong(susan))) | ~brave(mary) | [
"p4",
"p5",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3260004071429916751596623
% SZS output start Proof for 3260004071429916751596623
5. ! [X0] : (~tall(X0) <=> (curious(X0) <~> happy(X0))) [input p4]
6. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (rich(X0) | kind(X0))) [input p5]
13. ! [X0] : ((wise(X0) & happy(X0)) <=> kind(X0)) [input p12]
15. (~funny(mary) | brave(mary)) => ? [X0] : kind(X0) [input p14]
25. brave(mary) [input hypothesis]
37. ? [X0] : kind(X0) | (funny(mary) & ~brave(mary)) [ennf transformation 15]
45. ! [X0] : ((~tall(X0) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | tall(X0))) [nnf transformation 5]
46. ! [X0] : (((tall(X0) & ~curious(X0)) | (~rich(X0) & ~kind(X0))) & ((rich(X0) | kind(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 6]
47. ! [X0] : (((tall(X0) & ~curious(X0)) | (~rich(X0) & ~kind(X0))) & (rich(X0) | kind(X0) | ~tall(X0) | curious(X0))) [flattening 46]
57. ! [X0] : (((wise(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | (~wise(X0) | ~happy(X0)))) [nnf transformation 13]
58. ! [X0] : (((wise(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | ~wise(X0) | ~happy(X0))) [flattening 57]
64. ? [X0] : kind(X0) => kind(sK5) [choice axiom]
65. kind(sK5) | (funny(mary) & ~brave(mary)) [skolemisation 37,64]
93. ~happy(X0) | curious(X0) | ~tall(X0) [cnf transformation 45]
95. ~curious(X0) | ~kind(X0) [cnf transformation 47]
97. ~kind(X0) | tall(X0) [cnf transformation 47]
115. ~kind(X0) | happy(X0) [cnf transformation 58]
121. kind(sK5) | ~brave(mary) [cnf transformation 65]
143. brave(mary) [cnf transformation 25]
264. 27 <=> kind(sK5) [avatar definition]
266. kind(sK5) <- (27) [avatar component clause 264]
269. 28 <=> brave(mary) [avatar definition]
272. ~28 | 27 [avatar split clause 121,264,269]
324. 28 [avatar split clause 143,269]
328. tall(sK5) <- (27) [resolution 97,266]
332. happy(sK5) <- (27) [resolution 115,266]
376. curious(sK5) | ~tall(sK5) <- (27) [resolution 93,332]
379. curious(sK5) <- (27) [subsumption resolution 376,328]
440. ~kind(sK5) <- (27) [resolution 379,95]
441. $false <- (27) [subsumption resolution 440,266]
442. ~27 [avatar contradiction clause 441]
443. $false [avatar sat refutation 272,324,442]
% SZS output end Proof for 3260004071429916751596623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not tall or patient then someone is quiet and vice versa. If fred is both not wise and not patient then fred is brave and vice versa. Everyone who is funny is either not old or not quiet and vice versa. Everyone who is both not humble and old is generous or curious and vice versa. Everyone who is either not tall or not happy is both old and calm. Everyone who is not patient or not humble is not creative or not tall and vice versa. Everyone who is either quiet or funny is rich or kind. If john is either not old or not calm then alice is both not patient and not strong and vice versa. Everyone who is both not creative and not humble is creative or not funny and vice versa. Everyone who is funny is either strong or not creative and vice versa. If paul is rich or generous then paul is either not curious or not calm and vice versa. If fred is not rich then fred is either not creative or not strong. Everyone who is tall is both humble and not humble and vice versa. Everyone who is generous is patient or creative. If susan is both not funny and rich then someone is either not funny or curious. If someone is both patient and not curious then susan is both not old and quiet. Susan is either curious or calm. Someone is both wise and patient. Paul is either not tall or not rich. Susan is generous or not humble. Mary is both not funny and old. Someone is either wise or rich. Paul is not old. | Mary is humble. | contradiction | ((?[X]:((~tall(X)<~>patient(X))))<=>(?[X]:(quiet(X))))&
(((~wise(fred)&~patient(fred)))<=>(brave(fred)))&
(![X]:(funny(X)<=>(~old(X)<~>~quiet(X))))&
(![X]:((~humble(X)&old(X))<=>(generous(X)|curious(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(old(X)&calm(X))))&
(![X]:((~patient(X)|~humble(X))<=>(~creative(X)|~tall(X))))&
(![X]:((quiet(X)<~>funny(X))=>(rich(X)|kind(X))))&
(((~old(john)<~>~calm(john)))<=>((~patient(alice)&~strong(alice))))&
(![X]:((~creative(X)&~humble(X))<=>(creative(X)|~funny(X))))&
(![X]:(funny(X)<=>(strong(X)<~>~creative(X))))&
(((rich(paul)|generous(paul)))<=>((~curious(paul)<~>~calm(paul))))&
((~rich(fred))=>((~creative(fred)<~>~strong(fred))))&
(![X]:(tall(X)<=>(humble(X)&~humble(X))))&
(![X]:(generous(X)=>(patient(X)|creative(X))))&
(((~funny(susan)&rich(susan)))=>(?[X]:((~funny(X)<~>curious(X)))))&
((?[X]:((patient(X)&~curious(X))))=>((~old(susan)&quiet(susan))))&
((curious(susan)<~>calm(susan)))&
(?[X]:((wise(X)&patient(X))))&
((~tall(paul)<~>~rich(paul)))&
((generous(susan)|~humble(susan)))&
((~funny(mary)&old(mary)))&
(?[X]:((wise(X)<~>rich(X))))&
(~old(paul)) | humble(mary) | [
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2945808235332002549148573
% SZS output start Proof for 2945808235332002549148573
9. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> (~funny(X0) | creative(X0))) [input p8]
21. old(mary) & ~funny(mary) [input p20]
24. humble(mary) [input hypothesis]
49. ! [X0] : (((~humble(X0) & ~creative(X0)) | (funny(X0) & ~creative(X0))) & ((~funny(X0) | creative(X0)) | (humble(X0) | creative(X0)))) [nnf transformation 9]
50. ! [X0] : (((~humble(X0) & ~creative(X0)) | (funny(X0) & ~creative(X0))) & (~funny(X0) | creative(X0) | humble(X0) | creative(X0))) [flattening 49]
101. ~humble(X0) | funny(X0) [cnf transformation 50]
129. ~funny(mary) [cnf transformation 21]
134. humble(mary) [cnf transformation 24]
293. funny(mary) [resolution 101,134]
294. $false [subsumption resolution 293,129]
% SZS output end Proof for 2945808235332002549148573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not old or not wise then paul is either not patient or not wise. If someone is both not strong and brave then john is both patient and not creative and vice versa. If someone is either not tall or not old then someone is happy. Everyone who is either kind or wise is either not kind or not brave and vice versa. If someone is both humble and old then john is not tall or not wise and vice versa. If alice is not kind then someone is quiet or wise and vice versa. Everyone who is humble or tall is not strong and vice versa. If lucy is curious or not brave then alice is patient or not curious. If john is both happy and funny then alice is either not tall or not brave. Everyone who is not funny or quiet is either kind or brave and vice versa. Everyone who is both not kind and patient is both not funny and humble. Everyone who is calm or old is either kind or not brave. If john is either generous or rich then someone is either not funny or not curious and vice versa. Everyone who is not brave or strong is both not rich and curious. Everyone who is not wise or creative is both not rich and not happy. Everyone who is not brave is happy or not strong and vice versa. Fred is either not brave or not old. John is both not rich and kind. Someone is not happy or curious. Lucy is either curious or strong. Lucy is both not kind and not wise. Someone is either happy or generous. | Paul is tall. | contradiction | (((~old(paul)<~>~wise(paul)))=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~strong(X)&brave(X))))<=>((patient(john)&~creative(john))))&
((?[X]:((~tall(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>wise(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:((humble(X)&old(X))))<=>((~tall(john)|~wise(john))))&
((~kind(alice))<=>(?[X]:((quiet(X)|wise(X)))))&
(![X]:((humble(X)|tall(X))<=>~strong(X)))&
(((curious(lucy)|~brave(lucy)))=>((patient(alice)|~curious(alice))))&
(((happy(john)&funny(john)))=>((~tall(alice)<~>~brave(alice))))&
(![X]:((~funny(X)|quiet(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&patient(X))=>(~funny(X)&humble(X))))&
(![X]:((calm(X)|old(X))=>(kind(X)<~>~brave(X))))&
(((generous(john)<~>rich(john)))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((~brave(X)|strong(X))=>(~rich(X)&curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~rich(X)&~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)|~strong(X))))&
((~brave(fred)<~>~old(fred)))&
((~rich(john)&kind(john)))&
(?[X]:((~happy(X)|curious(X))))&
((curious(lucy)<~>strong(lucy)))&
((~kind(lucy)&~wise(lucy)))&
(?[X]:((happy(X)<~>generous(X)))) | tall(paul) | [
"p0",
"p2",
"p3",
"p6",
"p9",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2699378771993452884631088
% SZS output start Proof for 2699378771993452884631088
1. (~old(paul) <~> ~wise(paul)) => (~patient(paul) <~> ~wise(paul)) [input p0]
3. ? [X0] : (~tall(X0) <~> ~old(X0)) => ? [X0] : happy(X0) [input p2]
4. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (~kind(X0) <~> ~brave(X0))) [input p3]
7. ! [X0] : ((tall(X0) | humble(X0)) <=> ~strong(X0)) [input p6]
10. ! [X0] : ((quiet(X0) | ~funny(X0)) <=> (kind(X0) <~> brave(X0))) [input p9]
11. ! [X0] : ((patient(X0) & ~kind(X0)) => (humble(X0) & ~funny(X0))) [input p10]
12. ! [X0] : ((old(X0) | calm(X0)) => (kind(X0) <~> ~brave(X0))) [input p11]
15. ! [X0] : ((creative(X0) | ~wise(X0)) => (~happy(X0) & ~rich(X0))) [input p14]
16. ! [X0] : (~brave(X0) <=> (~strong(X0) | happy(X0))) [input p15]
23. tall(paul) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> ~old(X0)) => ? [X1] : happy(X1) [rectify 3]
25. ! [X0] : (old(X0) => (kind(X0) <~> ~brave(X0))) [pure predicate removal 12]
26. (~patient(paul) <~> ~wise(paul)) | (~old(paul) <=> ~wise(paul)) [ennf transformation 1]
27. ? [X1] : happy(X1) | ! [X0] : (~tall(X0) <=> ~old(X0)) [ennf transformation 24]
32. ! [X0] : ((humble(X0) & ~funny(X0)) | (~patient(X0) | kind(X0))) [ennf transformation 11]
33. ! [X0] : ((humble(X0) & ~funny(X0)) | ~patient(X0) | kind(X0)) [flattening 32]
34. ! [X0] : ((kind(X0) <~> ~brave(X0)) | ~old(X0)) [ennf transformation 25]
36. ! [X0] : ((~happy(X0) & ~rich(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 15]
37. ((wise(paul) | patient(paul)) & (~wise(paul) | ~patient(paul))) | ((~old(paul) | wise(paul)) & (~wise(paul) | old(paul))) [nnf transformation 26]
43. ? [X1] : happy(X1) | ! [X0] : ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))) [nnf transformation 27]
44. ? [X0] : happy(X0) | ! [X1] : ((~tall(X1) | old(X1)) & (~old(X1) | tall(X1))) [rectify 43]
45. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
46. happy(sK1) | ! [X1] : ((~tall(X1) | old(X1)) & (~old(X1) | tall(X1))) [skolemisation 44,45]
47. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 4]
57. ! [X0] : (((tall(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~humble(X0)))) [nnf transformation 7]
58. ! [X0] : ((tall(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~humble(X0)))) [flattening 57]
60. ! [X0] : (((quiet(X0) | ~funny(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (~quiet(X0) & funny(X0)))) [nnf transformation 10]
61. ! [X0] : ((quiet(X0) | ~funny(X0) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (~quiet(X0) & funny(X0)))) [flattening 60]
62. ! [X0] : (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~old(X0)) [nnf transformation 34]
67. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | brave(X0))) [nnf transformation 16]
68. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | brave(X0))) [flattening 67]
79. wise(paul) | patient(paul) | ~old(paul) | wise(paul) [cnf transformation 37]
85. happy(sK1) | ~tall(X1) | old(X1) [cnf transformation 46]
89. brave(X0) | kind(X0) | kind(X0) | ~wise(X0) [cnf transformation 47]
93. ~wise(X0) | ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 47]
103. ~tall(X0) | ~strong(X0) [cnf transformation 58]
109. funny(X0) | kind(X0) | brave(X0) [cnf transformation 61]
115. ~funny(X0) | ~patient(X0) | kind(X0) [cnf transformation 33]
118. ~kind(X0) | brave(X0) | ~old(X0) [cnf transformation 62]
133. ~happy(X0) | wise(X0) [cnf transformation 36]
136. ~happy(X0) | ~brave(X0) [cnf transformation 68]
137. ~brave(X0) | strong(X0) [cnf transformation 68]
149. tall(paul) [cnf transformation 23]
151. brave(X0) | kind(X0) | ~wise(X0) [duplicate literal removal 89]
153. ~kind(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 93]
155. wise(paul) | patient(paul) | ~old(paul) [duplicate literal removal 79]
157. 1 <=> old(paul) [avatar definition]
158. old(paul) <- (1) [avatar component clause 157]
159. ~old(paul) <- (~1) [avatar component clause 157]
161. 2 <=> patient(paul) [avatar definition]
163. patient(paul) <- (2) [avatar component clause 161]
165. 3 <=> wise(paul) [avatar definition]
167. wise(paul) <- (3) [avatar component clause 165]
168. ~1 | 2 | 3 [avatar split clause 155,165,161,157]
189. 8 <=> ! [X1] : (~brave(X1) | strong(X1)) [avatar definition]
190. ~brave(X1) | strong(X1) <- (8) [avatar component clause 189]
194. 9 <=> ! [X1] : (~tall(X1) | old(X1)) [avatar definition]
195. ~tall(X1) | old(X1) <- (9) [avatar component clause 194]
197. 10 <=> happy(sK1) [avatar definition]
199. happy(sK1) <- (10) [avatar component clause 197]
200. 9 | 10 [avatar split clause 85,197,194]
205. ~wise(X0) | brave(X0) [subsumption resolution 151,153]
318. 8 [avatar split clause 137,189]
353. ~strong(paul) [resolution 103,149]
363. old(paul) <- (9) [resolution 195,149]
364. $false <- (~1, 9) [subsumption resolution 363,159]
365. 1 | ~9 [avatar contradiction clause 364]
368. ~brave(sK1) <- (10) [resolution 199,136]
370. wise(sK1) <- (10) [resolution 199,133]
374. brave(sK1) <- (10) [resolution 370,205]
375. $false <- (10) [subsumption resolution 374,368]
376. ~10 [avatar contradiction clause 375]
378. brave(paul) <- (3) [resolution 167,205]
384. strong(paul) <- (3, 8) [resolution 378,190]
385. $false <- (3, 8) [subsumption resolution 384,353]
386. ~3 | ~8 [avatar contradiction clause 385]
415. ~patient(X0) | kind(X0) | kind(X0) | brave(X0) [resolution 115,109]
416. ~patient(X0) | kind(X0) | brave(X0) [duplicate literal removal 415]
435. 44 <=> kind(paul) [avatar definition]
437. kind(paul) <- (44) [avatar component clause 435]
492. brave(paul) | ~old(paul) <- (44) [resolution 437,118]
494. brave(paul) <- (1, 44) [subsumption resolution 492,158]
540. kind(paul) | brave(paul) <- (2) [resolution 416,163]
585. strong(paul) <- (1, 8, 44) [resolution 494,190]
588. $false <- (1, 8, 44) [subsumption resolution 585,353]
589. ~1 | ~8 | ~44 [avatar contradiction clause 588]
591. 55 <=> brave(paul) [avatar definition]
593. brave(paul) <- (55) [avatar component clause 591]
594. 55 | 44 | ~2 [avatar split clause 540,161,435,591]
617. strong(paul) <- (8, 55) [resolution 593,190]
626. $false <- (8, 55) [subsumption resolution 617,353]
627. ~8 | ~55 [avatar contradiction clause 626]
628. $false [avatar sat refutation 168,200,318,365,376,386,589,594,627]
% SZS output end Proof for 2699378771993452884631088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not curious then fred is both calm and humble.
If alice is either brave or not generous then alice is both humble and not humble and vice versa.
Everyone who is calm is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Paul is not generous or not wise.
Paul is either not curious or rich.
Someone is either not strong or not patient.
Someone is either rich or not happy.
Lucy is strong. | Alice is happy. | neutral | ((?[X]:((quiet(X)&~curious(X))))=>((calm(fred)&humble(fred))))&
(((brave(alice)<~>~generous(alice)))<=>((humble(alice)&~humble(alice))))&
(![X]:(calm(X)=>(~wise(X)&humble(X))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
((~generous(paul)|~wise(paul)))&
((~curious(paul)<~>rich(paul)))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(strong(lucy)) | happy(alice) | [] | null | 0 |
Everyone who is wise or brave is both not generous and funny and vice versa.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
If susan is generous then susan is happy and vice versa.
If someone is both kind and not humble then fred is either not funny or creative.
Everyone who is curious or wise is not curious.
Everyone who is both humble and rich is not brave and vice versa.
If mary is not patient or funny then john is either strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
Everyone who is not curious is creative or not patient and vice versa.
Everyone who is old or not quiet is either not creative or not curious and vice versa.
If someone is both not generous and not funny then someone is not quiet.
Someone is not curious.
Someone is either not kind or not old.
Susan is not wise or rich.
Someone is funny.
Someone is not strong or kind. | Fred is not brave. | neutral | (![X]:((wise(X)|brave(X))<=>(~generous(X)&funny(X))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~kind(X)<~>~old(X))))&
((~wise(susan)|rich(susan)))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)|kind(X)))) | ~brave(fred) | [] | null | 0 |
If susan is either tall or curious then someone is wise.
Everyone who is either not happy or not funny is not creative or tall and vice versa.
If susan is not funny or old then john is not old.
Everyone who is brave is both happy and not strong and vice versa.
If someone is humble then alice is both not calm and not wise.
Everyone who is either not curious or patient is both brave and quiet.
Everyone who is curious is calm or not brave.
Everyone who is either not humble or not creative is both old and funny and vice versa.
If alice is not generous or not tall then someone is either not curious or kind and vice versa.
Everyone who is not strong is both rich and generous and vice versa.
If fred is both not rich and not strong then mary is not curious or not quiet and vice versa.
Everyone who is both not funny and not rich is not kind or not happy.
If john is old then alice is not happy and vice versa.
If mary is both not humble and not brave then someone is tall or not quiet.
If someone is old or creative then someone is both not tall and quiet.
Everyone who is not strong is both not old and generous and vice versa.
Someone is both wise and not funny.
Someone is both not strong and not curious.
Someone is not patient or calm.
Someone is either not happy or not old.
Lucy is both humble and not kind.
Someone is not patient.
Someone is not curious or calm.
Fred is both wise and funny. | Susan is curious. | neutral | (((tall(susan)<~>curious(susan)))=>(?[X]:(wise(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(~creative(X)|tall(X))))&
(((~funny(susan)|old(susan)))=>(~old(john)))&
(![X]:(brave(X)<=>(happy(X)&~strong(X))))&
((?[X]:(humble(X)))=>((~calm(alice)&~wise(alice))))&
(![X]:((~curious(X)<~>patient(X))=>(brave(X)&quiet(X))))&
(![X]:(curious(X)=>(calm(X)|~brave(X))))&
(![X]:((~humble(X)<~>~creative(X))<=>(old(X)&funny(X))))&
(((~generous(alice)|~tall(alice)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(~strong(X)<=>(rich(X)&generous(X))))&
(((~rich(fred)&~strong(fred)))<=>((~curious(mary)|~quiet(mary))))&
(![X]:((~funny(X)&~rich(X))=>(~kind(X)|~happy(X))))&
((old(john))<=>(~happy(alice)))&
(((~humble(mary)&~brave(mary)))=>(?[X]:((tall(X)|~quiet(X)))))&
((?[X]:((old(X)|creative(X))))=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:(~strong(X)<=>(~old(X)&generous(X))))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:((~strong(X)&~curious(X))))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
((humble(lucy)&~kind(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:((~curious(X)|calm(X))))&
((wise(fred)&funny(fred))) | curious(susan) | [] | null | 0 |
Everyone who is happy or humble is both not old and not quiet.
Everyone who is happy or not wise is both funny and not calm.
Everyone who is wise or not old is both not patient and wise and vice versa.
If someone is not funny or old then someone is either not curious or brave and vice versa.
Everyone who is both tall and not old is both not quiet and happy and vice versa.
Everyone who is either humble or strong is either old or not quiet.
If someone is funny then mary is not funny.
If someone is not happy then someone is not calm or not patient.
Everyone who is brave is either not rich or tall.
Everyone who is both strong and not kind is both rich and curious.
Everyone who is not humble is both rich and not happy and vice versa.
Everyone who is both not old and not calm is either not tall or not curious and vice versa.
Everyone who is both not quiet and not kind is both rich and kind.
Everyone who is not strong is both humble and not patient and vice versa.
If susan is either not rich or not humble then someone is quiet and vice versa.
If paul is not generous or patient then someone is either kind or old.
Alice is either not curious or not creative.
Lucy is both strong and not old.
Someone is both curious and funny.
Mary is not calm.
Someone is tall or patient.
Someone is both not brave and not calm.
Someone is not old or old. | Lucy is not generous. | neutral | (![X]:((happy(X)|humble(X))=>(~old(X)&~quiet(X))))&
(![X]:((happy(X)|~wise(X))=>(funny(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))<=>(~patient(X)&wise(X))))&
((?[X]:((~funny(X)|old(X))))<=>(?[X]:((~curious(X)<~>brave(X)))))&
(![X]:((tall(X)&~old(X))<=>(~quiet(X)&happy(X))))&
(![X]:((humble(X)<~>strong(X))=>(old(X)<~>~quiet(X))))&
((?[X]:(funny(X)))=>(~funny(mary)))&
((?[X]:(~happy(X)))=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:(brave(X)=>(~rich(X)<~>tall(X))))&
(![X]:((strong(X)&~kind(X))=>(rich(X)&curious(X))))&
(![X]:(~humble(X)<=>(rich(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((~quiet(X)&~kind(X))=>(rich(X)&kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~patient(X))))&
(((~rich(susan)<~>~humble(susan)))<=>(?[X]:(quiet(X))))&
(((~generous(paul)|patient(paul)))=>(?[X]:((kind(X)<~>old(X)))))&
((~curious(alice)<~>~creative(alice)))&
((strong(lucy)&~old(lucy)))&
(?[X]:((curious(X)&funny(X))))&
(~calm(mary))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~brave(X)&~calm(X))))&
(?[X]:((~old(X)|old(X)))) | ~generous(lucy) | [] | null | 0 |
If john is both not brave and patient then someone is generous or not kind. If john is both not generous and not humble then alice is not curious and vice versa. Everyone who is both not generous and strong is not funny or funny. Everyone who is happy is funny. Everyone who is not patient is either tall or happy and vice versa. Everyone who is patient is not kind or curious and vice versa. If alice is both kind and not wise then susan is not quiet. Everyone who is either not strong or not rich is rich or funny and vice versa. If someone is both not creative and happy then someone is either not patient or not quiet and vice versa. If paul is both humble and not patient then someone is not old or not patient and vice versa. Everyone who is either not funny or not calm is kind or not humble and vice versa. Everyone who is humble or tall is either not calm or not curious. Everyone who is either not tall or curious is both brave and not generous and vice versa. Everyone who is curious is not generous or not tall. Everyone who is not funny or not rich is not brave or not funny and vice versa. If fred is either not strong or not generous then alice is tall or not creative and vice versa. Someone is old. Mary is strong. Alice is strong. John is generous. John is either strong or not old. Someone is not happy or curious. Someone is rich or humble. Lucy is generous. | Alice is not tall. | entailment | (((~brave(john)&patient(john)))=>(?[X]:((generous(X)|~kind(X)))))&
(((~generous(john)&~humble(john)))<=>(~curious(alice)))&
(![X]:((~generous(X)&strong(X))=>(~funny(X)|funny(X))))&
(![X]:(happy(X)=>funny(X)))&
(![X]:(~patient(X)<=>(tall(X)<~>happy(X))))&
(![X]:(patient(X)<=>(~kind(X)|curious(X))))&
(((kind(alice)&~wise(alice)))=>(~quiet(susan)))&
(![X]:((~strong(X)<~>~rich(X))<=>(rich(X)|funny(X))))&
((?[X]:((~creative(X)&happy(X))))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((humble(paul)&~patient(paul)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(kind(X)|~humble(X))))&
(![X]:((humble(X)|tall(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(brave(X)&~generous(X))))&
(![X]:(curious(X)=>(~generous(X)|~tall(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~brave(X)|~funny(X))))&
(((~strong(fred)<~>~generous(fred)))<=>((tall(alice)|~creative(alice))))&
(?[X]:(old(X)))&
(strong(mary))&
(strong(alice))&
(generous(john))&
((strong(john)<~>~old(john)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:((rich(X)|humble(X))))&
(generous(lucy)) | ~tall(alice) | [
"p1",
"p7",
"p12",
"p14",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 332340603246698754342543
% SZS output start Proof for 332340603246698754342543
2. (~humble(john) & ~generous(john)) <=> ~curious(alice) [input p1]
8. ! [X0] : ((~strong(X0) <~> ~rich(X0)) <=> (funny(X0) | rich(X0))) [input p7]
13. ! [X0] : ((~tall(X0) <~> curious(X0)) <=> (~generous(X0) & brave(X0))) [input p12]
15. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~funny(X0) | ~brave(X0))) [input p14]
19. strong(alice) [input p18]
20. generous(john) [input p19]
25. tall(alice) [input hypothesis]
38. ((~humble(john) & ~generous(john)) | curious(alice)) & (~curious(alice) | (humble(john) | generous(john))) [nnf transformation 2]
39. ((~humble(john) & ~generous(john)) | curious(alice)) & (~curious(alice) | humble(john) | generous(john)) [flattening 38]
43. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~funny(X0) & ~rich(X0))) & ((funny(X0) | rich(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [nnf transformation 8]
44. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~funny(X0) & ~rich(X0))) & (funny(X0) | rich(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [flattening 43]
58. ! [X0] : ((((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))))) [flattening 58]
60. ! [X0] : (((~rich(X0) | ~funny(X0)) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 15]
61. ! [X0] : ((~rich(X0) | ~funny(X0) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | (rich(X0) & funny(X0)))) [flattening 60]
73. ~generous(john) | curious(alice) [cnf transformation 39]
85. funny(X0) | rich(X0) | ~strong(X0) | rich(X0) [cnf transformation 44]
86. ~rich(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 44]
112. ~tall(X0) | brave(X0) | ~curious(X0) [cnf transformation 59]
119. ~funny(X0) | ~brave(X0) | rich(X0) [cnf transformation 61]
130. strong(alice) [cnf transformation 19]
131. generous(john) [cnf transformation 20]
137. tall(alice) [cnf transformation 25]
138. funny(X0) | rich(X0) | ~strong(X0) [duplicate literal removal 85]
139. ~rich(X0) | ~strong(X0) [duplicate literal removal 86]
158. 5 <=> curious(alice) [avatar definition]
160. curious(alice) <- (5) [avatar component clause 158]
167. 7 <=> generous(john) [avatar definition]
170. 5 | ~7 [avatar split clause 73,167,158]
172. ~strong(X0) | funny(X0) [subsumption resolution 138,139]
245. 24 <=> tall(alice) [avatar definition]
246. tall(alice) <- (24) [avatar component clause 245]
253. 7 [avatar split clause 131,167]
282. 24 [avatar split clause 137,245]
294. funny(alice) [resolution 172,130]
389. brave(alice) | ~curious(alice) <- (24) [resolution 112,246]
393. brave(alice) <- (5, 24) [subsumption resolution 389,160]
429. ~brave(alice) | rich(alice) [resolution 119,294]
433. rich(alice) <- (5, 24) [subsumption resolution 429,393]
658. ~strong(alice) <- (5, 24) [resolution 433,139]
662. $false <- (5, 24) [subsumption resolution 658,130]
663. ~5 | ~24 [avatar contradiction clause 662]
664. $false [avatar sat refutation 170,253,282,663]
% SZS output end Proof for 332340603246698754342543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is either not quiet or rich.
Everyone who is either not creative or calm is not curious or not strong and vice versa.
If mary is wise or rich then someone is humble.
Everyone who is not humble is not rich or rich.
Everyone who is not generous is calm or patient.
If someone is not strong then someone is both kind and old and vice versa.
Everyone who is either tall or not wise is both not quiet and not tall.
Everyone who is either patient or humble is not brave and vice versa.
If paul is kind or not tall then john is either not tall or not old and vice versa.
If someone is brave or tall then someone is either not humble or kind.
Everyone who is not happy or tall is both not curious and not creative and vice versa.
Everyone who is not wise is either not patient or not quiet and vice versa.
If someone is either not strong or patient then susan is not old and vice versa.
Everyone who is not quiet or calm is both funny and not funny.
If paul is both not wise and generous then someone is either rich or tall and vice versa.
Everyone who is creative is either not wise or strong and vice versa.
Mary is not generous.
John is both not creative and curious.
Someone is both not happy and old.
Paul is not kind.
John is either strong or quiet.
Someone is both patient and not kind.
John is tall or happy. | Paul is not wise. | entailment | (![X]:(quiet(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~curious(X)|~strong(X))))&
(((wise(mary)|rich(mary)))=>(?[X]:(humble(X))))&
(![X]:(~humble(X)=>(~rich(X)|rich(X))))&
(![X]:(~generous(X)=>(calm(X)|patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((tall(X)<~>~wise(X))=>(~quiet(X)&~tall(X))))&
(![X]:((patient(X)<~>humble(X))<=>~brave(X)))&
(((kind(paul)|~tall(paul)))<=>((~tall(john)<~>~old(john))))&
((?[X]:((brave(X)|tall(X))))=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~happy(X)|tall(X))<=>(~curious(X)&~creative(X))))&
(![X]:(~wise(X)<=>(~patient(X)<~>~quiet(X))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(~old(susan)))&
(![X]:((~quiet(X)|calm(X))=>(funny(X)&~funny(X))))&
(((~wise(paul)&generous(paul)))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:(creative(X)<=>(~wise(X)<~>strong(X))))&
(~generous(mary))&
((~creative(john)&curious(john)))&
(?[X]:((~happy(X)&old(X))))&
(~kind(paul))&
((strong(john)<~>quiet(john)))&
(?[X]:((patient(X)&~kind(X))))&
((tall(john)|happy(john))) | ~wise(paul) | [
"p0",
"p10",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3349522922491916565697208
% SZS output start Proof for 3349522922491916565697208
1. ! [X0] : (quiet(X0) => (~quiet(X0) <~> rich(X0))) [input p0]
11. ! [X0] : ((tall(X0) | ~happy(X0)) <=> (~creative(X0) & ~curious(X0))) [input p10]
14. ! [X0] : ((calm(X0) | ~quiet(X0)) => (~funny(X0) & funny(X0))) [input p13]
15. (generous(paul) & ~wise(paul)) <=> ? [X0] : (rich(X0) <~> tall(X0)) [input p14]
18. curious(john) & ~creative(john) [input p17]
24. wise(paul) [input hypothesis]
28. ! [X0] : ((~quiet(X0) <~> rich(X0)) | ~quiet(X0)) [ennf transformation 1]
37. ! [X0] : ((~funny(X0) & funny(X0)) | (~calm(X0) & quiet(X0))) [ennf transformation 14]
38. ! [X0] : (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ~quiet(X0)) [nnf transformation 28]
56. ! [X0] : (((tall(X0) | ~happy(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (~tall(X0) & happy(X0)))) [nnf transformation 11]
57. ! [X0] : ((tall(X0) | ~happy(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (~tall(X0) & happy(X0)))) [flattening 56]
63. ((generous(paul) & ~wise(paul)) | ! [X0] : ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (? [X0] : ((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (~generous(paul) | wise(paul))) [nnf transformation 15]
64. ((generous(paul) & ~wise(paul)) | ! [X0] : ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (? [X0] : ((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | ~generous(paul) | wise(paul)) [flattening 63]
65. ((generous(paul) & ~wise(paul)) | ! [X0] : ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (? [X1] : ((~tall(X1) | ~rich(X1)) & (tall(X1) | rich(X1))) | ~generous(paul) | wise(paul)) [rectify 64]
66. ? [X1] : ((~tall(X1) | ~rich(X1)) & (tall(X1) | rich(X1))) => ((~tall(sK5) | ~rich(sK5)) & (tall(sK5) | rich(sK5))) [choice axiom]
67. ((generous(paul) & ~wise(paul)) | ! [X0] : ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(sK5) | ~rich(sK5)) & (tall(sK5) | rich(sK5))) | ~generous(paul) | wise(paul)) [skolemisation 65,66]
74. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
106. ~tall(X0) | ~curious(X0) [cnf transformation 57]
118. funny(X0) | quiet(X0) [cnf transformation 37]
120. ~funny(X0) | quiet(X0) [cnf transformation 37]
124. ~wise(paul) | tall(X0) | ~rich(X0) [cnf transformation 67]
134. curious(john) [cnf transformation 18]
143. wise(paul) [cnf transformation 24]
145. ~quiet(X0) | rich(X0) [duplicate literal removal 74]
186. 10 <=> tall(john) [avatar definition]
187. tall(john) <- (10) [avatar component clause 186]
188. ~tall(john) <- (~10) [avatar component clause 186]
244. quiet(X0) [subsumption resolution 118,120]
254. 24 <=> ! [X0] : (tall(X0) | ~rich(X0)) [avatar definition]
255. ~rich(X0) | tall(X0) <- (24) [avatar component clause 254]
258. 25 <=> wise(paul) [avatar definition]
262. 24 | ~25 [avatar split clause 124,258,254]
280. 25 [avatar split clause 143,258]
289. ~curious(john) <- (10) [resolution 106,187]
290. $false <- (10) [subsumption resolution 289,134]
291. ~10 [avatar contradiction clause 290]
292. rich(X0) [resolution 145,244]
300. tall(X0) <- (24) [resolution 255,292]
306. $false <- (~10, 24) [resolution 300,188]
307. 10 | ~24 [avatar contradiction clause 306]
309. $false [avatar sat refutation 262,280,291,307]
% SZS output end Proof for 3349522922491916565697208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or not happy then someone is both not creative and funny.
If fred is either brave or not calm then fred is not generous or happy.
Everyone who is happy or not quiet is either not strong or rich.
Everyone who is either generous or not curious is not funny and vice versa.
Everyone who is both not quiet and funny is both happy and funny.
If someone is both not rich and not strong then fred is not tall and vice versa.
If mary is wise then lucy is not brave and vice versa.
Everyone who is both not kind and strong is kind and vice versa.
Everyone who is both not tall and not kind is both calm and not brave.
Everyone who is either not funny or not generous is either not brave or calm and vice versa.
If someone is funny then someone is not calm and vice versa.
Everyone who is both not kind and not brave is patient or kind and vice versa.
Everyone who is either not creative or not calm is both wise and curious.
Everyone who is both not tall and not brave is quiet and vice versa.
If mary is rich or strong then alice is patient.
If paul is either rich or not calm then mary is either calm or kind.
Someone is patient.
John is not creative.
Alice is not wise.
Someone is happy.
Lucy is either curious or not humble.
Someone is not happy or strong.
Someone is both not wise and funny. | Lucy is humble. | neutral | ((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(((brave(fred)<~>~calm(fred)))=>((~generous(fred)|happy(fred))))&
(![X]:((happy(X)|~quiet(X))=>(~strong(X)<~>rich(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~funny(X)))&
(![X]:((~quiet(X)&funny(X))=>(happy(X)&funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(~tall(fred)))&
((wise(mary))<=>(~brave(lucy)))&
(![X]:((~kind(X)&strong(X))<=>kind(X)))&
(![X]:((~tall(X)&~kind(X))=>(calm(X)&~brave(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~brave(X)<~>calm(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(patient(X)|kind(X))))&
(![X]:((~creative(X)<~>~calm(X))=>(wise(X)&curious(X))))&
(![X]:((~tall(X)&~brave(X))<=>quiet(X)))&
(((rich(mary)|strong(mary)))=>(patient(alice)))&
(((rich(paul)<~>~calm(paul)))=>((calm(mary)<~>kind(mary))))&
(?[X]:(patient(X)))&
(~creative(john))&
(~wise(alice))&
(?[X]:(happy(X)))&
((curious(lucy)<~>~humble(lucy)))&
(?[X]:((~happy(X)|strong(X))))&
(?[X]:((~wise(X)&funny(X)))) | humble(lucy) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa. Everyone who is calm is quiet and vice versa. Everyone who is tall is either not happy or funny. Everyone who is strong is either kind or not generous. Everyone who is not brave is not creative and vice versa. Everyone who is either not calm or happy is brave and vice versa. If mary is not patient or not creative then someone is both not curious and not humble. If alice is not brave or not funny then lucy is either not patient or curious. Everyone who is creative or funny is both humble and strong and vice versa. Everyone who is brave or not curious is both tall and not curious and vice versa. If someone is calm then someone is both not curious and not calm. If someone is both wise and generous then someone is either happy or not strong. Everyone who is humble is either not patient or wise. If someone is not kind then susan is both tall and not funny and vice versa. Everyone who is either strong or not brave is kind. If someone is happy then lucy is humble or not creative. Someone is either generous or not humble. Paul is either generous or not kind. Someone is not generous or not curious. Someone is wise or not old. Alice is either not rich or not quiet. John is kind or not kind. | John is not quiet. | entailment | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:(strong(X)=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(?[X]:((generous(X)<~>~humble(X))))&
((generous(paul)<~>~kind(paul)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((~rich(alice)<~>~quiet(alice)))&
((kind(john)|~kind(john))) | ~quiet(john) | [
"p0",
"p1",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4440497465505017750951075
% SZS output start Proof for 4440497465505017750951075
1. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~happy(X0))) [input p0]
2. ! [X0] : (calm(X0) <=> quiet(X0)) [input p1]
5. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p4]
6. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> brave(X0)) [input p5]
23. quiet(john) [input hypothesis]
37. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 37]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 2]
42. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 5]
43. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 6]
73. ~quiet(X0) | happy(X0) [cnf transformation 38]
74. ~creative(X0) | ~quiet(X0) [cnf transformation 38]
78. ~quiet(X0) | calm(X0) [cnf transformation 39]
84. ~brave(X0) | creative(X0) [cnf transformation 42]
86. ~calm(X0) | brave(X0) | ~happy(X0) [cnf transformation 43]
127. quiet(john) [cnf transformation 23]
251. happy(john) [resolution 73,127]
253. calm(john) [resolution 78,127]
297. brave(john) | ~happy(john) [resolution 86,253]
298. brave(john) [subsumption resolution 297,251]
303. creative(john) [resolution 298,84]
331. ~quiet(john) [resolution 303,74]
334. $false [subsumption resolution 331,127]
% SZS output end Proof for 4440497465505017750951075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not wise and generous then fred is either not creative or not tall and vice versa.
If someone is humble or not quiet then susan is funny or strong and vice versa.
Everyone who is both tall and rich is either not generous or creative and vice versa.
Everyone who is not generous or brave is either calm or old.
If mary is brave or not tall then mary is not funny.
If mary is either generous or creative then someone is either not tall or old.
If someone is both not humble and not patient then mary is both not kind and not strong and vice versa.
Everyone who is both funny and not rich is both not generous and not kind.
Everyone who is calm is both not wise and not quiet.
Everyone who is both not brave and curious is both tall and not creative and vice versa.
Everyone who is happy is brave.
If susan is not kind or not happy then paul is either not creative or not tall.
Everyone who is not wise or not rich is not humble or quiet.
If susan is not happy or not strong then alice is both not kind and calm.
If someone is both humble and not calm then mary is tall and vice versa.
If someone is both not rich and not kind then susan is both not creative and not happy and vice versa.
John is kind.
Alice is wise.
Someone is calm.
Mary is creative.
Alice is not kind.
Lucy is generous or humble.
John is not patient. | Lucy is humble. | neutral | (((~wise(paul)&generous(paul)))<=>((~creative(fred)<~>~tall(fred))))&
((?[X]:((humble(X)|~quiet(X))))<=>((funny(susan)|strong(susan))))&
(![X]:((tall(X)&rich(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((~generous(X)|brave(X))=>(calm(X)<~>old(X))))&
(((brave(mary)|~tall(mary)))=>(~funny(mary)))&
(((generous(mary)<~>creative(mary)))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((~humble(X)&~patient(X))))<=>((~kind(mary)&~strong(mary))))&
(![X]:((funny(X)&~rich(X))=>(~generous(X)&~kind(X))))&
(![X]:(calm(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~brave(X)&curious(X))<=>(tall(X)&~creative(X))))&
(![X]:(happy(X)=>brave(X)))&
(((~kind(susan)|~happy(susan)))=>((~creative(paul)<~>~tall(paul))))&
(![X]:((~wise(X)|~rich(X))=>(~humble(X)|quiet(X))))&
(((~happy(susan)|~strong(susan)))=>((~kind(alice)&calm(alice))))&
((?[X]:((humble(X)&~calm(X))))<=>(tall(mary)))&
((?[X]:((~rich(X)&~kind(X))))<=>((~creative(susan)&~happy(susan))))&
(kind(john))&
(wise(alice))&
(?[X]:(calm(X)))&
(creative(mary))&
(~kind(alice))&
((generous(lucy)|humble(lucy)))&
(~patient(john)) | humble(lucy) | [] | null | 0 |
Everyone who is both creative and not humble is either happy or not calm and vice versa.
Everyone who is both not wise and humble is either strong or rich and vice versa.
Everyone who is kind is curious.
If mary is brave then someone is not rich.
If someone is not calm or rich then someone is both not generous and not strong.
If someone is not curious then someone is not patient and vice versa.
Everyone who is either not creative or not calm is either not strong or not creative and vice versa.
Everyone who is both not patient and funny is not generous and vice versa.
Everyone who is not generous or curious is either curious or not quiet and vice versa.
Everyone who is curious or not old is both curious and not humble.
Everyone who is not old is kind.
If lucy is not tall then mary is both not old and not generous.
If john is either not old or brave then alice is curious or brave.
Everyone who is creative or not kind is either not patient or rich.
If paul is not curious then someone is either funny or not tall.
Everyone who is humble or not kind is either not old or not curious and vice versa.
Fred is both not curious and strong.
Someone is not calm.
Someone is both not kind and not happy.
Someone is either calm or happy.
Someone is not brave or not creative.
Someone is funny or not patient.
Paul is both calm and not patient.
Someone is either not old or old. | Paul is strong. | entailment | (![X]:((creative(X)&~humble(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~wise(X)&humble(X))<=>(strong(X)<~>rich(X))))&
(![X]:(kind(X)=>curious(X)))&
((brave(mary))=>(?[X]:(~rich(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~generous(X)&~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:(~patient(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(~strong(X)<~>~creative(X))))&
(![X]:((~patient(X)&funny(X))<=>~generous(X)))&
(![X]:((~generous(X)|curious(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((curious(X)|~old(X))=>(curious(X)&~humble(X))))&
(![X]:(~old(X)=>kind(X)))&
((~tall(lucy))=>((~old(mary)&~generous(mary))))&
(((~old(john)<~>brave(john)))=>((curious(alice)|brave(alice))))&
(![X]:((creative(X)|~kind(X))=>(~patient(X)<~>rich(X))))&
((~curious(paul))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((humble(X)|~kind(X))<=>(~old(X)<~>~curious(X))))&
((~curious(fred)&strong(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((~kind(X)&~happy(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~brave(X)|~creative(X))))&
(?[X]:((funny(X)|~patient(X))))&
((calm(paul)&~patient(paul)))&
(?[X]:((~old(X)<~>old(X)))) | strong(paul) | [
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3924536666331510700273468
% SZS output start Proof for 3924536666331510700273468
7. ! [X0] : ((~creative(X0) <~> ~calm(X0)) <=> (~strong(X0) <~> ~creative(X0))) [input p6]
23. ~patient(paul) & calm(paul) [input p22]
25. ~strong(paul) [input hypothesis]
52. ! [X0] : ((((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) & (((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0))))) [nnf transformation 7]
100. creative(X0) | strong(X0) | ~calm(X0) | creative(X0) [cnf transformation 52]
102. ~calm(X0) | ~creative(X0) | ~creative(X0) | strong(X0) [cnf transformation 52]
145. calm(paul) [cnf transformation 23]
149. ~strong(paul) [cnf transformation 25]
153. creative(X0) | strong(X0) | ~calm(X0) [duplicate literal removal 100]
154. ~calm(X0) | ~creative(X0) | strong(X0) [duplicate literal removal 102]
199. ~calm(X0) | strong(X0) [subsumption resolution 153,154]
284. strong(paul) [resolution 199,145]
286. $false [subsumption resolution 284,149]
% SZS output end Proof for 3924536666331510700273468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or rich is both not wise and not calm.
If susan is either rich or not curious then paul is both rich and kind and vice versa.
If someone is either creative or calm then john is both patient and not funny and vice versa.
Everyone who is not calm or not humble is not happy or generous and vice versa.
Everyone who is both generous and not brave is not patient or not quiet and vice versa.
Everyone who is not quiet is not curious or patient and vice versa.
Everyone who is both not generous and brave is either not funny or not calm.
If john is either not calm or strong then john is tall and vice versa.
Everyone who is both wise and not rich is either not creative or rich.
Everyone who is not wise is funny and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Fred is calm. | contradiction | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
(((rich(susan)<~>~curious(susan)))<=>((rich(paul)&kind(paul))))&
((?[X]:((creative(X)<~>calm(X))))<=>((patient(john)&~funny(john))))&
(![X]:((~calm(X)|~humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((generous(X)&~brave(X))<=>(~patient(X)|~quiet(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|patient(X))))&
(![X]:((~generous(X)&brave(X))=>(~funny(X)<~>~calm(X))))&
(((~calm(john)<~>strong(john)))<=>(tall(john)))&
(![X]:((wise(X)&~rich(X))=>(~creative(X)<~>rich(X))))&
(![X]:(~wise(X)<=>funny(X)))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | calm(fred) | [
"p0",
"p4",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4810725553142649574967934
% SZS output start Proof for 4810725553142649574967934
1. ! [X0] : ((rich(X0) | generous(X0)) => (~calm(X0) & ~wise(X0))) [input p0]
5. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p4]
14. ? [X0] : (~funny(X0) | ~brave(X0)) <=> ~tall(fred) [input p13]
21. ~rich(fred) <~> ~tall(fred) [input p20]
23. ~quiet(paul) & ~rich(paul) [input p22]
25. calm(fred) [input hypothesis]
28. ! [X0] : ((~calm(X0) & ~wise(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 1]
43. ! [X0] : (((~brave(X0) & generous(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~brave(X0) & generous(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | brave(X0) | ~generous(X0))) [flattening 43]
60. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X0] : (funny(X0) & brave(X0))) [nnf transformation 14]
61. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [rectify 60]
62. ? [X0] : (~funny(X0) | ~brave(X0)) => (~funny(sK4) | ~brave(sK4)) [choice axiom]
63. ((~funny(sK4) | ~brave(sK4)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [skolemisation 61,62]
71. (tall(fred) | rich(fred)) & (~tall(fred) | ~rich(fred)) [nnf transformation 21]
79. ~calm(X0) | ~rich(X0) [cnf transformation 28]
100. ~brave(X0) | quiet(X0) [cnf transformation 44]
121. ~tall(fred) | brave(X1) [cnf transformation 63]
145. tall(fred) | rich(fred) [cnf transformation 71]
149. ~quiet(paul) [cnf transformation 23]
151. calm(fred) [cnf transformation 25]
258. 22 <=> tall(fred) [avatar definition]
275. 26 <=> ! [X1] : brave(X1) [avatar definition]
276. brave(X1) <- (26) [avatar component clause 275]
277. 26 | ~22 [avatar split clause 121,258,275]
305. 31 <=> rich(fred) [avatar definition]
308. 31 | 22 [avatar split clause 145,258,305]
314. ~rich(fred) [resolution 79,151]
318. quiet(X0) <- (26) [resolution 100,276]
321. $false <- (26) [resolution 318,149]
325. ~26 [avatar contradiction clause 321]
326. ~31 [avatar split clause 314,305]
327. $false [avatar sat refutation 277,308,325,326]
% SZS output end Proof for 4810725553142649574967934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and strong then susan is tall or not curious.
If someone is not calm or generous then someone is not old.
If someone is not strong or brave then lucy is either old or tall and vice versa.
Everyone who is kind is either not patient or brave and vice versa.
Everyone who is not funny is both funny and generous.
If someone is either not patient or generous then alice is both tall and not calm and vice versa.
If susan is not generous or creative then lucy is both creative and not old and vice versa.
Everyone who is not tall or calm is both funny and not old and vice versa.
Everyone who is either not patient or brave is both strong and not patient.
Everyone who is both creative and not creative is both funny and not calm.
Everyone who is funny or strong is not generous or brave and vice versa.
If susan is either not happy or not kind then someone is either not humble or not wise.
If alice is rich then someone is both happy and not funny and vice versa.
If someone is generous or not old then fred is both not patient and not humble and vice versa.
If fred is calm then lucy is either not patient or humble and vice versa.
Everyone who is not humble or not rich is both creative and kind and vice versa.
Someone is either not happy or funny.
Someone is both patient and tall.
Someone is strong or patient.
Someone is patient.
Someone is curious.
Lucy is either humble or not quiet.
Someone is happy or not funny. | Alice is generous. | contradiction | ((?[X]:((old(X)&strong(X))))=>((tall(susan)|~curious(susan))))&
((?[X]:((~calm(X)|generous(X))))=>(?[X]:(~old(X))))&
((?[X]:((~strong(X)|brave(X))))<=>((old(lucy)<~>tall(lucy))))&
(![X]:(kind(X)<=>(~patient(X)<~>brave(X))))&
(![X]:(~funny(X)=>(funny(X)&generous(X))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((tall(alice)&~calm(alice))))&
(((~generous(susan)|creative(susan)))<=>((creative(lucy)&~old(lucy))))&
(![X]:((~tall(X)|calm(X))<=>(funny(X)&~old(X))))&
(![X]:((~patient(X)<~>brave(X))=>(strong(X)&~patient(X))))&
(![X]:((creative(X)&~creative(X))=>(funny(X)&~calm(X))))&
(![X]:((funny(X)|strong(X))<=>(~generous(X)|brave(X))))&
(((~happy(susan)<~>~kind(susan)))=>(?[X]:((~humble(X)<~>~wise(X)))))&
((rich(alice))<=>(?[X]:((happy(X)&~funny(X)))))&
((?[X]:((generous(X)|~old(X))))<=>((~patient(fred)&~humble(fred))))&
((calm(fred))<=>((~patient(lucy)<~>humble(lucy))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)&kind(X))))&
(?[X]:((~happy(X)<~>funny(X))))&
(?[X]:((patient(X)&tall(X))))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:(patient(X)))&
(?[X]:(curious(X)))&
((humble(lucy)<~>~quiet(lucy)))&
(?[X]:((happy(X)|~funny(X)))) | generous(alice) | [
"p3",
"p4",
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8334560180297995226711229
% SZS output start Proof for 8334560180297995226711229
4. ! [X0] : (kind(X0) <=> (~patient(X0) <~> brave(X0))) [input p3]
5. ! [X0] : (~funny(X0) => (generous(X0) & funny(X0))) [input p4]
9. ! [X0] : ((~patient(X0) <~> brave(X0)) => (~patient(X0) & strong(X0))) [input p8]
11. ! [X0] : ((strong(X0) | funny(X0)) <=> (brave(X0) | ~generous(X0))) [input p10]
13. rich(alice) <=> ? [X0] : (~funny(X0) & happy(X0)) [input p12]
16. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> (kind(X0) & creative(X0))) [input p15]
24. generous(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) & funny(X0)) | funny(X0)) [ennf transformation 5]
30. ! [X0] : ((~patient(X0) & strong(X0)) | (~patient(X0) <=> brave(X0))) [ennf transformation 9]
41. ! [X0] : ((kind(X0) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) & (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | ~kind(X0))) [nnf transformation 4]
51. ! [X0] : ((~patient(X0) & strong(X0)) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) [nnf transformation 30]
52. ! [X0] : (((strong(X0) | funny(X0)) | (~brave(X0) & generous(X0))) & ((brave(X0) | ~generous(X0)) | (~strong(X0) & ~funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((strong(X0) | funny(X0) | (~brave(X0) & generous(X0))) & (brave(X0) | ~generous(X0) | (~strong(X0) & ~funny(X0)))) [flattening 52]
57. (rich(alice) | ! [X0] : (funny(X0) | ~happy(X0))) & (? [X0] : (~funny(X0) & happy(X0)) | ~rich(alice)) [nnf transformation 13]
58. (rich(alice) | ! [X0] : (funny(X0) | ~happy(X0))) & (? [X1] : (~funny(X1) & happy(X1)) | ~rich(alice)) [rectify 57]
59. ? [X1] : (~funny(X1) & happy(X1)) => (~funny(sK4) & happy(sK4)) [choice axiom]
60. (rich(alice) | ! [X0] : (funny(X0) | ~happy(X0))) & ((~funny(sK4) & happy(sK4)) | ~rich(alice)) [skolemisation 58,59]
67. ! [X0] : (((~rich(X0) | ~humble(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [nnf transformation 16]
68. ! [X0] : ((~rich(X0) | ~humble(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [flattening 67]
93. ~kind(X0) | patient(X0) | ~brave(X0) [cnf transformation 41]
96. funny(X0) | funny(X0) [cnf transformation 29]
117. ~patient(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 51]
120. brave(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 53]
129. ~funny(sK4) | ~rich(alice) [cnf transformation 60]
143. rich(X0) | kind(X0) [cnf transformation 68]
155. generous(alice) [cnf transformation 24]
156. ~patient(X0) | ~brave(X0) [duplicate literal removal 117]
157. funny(X0) [duplicate literal removal 96]
256. ~generous(X0) | brave(X0) [subsumption resolution 120,157]
277. ~rich(alice) [subsumption resolution 129,157]
340. kind(alice) [resolution 143,277]
344. brave(alice) [resolution 256,155]
356. patient(alice) | ~brave(alice) [resolution 93,340]
359. patient(alice) [subsumption resolution 356,344]
502. ~brave(alice) [resolution 359,156]
505. $false [subsumption resolution 502,344]
% SZS output end Proof for 8334560180297995226711229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is quiet then someone is either humble or not patient and vice versa.
Everyone who is either wise or happy is both creative and not generous and vice versa.
Everyone who is generous is both not strong and not curious.
If someone is not calm or generous then alice is both wise and not humble.
Everyone who is not strong or not creative is not patient.
If someone is not old or generous then someone is not generous and vice versa.
Everyone who is not quiet or strong is both not rich and not tall.
Everyone who is rich is both rich and not generous and vice versa.
If someone is either not humble or creative then someone is calm and vice versa.
If lucy is not tall then someone is not brave.
If mary is either brave or curious then paul is both not kind and not quiet and vice versa.
Everyone who is both curious and generous is both strong and not old and vice versa.
Everyone who is either wise or creative is both not humble and tall and vice versa.
If someone is quiet then someone is either not rich or not strong.
Everyone who is not funny or brave is not curious.
Everyone who is tall or not happy is both calm and happy and vice versa.
Someone is both happy and not patient.
Someone is both not generous and curious.
Someone is either not rich or not wise.
Someone is not old.
Fred is either not creative or quiet.
Someone is not strong.
Someone is both tall and humble. | John is patient. | contradiction | ((quiet(john))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(creative(X)&~generous(X))))&
(![X]:(generous(X)=>(~strong(X)&~curious(X))))&
((?[X]:((~calm(X)|generous(X))))=>((wise(alice)&~humble(alice))))&
(![X]:((~strong(X)|~creative(X))=>~patient(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|strong(X))=>(~rich(X)&~tall(X))))&
(![X]:(rich(X)<=>(rich(X)&~generous(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>(?[X]:(calm(X))))&
((~tall(lucy))=>(?[X]:(~brave(X))))&
(((brave(mary)<~>curious(mary)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:((curious(X)&generous(X))<=>(strong(X)&~old(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~humble(X)&tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~funny(X)|brave(X))=>~curious(X)))&
(![X]:((tall(X)|~happy(X))<=>(calm(X)&happy(X))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(~old(X)))&
((~creative(fred)<~>quiet(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((tall(X)&humble(X)))) | patient(john) | [
"p1",
"p2",
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8284924939005934200274773
% SZS output start Proof for 8284924939005934200274773
2. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~generous(X0) & creative(X0))) [input p1]
3. ! [X0] : (generous(X0) => (~curious(X0) & ~strong(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~strong(X0)) => ~patient(X0)) [input p4]
7. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~tall(X0) & ~rich(X0))) [input p6]
13. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (tall(X0) & ~humble(X0))) [input p12]
16. ! [X0] : ((~happy(X0) | tall(X0)) <=> (happy(X0) & calm(X0))) [input p15]
24. patient(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~strong(X0)) | ~generous(X0)) [ennf transformation 3]
31. ! [X0] : (~patient(X0) | (creative(X0) & strong(X0))) [ennf transformation 5]
32. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 7]
40. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (generous(X0) | ~creative(X0))) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | generous(X0) | ~creative(X0)) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [flattening 40]
60. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [flattening 60]
66. ! [X0] : (((~happy(X0) | tall(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [nnf transformation 16]
67. ! [X0] : ((~happy(X0) | tall(X0) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [flattening 66]
91. ~creative(X0) | ~wise(X0) | generous(X0) | ~happy(X0) [cnf transformation 41]
92. ~strong(X0) | ~generous(X0) [cnf transformation 29]
98. ~patient(X0) | strong(X0) [cnf transformation 31]
99. ~patient(X0) | creative(X0) [cnf transformation 31]
106. ~tall(X0) | ~strong(X0) [cnf transformation 32]
128. ~creative(X0) | wise(X0) | tall(X0) [cnf transformation 61]
137. happy(X0) | happy(X0) [cnf transformation 67]
151. patient(john) [cnf transformation 24]
152. happy(X0) [duplicate literal removal 137]
307. strong(john) [resolution 98,151]
308. creative(john) [resolution 99,151]
309. ~generous(john) [resolution 307,92]
337. 35 <=> wise(john) [avatar definition]
345. wise(john) | tall(john) [resolution 128,308]
349. 36 <=> tall(john) [avatar definition]
351. tall(john) <- (36) [avatar component clause 349]
352. 36 | 35 [avatar split clause 345,337,349]
380. ~wise(john) | generous(john) | ~happy(john) [resolution 91,308]
389. ~wise(john) | ~happy(john) [subsumption resolution 380,309]
390. ~wise(john) [subsumption resolution 389,152]
391. ~35 [avatar split clause 390,337]
425. ~strong(john) <- (36) [resolution 351,106]
427. $false <- (36) [subsumption resolution 425,307]
428. ~36 [avatar contradiction clause 427]
429. $false [avatar sat refutation 352,391,428]
% SZS output end Proof for 8284924939005934200274773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not happy and not creative.
Everyone who is either happy or curious is both not happy and not strong and vice versa.
If alice is either not strong or patient then alice is not generous or not tall and vice versa.
Everyone who is generous is not rich or not generous and vice versa.
Everyone who is brave is not humble.
If someone is both brave and humble then someone is creative or not kind.
If susan is creative or tall then fred is quiet or not calm.
Everyone who is both strong and not brave is either happy or wise and vice versa.
If alice is either calm or wise then someone is not humble and vice versa.
Everyone who is either funny or not generous is not funny or tall.
If lucy is not wise then someone is not tall or tall and vice versa.
If fred is both not generous and old then alice is humble or not funny and vice versa.
If john is not old then someone is calm.
Everyone who is both not calm and not quiet is funny.
Everyone who is either not strong or tall is both strong and not wise and vice versa.
Susan is either kind or not calm.
Someone is not creative or tall.
Alice is either not wise or brave.
Fred is not quiet.
Someone is not tall. | Lucy is not rich. | entailment | (![X]:((strong(X)|wise(X))=>(~happy(X)&~creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>(~happy(X)&~strong(X))))&
(((~strong(alice)<~>patient(alice)))<=>((~generous(alice)|~tall(alice))))&
(![X]:(generous(X)<=>(~rich(X)|~generous(X))))&
(![X]:(brave(X)=>~humble(X)))&
((?[X]:((brave(X)&humble(X))))=>(?[X]:((creative(X)|~kind(X)))))&
(((creative(susan)|tall(susan)))=>((quiet(fred)|~calm(fred))))&
(![X]:((strong(X)&~brave(X))<=>(happy(X)<~>wise(X))))&
(((calm(alice)<~>wise(alice)))<=>(?[X]:(~humble(X))))&
(![X]:((funny(X)<~>~generous(X))=>(~funny(X)|tall(X))))&
((~wise(lucy))<=>(?[X]:((~tall(X)|tall(X)))))&
(((~generous(fred)&old(fred)))<=>((humble(alice)|~funny(alice))))&
((~old(john))=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&~quiet(X))=>funny(X)))&
(![X]:((~strong(X)<~>tall(X))<=>(strong(X)&~wise(X))))&
((kind(susan)<~>~calm(susan)))&
(?[X]:((~creative(X)|tall(X))))&
((~wise(alice)<~>brave(alice)))&
(~quiet(fred))&
(?[X]:(~tall(X))) | ~rich(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1712737091563825279728956
% SZS output start Proof for 1712737091563825279728956
4. ! [X0] : (generous(X0) <=> (~generous(X0) | ~rich(X0))) [input p3]
21. rich(lucy) [input hypothesis]
37. ! [X0] : ((generous(X0) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | ~generous(X0))) [nnf transformation 4]
38. ! [X0] : ((generous(X0) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~generous(X0))) [flattening 37]
81. ~generous(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 38]
83. generous(X0) | generous(X0) [cnf transformation 38]
123. rich(lucy) [cnf transformation 21]
127. ~generous(X0) | ~rich(X0) [duplicate literal removal 81]
128. generous(X0) [duplicate literal removal 83]
154. ~rich(X0) [subsumption resolution 127,128]
262. $false [subsumption resolution 123,154]
% SZS output end Proof for 1712737091563825279728956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and humble then lucy is either not patient or not wise and vice versa. Everyone who is not calm is either old or not humble and vice versa. If john is not quiet or not creative then someone is not old or not patient. Everyone who is not generous or not curious is brave or not old and vice versa. Everyone who is not happy is generous and vice versa. If someone is not strong or not brave then someone is both curious and not calm and vice versa. Everyone who is either not brave or kind is either wise or old and vice versa. If someone is calm then lucy is both quiet and creative. Everyone who is either not old or humble is both quiet and curious. Everyone who is curious is wise or not happy. Everyone who is quiet or not patient is both old and strong. Everyone who is rich is either tall or not curious and vice versa. Everyone who is not humble is kind. Everyone who is creative or rich is quiet and vice versa. Everyone who is both old and not brave is not wise or brave and vice versa. If someone is either funny or strong then john is either not rich or not kind and vice versa. Fred is either patient or not tall. Someone is funny or not generous. Someone is calm. John is either not old or not strong. Someone is either kind or happy. Someone is either not patient or quiet. Someone is both strong and not happy. | Fred is not humble. | contradiction | ((?[X]:((~happy(X)&humble(X))))<=>((~patient(lucy)<~>~wise(lucy))))&
(![X]:(~calm(X)<=>(old(X)<~>~humble(X))))&
(((~quiet(john)|~creative(john)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(brave(X)|~old(X))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>~strong(john)))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((strong(X)&~happy(X)))) | ~humble(fred) | [
"p6",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3065983149037908841663009
% SZS output start Proof for 3065983149037908841663009
7. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) <~> old(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> humble(X0)) => (curious(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((~patient(X0) | quiet(X0)) => (strong(X0) & old(X0))) [input p10]
13. ! [X0] : (~humble(X0) => kind(X0)) [input p12]
15. ! [X0] : ((~brave(X0) & old(X0)) <=> (brave(X0) | ~wise(X0))) [input p14]
24. ~humble(fred) [input hypothesis]
28. ! [X0] : ((curious(X0) & quiet(X0)) | (~old(X0) <=> humble(X0))) [ennf transformation 9]
31. ! [X0] : ((strong(X0) & old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 11]
32. ! [X0] : (kind(X0) | humble(X0)) [ennf transformation 13]
48. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 7]
49. ! [X0] : ((curious(X0) & quiet(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) [nnf transformation 28]
53. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 15]
54. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | brave(X0) | ~old(X0))) [flattening 53]
103. ~kind(X0) | brave(X0) | wise(X0) | ~old(X0) [cnf transformation 48]
106. quiet(X0) | humble(X0) | old(X0) [cnf transformation 49]
111. ~quiet(X0) | old(X0) [cnf transformation 31]
119. kind(X0) | humble(X0) [cnf transformation 32]
123. brave(X0) | ~wise(X0) | brave(X0) | ~old(X0) [cnf transformation 54]
124. old(X0) | wise(X0) [cnf transformation 54]
127. ~brave(X0) | ~brave(X0) [cnf transformation 54]
148. ~humble(fred) [cnf transformation 24]
149. brave(X0) | ~wise(X0) | ~old(X0) [duplicate literal removal 123]
150. ~brave(X0) [duplicate literal removal 127]
237. ~old(X0) | ~wise(X0) [subsumption resolution 149,150]
412. humble(X1) | old(X1) | old(X1) [resolution 106,111]
413. old(X1) | humble(X1) [duplicate literal removal 412]
533. brave(X1) | wise(X1) | ~old(X1) | humble(X1) [resolution 103,119]
541. wise(X1) | ~old(X1) | humble(X1) [subsumption resolution 533,150]
542. wise(X1) | humble(X1) [subsumption resolution 541,124]
663. humble(X7) | ~wise(X7) [resolution 413,237]
669. humble(X7) [subsumption resolution 663,542]
698. $false [resolution 669,148]
% SZS output end Proof for 3065983149037908841663009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either calm or quiet then lucy is both not happy and rich and vice versa.
If john is quiet or not tall then mary is either not wise or creative and vice versa.
Everyone who is both quiet and rich is generous or funny and vice versa.
If mary is both wise and rich then someone is both not quiet and brave and vice versa.
Everyone who is curious or funny is not rich.
If someone is either not old or wise then someone is both not humble and tall and vice versa.
If someone is both generous and not generous then paul is both creative and strong and vice versa.
Everyone who is rich is either not wise or not patient.
Everyone who is wise or curious is both curious and generous and vice versa.
Everyone who is not rich or generous is not generous or wise and vice versa.
If susan is either wise or not happy then someone is not humble.
If alice is patient or funny then lucy is patient or creative.
Everyone who is both not brave and not funny is curious or not curious and vice versa.
If someone is brave then john is both wise and not calm and vice versa.
If mary is humble then lucy is old or not calm.
If someone is either brave or not old then fred is either not calm or not strong.
Susan is both not quiet and calm.
Paul is not humble.
Lucy is creative or old.
Mary is both not strong and not calm.
Mary is not rich or not generous.
Someone is either not calm or generous. | Fred is not tall. | neutral | (((calm(paul)<~>quiet(paul)))<=>((~happy(lucy)&rich(lucy))))&
(((quiet(john)|~tall(john)))<=>((~wise(mary)<~>creative(mary))))&
(![X]:((quiet(X)&rich(X))<=>(generous(X)|funny(X))))&
(((wise(mary)&rich(mary)))<=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((curious(X)|funny(X))=>~rich(X)))&
((?[X]:((~old(X)<~>wise(X))))<=>(?[X]:((~humble(X)&tall(X)))))&
((?[X]:((generous(X)&~generous(X))))<=>((creative(paul)&strong(paul))))&
(![X]:(rich(X)=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|curious(X))<=>(curious(X)&generous(X))))&
(![X]:((~rich(X)|generous(X))<=>(~generous(X)|wise(X))))&
(((wise(susan)<~>~happy(susan)))=>(?[X]:(~humble(X))))&
(((patient(alice)|funny(alice)))=>((patient(lucy)|creative(lucy))))&
(![X]:((~brave(X)&~funny(X))<=>(curious(X)|~curious(X))))&
((?[X]:(brave(X)))<=>((wise(john)&~calm(john))))&
((humble(mary))=>((old(lucy)|~calm(lucy))))&
((?[X]:((brave(X)<~>~old(X))))=>((~calm(fred)<~>~strong(fred))))&
((~quiet(susan)&calm(susan)))&
(~humble(paul))&
((creative(lucy)|old(lucy)))&
((~strong(mary)&~calm(mary)))&
((~rich(mary)|~generous(mary)))&
(?[X]:((~calm(X)<~>generous(X)))) | ~tall(fred) | [] | null | 0 |
Everyone who is either generous or not rich is both quiet and not tall.
If someone is humble or not funny then paul is either rich or curious and vice versa.
Everyone who is both not quiet and not calm is both calm and not wise and vice versa.
If someone is generous then someone is both not brave and not quiet and vice versa.
If lucy is either strong or funny then lucy is not tall.
Everyone who is tall or wise is both not tall and not calm and vice versa.
Everyone who is either tall or old is either wise or not kind.
If john is either funny or wise then someone is not quiet or humble.
Everyone who is not generous or not strong is tall or not calm.
If paul is both not wise and brave then lucy is either not happy or happy.
Everyone who is not creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
If someone is either calm or not wise then someone is not tall.
Everyone who is both not calm and brave is kind and vice versa.
Susan is patient or not happy.
Someone is either not generous or not old.
Someone is not generous.
Susan is either humble or calm.
Someone is not patient or funny. | John is not strong. | contradiction | (![X]:((generous(X)<~>~rich(X))=>(quiet(X)&~tall(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((rich(paul)<~>curious(paul))))&
(![X]:((~quiet(X)&~calm(X))<=>(calm(X)&~wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(((strong(lucy)<~>funny(lucy)))=>(~tall(lucy)))&
(![X]:((tall(X)|wise(X))<=>(~tall(X)&~calm(X))))&
(![X]:((tall(X)<~>old(X))=>(wise(X)<~>~kind(X))))&
(((funny(john)<~>wise(john)))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~generous(X)|~strong(X))=>(tall(X)|~calm(X))))&
(((~wise(paul)&brave(paul)))=>((~happy(lucy)<~>happy(lucy))))&
(![X]:(~creative(X)=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)&brave(X))<=>kind(X)))&
((patient(susan)|~happy(susan)))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:(~generous(X)))&
((humble(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|funny(X)))) | ~strong(john) | [
"p2",
"p3",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1280339149352483139511041
% SZS output start Proof for 1280339149352483139511041
3. ! [X0] : ((~calm(X0) & ~quiet(X0)) <=> (~wise(X0) & calm(X0))) [input p2]
4. ? [X0] : generous(X0) <=> ? [X0] : (~quiet(X0) & ~brave(X0)) [input p3]
6. ! [X0] : ((wise(X0) | tall(X0)) <=> (~calm(X0) & ~tall(X0))) [input p5]
14. ! [X0] : ((~generous(X0) | kind(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p13]
22. ~strong(john) [input hypothesis]
23. ? [X0] : generous(X0) <=> ? [X1] : (~quiet(X1) & ~brave(X1)) [rectify 4]
41. ! [X0] : (((~calm(X0) & ~quiet(X0)) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | (calm(X0) | quiet(X0)))) [nnf transformation 3]
42. ! [X0] : (((~calm(X0) & ~quiet(X0)) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | calm(X0) | quiet(X0))) [flattening 41]
43. (? [X0] : generous(X0) | ! [X1] : (quiet(X1) | brave(X1))) & (? [X1] : (~quiet(X1) & ~brave(X1)) | ! [X0] : ~generous(X0)) [nnf transformation 23]
44. (? [X0] : generous(X0) | ! [X1] : (quiet(X1) | brave(X1))) & (? [X2] : (~quiet(X2) & ~brave(X2)) | ! [X3] : ~generous(X3)) [rectify 43]
45. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
46. ? [X2] : (~quiet(X2) & ~brave(X2)) => (~quiet(sK2) & ~brave(sK2)) [choice axiom]
47. (generous(sK1) | ! [X1] : (quiet(X1) | brave(X1))) & ((~quiet(sK2) & ~brave(sK2)) | ! [X3] : ~generous(X3)) [skolemisation 44,46,45]
49. ! [X0] : (((wise(X0) | tall(X0)) | (calm(X0) | tall(X0))) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [nnf transformation 6]
50. ! [X0] : ((wise(X0) | tall(X0) | calm(X0) | tall(X0)) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [flattening 49]
64. ! [X0] : (((~generous(X0) | kind(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (generous(X0) & ~kind(X0)))) [nnf transformation 14]
65. ! [X0] : ((~generous(X0) | kind(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (generous(X0) & ~kind(X0)))) [flattening 64]
90. calm(X0) | calm(X0) | quiet(X0) [cnf transformation 42]
93. ~calm(X0) | wise(X0) | ~calm(X0) [cnf transformation 42]
95. ~quiet(sK2) | ~generous(X3) [cnf transformation 47]
102. ~calm(X0) | ~wise(X0) [cnf transformation 50]
126. ~quiet(X0) | strong(X0) | generous(X0) [cnf transformation 65]
143. ~strong(john) [cnf transformation 22]
146. calm(X0) | quiet(X0) [duplicate literal removal 90]
147. ~calm(X0) | wise(X0) [duplicate literal removal 93]
185. 9 <=> ! [X3] : ~generous(X3) [avatar definition]
186. ~generous(X3) <- (9) [avatar component clause 185]
188. 10 <=> quiet(sK2) [avatar definition]
190. ~quiet(sK2) <- (~10) [avatar component clause 188]
191. 9 | ~10 [avatar split clause 95,188,185]
212. ~calm(X0) [subsumption resolution 102,147]
238. 19 <=> ! [X1] : quiet(X1) [avatar definition]
239. quiet(X1) <- (19) [avatar component clause 238]
284. quiet(X0) [resolution 146,212]
285. 19 [avatar split clause 284,238]
286. $false <- (~10, 19) [resolution 239,190]
291. 10 | ~19 [avatar contradiction clause 286]
314. strong(X1) | generous(X1) <- (19) [resolution 126,239]
316. strong(X1) <- (9, 19) [subsumption resolution 314,186]
317. $false <- (9, 19) [resolution 316,143]
318. ~9 | ~19 [avatar contradiction clause 317]
319. $false [avatar sat refutation 191,285,291,318]
% SZS output end Proof for 1280339149352483139511041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not happy is both rich and humble.
Everyone who is strong or not kind is not curious or not tall and vice versa.
If someone is both not funny and curious then mary is curious or not curious.
If someone is quiet then someone is calm or humble.
Everyone who is either creative or generous is both creative and not curious and vice versa.
If someone is both humble and not wise then someone is quiet.
Everyone who is quiet is both not calm and not generous and vice versa.
If someone is both old and brave then someone is not old or not tall and vice versa.
Everyone who is not old or not wise is both not tall and not kind and vice versa.
If paul is not rich then someone is both quiet and happy and vice versa.
Everyone who is not happy or not old is either not strong or funny and vice versa.
Everyone who is happy is either brave or not happy and vice versa.
If john is not happy then susan is both old and not rich.
If john is either quiet or happy then susan is wise or not happy.
Someone is not quiet.
Someone is not quiet or not calm.
Someone is not calm or not old.
Someone is humble.
Paul is either calm or kind.
John is either wise or not strong. | Paul is not generous. | neutral | (![X]:((~rich(X)<~>~happy(X))=>(rich(X)&humble(X))))&
(![X]:((strong(X)|~kind(X))<=>(~curious(X)|~tall(X))))&
((?[X]:((~funny(X)&curious(X))))=>((curious(mary)|~curious(mary))))&
((?[X]:(quiet(X)))=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(creative(X)&~curious(X))))&
((?[X]:((humble(X)&~wise(X))))=>(?[X]:(quiet(X))))&
(![X]:(quiet(X)<=>(~calm(X)&~generous(X))))&
((?[X]:((old(X)&brave(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~old(X)|~wise(X))<=>(~tall(X)&~kind(X))))&
((~rich(paul))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((~happy(X)|~old(X))<=>(~strong(X)<~>funny(X))))&
(![X]:(happy(X)<=>(brave(X)<~>~happy(X))))&
((~happy(john))=>((old(susan)&~rich(susan))))&
(((quiet(john)<~>happy(john)))=>((wise(susan)|~happy(susan))))&
(?[X]:(~quiet(X)))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:(humble(X)))&
((calm(paul)<~>kind(paul)))&
((wise(john)<~>~strong(john))) | ~generous(paul) | [] | null | 0 |
If someone is both not humble and rich then someone is either rich or not curious and vice versa.
Everyone who is brave is either not old or wise.
If john is either not kind or brave then someone is both creative and not funny and vice versa.
Everyone who is both old and wise is either not old or brave.
If someone is patient then someone is either not patient or quiet and vice versa.
Everyone who is not kind is calm.
If john is both brave and not quiet then lucy is not curious.
Everyone who is not old or humble is not generous and vice versa.
Everyone who is both not strong and kind is calm.
If someone is not humble then john is kind or not rich and vice versa.
If someone is happy or not humble then someone is both not humble and not quiet.
Everyone who is either happy or not rich is not brave or not patient and vice versa.
If lucy is old or not happy then someone is happy and vice versa.
Everyone who is both not brave and not generous is not brave or curious.
If someone is wise then susan is happy and vice versa.
Everyone who is either kind or not generous is not quiet and vice versa.
Susan is calm.
Someone is not creative or happy.
Someone is kind or wise.
Someone is both tall and curious.
Someone is either wise or happy.
Someone is either not brave or not tall.
Lucy is not creative.
Susan is either happy or strong. | Susan is wise. | neutral | ((?[X]:((~humble(X)&rich(X))))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(brave(X)=>(~old(X)<~>wise(X))))&
(((~kind(john)<~>brave(john)))<=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((old(X)&wise(X))=>(~old(X)<~>brave(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~patient(X)<~>quiet(X)))))&
(![X]:(~kind(X)=>calm(X)))&
(((brave(john)&~quiet(john)))=>(~curious(lucy)))&
(![X]:((~old(X)|humble(X))<=>~generous(X)))&
(![X]:((~strong(X)&kind(X))=>calm(X)))&
((?[X]:(~humble(X)))<=>((kind(john)|~rich(john))))&
((?[X]:((happy(X)|~humble(X))))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:((happy(X)<~>~rich(X))<=>(~brave(X)|~patient(X))))&
(((old(lucy)|~happy(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~brave(X)&~generous(X))=>(~brave(X)|curious(X))))&
((?[X]:(wise(X)))<=>(happy(susan)))&
(![X]:((kind(X)<~>~generous(X))<=>~quiet(X)))&
(calm(susan))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((tall(X)&curious(X))))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~tall(X))))&
(~creative(lucy))&
((happy(susan)<~>strong(susan))) | wise(susan) | [] | null | 0 |
Everyone who is not rich or not brave is not patient and vice versa. Everyone who is either not patient or kind is either patient or not kind. If someone is either rich or happy then someone is either brave or not patient and vice versa. If someone is not happy then someone is both generous and not brave and vice versa. If someone is either brave or curious then someone is not tall. If mary is not brave or wise then paul is both kind and not wise. If lucy is funny or humble then someone is either strong or not brave and vice versa. Everyone who is both generous and not calm is both quiet and old. Everyone who is calm is both not calm and not funny. Everyone who is either brave or not funny is either not creative or not wise. Everyone who is curious or patient is both calm and not wise and vice versa. Everyone who is either not calm or not generous is not happy or not old. If lucy is funny or not tall then mary is old and vice versa. Everyone who is either rich or not patient is patient. If someone is both humble and rich then paul is both kind and not brave and vice versa. Everyone who is humble is not creative. John is patient or humble. Alice is both not creative and not old. Lucy is not creative. Fred is both kind and not funny. | Paul is humble. | neutral | (![X]:((~rich(X)|~brave(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>kind(X))=>(patient(X)<~>~kind(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
((patient(john)|humble(john)))&
((~creative(alice)&~old(alice)))&
(~creative(lucy))&
((kind(fred)&~funny(fred))) | humble(paul) | [] | null | 0 |
If fred is both not funny and not patient then someone is either tall or humble and vice versa.
Everyone who is not strong or not happy is either not generous or kind.
Everyone who is not tall or kind is either not rich or quiet.
Everyone who is both not curious and creative is either not happy or humble and vice versa.
Everyone who is either tall or patient is both humble and wise.
If someone is both happy and tall then alice is either creative or not funny and vice versa.
Everyone who is either not rich or patient is rich or wise.
If someone is either humble or generous then someone is kind.
Everyone who is not tall or humble is patient and vice versa.
If someone is generous or not tall then alice is either not creative or calm and vice versa.
If someone is both not kind and not calm then someone is either happy or brave and vice versa.
Everyone who is either tall or not old is kind.
Everyone who is not generous is not calm and vice versa.
If lucy is patient or rich then someone is old or not rich and vice versa.
Everyone who is not quiet or not patient is both creative and not happy.
If paul is both strong and not tall then someone is not creative or not generous and vice versa.
Susan is either quiet or not tall.
Lucy is not brave.
Someone is funny.
Fred is not humble or not funny.
Someone is not strong or not funny.
Mary is both generous and quiet.
Someone is not curious.
Someone is not strong or not wise. | Susan is not creative. | contradiction | (((~funny(fred)&~patient(fred)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:((~strong(X)|~happy(X))=>(~generous(X)<~>kind(X))))&
(![X]:((~tall(X)|kind(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((~curious(X)&creative(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((tall(X)<~>patient(X))=>(humble(X)&wise(X))))&
((?[X]:((happy(X)&tall(X))))<=>((creative(alice)<~>~funny(alice))))&
(![X]:((~rich(X)<~>patient(X))=>(rich(X)|wise(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:((generous(X)|~tall(X))))<=>((~creative(alice)<~>calm(alice))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>kind(X)))&
(![X]:(~generous(X)<=>~calm(X)))&
(((patient(lucy)|rich(lucy)))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(creative(X)&~happy(X))))&
(((strong(paul)&~tall(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
((quiet(susan)<~>~tall(susan)))&
(~brave(lucy))&
(?[X]:(funny(X)))&
((~humble(fred)|~funny(fred)))&
(?[X]:((~strong(X)|~funny(X))))&
((generous(mary)&quiet(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)|~wise(X)))) | ~creative(susan) | [
"p0",
"p4",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7673856168957871849248924
% SZS output start Proof for 7673856168957871849248924
1. (~patient(fred) & ~funny(fred)) <=> ? [X0] : (tall(X0) <~> humble(X0)) [input p0]
5. ! [X0] : ((tall(X0) <~> patient(X0)) => (wise(X0) & humble(X0))) [input p4]
9. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p8]
16. (~tall(paul) & strong(paul)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p15]
25. ~creative(susan) [input hypothesis]
30. ! [X0] : ((wise(X0) & humble(X0)) | (tall(X0) <=> patient(X0))) [ennf transformation 5]
36. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (patient(fred) | funny(fred))) [nnf transformation 1]
37. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | patient(fred) | funny(fred)) [flattening 36]
38. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X1] : ((~humble(X1) | ~tall(X1)) & (humble(X1) | tall(X1))) | patient(fred) | funny(fred)) [rectify 37]
39. ? [X1] : ((~humble(X1) | ~tall(X1)) & (humble(X1) | tall(X1))) => ((~humble(sK0) | ~tall(sK0)) & (humble(sK0) | tall(sK0))) [choice axiom]
40. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(sK0) | ~tall(sK0)) & (humble(sK0) | tall(sK0))) | patient(fred) | funny(fred)) [skolemisation 38,39]
45. ! [X0] : ((wise(X0) & humble(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) [nnf transformation 30]
55. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 9]
56. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 55]
73. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | (tall(paul) | ~strong(paul))) [nnf transformation 16]
74. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | tall(paul) | ~strong(paul)) [flattening 73]
75. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | tall(paul) | ~strong(paul)) [rectify 74]
76. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK7) | ~creative(sK7)) [choice axiom]
77. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK7) | ~creative(sK7)) | tall(paul) | ~strong(paul)) [skolemisation 75,76]
92. ~patient(fred) | tall(X0) | ~humble(X0) [cnf transformation 40]
107. ~tall(X0) | patient(X0) | humble(X0) [cnf transformation 45]
108. ~patient(X0) | tall(X0) | humble(X0) [cnf transformation 45]
121. tall(X0) | patient(X0) [cnf transformation 56]
122. ~humble(X0) | patient(X0) [cnf transformation 56]
123. humble(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 56]
151. ~tall(paul) | creative(X0) [cnf transformation 77]
163. ~creative(susan) [cnf transformation 25]
166. 1 <=> ! [X0] : (tall(X0) | ~humble(X0)) [avatar definition]
167. tall(X0) | ~humble(X0) <- (1) [avatar component clause 166]
169. 2 <=> patient(fred) [avatar definition]
171. ~patient(fred) <- (~2) [avatar component clause 169]
172. 1 | ~2 [avatar split clause 92,169,166]
230. ~patient(X0) | humble(X0) [subsumption resolution 123,108]
246. 18 <=> ! [X1] : tall(X1) [avatar definition]
247. tall(X1) <- (18) [avatar component clause 246]
316. 34 <=> tall(paul) [avatar definition]
318. ~tall(paul) <- (~34) [avatar component clause 316]
321. 35 <=> ! [X0] : creative(X0) [avatar definition]
322. creative(X0) <- (35) [avatar component clause 321]
323. 35 | ~34 [avatar split clause 151,316,321]
374. $false <- (35) [resolution 322,163]
375. ~35 [avatar contradiction clause 374]
493. $false <- (18, ~34) [resolution 247,318]
494. ~18 | 34 [avatar contradiction clause 493]
542. patient(X0) | humble(X0) | patient(X0) [resolution 107,121]
547. patient(X0) | humble(X0) [duplicate literal removal 542]
548. humble(X0) [subsumption resolution 547,230]
551. patient(X1) [resolution 548,122]
707. $false <- (~2) [resolution 551,171]
711. 2 [avatar contradiction clause 707]
712. tall(X0) <- (1) [subsumption resolution 167,548]
713. 18 | ~1 [avatar split clause 712,166,246]
714. $false [avatar sat refutation 172,323,375,494,711,713]
% SZS output end Proof for 7673856168957871849248924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not calm or patient then paul is both happy and generous and vice versa.
Everyone who is both funny and not generous is either curious or quiet.
If john is not kind or not creative then susan is not creative and vice versa.
If someone is patient or not patient then susan is either happy or not humble and vice versa.
If someone is curious or not wise then someone is both not humble and not curious.
If someone is kind then john is both brave and calm and vice versa.
Everyone who is either strong or not humble is not patient or not brave and vice versa.
Everyone who is not curious or curious is either not quiet or patient and vice versa.
If someone is strong or generous then susan is happy or wise and vice versa.
Everyone who is either not calm or not brave is either patient or happy and vice versa.
If someone is either not humble or not creative then john is not happy or not quiet.
If someone is either not funny or not generous then john is not generous.
If susan is both not humble and not curious then susan is both patient and not brave and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is not quiet or funny is either humble or creative and vice versa.
Everyone who is both not tall and not strong is either not curious or not strong.
Susan is kind or not generous.
Someone is rich or not funny.
Susan is old or not patient.
Lucy is both generous and not patient.
Someone is either rich or not generous.
Alice is both curious and not rich.
Someone is both wise and kind.
Someone is both wise and humble. | John is not quiet. | entailment | (((~calm(mary)|patient(mary)))<=>((happy(paul)&generous(paul))))&
(![X]:((funny(X)&~generous(X))=>(curious(X)<~>quiet(X))))&
(((~kind(john)|~creative(john)))<=>(~creative(susan)))&
((?[X]:((patient(X)|~patient(X))))<=>((happy(susan)<~>~humble(susan))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((~humble(X)&~curious(X)))))&
((?[X]:(kind(X)))<=>((brave(john)&calm(john))))&
(![X]:((strong(X)<~>~humble(X))<=>(~patient(X)|~brave(X))))&
(![X]:((~curious(X)|curious(X))<=>(~quiet(X)<~>patient(X))))&
((?[X]:((strong(X)|generous(X))))<=>((happy(susan)|wise(susan))))&
(![X]:((~calm(X)<~>~brave(X))<=>(patient(X)<~>happy(X))))&
((?[X]:((~humble(X)<~>~creative(X))))=>((~happy(john)|~quiet(john))))&
((?[X]:((~funny(X)<~>~generous(X))))=>(~generous(john)))&
(((~humble(susan)&~curious(susan)))<=>((patient(susan)&~brave(susan))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((~quiet(X)|funny(X))<=>(humble(X)<~>creative(X))))&
(![X]:((~tall(X)&~strong(X))=>(~curious(X)<~>~strong(X))))&
((kind(susan)|~generous(susan)))&
(?[X]:((rich(X)|~funny(X))))&
((old(susan)|~patient(susan)))&
((generous(lucy)&~patient(lucy)))&
(?[X]:((rich(X)<~>~generous(X))))&
((curious(alice)&~rich(alice)))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:((wise(X)&humble(X)))) | ~quiet(john) | [
"p5",
"p7",
"p9",
"p10",
"p14",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4810755767336423149572283
% SZS output start Proof for 4810755767336423149572283
6. ? [X0] : kind(X0) <=> (calm(john) & brave(john)) [input p5]
8. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~quiet(X0) <~> patient(X0))) [input p7]
10. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> (patient(X0) <~> happy(X0))) [input p9]
11. ? [X0] : (~humble(X0) <~> ~creative(X0)) => (~quiet(john) | ~happy(john)) [input p10]
15. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (humble(X0) <~> creative(X0))) [input p14]
20. ~patient(lucy) & generous(lucy) [input p19]
23. ? [X0] : (kind(X0) & wise(X0)) [input p22]
25. quiet(john) [input hypothesis]
32. (~quiet(john) | ~happy(john)) | ! [X0] : (~humble(X0) <=> ~creative(X0)) [ennf transformation 11]
33. ~quiet(john) | ~happy(john) | ! [X0] : (~humble(X0) <=> ~creative(X0)) [flattening 32]
48. (? [X0] : kind(X0) | (~calm(john) | ~brave(john))) & ((calm(john) & brave(john)) | ! [X0] : ~kind(X0)) [nnf transformation 6]
49. (? [X0] : kind(X0) | ~calm(john) | ~brave(john)) & ((calm(john) & brave(john)) | ! [X0] : ~kind(X0)) [flattening 48]
50. (? [X0] : kind(X0) | ~calm(john) | ~brave(john)) & ((calm(john) & brave(john)) | ! [X1] : ~kind(X1)) [rectify 49]
51. ? [X0] : kind(X0) => kind(sK2) [choice axiom]
52. (kind(sK2) | ~calm(john) | ~brave(john)) & ((calm(john) & brave(john)) | ! [X1] : ~kind(X1)) [skolemisation 50,51]
55. ! [X0] : (((curious(X0) | ~curious(X0)) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) & (((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | (~curious(X0) & curious(X0)))) [nnf transformation 8]
56. ! [X0] : ((curious(X0) | ~curious(X0) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) & (((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | (~curious(X0) & curious(X0)))) [flattening 55]
62. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) & (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 10]
63. ~quiet(john) | ~happy(john) | ! [X0] : ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))) [nnf transformation 33]
67. ! [X0] : (((funny(X0) | ~quiet(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~funny(X0) & quiet(X0)))) [nnf transformation 15]
68. ! [X0] : ((funny(X0) | ~quiet(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~funny(X0) & quiet(X0)))) [flattening 67]
74. ? [X0] : (kind(X0) & wise(X0)) => (kind(sK6) & wise(sK6)) [choice axiom]
75. kind(sK6) & wise(sK6) [skolemisation 23,74]
98. brave(john) | ~kind(X1) [cnf transformation 52]
99. calm(john) | ~kind(X1) [cnf transformation 52]
107. patient(X0) | ~quiet(X0) | curious(X0) [cnf transformation 56]
108. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 56]
121. ~brave(X0) | ~calm(X0) | happy(X0) | ~patient(X0) [cnf transformation 62]
125. ~quiet(john) | ~happy(john) | ~creative(X0) | humble(X0) [cnf transformation 63]
126. ~quiet(john) | ~happy(john) | ~humble(X0) | creative(X0) [cnf transformation 63]
134. humble(X0) | creative(X0) | quiet(X0) [cnf transformation 68]
136. ~humble(X0) | ~creative(X0) | quiet(X0) [cnf transformation 68]
144. ~patient(lucy) [cnf transformation 20]
150. kind(sK6) [cnf transformation 75]
153. quiet(john) [cnf transformation 25]
191. 8 <=> ! [X1] : patient(X1) [avatar definition]
192. patient(X1) <- (8) [avatar component clause 191]
227. 16 <=> brave(john) [avatar definition]
228. brave(john) <- (16) [avatar component clause 227]
231. 17 <=> calm(john) [avatar definition]
232. calm(john) <- (17) [avatar component clause 231]
240. 19 <=> ! [X1] : ~kind(X1) [avatar definition]
241. ~kind(X1) <- (19) [avatar component clause 240]
242. 19 | 17 [avatar split clause 99,231,240]
243. 19 | 16 [avatar split clause 98,227,240]
245. ~quiet(X0) | patient(X0) [subsumption resolution 107,108]
269. 25 <=> ! [X0] : (~humble(X0) | creative(X0)) [avatar definition]
270. ~humble(X0) | creative(X0) <- (25) [avatar component clause 269]
272. 26 <=> happy(john) [avatar definition]
276. 27 <=> quiet(john) [avatar definition]
277. quiet(john) <- (27) [avatar component clause 276]
279. 25 | ~26 | ~27 [avatar split clause 126,276,272,269]
281. 28 <=> ! [X0] : (~creative(X0) | humble(X0)) [avatar definition]
282. ~creative(X0) | humble(X0) <- (28) [avatar component clause 281]
283. 28 | ~26 | ~27 [avatar split clause 125,276,272,281]
345. 27 [avatar split clause 153,276]
348. $false <- (19) [resolution 241,150]
349. ~19 [avatar contradiction clause 348]
350. patient(john) <- (27) [resolution 245,277]
516. ~calm(john) | happy(john) | ~patient(john) <- (16) [resolution 121,228]
519. happy(john) | ~patient(john) <- (16, 17) [subsumption resolution 516,232]
526. happy(john) <- (16, 17, 27) [subsumption resolution 519,350]
527. 26 | ~16 | ~17 | ~27 [avatar split clause 526,276,231,227,272]
530. creative(X1) | creative(X1) | quiet(X1) <- (25) [resolution 270,134]
534. creative(X1) | quiet(X1) <- (25) [duplicate literal removal 530]
600. humble(X1) | quiet(X1) <- (25, 28) [resolution 534,282]
632. quiet(X3) | ~creative(X3) | quiet(X3) <- (25, 28) [resolution 600,136]
636. quiet(X3) | ~creative(X3) <- (25, 28) [duplicate literal removal 632]
638. quiet(X3) <- (25, 28) [subsumption resolution 636,534]
655. patient(X2) <- (25, 28) [resolution 638,245]
656. 8 | ~25 | ~28 [avatar split clause 655,281,269,191]
660. $false <- (8) [resolution 192,144]
661. ~8 [avatar contradiction clause 660]
663. $false [avatar sat refutation 242,243,279,283,345,349,527,656,661]
% SZS output end Proof for 4810755767336423149572283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either generous or not calm then john is both not creative and patient and vice versa.
Everyone who is both happy and not strong is calm and vice versa.
If someone is not rich or not patient then susan is old and vice versa.
Everyone who is both generous and not creative is both old and rich.
Everyone who is either not creative or not quiet is funny.
Everyone who is happy is not wise or not brave.
If susan is either wise or not happy then mary is wise.
If someone is not creative or not quiet then someone is creative or calm and vice versa.
If alice is not funny or not brave then someone is not generous and vice versa.
Everyone who is not tall or tall is not curious and vice versa.
If lucy is both not creative and not calm then someone is both funny and not happy and vice versa.
Everyone who is both not calm and creative is not wise and vice versa.
Everyone who is both not happy and calm is either not humble or not kind.
If someone is either funny or not humble then someone is not old and vice versa.
Everyone who is either not patient or patient is not creative and vice versa.
Everyone who is either not patient or creative is not kind or not curious and vice versa.
John is either not calm or curious.
Fred is not old.
Paul is both not creative and not curious.
Someone is either strong or wise.
Someone is either not humble or not creative.
Paul is either not humble or not funny.
Someone is either not quiet or not rich. | Fred is rich. | neutral | (((generous(mary)<~>~calm(mary)))<=>((~creative(john)&patient(john))))&
(![X]:((happy(X)&~strong(X))<=>calm(X)))&
((?[X]:((~rich(X)|~patient(X))))<=>(old(susan)))&
(![X]:((generous(X)&~creative(X))=>(old(X)&rich(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>funny(X)))&
(![X]:(happy(X)=>(~wise(X)|~brave(X))))&
(((wise(susan)<~>~happy(susan)))=>(wise(mary)))&
((?[X]:((~creative(X)|~quiet(X))))<=>(?[X]:((creative(X)|calm(X)))))&
(((~funny(alice)|~brave(alice)))<=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)|tall(X))<=>~curious(X)))&
(((~creative(lucy)&~calm(lucy)))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((~calm(X)&creative(X))<=>~wise(X)))&
(![X]:((~happy(X)&calm(X))=>(~humble(X)<~>~kind(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:(~old(X))))&
(![X]:((~patient(X)<~>patient(X))<=>~creative(X)))&
(![X]:((~patient(X)<~>creative(X))<=>(~kind(X)|~curious(X))))&
((~calm(john)<~>curious(john)))&
(~old(fred))&
((~creative(paul)&~curious(paul)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~humble(X)<~>~creative(X))))&
((~humble(paul)<~>~funny(paul)))&
(?[X]:((~quiet(X)<~>~rich(X)))) | rich(fred) | [] | null | 0 |
If susan is either not humble or old then mary is both not humble and not generous and vice versa.
Everyone who is kind or not patient is both old and creative.
Everyone who is both not creative and not calm is creative.
Everyone who is not generous or not kind is not calm or wise and vice versa.
Everyone who is both not patient and happy is both not quiet and not brave.
Everyone who is not strong is both old and kind.
If someone is either funny or curious then someone is either not brave or old.
If fred is not brave then someone is either quiet or old and vice versa.
Everyone who is both not happy and not tall is not happy and vice versa.
Everyone who is both not quiet and kind is either brave or not calm and vice versa.
If someone is not strong then someone is both rich and kind and vice versa.
If someone is either creative or not patient then lucy is not brave.
Everyone who is not quiet or calm is both kind and old.
If someone is not calm or brave then someone is not tall or not creative.
If someone is calm then lucy is both old and tall and vice versa.
If someone is either not creative or not quiet then alice is either tall or not generous and vice versa.
Someone is not rich.
Alice is both not tall and creative.
Paul is wise or kind.
Someone is both curious and wise.
Someone is rich or patient.
Mary is both kind and tall.
Someone is either calm or funny. | Paul is kind. | neutral | (((~humble(susan)<~>old(susan)))<=>((~humble(mary)&~generous(mary))))&
(![X]:((kind(X)|~patient(X))=>(old(X)&creative(X))))&
(![X]:((~creative(X)&~calm(X))=>creative(X)))&
(![X]:((~generous(X)|~kind(X))<=>(~calm(X)|wise(X))))&
(![X]:((~patient(X)&happy(X))=>(~quiet(X)&~brave(X))))&
(![X]:(~strong(X)=>(old(X)&kind(X))))&
((?[X]:((funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>old(X)))))&
((~brave(fred))<=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:((~happy(X)&~tall(X))<=>~happy(X)))&
(![X]:((~quiet(X)&kind(X))<=>(brave(X)<~>~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:((creative(X)<~>~patient(X))))=>(~brave(lucy)))&
(![X]:((~quiet(X)|calm(X))=>(kind(X)&old(X))))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:((~tall(X)|~creative(X)))))&
((?[X]:(calm(X)))<=>((old(lucy)&tall(lucy))))&
((?[X]:((~creative(X)<~>~quiet(X))))<=>((tall(alice)<~>~generous(alice))))&
(?[X]:(~rich(X)))&
((~tall(alice)&creative(alice)))&
((wise(paul)|kind(paul)))&
(?[X]:((curious(X)&wise(X))))&
(?[X]:((rich(X)|patient(X))))&
((kind(mary)&tall(mary)))&
(?[X]:((calm(X)<~>funny(X)))) | kind(paul) | [] | null | 0 |
If someone is both not rich and not patient then alice is not brave and vice versa.
If someone is either strong or not old then someone is not funny or not strong and vice versa.
Everyone who is not old is not wise and vice versa.
Everyone who is both calm and not funny is both not brave and calm.
Everyone who is brave is either rich or curious.
Everyone who is generous is not curious or wise and vice versa.
If someone is not quiet then someone is rich or generous and vice versa.
Everyone who is not kind or not old is not creative or not happy and vice versa.
Everyone who is either strong or not generous is either not rich or not humble and vice versa.
If someone is both creative and quiet then someone is either wise or strong and vice versa.
Everyone who is not generous or not quiet is not creative.
If someone is old then someone is both not funny and old.
Everyone who is both curious and brave is old or generous.
Everyone who is both not happy and not creative is both not rich and creative and vice versa.
Everyone who is both not brave and not patient is either not patient or wise and vice versa.
Everyone who is not tall is not kind or not quiet and vice versa.
Alice is not strong.
Lucy is either not old or not funny.
Someone is either not brave or not generous.
Alice is both not funny and not strong.
Someone is either not wise or not patient.
Susan is either tall or rich.
Mary is not creative.
Someone is either creative or not rich. | Lucy is not funny. | neutral | ((?[X]:((~rich(X)&~patient(X))))<=>(~brave(alice)))&
((?[X]:((strong(X)<~>~old(X))))<=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:(~old(X)<=>~wise(X)))&
(![X]:((calm(X)&~funny(X))=>(~brave(X)&calm(X))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(![X]:(generous(X)<=>(~curious(X)|wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((~kind(X)|~old(X))<=>(~creative(X)|~happy(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~rich(X)<~>~humble(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~generous(X)|~quiet(X))=>~creative(X)))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)&old(X)))))&
(![X]:((curious(X)&brave(X))=>(old(X)|generous(X))))&
(![X]:((~happy(X)&~creative(X))<=>(~rich(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(~tall(X)<=>(~kind(X)|~quiet(X))))&
(~strong(alice))&
((~old(lucy)<~>~funny(lucy)))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~funny(alice)&~strong(alice)))&
(?[X]:((~wise(X)<~>~patient(X))))&
((tall(susan)<~>rich(susan)))&
(~creative(mary))&
(?[X]:((creative(X)<~>~rich(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is not creative is both happy and tall and vice versa.
Everyone who is both creative and patient is not creative or not calm and vice versa.
Everyone who is patient or not brave is both not curious and not quiet and vice versa.
If someone is curious or calm then someone is not funny or not tall and vice versa.
Everyone who is not tall or not wise is both not wise and wise.
If someone is both wise and creative then lucy is strong and vice versa.
Everyone who is both quiet and not funny is either not wise or tall.
Everyone who is either strong or tall is either strong or not kind.
Everyone who is both not funny and happy is either curious or creative and vice versa.
If someone is either not happy or not kind then fred is not funny or not curious.
Everyone who is not rich or not curious is either creative or not rich.
If mary is not kind then susan is not humble or not brave and vice versa.
If someone is creative then susan is wise or brave and vice versa.
If alice is either happy or not quiet then someone is both not happy and not humble and vice versa.
Everyone who is either not brave or old is both not generous and quiet.
Alice is both not strong and old.
Someone is quiet.
Someone is not brave or old.
Someone is funny. | Alice is not calm. | contradiction | (![X]:(~creative(X)<=>(happy(X)&tall(X))))&
(![X]:((creative(X)&patient(X))<=>(~creative(X)|~calm(X))))&
(![X]:((patient(X)|~brave(X))<=>(~curious(X)&~quiet(X))))&
((?[X]:((curious(X)|calm(X))))<=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((~tall(X)|~wise(X))=>(~wise(X)&wise(X))))&
((?[X]:((wise(X)&creative(X))))<=>(strong(lucy)))&
(![X]:((quiet(X)&~funny(X))=>(~wise(X)<~>tall(X))))&
(![X]:((strong(X)<~>tall(X))=>(strong(X)<~>~kind(X))))&
(![X]:((~funny(X)&happy(X))<=>(curious(X)<~>creative(X))))&
((?[X]:((~happy(X)<~>~kind(X))))=>((~funny(fred)|~curious(fred))))&
(![X]:((~rich(X)|~curious(X))=>(creative(X)<~>~rich(X))))&
((~kind(mary))<=>((~humble(susan)|~brave(susan))))&
((?[X]:(creative(X)))<=>((wise(susan)|brave(susan))))&
(((happy(alice)<~>~quiet(alice)))<=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((~brave(X)<~>old(X))=>(~generous(X)&quiet(X))))&
((~strong(alice)&old(alice)))&
(?[X]:(quiet(X)))&
(?[X]:((~brave(X)|old(X))))&
(?[X]:(funny(X))) | ~calm(alice) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5884844079184466467737346
% SZS output start Proof for 5884844079184466467737346
1. ! [X0] : (~creative(X0) <=> (tall(X0) & happy(X0))) [input p0]
2. ! [X0] : ((patient(X0) & creative(X0)) <=> (~calm(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | patient(X0)) <=> (~quiet(X0) & ~curious(X0))) [input p2]
5. ! [X0] : ((~wise(X0) | ~tall(X0)) => (wise(X0) & ~wise(X0))) [input p4]
9. ! [X0] : ((happy(X0) & ~funny(X0)) <=> (curious(X0) <~> creative(X0))) [input p8]
15. ! [X0] : ((~brave(X0) <~> old(X0)) => (quiet(X0) & ~generous(X0))) [input p14]
16. old(alice) & ~strong(alice) [input p15]
20. ~calm(alice) [input hypothesis]
22. ! [X0] : ((~brave(X0) <~> old(X0)) => quiet(X0)) [pure predicate removal 15]
23. ! [X0] : ((wise(X0) & ~wise(X0)) | (wise(X0) & tall(X0))) [ennf transformation 5]
30. ! [X0] : (quiet(X0) | (~brave(X0) <=> old(X0))) [ennf transformation 22]
31. ! [X0] : ((~creative(X0) | (~tall(X0) | ~happy(X0))) & ((tall(X0) & happy(X0)) | creative(X0))) [nnf transformation 1]
32. ! [X0] : ((~creative(X0) | ~tall(X0) | ~happy(X0)) & ((tall(X0) & happy(X0)) | creative(X0))) [flattening 31]
33. ! [X0] : (((patient(X0) & creative(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (~patient(X0) | ~creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((patient(X0) & creative(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | ~patient(X0) | ~creative(X0))) [flattening 33]
35. ! [X0] : (((~brave(X0) | patient(X0)) | (quiet(X0) | curious(X0))) & ((~quiet(X0) & ~curious(X0)) | (brave(X0) & ~patient(X0)))) [nnf transformation 3]
36. ! [X0] : ((~brave(X0) | patient(X0) | quiet(X0) | curious(X0)) & ((~quiet(X0) & ~curious(X0)) | (brave(X0) & ~patient(X0)))) [flattening 35]
48. ! [X0] : (((happy(X0) & ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~happy(X0) | funny(X0)))) [nnf transformation 9]
49. ! [X0] : (((happy(X0) & ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~happy(X0) | funny(X0))) [flattening 48]
63. ! [X0] : (quiet(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) [nnf transformation 30]
72. ~tall(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 32]
74. creative(X0) | creative(X0) [cnf transformation 34]
77. calm(X0) | patient(X0) [cnf transformation 34]
79. ~curious(X0) | brave(X0) [cnf transformation 36]
80. ~quiet(X0) | ~patient(X0) [cnf transformation 36]
87. ~wise(X0) | tall(X0) [cnf transformation 23]
90. wise(X0) | wise(X0) [cnf transformation 23]
105. happy(X0) | curious(X0) | ~creative(X0) [cnf transformation 49]
125. ~old(X0) | ~brave(X0) | quiet(X0) [cnf transformation 63]
127. old(alice) [cnf transformation 16]
131. ~calm(alice) [cnf transformation 20]
135. wise(X0) [duplicate literal removal 90]
137. creative(X0) [duplicate literal removal 74]
140. 1 <=> ! [X1] : tall(X1) [avatar definition]
141. tall(X1) <- (1) [avatar component clause 140]
171. tall(X0) [subsumption resolution 87,135]
172. 1 [avatar split clause 171,140]
176. curious(X0) | happy(X0) [subsumption resolution 105,137]
218. 17 <=> quiet(alice) [avatar definition]
219. ~quiet(alice) <- (~17) [avatar component clause 218]
220. quiet(alice) <- (17) [avatar component clause 218]
240. patient(alice) [resolution 77,131]
247. brave(X0) | happy(X0) [resolution 176,79]
255. ~creative(X1) | ~happy(X1) <- (1) [resolution 72,141]
256. ~happy(X1) <- (1) [subsumption resolution 255,137]
258. ~brave(alice) | quiet(alice) [resolution 125,127]
261. ~brave(alice) <- (~17) [subsumption resolution 258,219]
272. happy(alice) <- (~17) [resolution 247,261]
278. $false <- (1, ~17) [subsumption resolution 272,256]
279. ~1 | 17 [avatar contradiction clause 278]
289. ~patient(alice) <- (17) [resolution 220,80]
291. $false <- (17) [subsumption resolution 289,240]
292. ~17 [avatar contradiction clause 291]
293. $false [avatar sat refutation 172,279,292]
% SZS output end Proof for 5884844079184466467737346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not patient or not wise.
Everyone who is both not curious and humble is either not humble or not generous and vice versa.
Everyone who is both humble and creative is not calm and vice versa.
Everyone who is patient is both not wise and not patient.
Everyone who is both wise and kind is generous or not patient and vice versa.
If someone is both not wise and not calm then someone is both not old and not happy.
Everyone who is either not curious or humble is not humble.
If paul is not kind then lucy is both not strong and old.
Everyone who is either not calm or not old is creative or not brave.
Everyone who is both not old and not strong is both humble and brave.
If someone is either rich or quiet then alice is kind or not creative.
If someone is rich then mary is patient.
If someone is either not generous or not rich then paul is kind.
Everyone who is calm or strong is both not creative and humble and vice versa.
Everyone who is generous or not strong is both not calm and not rich.
If mary is not kind or curious then lucy is both not kind and wise and vice versa.
Fred is not generous or funny.
Mary is not patient.
Fred is both not generous and wise.
Mary is either not generous or calm.
Mary is either wise or not creative.
Someone is generous or not happy. | Lucy is not strong. | neutral | (![X]:(~kind(X)=>(~patient(X)<~>~wise(X))))&
(![X]:((~curious(X)&humble(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:((humble(X)&creative(X))<=>~calm(X)))&
(![X]:(patient(X)=>(~wise(X)&~patient(X))))&
(![X]:((wise(X)&kind(X))<=>(generous(X)|~patient(X))))&
((?[X]:((~wise(X)&~calm(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((~curious(X)<~>humble(X))=>~humble(X)))&
((~kind(paul))=>((~strong(lucy)&old(lucy))))&
(![X]:((~calm(X)<~>~old(X))=>(creative(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))=>(humble(X)&brave(X))))&
((?[X]:((rich(X)<~>quiet(X))))=>((kind(alice)|~creative(alice))))&
((?[X]:(rich(X)))=>(patient(mary)))&
((?[X]:((~generous(X)<~>~rich(X))))=>(kind(paul)))&
(![X]:((calm(X)|strong(X))<=>(~creative(X)&humble(X))))&
(![X]:((generous(X)|~strong(X))=>(~calm(X)&~rich(X))))&
(((~kind(mary)|curious(mary)))<=>((~kind(lucy)&wise(lucy))))&
((~generous(fred)|funny(fred)))&
(~patient(mary))&
((~generous(fred)&wise(fred)))&
((~generous(mary)<~>calm(mary)))&
((wise(mary)<~>~creative(mary)))&
(?[X]:((generous(X)|~happy(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is not calm or kind is either not brave or not quiet. Everyone who is not humble is either not calm or humble and vice versa. If susan is not brave or not rich then someone is old and vice versa. Everyone who is quiet or not rich is happy and vice versa. Everyone who is both funny and not kind is both rich and not kind. If someone is either brave or kind then someone is either tall or patient and vice versa. Everyone who is not curious is not generous and vice versa. If john is either kind or not generous then someone is not tall or happy. Everyone who is both happy and patient is either not strong or quiet. If someone is kind or brave then paul is not quiet. If someone is happy then someone is both not humble and curious. Everyone who is both not curious and happy is not quiet. Everyone who is not happy is either funny or kind. If someone is both not happy and not brave then someone is creative or happy and vice versa. If susan is either curious or not generous then someone is not wise or patient and vice versa. Everyone who is both wise and not calm is either not strong or curious. Lucy is both not strong and not generous. Someone is kind or happy. John is either creative or not wise. Susan is either quiet or not calm. Susan is both not calm and not wise. | Paul is brave. | entailment | (![X]:((~calm(X)|kind(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>humble(X))))&
(((~brave(susan)|~rich(susan)))<=>(?[X]:(old(X))))&
(![X]:((quiet(X)|~rich(X))<=>happy(X)))&
(![X]:((funny(X)&~kind(X))=>(rich(X)&~kind(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:(~curious(X)<=>~generous(X)))&
(((kind(john)<~>~generous(john)))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((happy(X)&patient(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((kind(X)|brave(X))))=>(~quiet(paul)))&
((?[X]:(happy(X)))=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((~curious(X)&happy(X))=>~quiet(X)))&
(![X]:(~happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:((~happy(X)&~brave(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(((curious(susan)<~>~generous(susan)))<=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((wise(X)&~calm(X))=>(~strong(X)<~>curious(X))))&
((~strong(lucy)&~generous(lucy)))&
(?[X]:((kind(X)|happy(X))))&
((creative(john)<~>~wise(john)))&
((quiet(susan)<~>~calm(susan)))&
((~calm(susan)&~wise(susan))) | brave(paul) | [
"p0",
"p1",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7920735883886612655686212
% SZS output start Proof for 7920735883886612655686212
1. ! [X0] : ((kind(X0) | ~calm(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : (~humble(X0) <=> (~calm(X0) <~> humble(X0))) [input p1]
10. ? [X0] : (brave(X0) | kind(X0)) => ~quiet(paul) [input p9]
20. quiet(susan) <~> ~calm(susan) [input p19]
22. ~brave(paul) [input hypothesis]
26. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 1]
32. ~quiet(paul) | ! [X0] : (~brave(X0) & ~kind(X0)) [ennf transformation 10]
39. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~kind(X0) & calm(X0))) [nnf transformation 26]
40. ! [X0] : ((~humble(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | humble(X0))) [nnf transformation 2]
75. (calm(susan) | ~quiet(susan)) & (~calm(susan) | quiet(susan)) [nnf transformation 20]
78. quiet(X0) | brave(X0) | calm(X0) [cnf transformation 39]
80. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 40]
83. ~humble(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 40]
107. ~quiet(paul) | ~brave(X0) [cnf transformation 32]
132. calm(susan) | ~quiet(susan) [cnf transformation 75]
135. ~brave(paul) [cnf transformation 22]
136. humble(X0) | ~calm(X0) [duplicate literal removal 80]
137. ~humble(X0) | ~calm(X0) [duplicate literal removal 83]
138. ~calm(X0) [subsumption resolution 136,137]
143. 2 <=> brave(susan) [avatar definition]
144. brave(susan) <- (2) [avatar component clause 143]
213. 17 <=> ! [X0] : ~brave(X0) [avatar definition]
214. ~brave(X0) <- (17) [avatar component clause 213]
216. 18 <=> quiet(paul) [avatar definition]
218. ~quiet(paul) <- (~18) [avatar component clause 216]
219. 17 | ~18 [avatar split clause 107,216,213]
302. ~quiet(susan) [subsumption resolution 132,138]
312. brave(paul) | calm(paul) <- (~18) [resolution 78,218]
313. brave(susan) | calm(susan) [resolution 78,302]
319. calm(paul) <- (~18) [subsumption resolution 312,135]
320. $false <- (~18) [subsumption resolution 319,138]
321. 18 [avatar contradiction clause 320]
322. brave(susan) [subsumption resolution 313,138]
323. 2 [avatar split clause 322,143]
327. $false <- (2, 17) [subsumption resolution 144,214]
328. ~2 | ~17 [avatar contradiction clause 327]
329. $false [avatar sat refutation 219,321,323,328]
% SZS output end Proof for 7920735883886612655686212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is not calm or rich and vice versa.
Everyone who is not creative or not brave is wise or funny and vice versa.
If fred is not quiet then paul is rich and vice versa.
Everyone who is patient or not funny is curious.
Everyone who is both not tall and not creative is both brave and happy.
Everyone who is both humble and kind is not happy and vice versa.
Everyone who is brave is rich or not wise and vice versa.
Everyone who is creative is creative or not quiet.
Everyone who is not brave is both not calm and calm and vice versa.
Everyone who is not old is both brave and not funny and vice versa.
Everyone who is either not patient or kind is both not funny and quiet and vice versa.
Everyone who is either old or not rich is both generous and not kind.
Everyone who is either not funny or kind is both strong and old.
If mary is either funny or not strong then someone is not creative or not old.
If susan is either humble or strong then someone is kind and vice versa.
Everyone who is calm or not rich is not generous and vice versa.
Someone is calm or not quiet.
Mary is either quiet or not funny.
Someone is not calm or not rich.
Fred is wise or strong.
Paul is tall or old.
Paul is either not calm or not wise.
Lucy is either not humble or not curious.
Someone is creative. | Mary is not patient. | neutral | (![X]:(brave(X)<=>(~calm(X)|rich(X))))&
(![X]:((~creative(X)|~brave(X))<=>(wise(X)|funny(X))))&
((~quiet(fred))<=>(rich(paul)))&
(![X]:((patient(X)|~funny(X))=>curious(X)))&
(![X]:((~tall(X)&~creative(X))=>(brave(X)&happy(X))))&
(![X]:((humble(X)&kind(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(rich(X)|~wise(X))))&
(![X]:(creative(X)=>(creative(X)|~quiet(X))))&
(![X]:(~brave(X)<=>(~calm(X)&calm(X))))&
(![X]:(~old(X)<=>(brave(X)&~funny(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((old(X)<~>~rich(X))=>(generous(X)&~kind(X))))&
(![X]:((~funny(X)<~>kind(X))=>(strong(X)&old(X))))&
(((funny(mary)<~>~strong(mary)))=>(?[X]:((~creative(X)|~old(X)))))&
(((humble(susan)<~>strong(susan)))<=>(?[X]:(kind(X))))&
(![X]:((calm(X)|~rich(X))<=>~generous(X)))&
(?[X]:((calm(X)|~quiet(X))))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:((~calm(X)|~rich(X))))&
((wise(fred)|strong(fred)))&
((tall(paul)|old(paul)))&
((~calm(paul)<~>~wise(paul)))&
((~humble(lucy)<~>~curious(lucy)))&
(?[X]:(creative(X))) | ~patient(mary) | [] | null | 0 |
If someone is both not happy and not quiet then someone is either not quiet or old.
Everyone who is both rich and not calm is not calm and vice versa.
If someone is either humble or not funny then someone is both rich and curious.
Everyone who is either not quiet or happy is either wise or not calm.
Everyone who is curious is not patient or not curious and vice versa.
If mary is not generous then someone is brave or not brave.
Everyone who is either not humble or not brave is not old.
Everyone who is either funny or calm is calm or not wise and vice versa.
If someone is not happy or not strong then someone is not funny or not tall.
Everyone who is either not kind or not old is both not wise and wise.
Everyone who is either rich or curious is either kind or funny.
If john is both not funny and creative then alice is not calm or not curious.
Everyone who is either calm or rich is either kind or not creative.
Everyone who is quiet is kind or quiet and vice versa.
Everyone who is both kind and not tall is both not funny and rich and vice versa.
Everyone who is kind is both patient and wise and vice versa.
Someone is either not curious or not humble.
Someone is not kind.
Someone is either not creative or old.
Susan is not brave.
Susan is either wise or not tall.
Someone is either not quiet or calm.
Lucy is either not happy or not generous. | Lucy is not calm. | entailment | ((?[X]:((~happy(X)&~quiet(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((rich(X)&~calm(X))<=>~calm(X)))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~quiet(X)<~>happy(X))=>(wise(X)<~>~calm(X))))&
(![X]:(curious(X)<=>(~patient(X)|~curious(X))))&
((~generous(mary))=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>~old(X)))&
(![X]:((funny(X)<~>calm(X))<=>(calm(X)|~wise(X))))&
((?[X]:((~happy(X)|~strong(X))))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((~kind(X)<~>~old(X))=>(~wise(X)&wise(X))))&
(![X]:((rich(X)<~>curious(X))=>(kind(X)<~>funny(X))))&
(((~funny(john)&creative(john)))=>((~calm(alice)|~curious(alice))))&
(![X]:((calm(X)<~>rich(X))=>(kind(X)<~>~creative(X))))&
(![X]:(quiet(X)<=>(kind(X)|quiet(X))))&
(![X]:((kind(X)&~tall(X))<=>(~funny(X)&rich(X))))&
(![X]:(kind(X)<=>(patient(X)&wise(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~creative(X)<~>old(X))))&
(~brave(susan))&
((wise(susan)<~>~tall(susan)))&
(?[X]:((~quiet(X)<~>calm(X))))&
((~happy(lucy)<~>~generous(lucy))) | ~calm(lucy) | [
"p4",
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2889812240280354870540051
% SZS output start Proof for 2889812240280354870540051
5. ! [X0] : (curious(X0) <=> (~curious(X0) | ~patient(X0))) [input p4]
8. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~wise(X0) | calm(X0))) [input p7]
11. ! [X0] : ((rich(X0) <~> curious(X0)) => (kind(X0) <~> funny(X0))) [input p10]
15. ! [X0] : ((~tall(X0) & kind(X0)) <=> (rich(X0) & ~funny(X0))) [input p14]
16. ! [X0] : (kind(X0) <=> (wise(X0) & patient(X0))) [input p15]
24. calm(lucy) [input hypothesis]
36. ! [X0] : ((kind(X0) <~> funny(X0)) | (rich(X0) <=> curious(X0))) [ennf transformation 11]
51. ! [X0] : ((curious(X0) | (curious(X0) & patient(X0))) & ((~curious(X0) | ~patient(X0)) | ~curious(X0))) [nnf transformation 5]
52. ! [X0] : ((curious(X0) | (curious(X0) & patient(X0))) & (~curious(X0) | ~patient(X0) | ~curious(X0))) [flattening 51]
56. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 8]
57. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [flattening 56]
62. ! [X0] : (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) [nnf transformation 36]
66. ! [X0] : (((~tall(X0) & kind(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (tall(X0) | ~kind(X0)))) [nnf transformation 15]
67. ! [X0] : (((~tall(X0) & kind(X0)) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | tall(X0) | ~kind(X0))) [flattening 66]
68. ! [X0] : ((kind(X0) | (~wise(X0) | ~patient(X0))) & ((wise(X0) & patient(X0)) | ~kind(X0))) [nnf transformation 16]
69. ! [X0] : ((kind(X0) | ~wise(X0) | ~patient(X0)) & ((wise(X0) & patient(X0)) | ~kind(X0))) [flattening 68]
96. ~curious(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 52]
98. curious(X0) | curious(X0) [cnf transformation 52]
106. ~calm(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 57]
114. funny(X0) | kind(X0) | rich(X0) | ~curious(X0) [cnf transformation 62]
127. kind(X0) | ~rich(X0) | funny(X0) [cnf transformation 67]
129. patient(X0) | ~kind(X0) [cnf transformation 69]
144. calm(lucy) [cnf transformation 24]
146. ~funny(X0) | ~calm(X0) [duplicate literal removal 106]
147. ~curious(X0) | ~patient(X0) [duplicate literal removal 96]
148. curious(X0) [duplicate literal removal 98]
180. ~patient(X0) [subsumption resolution 147,148]
197. funny(X0) | kind(X0) | rich(X0) [subsumption resolution 114,148]
216. kind(X0) | funny(X0) [subsumption resolution 127,197]
217. ~kind(X0) [subsumption resolution 129,180]
266. funny(X3) [resolution 216,217]
268. ~calm(X1) [resolution 266,146]
269. $false [resolution 268,144]
% SZS output end Proof for 2889812240280354870540051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then alice is both not wise and not funny and vice versa.
If paul is not happy or not patient then john is not wise.
If susan is not kind or not tall then mary is brave and vice versa.
Everyone who is either not old or happy is not kind and vice versa.
If someone is either not wise or generous then someone is not patient.
Everyone who is tall is not rich and vice versa.
Everyone who is humble is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
If john is either not happy or curious then someone is quiet.
If someone is both calm and not creative then someone is both not patient and brave.
If someone is not patient then someone is quiet and vice versa.
Everyone who is either not tall or not patient is both not calm and tall.
Someone is either patient or quiet.
Alice is not happy or creative.
Susan is not rich.
Someone is curious or not happy.
Someone is either not happy or not strong.
Someone is quiet. | Susan is not creative. | neutral | ((?[X]:(happy(X)))<=>((~wise(alice)&~funny(alice))))&
(((~happy(paul)|~patient(paul)))=>(~wise(john)))&
(((~kind(susan)|~tall(susan)))<=>(brave(mary)))&
(![X]:((~old(X)<~>happy(X))<=>~kind(X)))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:(~patient(X))))&
(![X]:(tall(X)<=>~rich(X)))&
(![X]:(humble(X)<=>(~wise(X)|~creative(X))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(((~happy(john)<~>curious(john)))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((~patient(X)&brave(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~calm(X)&tall(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
((~happy(alice)|creative(alice)))&
(~rich(susan))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(quiet(X))) | ~creative(susan) | [] | null | 0 |
Everyone who is not calm or not generous is either not happy or happy and vice versa.
Everyone who is both generous and creative is either humble or not generous and vice versa.
Everyone who is patient is either not creative or kind.
If someone is not quiet then paul is both quiet and not old.
If someone is not old then someone is tall or happy.
Everyone who is both rich and not curious is either not kind or not rich and vice versa.
Everyone who is both not quiet and wise is not calm or creative.
Everyone who is not curious or funny is not calm or calm.
If someone is patient or happy then someone is both strong and creative.
If someone is either not strong or generous then someone is old or calm and vice versa.
Everyone who is both not generous and not patient is both not strong and strong and vice versa.
Everyone who is both not generous and not strong is not kind.
Everyone who is either tall or quiet is both patient and brave.
If someone is wise then john is not kind or calm.
Everyone who is humble or not creative is both calm and not funny and vice versa.
Everyone who is curious is not brave or old and vice versa.
Mary is wise or not strong.
Someone is either creative or not creative.
Paul is wise.
Someone is both curious and not wise.
Someone is either not curious or not quiet.
Paul is not rich or tall.
Someone is either not generous or creative.
Susan is creative. | Susan is rich. | entailment | (![X]:((~calm(X)|~generous(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((generous(X)&creative(X))<=>(humble(X)<~>~generous(X))))&
(![X]:(patient(X)=>(~creative(X)<~>kind(X))))&
((?[X]:(~quiet(X)))=>((quiet(paul)&~old(paul))))&
((?[X]:(~old(X)))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((rich(X)&~curious(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((~quiet(X)&wise(X))=>(~calm(X)|creative(X))))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)|calm(X))))&
((?[X]:((patient(X)|happy(X))))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
(![X]:((tall(X)<~>quiet(X))=>(patient(X)&brave(X))))&
((?[X]:(wise(X)))=>((~kind(john)|calm(john))))&
(![X]:((humble(X)|~creative(X))<=>(calm(X)&~funny(X))))&
(![X]:(curious(X)<=>(~brave(X)|old(X))))&
((wise(mary)|~strong(mary)))&
(?[X]:((creative(X)<~>~creative(X))))&
(wise(paul))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((~rich(paul)|tall(paul)))&
(?[X]:((~generous(X)<~>creative(X))))&
(creative(susan)) | rich(susan) | [
"p0",
"p1",
"p2",
"p5",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1107724028176216022634651
% SZS output start Proof for 1107724028176216022634651
1. ! [X0] : ((~generous(X0) | ~calm(X0)) <=> (~happy(X0) <~> happy(X0))) [input p0]
2. ! [X0] : ((creative(X0) & generous(X0)) <=> (humble(X0) <~> ~generous(X0))) [input p1]
3. ! [X0] : (patient(X0) => (~creative(X0) <~> kind(X0))) [input p2]
6. ! [X0] : ((~curious(X0) & rich(X0)) <=> (~kind(X0) <~> ~rich(X0))) [input p5]
11. ! [X0] : ((~patient(X0) & ~generous(X0)) <=> (strong(X0) & ~strong(X0))) [input p10]
15. ! [X0] : ((~creative(X0) | humble(X0)) <=> (~funny(X0) & calm(X0))) [input p14]
24. creative(susan) [input p23]
25. ~rich(susan) [input hypothesis]
29. ! [X0] : ((~creative(X0) <~> kind(X0)) | ~patient(X0)) [ennf transformation 3]
42. ! [X0] : (((~generous(X0) | ~calm(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (generous(X0) & calm(X0)))) [nnf transformation 1]
43. ! [X0] : ((~generous(X0) | ~calm(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (generous(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (~creative(X0) | ~generous(X0)))) [nnf transformation 2]
45. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ~creative(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~patient(X0)) [nnf transformation 29]
50. ! [X0] : (((~curious(X0) & rich(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | (curious(X0) | ~rich(X0)))) [nnf transformation 6]
51. ! [X0] : (((~curious(X0) & rich(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | curious(X0) | ~rich(X0))) [flattening 50]
60. ! [X0] : (((~patient(X0) & ~generous(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (patient(X0) | generous(X0)))) [nnf transformation 11]
61. ! [X0] : (((~patient(X0) & ~generous(X0)) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | patient(X0) | generous(X0))) [flattening 60]
63. ! [X0] : (((~creative(X0) | humble(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 15]
64. ! [X0] : ((~creative(X0) | humble(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [flattening 63]
82. ~generous(X0) | ~calm(X0) | happy(X0) | happy(X0) [cnf transformation 43]
83. ~generous(X0) | ~calm(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 43]
84. ~generous(X0) | humble(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 45]
87. generous(X0) | humble(X0) | generous(X0) [cnf transformation 45]
90. ~patient(X0) | ~creative(X0) | kind(X0) [cnf transformation 46]
98. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 51]
114. ~strong(X0) | patient(X0) | generous(X0) [cnf transformation 61]
115. strong(X0) | patient(X0) | generous(X0) [cnf transformation 61]
124. ~humble(X0) | calm(X0) [cnf transformation 64]
125. creative(X0) | calm(X0) [cnf transformation 64]
143. creative(susan) [cnf transformation 24]
144. ~rich(susan) [cnf transformation 25]
146. ~kind(X0) | rich(X0) [duplicate literal removal 98]
147. ~generous(X0) | humble(X0) | ~creative(X0) [duplicate literal removal 84]
148. humble(X0) | generous(X0) [duplicate literal removal 87]
149. ~generous(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 82]
150. ~happy(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 83]
151. ~generous(X0) | ~calm(X0) [subsumption resolution 149,150]
152. ~creative(X0) | humble(X0) [subsumption resolution 147,148]
231. patient(X0) | generous(X0) [subsumption resolution 114,115]
294. humble(X0) | calm(X0) [resolution 152,125]
295. calm(X0) [subsumption resolution 294,124]
313. ~creative(X0) | kind(X0) | generous(X0) [resolution 90,231]
354. kind(susan) | generous(susan) [resolution 313,143]
358. 34 <=> generous(susan) [avatar definition]
360. generous(susan) <- (34) [avatar component clause 358]
362. 35 <=> kind(susan) [avatar definition]
364. kind(susan) <- (35) [avatar component clause 362]
365. 34 | 35 [avatar split clause 354,362,358]
379. rich(susan) <- (35) [resolution 364,146]
385. $false <- (35) [subsumption resolution 379,144]
386. ~35 [avatar contradiction clause 385]
387. ~calm(susan) <- (34) [resolution 360,151]
388. $false <- (34) [subsumption resolution 387,295]
389. ~34 [avatar contradiction clause 388]
390. $false [avatar sat refutation 365,386,389]
% SZS output end Proof for 1107724028176216022634651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and brave is creative and vice versa. Everyone who is both not brave and not old is both old and strong. If susan is either old or not creative then someone is curious or not quiet and vice versa. Everyone who is calm is happy or not tall. Everyone who is either kind or brave is both brave and not curious. If someone is curious then paul is both humble and not old and vice versa. If someone is not quiet or strong then someone is both funny and calm. If someone is both not brave and not funny then someone is either not brave or brave. Everyone who is either brave or not happy is both not wise and not humble and vice versa. Everyone who is both not calm and not old is both rich and not wise. If alice is not funny then someone is curious or humble and vice versa. Everyone who is happy is either not patient or not creative. If someone is not old or strong then john is both not creative and not kind and vice versa. Everyone who is strong or not wise is not brave and vice versa. If paul is both not calm and not humble then paul is not generous and vice versa. Everyone who is either not generous or not happy is either not kind or not old and vice versa. Someone is both creative and brave. Someone is curious. Mary is either not funny or creative. John is old or not quiet. Someone is not curious or not creative. Someone is both not funny and brave. Lucy is either not old or not quiet. Mary is not curious or happy. | Susan is strong. | contradiction | (![X]:((tall(X)&brave(X))<=>creative(X)))&
(![X]:((~brave(X)&~old(X))=>(old(X)&strong(X))))&
(((old(susan)<~>~creative(susan)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:(calm(X)=>(happy(X)|~tall(X))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&~curious(X))))&
((?[X]:(curious(X)))<=>((humble(paul)&~old(paul))))&
((?[X]:((~quiet(X)|strong(X))))=>(?[X]:((funny(X)&calm(X)))))&
((?[X]:((~brave(X)&~funny(X))))=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:((brave(X)<~>~happy(X))<=>(~wise(X)&~humble(X))))&
(![X]:((~calm(X)&~old(X))=>(rich(X)&~wise(X))))&
((~funny(alice))<=>(?[X]:((curious(X)|humble(X)))))&
(![X]:(happy(X)=>(~patient(X)<~>~creative(X))))&
((?[X]:((~old(X)|strong(X))))<=>((~creative(john)&~kind(john))))&
(![X]:((strong(X)|~wise(X))<=>~brave(X)))&
(((~calm(paul)&~humble(paul)))<=>(~generous(paul)))&
(![X]:((~generous(X)<~>~happy(X))<=>(~kind(X)<~>~old(X))))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:(curious(X)))&
((~funny(mary)<~>creative(mary)))&
((old(john)|~quiet(john)))&
(?[X]:((~curious(X)|~creative(X))))&
(?[X]:((~funny(X)&brave(X))))&
((~old(lucy)<~>~quiet(lucy)))&
((~curious(mary)|happy(mary))) | strong(susan) | [
"p0",
"p1",
"p2",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1969723913784556897873949
% SZS output start Proof for 1969723913784556897873949
1. ! [X0] : ((brave(X0) & tall(X0)) <=> creative(X0)) [input p0]
2. ! [X0] : ((~old(X0) & ~brave(X0)) => (strong(X0) & old(X0))) [input p1]
3. (old(susan) <~> ~creative(susan)) <=> ? [X0] : (~quiet(X0) | curious(X0)) [input p2]
14. ! [X0] : ((~wise(X0) | strong(X0)) <=> ~brave(X0)) [input p13]
18. ? [X0] : curious(X0) [input p17]
25. strong(susan) [input hypothesis]
29. ! [X0] : ((strong(X0) & old(X0)) | (old(X0) | brave(X0))) [ennf transformation 2]
30. ! [X0] : ((strong(X0) & old(X0)) | old(X0) | brave(X0)) [flattening 29]
39. ! [X0] : (((brave(X0) & tall(X0)) | ~creative(X0)) & (creative(X0) | (~brave(X0) | ~tall(X0)))) [nnf transformation 1]
40. ! [X0] : (((brave(X0) & tall(X0)) | ~creative(X0)) & (creative(X0) | ~brave(X0) | ~tall(X0))) [flattening 39]
41. (((creative(susan) | ~old(susan)) & (~creative(susan) | old(susan))) | ! [X0] : (quiet(X0) & ~curious(X0))) & (? [X0] : (~quiet(X0) | curious(X0)) | ((old(susan) | creative(susan)) & (~creative(susan) | ~old(susan)))) [nnf transformation 3]
42. (((creative(susan) | ~old(susan)) & (~creative(susan) | old(susan))) | ! [X0] : (quiet(X0) & ~curious(X0))) & (? [X1] : (~quiet(X1) | curious(X1)) | ((old(susan) | creative(susan)) & (~creative(susan) | ~old(susan)))) [rectify 41]
43. ? [X1] : (~quiet(X1) | curious(X1)) => (~quiet(sK0) | curious(sK0)) [choice axiom]
44. (((creative(susan) | ~old(susan)) & (~creative(susan) | old(susan))) | ! [X0] : (quiet(X0) & ~curious(X0))) & ((~quiet(sK0) | curious(sK0)) | ((old(susan) | creative(susan)) & (~creative(susan) | ~old(susan)))) [skolemisation 42,43]
70. ! [X0] : (((~wise(X0) | strong(X0)) | brave(X0)) & (~brave(X0) | (wise(X0) & ~strong(X0)))) [nnf transformation 14]
71. ! [X0] : ((~wise(X0) | strong(X0) | brave(X0)) & (~brave(X0) | (wise(X0) & ~strong(X0)))) [flattening 70]
77. ? [X0] : curious(X0) => curious(sK7) [choice axiom]
78. curious(sK7) [skolemisation 18,77]
87. ~creative(X0) | brave(X0) [cnf transformation 40]
88. old(X0) | old(X0) | brave(X0) [cnf transformation 30]
94. creative(susan) | ~old(susan) | ~curious(X0) [cnf transformation 44]
127. ~strong(X0) | ~brave(X0) [cnf transformation 71]
143. curious(sK7) [cnf transformation 78]
153. strong(susan) [cnf transformation 25]
155. old(X0) | brave(X0) [duplicate literal removal 88]
160. 2 <=> old(susan) [avatar definition]
162. ~old(susan) <- (~2) [avatar component clause 160]
164. 3 <=> creative(susan) [avatar definition]
166. creative(susan) <- (3) [avatar component clause 164]
169. 4 <=> ! [X0] : ~curious(X0) [avatar definition]
170. ~curious(X0) <- (4) [avatar component clause 169]
171. 4 | ~2 | 3 [avatar split clause 94,164,160,169]
314. $false <- (4) [resolution 170,143]
315. ~4 [avatar contradiction clause 314]
320. ~brave(susan) [resolution 127,153]
323. brave(susan) <- (~2) [resolution 155,162]
326. $false <- (~2) [subsumption resolution 323,320]
327. 2 [avatar contradiction clause 326]
328. brave(susan) <- (3) [resolution 166,87]
330. $false <- (3) [subsumption resolution 328,320]
331. ~3 [avatar contradiction clause 330]
332. $false [avatar sat refutation 171,315,327,331]
% SZS output end Proof for 1969723913784556897873949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not creative then someone is both not generous and brave. If someone is either happy or not kind then paul is not old. If lucy is both not brave and wise then lucy is either not strong or strong. Everyone who is either quiet or not quiet is old. Everyone who is curious is not strong. Everyone who is both not tall and brave is both not curious and curious. Everyone who is not brave is both old and not generous and vice versa. If someone is both wise and not brave then someone is either not calm or wise and vice versa. If alice is both patient and brave then someone is both not brave and funny and vice versa. Everyone who is not kind is brave or not funny and vice versa. If alice is either generous or strong then lucy is either not brave or not happy and vice versa. Everyone who is not calm is either not curious or not generous. Everyone who is either not patient or not tall is old and vice versa. Everyone who is either patient or not tall is humble or not humble. Everyone who is generous or strong is either not happy or not creative and vice versa. Everyone who is humble is strong. Someone is either not happy or quiet. Lucy is strong. Someone is happy or not kind. Fred is both not funny and calm. Someone is both not generous and not kind. John is either tall or not happy. Someone is either not patient or brave. | John is not tall. | contradiction | ((?[X]:((generous(X)&~creative(X))))=>(?[X]:((~generous(X)&brave(X)))))&
((?[X]:((happy(X)<~>~kind(X))))=>(~old(paul)))&
(((~brave(lucy)&wise(lucy)))=>((~strong(lucy)<~>strong(lucy))))&
(![X]:((quiet(X)<~>~quiet(X))=>old(X)))&
(![X]:(curious(X)=>~strong(X)))&
(![X]:((~tall(X)&brave(X))=>(~curious(X)&curious(X))))&
(![X]:(~brave(X)<=>(old(X)&~generous(X))))&
((?[X]:((wise(X)&~brave(X))))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(((patient(alice)&brave(alice)))<=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:(~kind(X)<=>(brave(X)|~funny(X))))&
(((generous(alice)<~>strong(alice)))<=>((~brave(lucy)<~>~happy(lucy))))&
(![X]:(~calm(X)=>(~curious(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>old(X)))&
(![X]:((patient(X)<~>~tall(X))=>(humble(X)|~humble(X))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(humble(X)=>strong(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(strong(lucy))&
(?[X]:((happy(X)|~kind(X))))&
((~funny(fred)&calm(fred)))&
(?[X]:((~generous(X)&~kind(X))))&
((tall(john)<~>~happy(john)))&
(?[X]:((~patient(X)<~>brave(X)))) | ~tall(john) | [
"p1",
"p3",
"p5",
"p8",
"p9",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6035920134502568852285160
% SZS output start Proof for 6035920134502568852285160
2. ? [X0] : (happy(X0) <~> ~kind(X0)) => ~old(paul) [input p1]
4. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => old(X0)) [input p3]
6. ! [X0] : ((brave(X0) & ~tall(X0)) => (curious(X0) & ~curious(X0))) [input p5]
9. (brave(alice) & patient(alice)) <=> ? [X0] : (funny(X0) & ~brave(X0)) [input p8]
10. ! [X0] : (~kind(X0) <=> (~funny(X0) | brave(X0))) [input p9]
13. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> old(X0)) [input p12]
22. tall(john) <~> ~happy(john) [input p21]
24. ~tall(john) [input hypothesis]
28. ~old(paul) | ! [X0] : (happy(X0) <=> ~kind(X0)) [ennf transformation 2]
31. ! [X0] : (old(X0) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 4]
33. ! [X0] : ((curious(X0) & ~curious(X0)) | (~brave(X0) | tall(X0))) [ennf transformation 6]
34. ! [X0] : ((curious(X0) & ~curious(X0)) | ~brave(X0) | tall(X0)) [flattening 33]
42. ~old(paul) | ! [X0] : ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0))) [nnf transformation 28]
44. ! [X0] : (old(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 31]
52. ((brave(alice) & patient(alice)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X0] : (funny(X0) & ~brave(X0)) | (~brave(alice) | ~patient(alice))) [nnf transformation 9]
53. ((brave(alice) & patient(alice)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X0] : (funny(X0) & ~brave(X0)) | ~brave(alice) | ~patient(alice)) [flattening 52]
54. ((brave(alice) & patient(alice)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X1] : (funny(X1) & ~brave(X1)) | ~brave(alice) | ~patient(alice)) [rectify 53]
55. ? [X1] : (funny(X1) & ~brave(X1)) => (funny(sK3) & ~brave(sK3)) [choice axiom]
56. ((brave(alice) & patient(alice)) | ! [X0] : (~funny(X0) | brave(X0))) & ((funny(sK3) & ~brave(sK3)) | ~brave(alice) | ~patient(alice)) [skolemisation 54,55]
57. ! [X0] : ((~kind(X0) | (funny(X0) & ~brave(X0))) & ((~funny(X0) | brave(X0)) | kind(X0))) [nnf transformation 10]
58. ! [X0] : ((~kind(X0) | (funny(X0) & ~brave(X0))) & (~funny(X0) | brave(X0) | kind(X0))) [flattening 57]
61. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~old(X0)) & (old(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 13]
72. (happy(john) | ~tall(john)) & (~happy(john) | tall(john)) [nnf transformation 22]
79. ~old(paul) | happy(X0) | kind(X0) [cnf transformation 42]
82. old(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 44]
83. old(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
85. ~curious(X0) | ~brave(X0) | tall(X0) [cnf transformation 34]
86. ~brave(X0) | curious(X0) | tall(X0) [cnf transformation 34]
98. patient(alice) | ~funny(X0) | brave(X0) [cnf transformation 56]
99. brave(alice) | ~funny(X0) | brave(X0) [cnf transformation 56]
101. ~kind(X0) | ~brave(X0) [cnf transformation 58]
102. ~kind(X0) | funny(X0) [cnf transformation 58]
115. ~tall(X0) | ~patient(X0) | ~old(X0) [cnf transformation 61]
134. ~happy(john) | tall(john) [cnf transformation 72]
138. ~tall(john) [cnf transformation 24]
139. old(X0) | ~quiet(X0) [duplicate literal removal 82]
140. quiet(X0) | old(X0) [duplicate literal removal 83]
155. 4 <=> ! [X0] : (happy(X0) | kind(X0)) [avatar definition]
156. kind(X0) | happy(X0) <- (4) [avatar component clause 155]
158. 5 <=> old(paul) [avatar definition]
160. ~old(paul) <- (~5) [avatar component clause 158]
161. 4 | ~5 [avatar split clause 79,158,155]
166. old(X0) [subsumption resolution 139,140]
167. ~brave(X0) | tall(X0) [subsumption resolution 85,86]
201. 14 <=> ! [X0] : (~funny(X0) | brave(X0)) [avatar definition]
202. ~funny(X0) | brave(X0) <- (14) [avatar component clause 201]
204. 15 <=> brave(alice) [avatar definition]
206. brave(alice) <- (15) [avatar component clause 204]
207. 14 | 15 [avatar split clause 99,204,201]
209. 16 <=> patient(alice) [avatar definition]
211. patient(alice) <- (16) [avatar component clause 209]
212. 14 | 16 [avatar split clause 98,209,201]
248. ~patient(X0) | ~tall(X0) [subsumption resolution 115,166]
269. 27 <=> tall(john) [avatar definition]
273. 28 <=> happy(john) [avatar definition]
274. ~happy(john) <- (~28) [avatar component clause 273]
277. 27 | ~28 [avatar split clause 134,273,269]
288. ~27 [avatar split clause 138,269]
289. $false <- (~5) [subsumption resolution 160,166]
290. 5 [avatar contradiction clause 289]
294. funny(X0) | happy(X0) <- (4) [resolution 156,102]
295. happy(X1) | ~brave(X1) <- (4) [resolution 156,101]
311. happy(X0) | brave(X0) <- (4, 14) [resolution 294,202]
312. happy(X0) <- (4, 14) [subsumption resolution 311,295]
316. $false <- (4, 14, ~28) [resolution 312,274]
317. ~4 | ~14 | 28 [avatar contradiction clause 316]
322. tall(alice) <- (15) [resolution 206,167]
324. 31 <=> tall(alice) [avatar definition]
326. tall(alice) <- (31) [avatar component clause 324]
334. 31 | ~15 [avatar split clause 322,204,324]
336. ~tall(alice) <- (16) [resolution 211,248]
337. $false <- (16, 31) [subsumption resolution 336,326]
338. ~16 | ~31 [avatar contradiction clause 337]
339. $false [avatar sat refutation 161,207,212,277,288,290,317,334,338]
% SZS output end Proof for 6035920134502568852285160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and humble is both not creative and old and vice versa.
If someone is not creative then mary is not creative or strong.
Everyone who is both creative and old is either not brave or quiet.
If someone is calm or rich then someone is either not funny or not brave.
Everyone who is either rich or generous is either not creative or not kind.
Everyone who is humble or not happy is both generous and not humble and vice versa.
Everyone who is both patient and rich is not calm or not happy.
Everyone who is both not old and happy is humble or not brave and vice versa.
If john is either brave or not humble then someone is both quiet and not patient.
Everyone who is both humble and brave is not brave or not curious and vice versa.
Everyone who is either not humble or humble is patient or not curious and vice versa.
Everyone who is both not kind and tall is both calm and not old and vice versa.
If paul is both not creative and funny then fred is rich and vice versa.
If someone is either generous or not happy then john is either humble or happy.
Someone is either funny or not humble.
Lucy is patient or not brave.
Paul is not wise or quiet.
Someone is creative or not old.
Someone is either not strong or rich.
Someone is not kind or not calm.
Someone is either not patient or not old.
Someone is either funny or not old. | Mary is tall. | neutral | (![X]:((quiet(X)&humble(X))<=>(~creative(X)&old(X))))&
((?[X]:(~creative(X)))=>((~creative(mary)|strong(mary))))&
(![X]:((creative(X)&old(X))=>(~brave(X)<~>quiet(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((rich(X)<~>generous(X))=>(~creative(X)<~>~kind(X))))&
(![X]:((humble(X)|~happy(X))<=>(generous(X)&~humble(X))))&
(![X]:((patient(X)&rich(X))=>(~calm(X)|~happy(X))))&
(![X]:((~old(X)&happy(X))<=>(humble(X)|~brave(X))))&
(((brave(john)<~>~humble(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((humble(X)&brave(X))<=>(~brave(X)|~curious(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(patient(X)|~curious(X))))&
(![X]:((~kind(X)&tall(X))<=>(calm(X)&~old(X))))&
(((~creative(paul)&funny(paul)))<=>(rich(fred)))&
((?[X]:((generous(X)<~>~happy(X))))=>((humble(john)<~>happy(john))))&
(?[X]:((funny(X)<~>~humble(X))))&
((patient(lucy)|~brave(lucy)))&
((~wise(paul)|quiet(paul)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((funny(X)<~>~old(X)))) | tall(mary) | [] | null | 0 |
Everyone who is not kind is either not calm or brave and vice versa. Everyone who is not patient is not strong or not wise and vice versa. If paul is either not quiet or not strong then someone is both not kind and happy. Everyone who is not funny or old is either happy or not happy. If someone is not creative or not humble then john is either not funny or rich. If fred is not funny then susan is not humble or not wise and vice versa. Everyone who is creative or not rich is both not kind and not humble. If john is either wise or not tall then someone is either kind or not creative. If paul is not curious then someone is either not calm or wise. If someone is not quiet or not patient then someone is both wise and not happy and vice versa. Everyone who is both not calm and not patient is either not happy or not generous and vice versa. Everyone who is funny or not rich is not old or strong and vice versa. Everyone who is either not old or strong is strong. Everyone who is strong or happy is kind. Everyone who is either rich or not calm is either not rich or old and vice versa. Everyone who is either not strong or generous is humble and vice versa. Lucy is not kind. Someone is either generous or tall. Someone is both rich and curious. Someone is wise or not old. Mary is calm or not tall. Someone is calm or creative. Paul is not quiet or not strong. | Mary is happy. | neutral | (![X]:(~kind(X)<=>(~calm(X)<~>brave(X))))&
(![X]:(~patient(X)<=>(~strong(X)|~wise(X))))&
(((~quiet(paul)<~>~strong(paul)))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((~funny(X)|old(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((~funny(john)<~>rich(john))))&
((~funny(fred))<=>((~humble(susan)|~wise(susan))))&
(![X]:((creative(X)|~rich(X))=>(~kind(X)&~humble(X))))&
(((wise(john)<~>~tall(john)))=>(?[X]:((kind(X)<~>~creative(X)))))&
((~curious(paul))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:((~quiet(X)|~patient(X))))<=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~calm(X)&~patient(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((funny(X)|~rich(X))<=>(~old(X)|strong(X))))&
(![X]:((~old(X)<~>strong(X))=>strong(X)))&
(![X]:((strong(X)|happy(X))=>kind(X)))&
(![X]:((rich(X)<~>~calm(X))<=>(~rich(X)<~>old(X))))&
(![X]:((~strong(X)<~>generous(X))<=>humble(X)))&
(~kind(lucy))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((calm(mary)|~tall(mary)))&
(?[X]:((calm(X)|creative(X))))&
((~quiet(paul)|~strong(paul))) | happy(mary) | [] | null | 0 |
If someone is either not kind or funny then someone is both not tall and funny.
If john is not funny then someone is rich or not tall.
If mary is kind or old then fred is not patient or quiet and vice versa.
If fred is both creative and not quiet then susan is not strong or not funny.
Everyone who is either not curious or not tall is either not kind or not creative.
If someone is both not quiet and patient then paul is quiet or creative and vice versa.
Everyone who is either not rich or not quiet is either not strong or happy and vice versa.
Everyone who is not happy is brave.
Everyone who is both old and not old is strong or curious and vice versa.
If someone is both happy and not calm then alice is quiet and vice versa.
Everyone who is wise is both curious and not rich.
Everyone who is both old and humble is both quiet and not tall and vice versa.
Everyone who is either not humble or not happy is both not humble and strong and vice versa.
Everyone who is both patient and not curious is both not curious and patient.
Everyone who is strong is both old and wise and vice versa.
If john is both brave and not quiet then paul is not kind.
Mary is quiet.
Lucy is either patient or not wise.
Mary is either not curious or kind.
Someone is both happy and brave.
Lucy is not strong.
Someone is calm or not strong.
Alice is not funny. | Alice is not wise. | entailment | ((?[X]:((~kind(X)<~>funny(X))))=>(?[X]:((~tall(X)&funny(X)))))&
((~funny(john))=>(?[X]:((rich(X)|~tall(X)))))&
(((kind(mary)|old(mary)))<=>((~patient(fred)|quiet(fred))))&
(((creative(fred)&~quiet(fred)))=>((~strong(susan)|~funny(susan))))&
(![X]:((~curious(X)<~>~tall(X))=>(~kind(X)<~>~creative(X))))&
((?[X]:((~quiet(X)&patient(X))))<=>((quiet(paul)|creative(paul))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~strong(X)<~>happy(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((old(X)&~old(X))<=>(strong(X)|curious(X))))&
((?[X]:((happy(X)&~calm(X))))<=>(quiet(alice)))&
(![X]:(wise(X)=>(curious(X)&~rich(X))))&
(![X]:((old(X)&humble(X))<=>(quiet(X)&~tall(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~humble(X)&strong(X))))&
(![X]:((patient(X)&~curious(X))=>(~curious(X)&patient(X))))&
(![X]:(strong(X)<=>(old(X)&wise(X))))&
(((brave(john)&~quiet(john)))=>(~kind(paul)))&
(quiet(mary))&
((patient(lucy)<~>~wise(lucy)))&
((~curious(mary)<~>kind(mary)))&
(?[X]:((happy(X)&brave(X))))&
(~strong(lucy))&
(?[X]:((calm(X)|~strong(X))))&
(~funny(alice)) | ~wise(alice) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4916642649417139201830687
% SZS output start Proof for 4916642649417139201830687
9. ! [X0] : ((~old(X0) & old(X0)) <=> (curious(X0) | strong(X0))) [input p8]
11. ! [X0] : (wise(X0) => (~rich(X0) & curious(X0))) [input p10]
24. wise(alice) [input hypothesis]
32. ! [X0] : ((~rich(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 11]
52. ! [X0] : (((~old(X0) & old(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (old(X0) | ~old(X0)))) [nnf transformation 9]
53. ! [X0] : (((~old(X0) & old(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | old(X0) | ~old(X0))) [flattening 52]
100. old(X0) | ~curious(X0) [cnf transformation 53]
102. ~old(X0) | ~curious(X0) [cnf transformation 53]
106. curious(X0) | ~wise(X0) [cnf transformation 32]
134. wise(alice) [cnf transformation 24]
225. ~curious(X0) [subsumption resolution 100,102]
245. ~wise(X0) [subsumption resolution 106,225]
264. $false [subsumption resolution 134,245]
% SZS output end Proof for 4916642649417139201830687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either happy or not creative and vice versa. If alice is either strong or not happy then someone is not generous. If someone is patient then someone is old. Everyone who is either humble or brave is kind or not generous. Everyone who is wise or not brave is either not tall or wise and vice versa. If someone is either not kind or rich then someone is not patient or calm and vice versa. If someone is strong then mary is not funny or not creative. If someone is calm then someone is not generous and vice versa. Everyone who is both strong and not calm is curious. Everyone who is not wise is kind and vice versa. Everyone who is curious or not strong is either strong or patient. Everyone who is quiet is not funny and vice versa. Everyone who is either creative or wise is not calm. If someone is either not patient or creative then lucy is not wise or not curious and vice versa. If mary is either not creative or not calm then someone is both not generous and not wise. If someone is patient then someone is not generous or patient. Alice is not kind or not rich. Paul is both tall and rich. Someone is not funny or not curious. Someone is tall or rich. Someone is not humble or humble. Someone is old. Someone is not kind. Someone is both not creative and funny. | Paul is not patient. | neutral | (![X]:((quiet(X)<~>calm(X))<=>(happy(X)<~>~creative(X))))&
(((strong(alice)<~>~happy(alice)))=>(?[X]:(~generous(X))))&
((?[X]:(patient(X)))=>(?[X]:(old(X))))&
(![X]:((humble(X)<~>brave(X))=>(kind(X)|~generous(X))))&
(![X]:((wise(X)|~brave(X))<=>(~tall(X)<~>wise(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:(strong(X)))=>((~funny(mary)|~creative(mary))))&
((?[X]:(calm(X)))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)&~calm(X))=>curious(X)))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((curious(X)|~strong(X))=>(strong(X)<~>patient(X))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:((creative(X)<~>wise(X))=>~calm(X)))&
((?[X]:((~patient(X)<~>creative(X))))<=>((~wise(lucy)|~curious(lucy))))&
(((~creative(mary)<~>~calm(mary)))=>(?[X]:((~generous(X)&~wise(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~generous(X)|patient(X)))))&
((~kind(alice)|~rich(alice)))&
((tall(paul)&rich(paul)))&
(?[X]:((~funny(X)|~curious(X))))&
(?[X]:((tall(X)|rich(X))))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:(old(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~creative(X)&funny(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is not creative is generous or not rich and vice versa.
If john is not quiet then paul is curious and vice versa.
If someone is both not patient and not quiet then someone is either not kind or not calm and vice versa.
Everyone who is not generous is not humble.
If someone is rich or not funny then alice is not happy.
Everyone who is both patient and not humble is not curious or not creative.
Everyone who is both not tall and not happy is both old and not happy and vice versa.
Everyone who is both not old and not calm is calm and vice versa.
If susan is strong then alice is not patient and vice versa.
Everyone who is either not humble or not patient is quiet or tall and vice versa.
If susan is not quiet then someone is both not funny and not creative.
Everyone who is old is both funny and brave and vice versa.
If someone is either patient or not calm then mary is both creative and not brave and vice versa.
Everyone who is both not generous and rich is not brave.
Everyone who is not old is both not rich and happy.
If john is strong or quiet then mary is both kind and old and vice versa.
Someone is either creative or strong.
Someone is either funny or not patient.
Paul is not creative.
Paul is rich.
Someone is both not wise and generous. | Susan is creative. | contradiction | (![X]:(~creative(X)<=>(generous(X)|~rich(X))))&
((~quiet(john))<=>(curious(paul)))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~generous(X)=>~humble(X)))&
((?[X]:((rich(X)|~funny(X))))=>(~happy(alice)))&
(![X]:((patient(X)&~humble(X))=>(~curious(X)|~creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>(old(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>calm(X)))&
((strong(susan))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~patient(X))<=>(quiet(X)|tall(X))))&
((~quiet(susan))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(old(X)<=>(funny(X)&brave(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((creative(mary)&~brave(mary))))&
(![X]:((~generous(X)&rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~rich(X)&happy(X))))&
(((strong(john)|quiet(john)))<=>((kind(mary)&old(mary))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(~creative(paul))&
(rich(paul))&
(?[X]:((~wise(X)&generous(X)))) | creative(susan) | [
"p0",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5669743191583025658307169
% SZS output start Proof for 5669743191583025658307169
1. ! [X0] : (~creative(X0) <=> (~rich(X0) | generous(X0))) [input p0]
8. ! [X0] : ((~calm(X0) & ~old(X0)) <=> calm(X0)) [input p7]
12. ! [X0] : (old(X0) <=> (brave(X0) & funny(X0))) [input p11]
14. ! [X0] : ((rich(X0) & ~generous(X0)) => ~brave(X0)) [input p13]
22. creative(susan) [input hypothesis]
30. ! [X0] : (~brave(X0) | (~rich(X0) | generous(X0))) [ennf transformation 14]
31. ! [X0] : (~brave(X0) | ~rich(X0) | generous(X0)) [flattening 30]
33. ! [X0] : ((~creative(X0) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | creative(X0))) [nnf transformation 1]
34. ! [X0] : ((~creative(X0) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | creative(X0))) [flattening 33]
43. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | old(X0)))) [nnf transformation 8]
44. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | old(X0))) [flattening 43]
50. ! [X0] : ((old(X0) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | ~old(X0))) [nnf transformation 12]
51. ! [X0] : ((old(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | ~old(X0))) [flattening 50]
68. ~generous(X0) | ~creative(X0) [cnf transformation 34]
69. ~creative(X0) | rich(X0) [cnf transformation 34]
86. calm(X0) | calm(X0) | old(X0) [cnf transformation 44]
88. ~calm(X0) | ~calm(X0) [cnf transformation 44]
100. brave(X0) | ~old(X0) [cnf transformation 51]
108. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 31]
123. creative(susan) [cnf transformation 22]
124. calm(X0) | old(X0) [duplicate literal removal 86]
125. ~calm(X0) [duplicate literal removal 88]
179. old(X0) [subsumption resolution 124,125]
204. brave(X0) [subsumption resolution 100,179]
209. ~rich(X0) | generous(X0) [subsumption resolution 108,204]
241. rich(susan) [resolution 69,123]
244. generous(susan) [resolution 209,241]
250. ~creative(susan) [resolution 244,68]
251. $false [subsumption resolution 250,123]
% SZS output end Proof for 5669743191583025658307169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both old and not brave then someone is both happy and not funny.
Everyone who is not rich is either calm or creative and vice versa.
Everyone who is either old or not patient is either not funny or calm.
Everyone who is either not happy or not kind is not rich or not old.
Everyone who is either not calm or not humble is humble or not wise.
If lucy is both strong and not quiet then paul is not humble or rich.
Everyone who is either not funny or not curious is not kind or tall and vice versa.
Everyone who is old or creative is old and vice versa.
Everyone who is both kind and not curious is not patient and vice versa.
If fred is either funny or not old then someone is not patient and vice versa.
Everyone who is either quiet or not funny is both not brave and quiet.
Everyone who is either not happy or happy is either wise or happy and vice versa.
Everyone who is both strong and not kind is both not kind and wise and vice versa.
Everyone who is old is both not rich and not happy.
Everyone who is either not curious or happy is not happy or happy and vice versa.
If someone is both not patient and not calm then someone is both generous and not funny.
Paul is both not old and kind.
Alice is not patient.
Lucy is curious.
Someone is either rich or old.
Mary is wise or humble.
Fred is funny.
Mary is not tall or generous.
Mary is either kind or not kind. | Fred is curious. | contradiction | (((old(alice)&~brave(alice)))=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(~rich(X)<=>(calm(X)<~>creative(X))))&
(![X]:((old(X)<~>~patient(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~kind(X))=>(~rich(X)|~old(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(humble(X)|~wise(X))))&
(((strong(lucy)&~quiet(lucy)))=>((~humble(paul)|rich(paul))))&
(![X]:((~funny(X)<~>~curious(X))<=>(~kind(X)|tall(X))))&
(![X]:((old(X)|creative(X))<=>old(X)))&
(![X]:((kind(X)&~curious(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(~brave(X)&quiet(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(wise(X)<~>happy(X))))&
(![X]:((strong(X)&~kind(X))<=>(~kind(X)&wise(X))))&
(![X]:(old(X)=>(~rich(X)&~happy(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(~happy(X)|happy(X))))&
((?[X]:((~patient(X)&~calm(X))))=>(?[X]:((generous(X)&~funny(X)))))&
((~old(paul)&kind(paul)))&
(~patient(alice))&
(curious(lucy))&
(?[X]:((rich(X)<~>old(X))))&
((wise(mary)|humble(mary)))&
(funny(fred))&
((~tall(mary)|generous(mary)))&
((kind(mary)<~>~kind(mary))) | curious(fred) | [
"p9",
"p13",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5821787596612916726433990
% SZS output start Proof for 5821787596612916726433990
10. (funny(fred) <~> ~old(fred)) <=> ? [X0] : ~patient(X0) [input p9]
14. ! [X0] : (old(X0) => (~happy(X0) & ~rich(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (happy(X0) | ~happy(X0))) [input p14]
18. ~patient(alice) [input p17]
22. funny(fred) [input p21]
25. curious(fred) [input hypothesis]
39. ! [X0] : ((~happy(X0) & ~rich(X0)) | ~old(X0)) [ennf transformation 14]
53. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [nnf transformation 10]
54. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [rectify 53]
55. ? [X1] : ~patient(X1) => ~patient(sK1) [choice axiom]
56. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (~patient(sK1) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [skolemisation 54,55]
61. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 61]
100. old(fred) | ~funny(fred) | patient(X0) [cnf transformation 56]
118. ~happy(X0) | ~old(X0) [cnf transformation 39]
121. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 62]
128. ~patient(alice) [cnf transformation 18]
133. funny(fred) [cnf transformation 22]
136. curious(fred) [cnf transformation 25]
139. ~curious(X0) | happy(X0) [duplicate literal removal 121]
187. 9 <=> ! [X0] : patient(X0) [avatar definition]
188. patient(X0) <- (9) [avatar component clause 187]
190. 10 <=> funny(fred) [avatar definition]
194. 11 <=> old(fred) [avatar definition]
196. old(fred) <- (11) [avatar component clause 194]
197. 9 | ~10 | 11 [avatar split clause 100,194,190,187]
231. 10 [avatar split clause 133,190]
232. $false <- (9) [resolution 188,128]
233. ~9 [avatar contradiction clause 232]
239. happy(fred) [resolution 139,136]
243. ~old(fred) [resolution 239,118]
244. $false <- (11) [subsumption resolution 243,196]
245. ~11 [avatar contradiction clause 244]
246. $false [avatar sat refutation 197,231,233,245]
% SZS output end Proof for 5821787596612916726433990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not brave is either not wise or generous.
If someone is not strong then alice is generous or rich and vice versa.
Everyone who is not calm or not generous is both not wise and happy.
Everyone who is either not rich or not tall is both happy and not kind.
If someone is either wise or calm then lucy is both quiet and not quiet and vice versa.
Everyone who is creative or curious is both kind and not curious.
If someone is not wise then fred is calm.
If someone is not rich or not curious then alice is not kind.
Everyone who is quiet or not old is happy or not old and vice versa.
If alice is either not curious or not calm then fred is either not curious or not kind and vice versa.
If someone is happy or not curious then alice is either not kind or not wise.
If someone is calm then someone is wise or not wise.
Everyone who is not patient or not kind is either quiet or happy.
If someone is either calm or humble then someone is happy.
Everyone who is not tall is curious or not strong.
Everyone who is not quiet or not generous is both patient and kind and vice versa.
Paul is rich.
Someone is both quiet and not kind.
Someone is both not brave and rich.
Lucy is not kind.
Someone is not wise or not calm.
Someone is kind or not generous.
Mary is both funny and kind.
Someone is both wise and calm. | Fred is kind. | entailment | (![X]:((curious(X)|~brave(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(~strong(X)))<=>((generous(alice)|rich(alice))))&
(![X]:((~calm(X)|~generous(X))=>(~wise(X)&happy(X))))&
(![X]:((~rich(X)<~>~tall(X))=>(happy(X)&~kind(X))))&
((?[X]:((wise(X)<~>calm(X))))<=>((quiet(lucy)&~quiet(lucy))))&
(![X]:((creative(X)|curious(X))=>(kind(X)&~curious(X))))&
((?[X]:(~wise(X)))=>(calm(fred)))&
((?[X]:((~rich(X)|~curious(X))))=>(~kind(alice)))&
(![X]:((quiet(X)|~old(X))<=>(happy(X)|~old(X))))&
(((~curious(alice)<~>~calm(alice)))<=>((~curious(fred)<~>~kind(fred))))&
((?[X]:((happy(X)|~curious(X))))=>((~kind(alice)<~>~wise(alice))))&
((?[X]:(calm(X)))=>(?[X]:((wise(X)|~wise(X)))))&
(![X]:((~patient(X)|~kind(X))=>(quiet(X)<~>happy(X))))&
((?[X]:((calm(X)<~>humble(X))))=>(?[X]:(happy(X))))&
(![X]:(~tall(X)=>(curious(X)|~strong(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(patient(X)&kind(X))))&
(rich(paul))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~brave(X)&rich(X))))&
(~kind(lucy))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((kind(X)|~generous(X))))&
((funny(mary)&kind(mary)))&
(?[X]:((wise(X)&calm(X)))) | kind(fred) | [
"p2",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 297545387891771304840298
% SZS output start Proof for 297545387891771304840298
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => (happy(X0) & ~wise(X0))) [input p2]
6. ! [X0] : ((curious(X0) | creative(X0)) => (~curious(X0) & kind(X0))) [input p5]
8. ? [X0] : (~curious(X0) | ~rich(X0)) => ~kind(alice) [input p7]
10. (~curious(alice) <~> ~calm(alice)) <=> (~curious(fred) <~> ~kind(fred)) [input p9]
11. ? [X0] : (~curious(X0) | happy(X0)) => (~kind(alice) <~> ~wise(alice)) [input p10]
25. ~kind(fred) [input hypothesis]
29. ! [X0] : (curious(X0) => (~curious(X0) & kind(X0))) [pure predicate removal 6]
31. ! [X0] : ((happy(X0) & ~wise(X0)) | (generous(X0) & calm(X0))) [ennf transformation 3]
33. ! [X0] : ((~curious(X0) & kind(X0)) | ~curious(X0)) [ennf transformation 29]
35. ~kind(alice) | ! [X0] : (curious(X0) & rich(X0)) [ennf transformation 8]
36. (~kind(alice) <~> ~wise(alice)) | ! [X0] : (curious(X0) & ~happy(X0)) [ennf transformation 11]
56. (((calm(alice) | curious(alice)) & (~calm(alice) | ~curious(alice))) | ((~curious(fred) | kind(fred)) & (~kind(fred) | curious(fred)))) & (((kind(fred) | curious(fred)) & (~kind(fred) | ~curious(fred))) | ((~curious(alice) | calm(alice)) & (~calm(alice) | curious(alice)))) [nnf transformation 10]
57. ((wise(alice) | kind(alice)) & (~wise(alice) | ~kind(alice))) | ! [X0] : (curious(X0) & ~happy(X0)) [nnf transformation 36]
85. ~wise(X0) | calm(X0) [cnf transformation 31]
100. ~curious(X0) | ~curious(X0) [cnf transformation 33]
103. ~kind(alice) | curious(X0) [cnf transformation 35]
110. kind(fred) | curious(fred) | ~calm(alice) | curious(alice) [cnf transformation 56]
119. wise(alice) | kind(alice) | curious(X0) [cnf transformation 57]
144. ~kind(fred) [cnf transformation 25]
145. ~curious(X0) [duplicate literal removal 100]
181. ~kind(alice) [subsumption resolution 103,145]
185. 9 <=> kind(fred) [avatar definition]
189. 10 <=> calm(alice) [avatar definition]
190. ~calm(alice) <- (~10) [avatar component clause 189]
193. kind(fred) | ~calm(alice) | curious(alice) [subsumption resolution 110,145]
194. kind(fred) | ~calm(alice) [subsumption resolution 193,145]
195. ~10 | 9 [avatar split clause 194,185,189]
196. wise(alice) | curious(X0) [subsumption resolution 119,181]
197. wise(alice) [subsumption resolution 196,145]
213. ~9 [avatar split clause 144,185]
217. calm(alice) [resolution 85,197]
218. $false <- (~10) [subsumption resolution 217,190]
219. 10 [avatar contradiction clause 218]
220. $false [avatar sat refutation 195,213,219]
% SZS output end Proof for 297545387891771304840298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not curious is not old or calm and vice versa.
Everyone who is either not humble or brave is not curious and vice versa.
If mary is either rich or not brave then someone is either quiet or not rich and vice versa.
Everyone who is either curious or funny is calm.
If someone is either curious or not funny then john is calm.
If alice is not strong then alice is not creative or creative and vice versa.
Everyone who is both not tall and rich is either not happy or brave and vice versa.
If john is not funny then fred is either not humble or wise and vice versa.
If john is either not calm or not wise then lucy is calm and vice versa.
Everyone who is both humble and not creative is curious or happy.
Everyone who is funny or not humble is either not generous or not rich and vice versa.
Everyone who is not calm or old is not wise or patient.
Everyone who is not funny is either not patient or not quiet and vice versa.
If alice is curious then mary is strong and vice versa.
If someone is both not happy and not humble then someone is not creative or kind.
Everyone who is either humble or happy is kind and vice versa.
Someone is curious or not happy.
Mary is both brave and not wise.
Susan is happy.
Someone is not creative or not happy.
Alice is not patient.
Paul is either not funny or not patient.
Someone is not old. | Paul is brave. | neutral | (![X]:((old(X)<~>~curious(X))<=>(~old(X)|calm(X))))&
(![X]:((~humble(X)<~>brave(X))<=>~curious(X)))&
(((rich(mary)<~>~brave(mary)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((curious(X)<~>funny(X))=>calm(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>(calm(john)))&
((~strong(alice))<=>((~creative(alice)|creative(alice))))&
(![X]:((~tall(X)&rich(X))<=>(~happy(X)<~>brave(X))))&
((~funny(john))<=>((~humble(fred)<~>wise(fred))))&
(((~calm(john)<~>~wise(john)))<=>(calm(lucy)))&
(![X]:((humble(X)&~creative(X))=>(curious(X)|happy(X))))&
(![X]:((funny(X)|~humble(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)|patient(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~quiet(X))))&
((curious(alice))<=>(strong(mary)))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((humble(X)<~>happy(X))<=>kind(X)))&
(?[X]:((curious(X)|~happy(X))))&
((brave(mary)&~wise(mary)))&
(happy(susan))&
(?[X]:((~creative(X)|~happy(X))))&
(~patient(alice))&
((~funny(paul)<~>~patient(paul)))&
(?[X]:(~old(X))) | brave(paul) | [] | null | 0 |
Everyone who is quiet or not strong is patient. If john is humble or not rich then someone is either not happy or not curious. Everyone who is not generous is generous. Everyone who is rich or not creative is both brave and creative. Everyone who is not wise or strong is either kind or not funny. If someone is either not patient or rich then mary is both quiet and not calm and vice versa. If paul is not tall then fred is either rich or not brave and vice versa. Everyone who is either not rich or quiet is either rich or wise. If mary is both brave and generous then someone is either generous or humble. If lucy is not rich then mary is either not brave or not creative. Everyone who is both strong and generous is not strong or funny. Everyone who is not old is either brave or humble and vice versa. Everyone who is not brave is kind. Everyone who is not rich is either not wise or not strong and vice versa. If someone is either creative or not tall then someone is not calm or humble. Everyone who is humble or generous is quiet. Fred is both curious and happy. Someone is both old and not happy. Paul is not happy. Someone is both curious and creative. Someone is either funny or generous. Lucy is both kind and not rich. | Paul is patient. | entailment | (![X]:((quiet(X)|~strong(X))=>patient(X)))&
(((humble(john)|~rich(john)))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:((rich(X)|~creative(X))=>(brave(X)&creative(X))))&
(![X]:((~wise(X)|strong(X))=>(kind(X)<~>~funny(X))))&
((?[X]:((~patient(X)<~>rich(X))))<=>((quiet(mary)&~calm(mary))))&
((~tall(paul))<=>((rich(fred)<~>~brave(fred))))&
(![X]:((~rich(X)<~>quiet(X))=>(rich(X)<~>wise(X))))&
(((brave(mary)&generous(mary)))=>(?[X]:((generous(X)<~>humble(X)))))&
((~rich(lucy))=>((~brave(mary)<~>~creative(mary))))&
(![X]:((strong(X)&generous(X))=>(~strong(X)|funny(X))))&
(![X]:(~old(X)<=>(brave(X)<~>humble(X))))&
(![X]:(~brave(X)=>kind(X)))&
(![X]:(~rich(X)<=>(~wise(X)<~>~strong(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((humble(X)|generous(X))=>quiet(X)))&
((curious(fred)&happy(fred)))&
(?[X]:((old(X)&~happy(X))))&
(~happy(paul))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:((funny(X)<~>generous(X))))&
((kind(lucy)&~rich(lucy))) | patient(paul) | [
"p0",
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4506817565090815793309110
% SZS output start Proof for 4506817565090815793309110
1. ! [X0] : ((~strong(X0) | quiet(X0)) => patient(X0)) [input p0]
3. ! [X0] : (~generous(X0) => generous(X0)) [input p2]
16. ! [X0] : ((generous(X0) | humble(X0)) => quiet(X0)) [input p15]
23. ~patient(paul) [input hypothesis]
26. ! [X0] : (patient(X0) | (strong(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 3]
40. ! [X0] : (quiet(X0) | (~generous(X0) & ~humble(X0))) [ennf transformation 16]
69. ~quiet(X0) | patient(X0) [cnf transformation 26]
75. generous(X0) | generous(X0) [cnf transformation 28]
113. quiet(X0) | ~generous(X0) [cnf transformation 40]
125. ~patient(paul) [cnf transformation 23]
130. generous(X0) [duplicate literal removal 75]
227. quiet(X0) [subsumption resolution 113,130]
230. patient(X0) [resolution 69,227]
233. $false [resolution 230,125]
% SZS output end Proof for 4506817565090815793309110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not calm is not patient and vice versa. Everyone who is kind is both wise and not funny and vice versa. Everyone who is not quiet or not wise is not strong. Everyone who is both not calm and not kind is kind and vice versa. Everyone who is either strong or not humble is patient or wise. If lucy is not patient then someone is not kind and vice versa. Everyone who is patient or generous is both not generous and not curious and vice versa. If john is rich or strong then someone is not humble or tall and vice versa. Everyone who is either creative or patient is not brave or not creative and vice versa. If fred is either not brave or brave then someone is either funny or not creative and vice versa. Everyone who is both curious and not tall is not wise. If lucy is brave or kind then someone is not old. If mary is both humble and not generous then someone is both not kind and not strong. Everyone who is either creative or funny is not calm or rich. Everyone who is both not rich and wise is either generous or not calm and vice versa. Someone is curious. John is both funny and brave. Mary is not brave or kind. Paul is not quiet. Someone is quiet or not kind. Susan is both not old and strong. Alice is not calm or not old. | Susan is not kind. | entailment | (![X]:((~brave(X)<~>~calm(X))<=>~patient(X)))&
(![X]:(kind(X)<=>(wise(X)&~funny(X))))&
(![X]:((~quiet(X)|~wise(X))=>~strong(X)))&
(![X]:((~calm(X)&~kind(X))<=>kind(X)))&
(![X]:((strong(X)<~>~humble(X))=>(patient(X)|wise(X))))&
((~patient(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((patient(X)|generous(X))<=>(~generous(X)&~curious(X))))&
(((rich(john)|strong(john)))<=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((creative(X)<~>patient(X))<=>(~brave(X)|~creative(X))))&
(((~brave(fred)<~>brave(fred)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((curious(X)&~tall(X))=>~wise(X)))&
(((brave(lucy)|kind(lucy)))=>(?[X]:(~old(X))))&
(((humble(mary)&~generous(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((creative(X)<~>funny(X))=>(~calm(X)|rich(X))))&
(![X]:((~rich(X)&wise(X))<=>(generous(X)<~>~calm(X))))&
(?[X]:(curious(X)))&
((funny(john)&brave(john)))&
((~brave(mary)|kind(mary)))&
(~quiet(paul))&
(?[X]:((quiet(X)|~kind(X))))&
((~old(susan)&strong(susan)))&
((~calm(alice)|~old(alice))) | ~kind(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2758302498525160918727890
% SZS output start Proof for 2758302498525160918727890
4. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> kind(X0)) [input p3]
23. kind(susan) [input hypothesis]
39. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | calm(X0))) [flattening 39]
79. ~kind(X0) | ~kind(X0) [cnf transformation 40]
125. kind(susan) [cnf transformation 23]
135. ~kind(X0) [duplicate literal removal 79]
197. $false [subsumption resolution 125,135]
% SZS output end Proof for 2758302498525160918727890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then fred is either quiet or wise and vice versa.
Everyone who is either not humble or not tall is both not wise and not tall.
Everyone who is wise is not patient or curious and vice versa.
If someone is either curious or not kind then alice is both creative and not tall.
If john is kind then someone is wise.
Everyone who is both not creative and quiet is either not calm or not kind.
If someone is both not kind and kind then mary is calm.
Everyone who is either not quiet or not old is humble and vice versa.
If someone is generous then lucy is either brave or not patient and vice versa.
Everyone who is rich or not brave is calm or not strong.
If fred is both generous and not tall then susan is not brave or not rich.
If someone is either not happy or not old then susan is both patient and brave and vice versa.
If someone is tall or not creative then someone is brave or not tall and vice versa.
Everyone who is old is tall and vice versa.
If someone is both wise and happy then someone is not generous or strong and vice versa.
Everyone who is humble or generous is either happy or not creative.
Someone is both not happy and not quiet.
Someone is not old or rich.
Fred is either not generous or brave.
Lucy is not humble or tall.
Someone is both rich and not humble.
Someone is brave.
Alice is old or quiet. | Alice is humble. | entailment | ((?[X]:(wise(X)))<=>((quiet(fred)<~>wise(fred))))&
(![X]:((~humble(X)<~>~tall(X))=>(~wise(X)&~tall(X))))&
(![X]:(wise(X)<=>(~patient(X)|curious(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>((creative(alice)&~tall(alice))))&
((kind(john))=>(?[X]:(wise(X))))&
(![X]:((~creative(X)&quiet(X))=>(~calm(X)<~>~kind(X))))&
((?[X]:((~kind(X)&kind(X))))=>(calm(mary)))&
(![X]:((~quiet(X)<~>~old(X))<=>humble(X)))&
((?[X]:(generous(X)))<=>((brave(lucy)<~>~patient(lucy))))&
(![X]:((rich(X)|~brave(X))=>(calm(X)|~strong(X))))&
(((generous(fred)&~tall(fred)))=>((~brave(susan)|~rich(susan))))&
((?[X]:((~happy(X)<~>~old(X))))<=>((patient(susan)&brave(susan))))&
((?[X]:((tall(X)|~creative(X))))<=>(?[X]:((brave(X)|~tall(X)))))&
(![X]:(old(X)<=>tall(X)))&
((?[X]:((wise(X)&happy(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((humble(X)|generous(X))=>(happy(X)<~>~creative(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
(?[X]:((~old(X)|rich(X))))&
((~generous(fred)<~>brave(fred)))&
((~humble(lucy)|tall(lucy)))&
(?[X]:((rich(X)&~humble(X))))&
(?[X]:(brave(X)))&
((old(alice)|quiet(alice))) | humble(alice) | [
"p1",
"p7",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 733199593415387305420444
% SZS output start Proof for 733199593415387305420444
2. ! [X0] : ((~humble(X0) <~> ~tall(X0)) => (~tall(X0) & ~wise(X0))) [input p1]
8. ! [X0] : ((~quiet(X0) <~> ~old(X0)) <=> humble(X0)) [input p7]
14. ! [X0] : (old(X0) <=> tall(X0)) [input p13]
23. quiet(alice) | old(alice) [input p22]
24. ~humble(alice) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~wise(X0)) | (~humble(X0) <=> ~tall(X0))) [ennf transformation 2]
42. ! [X0] : ((~tall(X0) & ~wise(X0)) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) [nnf transformation 27]
49. ! [X0] : ((((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | ~humble(X0)) & (humble(X0) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0))))) [nnf transformation 8]
64. ! [X0] : ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0))) [nnf transformation 14]
86. ~tall(X0) | ~tall(X0) | humble(X0) [cnf transformation 42]
100. ~quiet(X0) | humble(X0) | old(X0) [cnf transformation 49]
120. ~old(X0) | tall(X0) [cnf transformation 64]
140. quiet(alice) | old(alice) [cnf transformation 23]
141. ~humble(alice) [cnf transformation 24]
142. ~tall(X0) | humble(X0) [duplicate literal removal 86]
166. 6 <=> tall(alice) [avatar definition]
167. tall(alice) <- (6) [avatar component clause 166]
336. 44 <=> old(alice) [avatar definition]
338. old(alice) <- (44) [avatar component clause 336]
340. 45 <=> quiet(alice) [avatar definition]
342. quiet(alice) <- (45) [avatar component clause 340]
343. 44 | 45 [avatar split clause 140,340,336]
349. tall(alice) <- (44) [resolution 120,338]
350. 6 | ~44 [avatar split clause 349,336,166]
366. humble(alice) | old(alice) <- (45) [resolution 100,342]
376. old(alice) <- (45) [subsumption resolution 366,141]
379. 44 | ~45 [avatar split clause 376,340,336]
380. humble(alice) <- (6) [resolution 167,142]
382. $false <- (6) [subsumption resolution 380,141]
383. ~6 [avatar contradiction clause 382]
384. $false [avatar sat refutation 343,350,379,383]
% SZS output end Proof for 733199593415387305420444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or kind then someone is either happy or not patient and vice versa.
Everyone who is either patient or kind is both calm and not curious.
Everyone who is happy or not kind is not rich.
Everyone who is curious or brave is both calm and brave.
If someone is not calm or not old then fred is not happy.
If john is either not old or wise then someone is either not calm or not quiet.
Everyone who is not humble is both not humble and humble and vice versa.
Everyone who is either not rich or creative is both patient and funny.
If susan is both not calm and not patient then someone is either old or not curious and vice versa.
If someone is generous then susan is funny.
If lucy is both not tall and creative then someone is strong or tall.
If someone is either not kind or humble then someone is both old and quiet and vice versa.
If john is either funny or curious then alice is not rich and vice versa.
Everyone who is calm or not old is both not strong and strong and vice versa.
Everyone who is not generous is not tall or quiet and vice versa.
If someone is either curious or not kind then lucy is quiet or funny.
Paul is patient or not calm.
Someone is not rich.
Someone is not curious.
Paul is brave or not curious.
Alice is both not funny and wise.
Lucy is tall or happy.
Someone is creative or not funny.
Mary is either brave or not tall. | Alice is old. | entailment | (((~wise(mary)|kind(mary)))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((patient(X)<~>kind(X))=>(calm(X)&~curious(X))))&
(![X]:((happy(X)|~kind(X))=>~rich(X)))&
(![X]:((curious(X)|brave(X))=>(calm(X)&brave(X))))&
((?[X]:((~calm(X)|~old(X))))=>(~happy(fred)))&
(((~old(john)<~>wise(john)))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(patient(X)&funny(X))))&
(((~calm(susan)&~patient(susan)))<=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:(generous(X)))=>(funny(susan)))&
(((~tall(lucy)&creative(lucy)))=>(?[X]:((strong(X)|tall(X)))))&
((?[X]:((~kind(X)<~>humble(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(((funny(john)<~>curious(john)))<=>(~rich(alice)))&
(![X]:((calm(X)|~old(X))<=>(~strong(X)&strong(X))))&
(![X]:(~generous(X)<=>(~tall(X)|quiet(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>((quiet(lucy)|funny(lucy))))&
((patient(paul)|~calm(paul)))&
(?[X]:(~rich(X)))&
(?[X]:(~curious(X)))&
((brave(paul)|~curious(paul)))&
((~funny(alice)&wise(alice)))&
((tall(lucy)|happy(lucy)))&
(?[X]:((creative(X)|~funny(X))))&
((brave(mary)<~>~tall(mary))) | old(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6985324087896082423991545
% SZS output start Proof for 6985324087896082423991545
14. ! [X0] : ((~old(X0) | calm(X0)) <=> (strong(X0) & ~strong(X0))) [input p13]
25. ~old(alice) [input hypothesis]
66. ! [X0] : (((~old(X0) | calm(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (old(X0) & ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : ((~old(X0) | calm(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (old(X0) & ~calm(X0)))) [flattening 66]
124. ~strong(X0) | old(X0) [cnf transformation 67]
126. strong(X0) | old(X0) [cnf transformation 67]
141. ~old(alice) [cnf transformation 25]
173. 7 <=> ! [X0] : old(X0) [avatar definition]
174. old(X0) <- (7) [avatar component clause 173]
297. old(X0) [subsumption resolution 124,126]
298. 7 [avatar split clause 297,173]
340. $false <- (7) [resolution 174,141]
341. ~7 [avatar contradiction clause 340]
342. $false [avatar sat refutation 298,341]
% SZS output end Proof for 6985324087896082423991545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not happy is patient or not quiet.
Everyone who is not tall is patient or tall.
Everyone who is either quiet or generous is both not rich and not funny.
Everyone who is either not strong or patient is humble or wise and vice versa.
If lucy is both quiet and not quiet then susan is curious and vice versa.
Everyone who is either not quiet or not tall is either not brave or not creative and vice versa.
If someone is either kind or not brave then someone is patient or kind and vice versa.
If someone is both quiet and not tall then alice is both tall and happy and vice versa.
If susan is either not patient or brave then john is old or strong and vice versa.
Everyone who is not old or not strong is both funny and kind and vice versa.
Everyone who is either not curious or happy is not calm.
Everyone who is not generous is brave or kind and vice versa.
Everyone who is strong or calm is quiet and vice versa.
Everyone who is not generous is humble.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is not calm is not rich and vice versa.
Someone is not wise.
Susan is not strong or generous.
Alice is brave or patient.
John is either wise or not brave.
John is either not patient or not quiet.
Someone is funny or not creative.
John is not brave.
Lucy is not tall. | Lucy is not calm. | entailment | (![X]:((~patient(X)<~>~happy(X))=>(patient(X)|~quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|tall(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)&~funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|wise(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>(curious(susan)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((quiet(X)&~tall(X))))<=>((tall(alice)&happy(alice))))&
(((~patient(susan)<~>brave(susan)))<=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(?[X]:(~wise(X)))&
((~strong(susan)|generous(susan)))&
((brave(alice)|patient(alice)))&
((wise(john)<~>~brave(john)))&
((~patient(john)<~>~quiet(john)))&
(?[X]:((funny(X)|~creative(X))))&
(~brave(john))&
(~tall(lucy)) | ~calm(lucy) | [
"p2",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7982282840672482545891661
% SZS output start Proof for 7982282840672482545891661
3. ! [X0] : ((quiet(X0) <~> generous(X0)) => (~funny(X0) & ~rich(X0))) [input p2]
12. ! [X0] : (~generous(X0) <=> (kind(X0) | brave(X0))) [input p11]
13. ! [X0] : ((calm(X0) | strong(X0)) <=> quiet(X0)) [input p12]
15. ! [X0] : ((generous(X0) & ~rich(X0)) <=> ~kind(X0)) [input p14]
16. ! [X0] : (~calm(X0) <=> ~rich(X0)) [input p15]
25. calm(lucy) [input hypothesis]
31. ! [X0] : ((~funny(X0) & ~rich(X0)) | (quiet(X0) <=> generous(X0))) [ennf transformation 3]
35. ! [X0] : ((~funny(X0) & ~rich(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) [nnf transformation 31]
56. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | generous(X0))) [nnf transformation 12]
57. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | generous(X0))) [flattening 56]
58. ! [X0] : (((calm(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 13]
59. ! [X0] : ((calm(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [flattening 58]
60. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) | rich(X0)))) [nnf transformation 15]
61. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | ~generous(X0) | rich(X0))) [flattening 60]
62. ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))) [nnf transformation 16]
72. ~rich(X0) | generous(X0) | ~quiet(X0) [cnf transformation 35]
118. ~kind(X0) | ~generous(X0) [cnf transformation 57]
120. ~calm(X0) | quiet(X0) [cnf transformation 59]
124. ~rich(X0) | kind(X0) [cnf transformation 61]
127. ~calm(X0) | rich(X0) [cnf transformation 62]
138. calm(lucy) [cnf transformation 25]
146. 2 <=> quiet(lucy) [avatar definition]
147. quiet(lucy) <- (2) [avatar component clause 146]
290. quiet(lucy) [resolution 120,138]
291. 2 [avatar split clause 290,146]
295. rich(lucy) [resolution 127,138]
297. kind(lucy) [resolution 295,124]
300. generous(lucy) | ~quiet(lucy) [resolution 72,295]
301. generous(lucy) <- (2) [subsumption resolution 300,147]
303. ~generous(lucy) [resolution 297,118]
304. $false <- (2) [subsumption resolution 303,301]
305. ~2 [avatar contradiction clause 304]
306. $false [avatar sat refutation 291,305]
% SZS output end Proof for 7982282840672482545891661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not happy then susan is not brave. Everyone who is either brave or not creative is kind and vice versa. Everyone who is both not old and quiet is happy. If lucy is both quiet and not wise then mary is both wise and not patient. Everyone who is creative or humble is either not patient or rich. Everyone who is either not creative or generous is not brave. Everyone who is brave is not calm or humble and vice versa. If fred is either not strong or not wise then paul is both strong and old. Everyone who is old is either not funny or not brave. Everyone who is both not brave and patient is both not wise and brave and vice versa. If someone is not quiet or not brave then someone is both not kind and humble. Everyone who is patient or not tall is either not humble or wise. Everyone who is both kind and not funny is not patient and vice versa. If someone is not calm or patient then paul is generous. Everyone who is either not wise or not strong is either not rich or strong and vice versa. Someone is brave. Mary is either funny or curious. Someone is creative. Someone is not patient or wise. Someone is either happy or not old. Mary is not tall or not kind. | Paul is quiet. | entailment | ((?[X]:((strong(X)&~happy(X))))=>(~brave(susan)))&
(![X]:((brave(X)<~>~creative(X))<=>kind(X)))&
(![X]:((~old(X)&quiet(X))=>happy(X)))&
(((quiet(lucy)&~wise(lucy)))=>((wise(mary)&~patient(mary))))&
(![X]:((creative(X)|humble(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~creative(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)<=>(~calm(X)|humble(X))))&
(((~strong(fred)<~>~wise(fred)))=>((strong(paul)&old(paul))))&
(![X]:(old(X)=>(~funny(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~wise(X)&brave(X))))&
((?[X]:((~quiet(X)|~brave(X))))=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((patient(X)|~tall(X))=>(~humble(X)<~>wise(X))))&
(![X]:((kind(X)&~funny(X))<=>~patient(X)))&
((?[X]:((~calm(X)|patient(X))))=>(generous(paul)))&
(![X]:((~wise(X)<~>~strong(X))<=>(~rich(X)<~>strong(X))))&
(?[X]:(brave(X)))&
((funny(mary)<~>curious(mary)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
((~tall(mary)|~kind(mary))) | quiet(paul) | [
"p4",
"p6",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 211134369680759162341545
% SZS output start Proof for 211134369680759162341545
5. ! [X0] : ((humble(X0) | creative(X0)) => (~patient(X0) <~> rich(X0))) [input p4]
7. ! [X0] : (brave(X0) <=> (humble(X0) | ~calm(X0))) [input p6]
10. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (brave(X0) & ~wise(X0))) [input p9]
11. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X0] : (humble(X0) & ~kind(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & kind(X0)) <=> ~patient(X0)) [input p12]
15. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~rich(X0) <~> strong(X0))) [input p14]
22. ~quiet(paul) [input hypothesis]
23. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X1] : (humble(X1) & ~kind(X1)) [rectify 11]
29. ! [X0] : ((~patient(X0) <~> rich(X0)) | (~humble(X0) & ~creative(X0))) [ennf transformation 5]
33. ? [X1] : (humble(X1) & ~kind(X1)) | ! [X0] : (brave(X0) & quiet(X0)) [ennf transformation 23]
37. ! [X0] : (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~humble(X0) & ~creative(X0))) [nnf transformation 29]
39. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 7]
40. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : (((patient(X0) & ~brave(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 10]
44. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | ~patient(X0) | brave(X0))) [flattening 43]
45. ? [X0] : (humble(X0) & ~kind(X0)) | ! [X1] : (brave(X1) & quiet(X1)) [rectify 33]
46. ? [X0] : (humble(X0) & ~kind(X0)) => (humble(sK0) & ~kind(sK0)) [choice axiom]
47. (humble(sK0) & ~kind(sK0)) | ! [X1] : (brave(X1) & quiet(X1)) [skolemisation 45,46]
49. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | (funny(X0) | ~kind(X0)))) [nnf transformation 13]
50. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | funny(X0) | ~kind(X0))) [flattening 49]
51. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 15]
71. ~humble(X0) | ~patient(X0) | rich(X0) [cnf transformation 37]
78. ~humble(X0) | brave(X0) [cnf transformation 40]
87. ~brave(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
89. ~kind(sK0) | quiet(X1) [cnf transformation 47]
91. humble(sK0) | quiet(X1) [cnf transformation 47]
98. patient(X0) | kind(X0) [cnf transformation 50]
103. strong(X0) | ~rich(X0) | ~wise(X0) | strong(X0) [cnf transformation 51]
107. ~strong(X0) | ~wise(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 51]
118. ~quiet(paul) [cnf transformation 22]
119. strong(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 103]
121. ~strong(X0) | ~wise(X0) | ~rich(X0) [duplicate literal removal 107]
124. ~brave(X0) | wise(X0) [duplicate literal removal 87]
175. 12 <=> humble(sK0) [avatar definition]
177. humble(sK0) <- (12) [avatar component clause 175]
180. 13 <=> ! [X1] : quiet(X1) [avatar definition]
181. quiet(X1) <- (13) [avatar component clause 180]
182. 13 | 12 [avatar split clause 91,175,180]
184. 14 <=> kind(sK0) [avatar definition]
186. ~kind(sK0) <- (~14) [avatar component clause 184]
188. 13 | ~14 [avatar split clause 89,184,180]
202. ~rich(X0) | ~wise(X0) [subsumption resolution 119,121]
241. brave(sK0) <- (12) [resolution 78,177]
248. wise(sK0) <- (12) [resolution 124,241]
291. ~patient(sK0) | rich(sK0) <- (12) [resolution 71,177]
293. 30 <=> rich(sK0) [avatar definition]
295. rich(sK0) <- (30) [avatar component clause 293]
297. 31 <=> patient(sK0) [avatar definition]
299. ~patient(sK0) <- (~31) [avatar component clause 297]
300. 30 | ~31 | ~12 [avatar split clause 291,175,297,293]
301. kind(sK0) <- (~31) [resolution 299,98]
302. $false <- (~14, ~31) [subsumption resolution 301,186]
303. 14 | 31 [avatar contradiction clause 302]
306. ~wise(sK0) <- (30) [resolution 295,202]
307. $false <- (12, 30) [subsumption resolution 306,248]
308. ~12 | ~30 [avatar contradiction clause 307]
314. $false <- (13) [resolution 181,118]
318. ~13 [avatar contradiction clause 314]
319. $false [avatar sat refutation 182,188,300,303,308,318]
% SZS output end Proof for 211134369680759162341545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and kind is not brave or not wise and vice versa.
Everyone who is not strong or tall is not happy or not generous.
Everyone who is both calm and generous is either not funny or creative and vice versa.
Everyone who is not creative is not humble.
Everyone who is both humble and quiet is not generous.
Everyone who is either strong or not happy is either quiet or creative and vice versa.
Everyone who is creative is funny or kind.
If alice is not patient then paul is creative.
If someone is either not rich or patient then someone is kind.
If john is not quiet then paul is strong.
Everyone who is not quiet is either funny or happy.
If someone is funny or humble then someone is either not patient or not rich.
If someone is quiet then mary is creative and vice versa.
Everyone who is creative is not kind or strong.
Everyone who is either not humble or creative is either quiet or not brave and vice versa.
If fred is both not patient and not brave then fred is either humble or tall.
Paul is either calm or not calm.
Someone is happy.
Someone is not patient.
John is not wise or old.
Paul is generous or funny.
Lucy is both happy and not old.
Someone is either not happy or not strong. | Fred is not patient. | neutral | (![X]:((~kind(X)&kind(X))<=>(~brave(X)|~wise(X))))&
(![X]:((~strong(X)|tall(X))=>(~happy(X)|~generous(X))))&
(![X]:((calm(X)&generous(X))<=>(~funny(X)<~>creative(X))))&
(![X]:(~creative(X)=>~humble(X)))&
(![X]:((humble(X)&quiet(X))=>~generous(X)))&
(![X]:((strong(X)<~>~happy(X))<=>(quiet(X)<~>creative(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
((~patient(alice))=>(creative(paul)))&
((?[X]:((~rich(X)<~>patient(X))))=>(?[X]:(kind(X))))&
((~quiet(john))=>(strong(paul)))&
(![X]:(~quiet(X)=>(funny(X)<~>happy(X))))&
((?[X]:((funny(X)|humble(X))))=>(?[X]:((~patient(X)<~>~rich(X)))))&
((?[X]:(quiet(X)))<=>(creative(mary)))&
(![X]:(creative(X)=>(~kind(X)|strong(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(quiet(X)<~>~brave(X))))&
(((~patient(fred)&~brave(fred)))=>((humble(fred)<~>tall(fred))))&
((calm(paul)<~>~calm(paul)))&
(?[X]:(happy(X)))&
(?[X]:(~patient(X)))&
((~wise(john)|old(john)))&
((generous(paul)|funny(paul)))&
((happy(lucy)&~old(lucy)))&
(?[X]:((~happy(X)<~>~strong(X)))) | ~patient(fred) | [] | null | 0 |
If lucy is not funny or not wise then john is either not calm or wise and vice versa.
Everyone who is either strong or not old is both patient and not brave and vice versa.
If paul is either not brave or not generous then someone is either quiet or not humble and vice versa.
Everyone who is both quiet and not kind is not creative or funny and vice versa.
Everyone who is either humble or not happy is either calm or brave.
Everyone who is both wise and happy is not kind or not humble.
Everyone who is both rich and happy is not humble or not rich and vice versa.
Everyone who is generous is not funny and vice versa.
Everyone who is not quiet or funny is happy.
If someone is either humble or not funny then someone is not funny.
If someone is either generous or happy then someone is either not funny or happy and vice versa.
Everyone who is either not happy or not humble is not patient or not strong and vice versa.
If someone is creative then someone is funny.
If alice is both not generous and not tall then someone is both not patient and strong.
Everyone who is wise or not wise is both not generous and not humble and vice versa.
If john is both not calm and strong then someone is both tall and humble.
Susan is either calm or not patient.
Someone is not tall or not kind.
Someone is not old.
Susan is either not tall or not brave.
Someone is either wise or not old.
Susan is either patient or not generous.
Someone is quiet. | Susan is not creative. | neutral | (((~funny(lucy)|~wise(lucy)))<=>((~calm(john)<~>wise(john))))&
(![X]:((strong(X)<~>~old(X))<=>(patient(X)&~brave(X))))&
(((~brave(paul)<~>~generous(paul)))<=>(?[X]:((quiet(X)<~>~humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~creative(X)|funny(X))))&
(![X]:((humble(X)<~>~happy(X))=>(calm(X)<~>brave(X))))&
(![X]:((wise(X)&happy(X))=>(~kind(X)|~humble(X))))&
(![X]:((rich(X)&happy(X))<=>(~humble(X)|~rich(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(![X]:((~quiet(X)|funny(X))=>happy(X)))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:(~funny(X))))&
((?[X]:((generous(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~patient(X)|~strong(X))))&
((?[X]:(creative(X)))=>(?[X]:(funny(X))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
((calm(susan)<~>~patient(susan)))&
(?[X]:((~tall(X)|~kind(X))))&
(?[X]:(~old(X)))&
((~tall(susan)<~>~brave(susan)))&
(?[X]:((wise(X)<~>~old(X))))&
((patient(susan)<~>~generous(susan)))&
(?[X]:(quiet(X))) | ~creative(susan) | [] | null | 0 |
If someone is funny then lucy is kind or not patient.
If someone is either not old or old then john is either not happy or strong and vice versa.
Everyone who is funny or not kind is both not old and generous and vice versa.
Everyone who is strong or curious is both patient and brave and vice versa.
If someone is not old or not kind then alice is calm and vice versa.
If alice is not tall then lucy is not generous and vice versa.
Everyone who is calm or not patient is either strong or not calm and vice versa.
Everyone who is not calm or not quiet is either not generous or not creative.
If paul is either calm or rich then someone is either tall or not humble and vice versa.
If john is not tall or calm then paul is both calm and old and vice versa.
If lucy is not tall then someone is brave and vice versa.
Everyone who is both not funny and quiet is not strong.
Everyone who is not creative or not curious is tall.
If john is either curious or not rich then someone is creative and vice versa.
If mary is both not old and strong then fred is quiet or not wise and vice versa.
If someone is both kind and old then lucy is not patient or curious and vice versa.
Lucy is not curious.
Someone is not brave.
Someone is both not happy and not quiet.
Paul is not calm.
Someone is either kind or not humble.
Someone is either not happy or patient. | Mary is not calm. | entailment | ((?[X]:(funny(X)))=>((kind(lucy)|~patient(lucy))))&
((?[X]:((~old(X)<~>old(X))))<=>((~happy(john)<~>strong(john))))&
(![X]:((funny(X)|~kind(X))<=>(~old(X)&generous(X))))&
(![X]:((strong(X)|curious(X))<=>(patient(X)&brave(X))))&
((?[X]:((~old(X)|~kind(X))))<=>(calm(alice)))&
((~tall(alice))<=>(~generous(lucy)))&
(![X]:((calm(X)|~patient(X))<=>(strong(X)<~>~calm(X))))&
(![X]:((~calm(X)|~quiet(X))=>(~generous(X)<~>~creative(X))))&
(((calm(paul)<~>rich(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~tall(john)|calm(john)))<=>((calm(paul)&old(paul))))&
((~tall(lucy))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)&quiet(X))=>~strong(X)))&
(![X]:((~creative(X)|~curious(X))=>tall(X)))&
(((curious(john)<~>~rich(john)))<=>(?[X]:(creative(X))))&
(((~old(mary)&strong(mary)))<=>((quiet(fred)|~wise(fred))))&
((?[X]:((kind(X)&old(X))))<=>((~patient(lucy)|curious(lucy))))&
(~curious(lucy))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)&~quiet(X))))&
(~calm(paul))&
(?[X]:((kind(X)<~>~humble(X))))&
(?[X]:((~happy(X)<~>patient(X)))) | ~calm(mary) | [
"p3",
"p6",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3878195109831493688712972
% SZS output start Proof for 3878195109831493688712972
4. ! [X0] : ((curious(X0) | strong(X0)) <=> (brave(X0) & patient(X0))) [input p3]
7. ! [X0] : ((~patient(X0) | calm(X0)) <=> (strong(X0) <~> ~calm(X0))) [input p6]
11. ~tall(lucy) <=> ? [X0] : brave(X0) [input p10]
13. ! [X0] : ((~curious(X0) | ~creative(X0)) => tall(X0)) [input p12]
17. ~curious(lucy) [input p16]
23. calm(mary) [input hypothesis]
29. ! [X0] : (tall(X0) | (curious(X0) & creative(X0))) [ennf transformation 13]
36. ! [X0] : (((curious(X0) | strong(X0)) | (~brave(X0) | ~patient(X0))) & ((brave(X0) & patient(X0)) | (~curious(X0) & ~strong(X0)))) [nnf transformation 4]
37. ! [X0] : ((curious(X0) | strong(X0) | ~brave(X0) | ~patient(X0)) & ((brave(X0) & patient(X0)) | (~curious(X0) & ~strong(X0)))) [flattening 36]
43. ! [X0] : (((~patient(X0) | calm(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (patient(X0) & ~calm(X0)))) [nnf transformation 7]
44. ! [X0] : ((~patient(X0) | calm(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (patient(X0) & ~calm(X0)))) [flattening 43]
52. (~tall(lucy) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | tall(lucy)) [nnf transformation 11]
53. (~tall(lucy) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | tall(lucy)) [rectify 52]
54. ? [X1] : brave(X1) => brave(sK3) [choice axiom]
55. (~tall(lucy) | ! [X0] : ~brave(X0)) & (brave(sK3) | tall(lucy)) [skolemisation 53,54]
93. ~strong(X0) | brave(X0) [cnf transformation 37]
101. ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 44]
125. ~tall(lucy) | ~brave(X0) [cnf transformation 55]
128. tall(X0) | curious(X0) [cnf transformation 29]
143. ~curious(lucy) [cnf transformation 17]
152. calm(mary) [cnf transformation 23]
153. ~calm(X0) | strong(X0) [duplicate literal removal 101]
263. 22 <=> ! [X0] : ~brave(X0) [avatar definition]
264. ~brave(X0) <- (22) [avatar component clause 263]
266. 23 <=> tall(lucy) [avatar definition]
268. ~tall(lucy) <- (~23) [avatar component clause 266]
269. 22 | ~23 [avatar split clause 125,266,263]
299. 30 <=> strong(mary) [avatar definition]
301. strong(mary) <- (30) [avatar component clause 299]
316. 33 <=> curious(lucy) [avatar definition]
318. ~curious(lucy) <- (~33) [avatar component clause 316]
333. ~33 [avatar split clause 143,316]
363. curious(lucy) <- (~23) [resolution 128,268]
364. $false <- (~23, ~33) [subsumption resolution 363,318]
365. 23 | 33 [avatar contradiction clause 364]
368. strong(mary) [resolution 153,152]
372. 30 [avatar split clause 368,299]
373. brave(mary) <- (30) [resolution 301,93]
375. $false <- (22, 30) [subsumption resolution 373,264]
376. ~22 | ~30 [avatar contradiction clause 375]
377. $false [avatar sat refutation 269,333,365,372,376]
% SZS output end Proof for 3878195109831493688712972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then paul is not calm or not wise.
Everyone who is not rich is both not happy and creative.
If someone is not kind then alice is both not creative and happy and vice versa.
Everyone who is generous is not rich or not old and vice versa.
Everyone who is happy or curious is generous or calm and vice versa.
If someone is not strong or rich then paul is not tall and vice versa.
Everyone who is happy is funny or rich.
If paul is both strong and not generous then susan is either happy or not wise.
Everyone who is not old or happy is wise or kind and vice versa.
If lucy is not creative or not rich then someone is generous and vice versa.
Everyone who is either calm or not rich is either generous or patient.
Everyone who is either not creative or strong is not creative and vice versa.
Everyone who is not patient is not funny or not quiet.
Everyone who is either not funny or not curious is either wise or funny.
If someone is wise or not happy then john is both happy and curious and vice versa.
Susan is not patient.
Fred is kind.
Someone is either not brave or rich.
John is quiet.
Alice is not strong. | Paul is not funny. | neutral | ((?[X]:(humble(X)))=>((~calm(paul)|~wise(paul))))&
(![X]:(~rich(X)=>(~happy(X)&creative(X))))&
((?[X]:(~kind(X)))<=>((~creative(alice)&happy(alice))))&
(![X]:(generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((happy(X)|curious(X))<=>(generous(X)|calm(X))))&
((?[X]:((~strong(X)|rich(X))))<=>(~tall(paul)))&
(![X]:(happy(X)=>(funny(X)|rich(X))))&
(((strong(paul)&~generous(paul)))=>((happy(susan)<~>~wise(susan))))&
(![X]:((~old(X)|happy(X))<=>(wise(X)|kind(X))))&
(((~creative(lucy)|~rich(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>~rich(X))=>(generous(X)<~>patient(X))))&
(![X]:((~creative(X)<~>strong(X))<=>~creative(X)))&
(![X]:(~patient(X)=>(~funny(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~curious(X))=>(wise(X)<~>funny(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((happy(john)&curious(john))))&
(~patient(susan))&
(kind(fred))&
(?[X]:((~brave(X)<~>rich(X))))&
(quiet(john))&
(~strong(alice)) | ~funny(paul) | [] | null | 0 |
If susan is either not creative or calm then mary is both brave and not quiet and vice versa.
If mary is either not kind or generous then someone is happy.
If someone is both tall and funny then john is either not tall or not wise and vice versa.
If someone is not strong or creative then mary is not old and vice versa.
If fred is both not brave and not kind then john is generous or brave.
Everyone who is both not humble and tall is both wise and humble and vice versa.
Everyone who is generous is either brave or funny and vice versa.
If someone is either not strong or calm then someone is either not tall or strong.
Everyone who is both brave and not quiet is strong or not humble.
If someone is not kind or not old then someone is not quiet.
Everyone who is not quiet or not wise is old and vice versa.
Everyone who is not patient or generous is not kind.
Everyone who is both curious and happy is humble or not happy.
Everyone who is either brave or not calm is both not funny and not strong and vice versa.
Everyone who is not tall is both not quiet and curious.
If john is either wise or happy then alice is both not kind and not wise and vice versa.
Mary is patient.
Someone is not wise or wise.
Someone is either not curious or kind.
Someone is not happy.
Mary is either not patient or calm.
Susan is both funny and wise. | John is strong. | entailment | (((~creative(susan)<~>calm(susan)))<=>((brave(mary)&~quiet(mary))))&
(((~kind(mary)<~>generous(mary)))=>(?[X]:(happy(X))))&
((?[X]:((tall(X)&funny(X))))<=>((~tall(john)<~>~wise(john))))&
((?[X]:((~strong(X)|creative(X))))<=>(~old(mary)))&
(((~brave(fred)&~kind(fred)))=>((generous(john)|brave(john))))&
(![X]:((~humble(X)&tall(X))<=>(wise(X)&humble(X))))&
(![X]:(generous(X)<=>(brave(X)<~>funny(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((brave(X)&~quiet(X))=>(strong(X)|~humble(X))))&
((?[X]:((~kind(X)|~old(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)|~wise(X))<=>old(X)))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((curious(X)&happy(X))=>(humble(X)|~happy(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~funny(X)&~strong(X))))&
(![X]:(~tall(X)=>(~quiet(X)&curious(X))))&
(((wise(john)<~>happy(john)))<=>((~kind(alice)&~wise(alice))))&
(patient(mary))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:(~happy(X)))&
((~patient(mary)<~>calm(mary)))&
((funny(susan)&wise(susan))) | strong(john) | [
"p3",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 555928780890039804597708
% SZS output start Proof for 555928780890039804597708
4. ? [X0] : (creative(X0) | ~strong(X0)) <=> ~old(mary) [input p3]
6. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (humble(X0) & wise(X0))) [input p5]
11. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> old(X0)) [input p10]
15. ! [X0] : (~tall(X0) => (curious(X0) & ~quiet(X0))) [input p14]
23. ~strong(john) [input hypothesis]
36. ! [X0] : ((curious(X0) & ~quiet(X0)) | tall(X0)) [ennf transformation 15]
46. (? [X0] : (creative(X0) | ~strong(X0)) | old(mary)) & (~old(mary) | ! [X0] : (~creative(X0) & strong(X0))) [nnf transformation 4]
47. (? [X0] : (creative(X0) | ~strong(X0)) | old(mary)) & (~old(mary) | ! [X1] : (~creative(X1) & strong(X1))) [rectify 46]
48. ? [X0] : (creative(X0) | ~strong(X0)) => (creative(sK2) | ~strong(sK2)) [choice axiom]
49. ((creative(sK2) | ~strong(sK2)) | old(mary)) & (~old(mary) | ! [X1] : (~creative(X1) & strong(X1))) [skolemisation 47,48]
50. ! [X0] : (((tall(X0) & ~humble(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (~tall(X0) | humble(X0)))) [nnf transformation 6]
51. ! [X0] : (((tall(X0) & ~humble(X0)) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | ~tall(X0) | humble(X0))) [flattening 50]
60. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ~old(X0)) & (old(X0) | (wise(X0) & quiet(X0)))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~old(X0)) & (old(X0) | (wise(X0) & quiet(X0)))) [flattening 60]
88. ~old(mary) | strong(X1) [cnf transformation 49]
93. humble(X0) | ~tall(X0) | humble(X0) [cnf transformation 51]
94. ~humble(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 51]
107. old(X0) | quiet(X0) [cnf transformation 61]
108. old(X0) | wise(X0) [cnf transformation 61]
119. ~quiet(X0) | tall(X0) [cnf transformation 36]
136. ~strong(john) [cnf transformation 23]
138. ~tall(X0) | humble(X0) [duplicate literal removal 93]
139. ~humble(X0) | ~wise(X0) [duplicate literal removal 94]
145. 2 <=> quiet(mary) [avatar definition]
147. quiet(mary) <- (2) [avatar component clause 145]
202. 13 <=> old(mary) [avatar definition]
203. ~old(mary) <- (~13) [avatar component clause 202]
219. 17 <=> ! [X1] : strong(X1) [avatar definition]
220. strong(X1) <- (17) [avatar component clause 219]
221. 17 | ~13 [avatar split clause 88,202,219]
298. quiet(mary) <- (~13) [resolution 107,203]
299. 2 | 13 [avatar split clause 298,202,145]
303. $false <- (17) [resolution 220,136]
308. ~17 [avatar contradiction clause 303]
309. wise(mary) <- (~13) [resolution 108,203]
311. tall(mary) <- (2) [resolution 119,147]
314. humble(mary) <- (2) [resolution 138,311]
319. ~wise(mary) <- (2) [resolution 314,139]
320. $false <- (2, ~13) [subsumption resolution 319,309]
321. ~2 | 13 [avatar contradiction clause 320]
322. $false [avatar sat refutation 221,299,308,321]
% SZS output end Proof for 555928780890039804597708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either kind or not patient then john is either not generous or not happy and vice versa.
If fred is brave then alice is both rich and strong and vice versa.
Everyone who is both not rich and happy is either funny or kind and vice versa.
Everyone who is either patient or not tall is not patient or wise and vice versa.
Everyone who is happy is quiet.
If someone is either quiet or not rich then susan is not old.
Everyone who is both brave and funny is curious or generous and vice versa.
Everyone who is both strong and funny is either humble or wise.
Everyone who is either not curious or happy is either kind or not old.
Everyone who is either not old or calm is quiet.
Everyone who is either not patient or old is both not wise and generous.
If paul is not calm or not patient then paul is both not brave and not kind and vice versa.
If someone is either not kind or generous then someone is not kind and vice versa.
Everyone who is not creative or humble is either generous or brave and vice versa.
Everyone who is either not kind or happy is generous.
If fred is creative then fred is either calm or not patient and vice versa.
Mary is either quiet or kind.
Mary is both not generous and not kind.
Susan is old.
Someone is either tall or not curious.
Someone is not creative or creative.
Paul is either not tall or brave.
Someone is either kind or calm.
Someone is either not brave or tall. | Paul is funny. | entailment | (((kind(mary)<~>~patient(mary)))<=>((~generous(john)<~>~happy(john))))&
((brave(fred))<=>((rich(alice)&strong(alice))))&
(![X]:((~rich(X)&happy(X))<=>(funny(X)<~>kind(X))))&
(![X]:((patient(X)<~>~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((quiet(X)<~>~rich(X))))=>(~old(susan)))&
(![X]:((brave(X)&funny(X))<=>(curious(X)|generous(X))))&
(![X]:((strong(X)&funny(X))=>(humble(X)<~>wise(X))))&
(![X]:((~curious(X)<~>happy(X))=>(kind(X)<~>~old(X))))&
(![X]:((~old(X)<~>calm(X))=>quiet(X)))&
(![X]:((~patient(X)<~>old(X))=>(~wise(X)&generous(X))))&
(((~calm(paul)|~patient(paul)))<=>((~brave(paul)&~kind(paul))))&
((?[X]:((~kind(X)<~>generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(generous(X)<~>brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>generous(X)))&
((creative(fred))<=>((calm(fred)<~>~patient(fred))))&
((quiet(mary)<~>kind(mary)))&
((~generous(mary)&~kind(mary)))&
(old(susan))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~creative(X)|creative(X))))&
((~tall(paul)<~>brave(paul)))&
(?[X]:((kind(X)<~>calm(X))))&
(?[X]:((~brave(X)<~>tall(X)))) | funny(paul) | [
"p2",
"p4",
"p5",
"p6",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2674595890753051849926490
% SZS output start Proof for 2674595890753051849926490
3. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (funny(X0) <~> kind(X0))) [input p2]
5. ! [X0] : (happy(X0) => quiet(X0)) [input p4]
6. ? [X0] : (quiet(X0) <~> ~rich(X0)) => ~old(susan) [input p5]
7. ! [X0] : ((funny(X0) & brave(X0)) <=> (generous(X0) | curious(X0))) [input p6]
15. ! [X0] : ((~kind(X0) <~> happy(X0)) => generous(X0)) [input p14]
19. old(susan) [input p18]
25. ~funny(paul) [input hypothesis]
27. ! [X0] : (quiet(X0) | ~happy(X0)) [ennf transformation 5]
28. ~old(susan) | ! [X0] : (quiet(X0) <=> ~rich(X0)) [ennf transformation 6]
34. ! [X0] : (generous(X0) | (~kind(X0) <=> happy(X0))) [ennf transformation 15]
38. ! [X0] : (((happy(X0) & ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (~happy(X0) | rich(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | ~happy(X0) | rich(X0))) [flattening 38]
42. ~old(susan) | ! [X0] : ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))) [nnf transformation 28]
43. ! [X0] : (((funny(X0) & brave(X0)) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | (~funny(X0) | ~brave(X0)))) [nnf transformation 7]
44. ! [X0] : (((funny(X0) & brave(X0)) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ~funny(X0) | ~brave(X0))) [flattening 43]
58. ! [X0] : (generous(X0) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 34]
84. ~happy(X0) | funny(X0) | kind(X0) | rich(X0) [cnf transformation 39]
89. ~kind(X0) | funny(X0) | happy(X0) [cnf transformation 39]
96. ~happy(X0) | quiet(X0) [cnf transformation 27]
97. ~old(susan) | ~rich(X0) | ~quiet(X0) [cnf transformation 42]
103. ~generous(X0) | funny(X0) [cnf transformation 44]
131. happy(X0) | generous(X0) | kind(X0) [cnf transformation 58]
132. ~happy(X0) | ~kind(X0) | generous(X0) [cnf transformation 58]
141. old(susan) [cnf transformation 19]
151. ~funny(paul) [cnf transformation 25]
198. 9 <=> old(susan) [avatar definition]
203. 10 <=> ! [X0] : (~rich(X0) | ~quiet(X0)) [avatar definition]
204. ~quiet(X0) | ~rich(X0) <- (10) [avatar component clause 203]
205. 10 | ~9 [avatar split clause 97,198,203]
211. 12 <=> kind(paul) [avatar definition]
212. ~kind(paul) <- (~12) [avatar component clause 211]
213. kind(paul) <- (12) [avatar component clause 211]
279. 9 [avatar split clause 141,198]
368. 39 <=> quiet(paul) [avatar definition]
369. ~quiet(paul) <- (~39) [avatar component clause 368]
370. quiet(paul) <- (39) [avatar component clause 368]
434. quiet(X0) | kind(X0) | generous(X0) [resolution 131,96]
442. funny(X0) | kind(X0) | rich(X0) | generous(X0) | kind(X0) [resolution 84,131]
443. funny(X0) | kind(X0) | rich(X0) | generous(X0) [duplicate literal removal 442]
444. funny(X0) | kind(X0) | rich(X0) [subsumption resolution 443,103]
504. 57 <=> generous(paul) [avatar definition]
505. ~generous(paul) <- (~57) [avatar component clause 504]
506. generous(paul) <- (57) [avatar component clause 504]
536. 63 <=> happy(paul) [avatar definition]
538. happy(paul) <- (63) [avatar component clause 536]
569. kind(paul) | rich(paul) [resolution 444,151]
578. rich(paul) <- (~12) [subsumption resolution 569,212]
581. funny(paul) <- (57) [resolution 506,103]
583. $false <- (57) [subsumption resolution 581,151]
584. ~57 [avatar contradiction clause 583]
599. ~rich(paul) <- (10, 39) [resolution 370,204]
600. $false <- (10, ~12, 39) [subsumption resolution 599,578]
601. ~10 | 12 | ~39 [avatar contradiction clause 600]
609. kind(paul) | generous(paul) <- (~39) [resolution 369,434]
614. kind(paul) <- (~39, ~57) [subsumption resolution 609,505]
615. 12 | 39 | 57 [avatar split clause 614,504,368,211]
617. funny(paul) | happy(paul) <- (12) [resolution 213,89]
622. happy(paul) <- (12) [subsumption resolution 617,151]
625. 63 | ~12 [avatar split clause 622,211,536]
633. ~kind(paul) | generous(paul) <- (63) [resolution 538,132]
635. generous(paul) <- (12, 63) [subsumption resolution 633,213]
636. $false <- (12, ~57, 63) [subsumption resolution 635,505]
637. ~12 | 57 | ~63 [avatar contradiction clause 636]
638. $false [avatar sat refutation 205,279,584,601,615,625,637]
% SZS output end Proof for 2674595890753051849926490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or funny then john is brave and vice versa.
If lucy is calm then someone is both quiet and not patient.
Everyone who is either kind or not tall is not tall or not creative.
Everyone who is not quiet or kind is both humble and quiet and vice versa.
Everyone who is not happy is generous.
Everyone who is creative or not patient is kind.
Everyone who is both curious and not funny is both not generous and brave.
If lucy is not happy or humble then paul is wise.
If someone is not rich or not brave then fred is both not creative and not happy and vice versa.
If susan is curious then someone is either curious or humble and vice versa.
Everyone who is either not patient or not old is not happy or not humble.
Everyone who is happy or tall is either creative or not kind and vice versa.
Everyone who is both calm and not curious is not happy or not generous and vice versa.
If paul is strong or brave then lucy is tall and vice versa.
Everyone who is wise or not strong is not calm or not humble.
If someone is not rich or not creative then lucy is either not tall or patient and vice versa.
Someone is both not happy and not curious.
Someone is both not patient and quiet.
Someone is patient or not quiet.
Someone is either not curious or not quiet.
Someone is not wise or rich.
Lucy is both creative and not curious.
Alice is both not rich and curious.
Someone is not patient. | Paul is not strong. | entailment | ((?[X]:((~humble(X)|funny(X))))<=>(brave(john)))&
((calm(lucy))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((kind(X)<~>~tall(X))=>(~tall(X)|~creative(X))))&
(![X]:((~quiet(X)|kind(X))<=>(humble(X)&quiet(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>kind(X)))&
(![X]:((curious(X)&~funny(X))=>(~generous(X)&brave(X))))&
(((~happy(lucy)|humble(lucy)))=>(wise(paul)))&
((?[X]:((~rich(X)|~brave(X))))<=>((~creative(fred)&~happy(fred))))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~tall(lucy)<~>patient(lucy))))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~wise(X)|rich(X))))&
((creative(lucy)&~curious(lucy)))&
((~rich(alice)&curious(alice)))&
(?[X]:(~patient(X))) | ~strong(paul) | [
"p2",
"p5",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8364048835162616154255404
% SZS output start Proof for 8364048835162616154255404
3. ! [X0] : ((kind(X0) <~> ~tall(X0)) => (~creative(X0) | ~tall(X0))) [input p2]
6. ! [X0] : ((~patient(X0) | creative(X0)) => kind(X0)) [input p5]
12. ! [X0] : ((tall(X0) | happy(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p11]
14. (brave(paul) | strong(paul)) <=> tall(lucy) [input p13]
22. ~curious(lucy) & creative(lucy) [input p21]
25. strong(paul) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (kind(X0) <=> ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (kind(X0) <=> ~tall(X0))) [flattening 27]
30. ! [X0] : (kind(X0) | (patient(X0) & ~creative(X0))) [ennf transformation 6]
44. ! [X0] : (~creative(X0) | ~tall(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) [nnf transformation 28]
57. ! [X0] : (((tall(X0) | happy(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((tall(X0) | happy(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [flattening 57]
61. ((brave(paul) | strong(paul)) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [nnf transformation 14]
62. (brave(paul) | strong(paul) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [flattening 61]
85. ~creative(X0) | ~tall(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 44]
93. ~creative(X0) | kind(X0) [cnf transformation 30]
111. ~kind(X0) | creative(X0) | ~tall(X0) [cnf transformation 58]
121. tall(lucy) | ~strong(paul) [cnf transformation 62]
140. creative(lucy) [cnf transformation 22]
145. strong(paul) [cnf transformation 25]
148. ~creative(X0) | ~tall(X0) | ~kind(X0) [duplicate literal removal 85]
249. ~tall(X0) | ~kind(X0) [subsumption resolution 111,148]
251. 23 <=> tall(lucy) [avatar definition]
252. tall(lucy) <- (23) [avatar component clause 251]
255. 24 <=> strong(paul) [avatar definition]
264. ~24 | 23 [avatar split clause 121,251,255]
297. 24 [avatar split clause 145,255]
300. kind(lucy) [resolution 93,140]
322. ~kind(lucy) <- (23) [resolution 249,252]
323. $false <- (23) [subsumption resolution 322,300]
324. ~23 [avatar contradiction clause 323]
325. $false [avatar sat refutation 264,297,324]
% SZS output end Proof for 8364048835162616154255404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not strong then paul is not rich or old. If fred is not brave then someone is not creative or not funny and vice versa. If fred is either not wise or old then someone is both not funny and not tall. Everyone who is old is not wise or not patient. If lucy is either not patient or not creative then someone is brave or wise and vice versa. Everyone who is not rich is not humble or strong and vice versa. If paul is not strong then mary is not funny or not happy. Everyone who is not creative or not curious is both not strong and not patient and vice versa. If paul is either not curious or humble then someone is generous. If mary is not rich then someone is either generous or not rich. Everyone who is either quiet or not strong is either humble or quiet. If someone is quiet then alice is either not creative or creative and vice versa. If mary is not kind then lucy is happy or not kind. Everyone who is either kind or not strong is not calm or patient. If someone is old then someone is both old and not kind. Everyone who is funny or not brave is not calm or old. Someone is either not curious or generous. Fred is funny. Susan is both creative and tall. Someone is not wise or generous. Someone is both quiet and funny. Fred is rich or calm. Alice is kind or not tall. | Paul is strong. | neutral | ((?[X]:((~patient(X)|~strong(X))))=>((~rich(paul)|old(paul))))&
((~brave(fred))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((~wise(fred)<~>old(fred)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(old(X)=>(~wise(X)|~patient(X))))&
(((~patient(lucy)<~>~creative(lucy)))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(~rich(X)<=>(~humble(X)|strong(X))))&
((~strong(paul))=>((~funny(mary)|~happy(mary))))&
(![X]:((~creative(X)|~curious(X))<=>(~strong(X)&~patient(X))))&
(((~curious(paul)<~>humble(paul)))=>(?[X]:(generous(X))))&
((~rich(mary))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:((quiet(X)<~>~strong(X))=>(humble(X)<~>quiet(X))))&
((?[X]:(quiet(X)))<=>((~creative(alice)<~>creative(alice))))&
((~kind(mary))=>((happy(lucy)|~kind(lucy))))&
(![X]:((kind(X)<~>~strong(X))=>(~calm(X)|patient(X))))&
((?[X]:(old(X)))=>(?[X]:((old(X)&~kind(X)))))&
(![X]:((funny(X)|~brave(X))=>(~calm(X)|old(X))))&
(?[X]:((~curious(X)<~>generous(X))))&
(funny(fred))&
((creative(susan)&tall(susan)))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((quiet(X)&funny(X))))&
((rich(fred)|calm(fred)))&
((kind(alice)|~tall(alice))) | strong(paul) | [] | null | 0 |
If someone is not kind then mary is kind or old and vice versa.
Everyone who is not old is both patient and not tall.
Everyone who is not happy is both wise and not funny.
Everyone who is brave is wise or patient and vice versa.
If someone is either humble or funny then someone is patient or not brave.
If susan is brave or not rich then someone is not brave or not kind.
Everyone who is not strong or funny is not wise or happy and vice versa.
Everyone who is either not patient or not quiet is either quiet or happy and vice versa.
If susan is either not generous or not humble then someone is not wise and vice versa.
If someone is both patient and not tall then someone is not strong and vice versa.
If someone is either not tall or curious then someone is not old or strong and vice versa.
If paul is brave or generous then alice is either not curious or not humble.
Everyone who is both brave and strong is either funny or not creative and vice versa.
Everyone who is creative or not quiet is both old and not creative and vice versa.
If someone is not curious then someone is generous and vice versa.
Someone is both brave and not patient.
Lucy is either not humble or generous.
Someone is either humble or quiet.
Someone is both wise and not happy.
Someone is brave.
Lucy is either generous or not tall.
Someone is not strong or not patient. | Mary is not patient. | neutral | ((?[X]:(~kind(X)))<=>((kind(mary)|old(mary))))&
(![X]:(~old(X)=>(patient(X)&~tall(X))))&
(![X]:(~happy(X)=>(wise(X)&~funny(X))))&
(![X]:(brave(X)<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((brave(susan)|~rich(susan)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)|funny(X))<=>(~wise(X)|happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(quiet(X)<~>happy(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((brave(paul)|generous(paul)))=>((~curious(alice)<~>~humble(alice))))&
(![X]:((brave(X)&strong(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~quiet(X))<=>(old(X)&~creative(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(generous(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~humble(lucy)<~>generous(lucy)))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:(brave(X)))&
((generous(lucy)<~>~tall(lucy)))&
(?[X]:((~strong(X)|~patient(X)))) | ~patient(mary) | [] | null | 0 |
If mary is not calm then someone is not tall or not generous and vice versa. If someone is not brave then lucy is not brave and vice versa. Everyone who is wise or not patient is wise or not generous and vice versa. Everyone who is both brave and not rich is both curious and not old and vice versa. Everyone who is either wise or kind is both not brave and kind and vice versa. Everyone who is not patient or patient is quiet. If john is either not generous or not brave then someone is either not quiet or quiet and vice versa. If susan is both calm and not old then someone is both wise and not old. Everyone who is both quiet and not creative is curious or calm and vice versa. If someone is funny then someone is not calm and vice versa. If someone is either brave or rich then paul is both not generous and kind and vice versa. If someone is both strong and quiet then someone is both not rich and humble and vice versa. Everyone who is both not strong and not kind is either happy or not calm. If john is either old or not tall then paul is not curious. Everyone who is old or not kind is not rich or not tall. If alice is both not creative and generous then paul is both not generous and not kind. Someone is either rich or old. Someone is not old or creative. Alice is either not old or kind. Paul is strong. Someone is not patient or not wise. Someone is both calm and curious. Someone is either not quiet or not strong. Lucy is wise or humble. | John is calm. | neutral | ((~calm(mary))<=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:(~brave(X)))<=>(~brave(lucy)))&
(![X]:((wise(X)|~patient(X))<=>(wise(X)|~generous(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)&~old(X))))&
(![X]:((wise(X)<~>kind(X))<=>(~brave(X)&kind(X))))&
(![X]:((~patient(X)|patient(X))=>quiet(X)))&
(((~generous(john)<~>~brave(john)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((calm(susan)&~old(susan)))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((quiet(X)&~creative(X))<=>(curious(X)|calm(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~calm(X))))&
((?[X]:((brave(X)<~>rich(X))))<=>((~generous(paul)&kind(paul))))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~strong(X)&~kind(X))=>(happy(X)<~>~calm(X))))&
(((old(john)<~>~tall(john)))=>(~curious(paul)))&
(![X]:((old(X)|~kind(X))=>(~rich(X)|~tall(X))))&
(((~creative(alice)&generous(alice)))=>((~generous(paul)&~kind(paul))))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~old(X)|creative(X))))&
((~old(alice)<~>kind(alice)))&
(strong(paul))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:((calm(X)&curious(X))))&
(?[X]:((~quiet(X)<~>~strong(X))))&
((wise(lucy)|humble(lucy))) | calm(john) | [] | null | 0 |
If someone is both tall and not humble then someone is wise or not patient and vice versa. Everyone who is both strong and generous is both humble and not creative and vice versa. Everyone who is either not kind or not brave is not creative. If someone is not curious then mary is not calm or not generous and vice versa. Everyone who is either not old or curious is both curious and not tall. Everyone who is both not creative and strong is humble or not tall. Everyone who is both strong and not funny is happy or not calm and vice versa. If someone is rich then someone is both happy and not brave and vice versa. Everyone who is either not old or not generous is not creative and vice versa. Everyone who is both not creative and not humble is tall and vice versa. Everyone who is both rich and not humble is either not humble or curious. If someone is both strong and old then someone is brave or not happy and vice versa. If paul is not tall then john is rich or not funny and vice versa. If someone is old or not happy then john is not curious or kind. Everyone who is not kind is not generous or creative. Everyone who is old or not calm is quiet or not tall. Someone is not old or not curious. John is brave or happy. John is calm or not happy. Alice is not strong or not rich. Someone is not old or not kind. | Paul is not patient. | contradiction | ((?[X]:((tall(X)&~humble(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((strong(X)&generous(X))<=>(humble(X)&~creative(X))))&
(![X]:((~kind(X)<~>~brave(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>((~calm(mary)|~generous(mary))))&
(![X]:((~old(X)<~>curious(X))=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)&strong(X))=>(humble(X)|~tall(X))))&
(![X]:((strong(X)&~funny(X))<=>(happy(X)|~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~creative(X)&~humble(X))<=>tall(X)))&
(![X]:((rich(X)&~humble(X))=>(~humble(X)<~>curious(X))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
((~tall(paul))<=>((rich(john)|~funny(john))))&
((?[X]:((old(X)|~happy(X))))=>((~curious(john)|kind(john))))&
(![X]:(~kind(X)=>(~generous(X)|creative(X))))&
(![X]:((old(X)|~calm(X))=>(quiet(X)|~tall(X))))&
(?[X]:((~old(X)|~curious(X))))&
((brave(john)|happy(john)))&
((calm(john)|~happy(john)))&
((~strong(alice)|~rich(alice)))&
(?[X]:((~old(X)|~kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3940139520691971781155530
% SZS output start Proof for 3940139520691971781155530
1. ? [X0] : (~humble(X0) & tall(X0)) <=> ? [X0] : (~patient(X0) | wise(X0)) [input p0]
2. ! [X0] : ((generous(X0) & strong(X0)) <=> (~creative(X0) & humble(X0))) [input p1]
5. ! [X0] : ((~old(X0) <~> curious(X0)) => (~tall(X0) & curious(X0))) [input p4]
6. ! [X0] : ((strong(X0) & ~creative(X0)) => (~tall(X0) | humble(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & strong(X0)) <=> (~calm(X0) | happy(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> tall(X0)) [input p9]
12. ? [X0] : (old(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | brave(X0)) [input p11]
22. ~patient(paul) [input hypothesis]
23. ? [X0] : (~humble(X0) & tall(X0)) <=> ? [X1] : (~patient(X1) | wise(X1)) [rectify 1]
25. ? [X0] : (old(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | brave(X1)) [rectify 12]
28. ! [X0] : ((~tall(X0) & curious(X0)) | (~old(X0) <=> curious(X0))) [ennf transformation 5]
29. ! [X0] : ((~tall(X0) | humble(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 6]
30. ! [X0] : (~tall(X0) | humble(X0) | ~strong(X0) | creative(X0)) [flattening 29]
37. (? [X0] : (~humble(X0) & tall(X0)) | ! [X1] : (patient(X1) & ~wise(X1))) & (? [X1] : (~patient(X1) | wise(X1)) | ! [X0] : (humble(X0) | ~tall(X0))) [nnf transformation 23]
38. (? [X0] : (~humble(X0) & tall(X0)) | ! [X1] : (patient(X1) & ~wise(X1))) & (? [X2] : (~patient(X2) | wise(X2)) | ! [X3] : (humble(X3) | ~tall(X3))) [rectify 37]
39. ? [X0] : (~humble(X0) & tall(X0)) => (~humble(sK0) & tall(sK0)) [choice axiom]
40. ? [X2] : (~patient(X2) | wise(X2)) => (~patient(sK1) | wise(sK1)) [choice axiom]
41. ((~humble(sK0) & tall(sK0)) | ! [X1] : (patient(X1) & ~wise(X1))) & ((~patient(sK1) | wise(sK1)) | ! [X3] : (humble(X3) | ~tall(X3))) [skolemisation 38,40,39]
42. ! [X0] : (((generous(X0) & strong(X0)) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | (~generous(X0) | ~strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((generous(X0) & strong(X0)) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | ~generous(X0) | ~strong(X0))) [flattening 42]
50. ! [X0] : ((~tall(X0) & curious(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) [nnf transformation 28]
51. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | (funny(X0) | ~strong(X0)))) [nnf transformation 7]
52. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | funny(X0) | ~strong(X0))) [flattening 51]
58. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | creative(X0)) & (~creative(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 9]
59. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) | creative(X0)))) [nnf transformation 10]
60. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | humble(X0) | creative(X0))) [flattening 59]
62. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X1] : (~happy(X1) | brave(X1)) | ! [X0] : (~old(X0) | ~strong(X0))) [nnf transformation 25]
63. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X2] : (~happy(X2) | brave(X2)) | ! [X3] : (~old(X3) | ~strong(X3))) [rectify 62]
64. ? [X0] : (old(X0) & strong(X0)) => (old(sK5) & strong(sK5)) [choice axiom]
65. ? [X2] : (~happy(X2) | brave(X2)) => (~happy(sK6) | brave(sK6)) [choice axiom]
66. ((old(sK5) & strong(sK5)) | ! [X1] : (happy(X1) & ~brave(X1))) & ((~happy(sK6) | brave(sK6)) | ! [X3] : (~old(X3) | ~strong(X3))) [skolemisation 63,65,64]
75. tall(sK0) | patient(X1) [cnf transformation 41]
77. ~humble(sK0) | patient(X1) [cnf transformation 41]
78. ~generous(X0) | humble(X0) | ~strong(X0) [cnf transformation 43]
79. ~creative(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 43]
81. ~humble(X0) | creative(X0) | generous(X0) [cnf transformation 43]
87. curious(X0) | curious(X0) | old(X0) [cnf transformation 50]
90. ~old(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 50]
91. ~strong(X0) | humble(X0) | ~tall(X0) | creative(X0) [cnf transformation 30]
93. ~happy(X0) | strong(X0) [cnf transformation 52]
101. ~old(X0) | ~creative(X0) | generous(X0) [cnf transformation 58]
102. ~old(X0) | ~generous(X0) | creative(X0) [cnf transformation 58]
103. old(X0) | generous(X0) | creative(X0) [cnf transformation 58]
104. creative(X0) | humble(X0) | tall(X0) [cnf transformation 60]
105. ~creative(X0) | ~tall(X0) [cnf transformation 60]
109. ~happy(sK6) | brave(sK6) | ~old(X3) | ~strong(X3) [cnf transformation 66]
110. strong(sK5) | ~brave(X1) [cnf transformation 66]
111. strong(sK5) | happy(X1) [cnf transformation 66]
112. old(sK5) | ~brave(X1) [cnf transformation 66]
113. old(sK5) | happy(X1) [cnf transformation 66]
125. ~patient(paul) [cnf transformation 22]
127. old(X0) | curious(X0) [duplicate literal removal 87]
129. 1 <=> ! [X1] : patient(X1) [avatar definition]
130. patient(X1) <- (1) [avatar component clause 129]
132. 2 <=> humble(sK0) [avatar definition]
134. ~humble(sK0) <- (~2) [avatar component clause 132]
135. 1 | ~2 [avatar split clause 77,132,129]
141. 4 <=> tall(sK0) [avatar definition]
143. tall(sK0) <- (4) [avatar component clause 141]
144. 1 | 4 [avatar split clause 75,141,129]
173. 11 <=> ! [X1] : curious(X1) [avatar definition]
174. curious(X1) <- (11) [avatar component clause 173]
198. 17 <=> ! [X1] : happy(X1) [avatar definition]
199. happy(X1) <- (17) [avatar component clause 198]
201. 18 <=> old(sK5) [avatar definition]
203. old(sK5) <- (18) [avatar component clause 201]
204. 17 | 18 [avatar split clause 113,201,198]
206. 19 <=> ! [X1] : ~brave(X1) [avatar definition]
207. ~brave(X1) <- (19) [avatar component clause 206]
208. 19 | 18 [avatar split clause 112,201,206]
210. 20 <=> strong(sK5) [avatar definition]
212. strong(sK5) <- (20) [avatar component clause 210]
213. 17 | 20 [avatar split clause 111,210,198]
214. 19 | 20 [avatar split clause 110,210,206]
216. 21 <=> ! [X3] : (~old(X3) | ~strong(X3)) [avatar definition]
217. ~old(X3) | ~strong(X3) <- (21) [avatar component clause 216]
219. 22 <=> brave(sK6) [avatar definition]
221. brave(sK6) <- (22) [avatar component clause 219]
223. 23 <=> happy(sK6) [avatar definition]
225. ~happy(sK6) <- (~23) [avatar component clause 223]
226. 21 | 22 | ~23 [avatar split clause 109,223,219,216]
252. 29 <=> ! [X0] : ~old(X0) [avatar definition]
253. ~old(X0) <- (29) [avatar component clause 252]
301. $false <- (17, ~23) [resolution 225,199]
302. ~17 | 23 [avatar contradiction clause 301]
324. 41 <=> tall(sK5) [avatar definition]
325. tall(sK5) <- (41) [avatar component clause 324]
332. 42 <=> generous(sK5) [avatar definition]
334. generous(sK5) <- (42) [avatar component clause 332]
336. 43 <=> creative(sK5) [avatar definition]
337. creative(sK5) <- (43) [avatar component clause 336]
338. ~creative(sK5) <- (~43) [avatar component clause 336]
358. generous(X2) | creative(X2) | ~tall(X2) | ~curious(X2) [resolution 103,90]
361. ~curious(X2) | ~tall(X2) | generous(X2) [subsumption resolution 358,105]
366. humble(sK5) | tall(sK5) <- (~43) [resolution 104,338]
377. 48 <=> humble(sK5) [avatar definition]
379. humble(sK5) <- (48) [avatar component clause 377]
380. 41 | 48 | 43 [avatar split clause 366,336,377,324]
411. humble(sK5) | ~tall(sK5) | creative(sK5) <- (20) [resolution 91,212]
413. humble(sK5) | creative(sK5) <- (20, 41) [subsumption resolution 411,325]
426. 43 | 48 | ~20 | ~41 [avatar split clause 413,324,210,377,336]
429. humble(sK5) | ~strong(sK5) <- (42) [resolution 334,78]
430. humble(sK5) <- (20, 42) [subsumption resolution 429,212]
431. 48 | ~20 | ~42 [avatar split clause 430,332,210,377]
436. strong(X1) <- (17) [resolution 199,93]
442. $false <- (19, 22) [resolution 221,207]
444. ~19 | ~22 [avatar contradiction clause 442]
454. ~old(X3) <- (17, 21) [subsumption resolution 217,436]
455. 29 | ~17 | ~21 [avatar split clause 454,216,198,252]
460. curious(X1) <- (29) [resolution 253,127]
462. 11 | ~29 [avatar split clause 460,252,173]
504. ~generous(sK5) | creative(sK5) <- (18) [resolution 203,102]
505. ~creative(sK5) | generous(sK5) <- (18) [resolution 203,101]
571. creative(sK5) | generous(sK5) <- (48) [resolution 379,81]
580. 43 | ~42 | ~18 [avatar split clause 504,201,332,336]
581. 42 | 43 | ~48 [avatar split clause 571,377,336,332]
582. 42 | ~43 | ~18 [avatar split clause 505,201,336,332]
588. ~generous(sK5) | ~strong(sK5) <- (43) [resolution 337,79]
620. ~generous(sK5) <- (20, 43) [subsumption resolution 588,212]
621. ~42 | ~20 | ~43 [avatar split clause 620,336,210,332]
627. ~tall(X0) | generous(X0) <- (11) [resolution 174,361]
631. strong(X1) <- (17) [resolution 199,93]
700. generous(sK0) <- (4, 11) [resolution 627,143]
704. humble(sK0) | ~strong(sK0) <- (4, 11) [resolution 700,78]
714. ~strong(sK0) <- (~2, 4, 11) [subsumption resolution 704,134]
715. $false <- (~2, 4, 11, 17) [subsumption resolution 714,631]
716. 2 | ~4 | ~11 | ~17 [avatar contradiction clause 715]
717. $false <- (1) [resolution 130,125]
720. ~1 [avatar contradiction clause 717]
721. $false [avatar sat refutation 135,144,204,208,213,214,226,302,380,426,431,444,455,462,580,581,582,621,716,720]
% SZS output end Proof for 3940139520691971781155530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either patient or quiet then someone is both patient and calm and vice versa. Everyone who is both wise and old is both calm and not curious. Everyone who is strong is not calm. Everyone who is tall or generous is either rich or not strong. Everyone who is both generous and not generous is both patient and not old. Everyone who is strong or humble is calm or creative. If someone is both not kind and curious then someone is rich and vice versa. Everyone who is not funny or not kind is both kind and quiet. Everyone who is either not creative or rich is patient or quiet. If fred is either generous or not old then someone is brave. Everyone who is both not rich and not patient is either not wise or funny and vice versa. Everyone who is both not brave and not curious is old or not creative. Everyone who is not rich or generous is not rich. Everyone who is either not wise or rich is not rich and vice versa. Everyone who is both old and humble is not humble or quiet. Everyone who is either not happy or calm is both happy and curious. Susan is either rich or not humble. Paul is rich or not humble. Someone is funny. Susan is not strong. John is both calm and not humble. Someone is either not calm or curious. John is quiet or rich. Alice is not kind or tall. | Susan is rich. | contradiction | (((patient(alice)<~>quiet(alice)))<=>(?[X]:((patient(X)&calm(X)))))&
(![X]:((wise(X)&old(X))=>(calm(X)&~curious(X))))&
(![X]:(strong(X)=>~calm(X)))&
(![X]:((tall(X)|generous(X))=>(rich(X)<~>~strong(X))))&
(![X]:((generous(X)&~generous(X))=>(patient(X)&~old(X))))&
(![X]:((strong(X)|humble(X))=>(calm(X)|creative(X))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:(rich(X))))&
(![X]:((~funny(X)|~kind(X))=>(kind(X)&quiet(X))))&
(![X]:((~creative(X)<~>rich(X))=>(patient(X)|quiet(X))))&
(((generous(fred)<~>~old(fred)))=>(?[X]:(brave(X))))&
(![X]:((~rich(X)&~patient(X))<=>(~wise(X)<~>funny(X))))&
(![X]:((~brave(X)&~curious(X))=>(old(X)|~creative(X))))&
(![X]:((~rich(X)|generous(X))=>~rich(X)))&
(![X]:((~wise(X)<~>rich(X))<=>~rich(X)))&
(![X]:((old(X)&humble(X))=>(~humble(X)|quiet(X))))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)&curious(X))))&
((rich(susan)<~>~humble(susan)))&
((rich(paul)|~humble(paul)))&
(?[X]:(funny(X)))&
(~strong(susan))&
((calm(john)&~humble(john)))&
(?[X]:((~calm(X)<~>curious(X))))&
((quiet(john)|rich(john)))&
((~kind(alice)|tall(alice))) | rich(susan) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 343890065787865677825123
% SZS output start Proof for 343890065787865677825123
7. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : rich(X0) [input p6]
8. ! [X0] : ((~kind(X0) | ~funny(X0)) => (quiet(X0) & kind(X0))) [input p7]
25. rich(susan) [input hypothesis]
26. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : rich(X1) [rectify 7]
38. ! [X0] : ((quiet(X0) & kind(X0)) | (kind(X0) & funny(X0))) [ennf transformation 8]
48. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 26]
49. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 48]
50. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK1) & ~kind(sK1)) [choice axiom]
51. ? [X2] : rich(X2) => rich(sK2) [choice axiom]
52. ((curious(sK1) & ~kind(sK1)) | ! [X1] : ~rich(X1)) & (rich(sK2) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 49,51,50]
79. ~kind(sK1) | ~rich(X1) [cnf transformation 52]
82. kind(X0) | kind(X0) [cnf transformation 38]
114. rich(susan) [cnf transformation 25]
118. kind(X0) [duplicate literal removal 82]
146. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
147. ~rich(X1) <- (6) [avatar component clause 146]
154. 8 <=> kind(sK1) [avatar definition]
156. ~kind(sK1) <- (~8) [avatar component clause 154]
157. 6 | ~8 [avatar split clause 79,154,146]
168. 11 <=> rich(susan) [avatar definition]
169. rich(susan) <- (11) [avatar component clause 168]
206. 11 [avatar split clause 114,168]
207. $false <- (6, 11) [resolution 169,147]
208. ~6 | ~11 [avatar contradiction clause 207]
209. $false <- (~8) [subsumption resolution 156,118]
210. 8 [avatar contradiction clause 209]
211. $false [avatar sat refutation 157,206,208,210]
% SZS output end Proof for 343890065787865677825123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not kind and humble then someone is both old and tall.
Everyone who is not old or not wise is both not humble and creative.
Everyone who is not wise or not happy is not brave or tall and vice versa.
If alice is both creative and not strong then mary is rich or not tall and vice versa.
Everyone who is not strong is not funny.
Everyone who is not happy is calm or kind.
Everyone who is both not kind and tall is either not humble or patient.
If lucy is not patient then paul is either not old or quiet and vice versa.
Everyone who is both rich and not creative is both curious and calm.
Everyone who is either not patient or humble is either not strong or calm and vice versa.
If lucy is both wise and kind then someone is both not wise and strong and vice versa.
If someone is old then alice is calm.
If john is either creative or not funny then someone is both rich and not old.
If fred is calm or patient then lucy is either calm or generous and vice versa.
Everyone who is either not old or not curious is either creative or not wise and vice versa.
Everyone who is either not patient or curious is quiet or not tall.
Someone is both not generous and calm.
Someone is both happy and calm.
Paul is both patient and strong.
Someone is not old or brave.
Someone is either tall or humble.
Paul is old or not creative.
Someone is both not brave and kind.
Someone is not kind or not rich. | Paul is not creative. | neutral | (((~kind(mary)&humble(mary)))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((~old(X)|~wise(X))=>(~humble(X)&creative(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~brave(X)|tall(X))))&
(((creative(alice)&~strong(alice)))<=>((rich(mary)|~tall(mary))))&
(![X]:(~strong(X)=>~funny(X)))&
(![X]:(~happy(X)=>(calm(X)|kind(X))))&
(![X]:((~kind(X)&tall(X))=>(~humble(X)<~>patient(X))))&
((~patient(lucy))<=>((~old(paul)<~>quiet(paul))))&
(![X]:((rich(X)&~creative(X))=>(curious(X)&calm(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~strong(X)<~>calm(X))))&
(((wise(lucy)&kind(lucy)))<=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:(old(X)))=>(calm(alice)))&
(((creative(john)<~>~funny(john)))=>(?[X]:((rich(X)&~old(X)))))&
(((calm(fred)|patient(fred)))<=>((calm(lucy)<~>generous(lucy))))&
(![X]:((~old(X)<~>~curious(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((~patient(X)<~>curious(X))=>(quiet(X)|~tall(X))))&
(?[X]:((~generous(X)&calm(X))))&
(?[X]:((happy(X)&calm(X))))&
((patient(paul)&strong(paul)))&
(?[X]:((~old(X)|brave(X))))&
(?[X]:((tall(X)<~>humble(X))))&
((old(paul)|~creative(paul)))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:((~kind(X)|~rich(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is either strong or not generous is funny or not strong and vice versa.
Everyone who is kind is both not quiet and not tall.
Everyone who is both old and not wise is not calm or not humble.
Everyone who is either tall or not generous is not generous and vice versa.
If susan is both not humble and not wise then someone is humble or rich and vice versa.
If someone is not generous then someone is both generous and not curious.
If someone is both happy and tall then someone is both creative and not curious.
Everyone who is not calm is either brave or not humble.
If someone is both curious and not creative then someone is either happy or not brave.
Everyone who is old or tall is both not quiet and not humble.
If mary is curious or old then someone is not brave or not kind.
Everyone who is not curious or calm is not quiet.
If someone is either humble or not patient then someone is not wise or curious and vice versa.
If mary is strong then paul is rich or brave.
If fred is both not funny and old then someone is funny and vice versa.
Everyone who is either not quiet or not brave is not quiet and vice versa.
Someone is happy or tall.
Susan is calm or not generous.
Someone is both not happy and calm.
Fred is not happy.
Someone is not kind.
Someone is both wise and not quiet. | Mary is wise. | neutral | (![X]:((strong(X)<~>~generous(X))<=>(funny(X)|~strong(X))))&
(![X]:(kind(X)=>(~quiet(X)&~tall(X))))&
(![X]:((old(X)&~wise(X))=>(~calm(X)|~humble(X))))&
(![X]:((tall(X)<~>~generous(X))<=>~generous(X)))&
(((~humble(susan)&~wise(susan)))<=>(?[X]:((humble(X)|rich(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:(~calm(X)=>(brave(X)<~>~humble(X))))&
((?[X]:((curious(X)&~creative(X))))=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((old(X)|tall(X))=>(~quiet(X)&~humble(X))))&
(((curious(mary)|old(mary)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~curious(X)|calm(X))=>~quiet(X)))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
((strong(mary))=>((rich(paul)|brave(paul))))&
(((~funny(fred)&old(fred)))<=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>~quiet(X)))&
(?[X]:((happy(X)|tall(X))))&
((calm(susan)|~generous(susan)))&
(?[X]:((~happy(X)&calm(X))))&
(~happy(fred))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)&~quiet(X)))) | wise(mary) | [] | null | 0 |
Everyone who is not old is happy or not curious. Everyone who is not old is not kind and vice versa. Everyone who is not strong or not happy is either not quiet or wise and vice versa. If alice is strong or not tall then lucy is not brave. Everyone who is both strong and not wise is patient. If mary is either not calm or not patient then lucy is either not happy or rich and vice versa. If someone is either not humble or calm then susan is happy or not wise. Everyone who is not brave is either quiet or not curious. Everyone who is generous or curious is either strong or old and vice versa. Everyone who is both not wise and tall is rich. If someone is either humble or not strong then someone is either not kind or not tall and vice versa. Everyone who is not old or not funny is not creative and vice versa. Everyone who is calm or tall is both curious and not patient and vice versa. Everyone who is either brave or not tall is not wise and vice versa. Everyone who is strong or not kind is not rich and vice versa. Everyone who is not kind or funny is either funny or wise and vice versa. Fred is brave or not quiet. Someone is not rich. Someone is either tall or not kind. Susan is quiet. Someone is both funny and happy. Someone is not wise or not curious. Alice is either not kind or not tall. | Mary is funny. | neutral | (![X]:(~old(X)=>(happy(X)|~curious(X))))&
(![X]:(~old(X)<=>~kind(X)))&
(![X]:((~strong(X)|~happy(X))<=>(~quiet(X)<~>wise(X))))&
(((strong(alice)|~tall(alice)))=>(~brave(lucy)))&
(![X]:((strong(X)&~wise(X))=>patient(X)))&
(((~calm(mary)<~>~patient(mary)))<=>((~happy(lucy)<~>rich(lucy))))&
((?[X]:((~humble(X)<~>calm(X))))=>((happy(susan)|~wise(susan))))&
(![X]:(~brave(X)=>(quiet(X)<~>~curious(X))))&
(![X]:((generous(X)|curious(X))<=>(strong(X)<~>old(X))))&
(![X]:((~wise(X)&tall(X))=>rich(X)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((~old(X)|~funny(X))<=>~creative(X)))&
(![X]:((calm(X)|tall(X))<=>(curious(X)&~patient(X))))&
(![X]:((brave(X)<~>~tall(X))<=>~wise(X)))&
(![X]:((strong(X)|~kind(X))<=>~rich(X)))&
(![X]:((~kind(X)|funny(X))<=>(funny(X)<~>wise(X))))&
((brave(fred)|~quiet(fred)))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)<~>~kind(X))))&
(quiet(susan))&
(?[X]:((funny(X)&happy(X))))&
(?[X]:((~wise(X)|~curious(X))))&
((~kind(alice)<~>~tall(alice))) | funny(mary) | [] | null | 0 |
Everyone who is either not tall or not humble is either brave or not humble and vice versa.
Everyone who is not wise or not quiet is kind.
Everyone who is both not generous and not funny is either wise or humble and vice versa.
If john is both curious and not strong then lucy is calm or strong and vice versa.
Everyone who is not calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
If fred is not generous then fred is either not tall or patient and vice versa.
Someone is not brave or happy.
Susan is not patient.
Fred is calm.
Alice is both kind and humble.
Someone is both kind and patient. | John is not generous. | contradiction | (![X]:((~tall(X)<~>~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)<~>humble(X))))&
(((curious(john)&~strong(john)))<=>((calm(lucy)|strong(lucy))))&
(![X]:(~calm(X)<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(?[X]:((~brave(X)|happy(X))))&
(~patient(susan))&
(calm(fred))&
((kind(alice)&humble(alice)))&
(?[X]:((kind(X)&patient(X)))) | ~generous(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7175622728014371057748334
% SZS output start Proof for 7175622728014371057748334
13. ! [X0] : ((wise(X0) & generous(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p12]
21. ~generous(john) [input hypothesis]
49. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 13]
50. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | ~wise(X0) | ~generous(X0))) [flattening 49]
107. generous(X0) | generous(X0) [cnf transformation 50]
124. ~generous(john) [cnf transformation 21]
126. generous(X0) [duplicate literal removal 107]
227. $false [subsumption resolution 124,126]
% SZS output end Proof for 7175622728014371057748334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is wise or not humble and vice versa.
Everyone who is quiet is strong and vice versa.
If someone is both not curious and strong then paul is both generous and not calm.
Everyone who is both not curious and happy is either not old or not wise and vice versa.
Everyone who is both not happy and strong is strong or not happy and vice versa.
If mary is either quiet or not quiet then someone is not strong or not curious.
If fred is not brave then someone is both not kind and patient.
Everyone who is both patient and brave is both old and not strong.
If someone is both not creative and quiet then someone is old or not old and vice versa.
If mary is either generous or humble then someone is tall or calm.
If mary is either not creative or creative then paul is either not humble or kind.
If someone is both not rich and not patient then someone is either not tall or humble and vice versa.
If someone is not wise or not rich then paul is not brave or not humble.
If someone is wise or curious then paul is either strong or not kind.
Everyone who is old is both not quiet and strong and vice versa.
Someone is humble or curious.
Alice is either not strong or brave.
Paul is brave.
Fred is either quiet or wise.
Someone is both not brave and not humble.
Someone is either not quiet or curious.
Someone is either tall or not humble. | Alice is wise. | neutral | (![X]:(~quiet(X)<=>(wise(X)|~humble(X))))&
(![X]:(quiet(X)<=>strong(X)))&
((?[X]:((~curious(X)&strong(X))))=>((generous(paul)&~calm(paul))))&
(![X]:((~curious(X)&happy(X))<=>(~old(X)<~>~wise(X))))&
(![X]:((~happy(X)&strong(X))<=>(strong(X)|~happy(X))))&
(((quiet(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|~curious(X)))))&
((~brave(fred))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((patient(X)&brave(X))=>(old(X)&~strong(X))))&
((?[X]:((~creative(X)&quiet(X))))<=>(?[X]:((old(X)|~old(X)))))&
(((generous(mary)<~>humble(mary)))=>(?[X]:((tall(X)|calm(X)))))&
(((~creative(mary)<~>creative(mary)))=>((~humble(paul)<~>kind(paul))))&
((?[X]:((~rich(X)&~patient(X))))<=>(?[X]:((~tall(X)<~>humble(X)))))&
((?[X]:((~wise(X)|~rich(X))))=>((~brave(paul)|~humble(paul))))&
((?[X]:((wise(X)|curious(X))))=>((strong(paul)<~>~kind(paul))))&
(![X]:(old(X)<=>(~quiet(X)&strong(X))))&
(?[X]:((humble(X)|curious(X))))&
((~strong(alice)<~>brave(alice)))&
(brave(paul))&
((quiet(fred)<~>wise(fred)))&
(?[X]:((~brave(X)&~humble(X))))&
(?[X]:((~quiet(X)<~>curious(X))))&
(?[X]:((tall(X)<~>~humble(X)))) | wise(alice) | [] | null | 0 |
Everyone who is wise is either not old or generous. If lucy is curious then someone is both not funny and not calm. If someone is rich or tall then someone is generous or not old. Everyone who is either patient or calm is either not old or not kind and vice versa. Everyone who is either wise or not happy is both not old and not patient and vice versa. Everyone who is kind or old is both funny and rich. If mary is generous then paul is both not funny and not generous. Everyone who is both rich and not curious is not rich or not generous. Everyone who is patient is either not patient or not quiet and vice versa. If susan is brave then paul is not humble or not wise. Everyone who is either not creative or generous is either brave or not rich and vice versa. Everyone who is not funny or not kind is either not generous or not patient and vice versa. If john is both not tall and rich then mary is either wise or not tall. Everyone who is either generous or not creative is not funny or not rich and vice versa. Everyone who is either not calm or patient is both not patient and wise and vice versa. If alice is not old or not creative then someone is strong or not old and vice versa. Paul is funny. Susan is not quiet. Someone is either not wise or not humble. Someone is not kind. Paul is either kind or not humble. Someone is either funny or wise. | Alice is not wise. | entailment | (![X]:(wise(X)=>(~old(X)<~>generous(X))))&
((curious(lucy))=>(?[X]:((~funny(X)&~calm(X)))))&
((?[X]:((rich(X)|tall(X))))=>(?[X]:((generous(X)|~old(X)))))&
(![X]:((patient(X)<~>calm(X))<=>(~old(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~happy(X))<=>(~old(X)&~patient(X))))&
(![X]:((kind(X)|old(X))=>(funny(X)&rich(X))))&
((generous(mary))=>((~funny(paul)&~generous(paul))))&
(![X]:((rich(X)&~curious(X))=>(~rich(X)|~generous(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>~quiet(X))))&
((brave(susan))=>((~humble(paul)|~wise(paul))))&
(![X]:((~creative(X)<~>generous(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((~funny(X)|~kind(X))<=>(~generous(X)<~>~patient(X))))&
(((~tall(john)&rich(john)))=>((wise(mary)<~>~tall(mary))))&
(![X]:((generous(X)<~>~creative(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)<~>patient(X))<=>(~patient(X)&wise(X))))&
(((~old(alice)|~creative(alice)))<=>(?[X]:((strong(X)|~old(X)))))&
(funny(paul))&
(~quiet(susan))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((funny(X)<~>wise(X)))) | ~wise(alice) | [
"p0",
"p3",
"p5",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4054471452395753171665897
% SZS output start Proof for 4054471452395753171665897
1. ! [X0] : (wise(X0) => (~old(X0) <~> generous(X0))) [input p0]
4. ! [X0] : ((patient(X0) <~> calm(X0)) <=> (~old(X0) <~> ~kind(X0))) [input p3]
6. ! [X0] : ((old(X0) | kind(X0)) => (rich(X0) & funny(X0))) [input p5]
12. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (~generous(X0) <~> ~patient(X0))) [input p11]
15. ! [X0] : ((~calm(X0) <~> patient(X0)) <=> (wise(X0) & ~patient(X0))) [input p14]
23. wise(alice) [input hypothesis]
25. ! [X0] : ((~old(X0) <~> generous(X0)) | ~wise(X0)) [ennf transformation 1]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~old(X0) & ~kind(X0))) [ennf transformation 6]
36. ! [X0] : (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~wise(X0)) [nnf transformation 25]
42. ! [X0] : ((((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0))))) [nnf transformation 4]
47. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 12]
48. ! [X0] : ((~kind(X0) | ~funny(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (kind(X0) & funny(X0)))) [flattening 47]
52. ! [X0] : ((((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))))) [nnf transformation 15]
53. ! [X0] : ((((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))))) [flattening 52]
68. ~old(X0) | generous(X0) | ~wise(X0) [cnf transformation 36]
69. ~generous(X0) | old(X0) | ~wise(X0) [cnf transformation 36]
74. ~kind(X0) | ~old(X0) | calm(X0) | ~patient(X0) [cnf transformation 42]
76. ~patient(X0) | old(X0) | calm(X0) | kind(X0) [cnf transformation 42]
78. ~kind(X0) | patient(X0) | calm(X0) | old(X0) [cnf transformation 42]
79. ~old(X0) | patient(X0) | calm(X0) | kind(X0) [cnf transformation 42]
88. ~kind(X0) | funny(X0) [cnf transformation 28]
109. ~patient(X0) | ~generous(X0) | kind(X0) [cnf transformation 48]
111. kind(X0) | generous(X0) | patient(X0) [cnf transformation 48]
112. ~kind(X0) | ~funny(X0) | ~patient(X0) | generous(X0) [cnf transformation 48]
113. ~kind(X0) | ~funny(X0) | ~generous(X0) | patient(X0) [cnf transformation 48]
123. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 53]
126. patient(X0) | ~calm(X0) | ~wise(X0) | patient(X0) [cnf transformation 53]
141. wise(alice) [cnf transformation 23]
142. ~patient(X0) | ~calm(X0) [duplicate literal removal 123]
143. ~calm(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 126]
205. ~kind(X0) | ~generous(X0) | patient(X0) [subsumption resolution 113,88]
206. ~kind(X0) | ~patient(X0) | generous(X0) [subsumption resolution 112,88]
229. 19 <=> old(alice) [avatar definition]
230. old(alice) <- (19) [avatar component clause 229]
231. ~old(alice) <- (~19) [avatar component clause 229]
443. patient(X0) | calm(X0) | old(X0) | generous(X0) | patient(X0) [resolution 78,111]
445. patient(X0) | calm(X0) | old(X0) | generous(X0) [duplicate literal removal 443]
469. 43 <=> patient(alice) [avatar definition]
470. ~patient(alice) <- (~43) [avatar component clause 469]
471. patient(alice) <- (43) [avatar component clause 469]
656. calm(alice) | old(alice) | generous(alice) <- (~43) [resolution 445,470]
659. calm(alice) | generous(alice) <- (~19, ~43) [subsumption resolution 656,231]
661. 53 <=> generous(alice) [avatar definition]
663. generous(alice) <- (53) [avatar component clause 661]
665. 54 <=> calm(alice) [avatar definition]
666. ~calm(alice) <- (~54) [avatar component clause 665]
667. calm(alice) <- (54) [avatar component clause 665]
668. 53 | 54 | 19 | 43 [avatar split clause 659,469,229,665,661]
677. old(alice) | ~wise(alice) <- (53) [resolution 663,69]
696. old(alice) <- (53) [subsumption resolution 677,141]
697. 19 | ~53 [avatar split clause 696,661,229]
702. generous(alice) | ~wise(alice) <- (19) [resolution 230,68]
707. 58 <=> kind(alice) [avatar definition]
709. kind(alice) <- (58) [avatar component clause 707]
712. old(alice) | calm(alice) | kind(alice) <- (43) [resolution 471,76]
716. ~generous(alice) | kind(alice) <- (43) [resolution 471,109]
718. ~calm(alice) <- (43) [resolution 471,142]
723. ~54 | ~43 [avatar split clause 718,469,665]
724. 58 | ~53 | ~43 [avatar split clause 716,469,661,707]
725. generous(alice) <- (19) [subsumption resolution 702,141]
726. 53 | ~19 [avatar split clause 725,229,661]
729. ~old(alice) | calm(alice) | ~patient(alice) <- (58) [resolution 709,74]
736. ~patient(alice) | generous(alice) <- (58) [resolution 709,206]
741. ~old(alice) | ~patient(alice) <- (~54, 58) [subsumption resolution 729,666]
742. ~old(alice) <- (43, ~54, 58) [subsumption resolution 741,471]
743. ~19 | ~43 | 54 | ~58 [avatar split clause 742,707,665,469,229]
744. generous(alice) <- (43, 58) [subsumption resolution 736,471]
745. 53 | ~43 | ~58 [avatar split clause 744,707,469,661]
746. calm(alice) | kind(alice) <- (~19, 43) [subsumption resolution 712,231]
747. kind(alice) <- (~19, 43, ~54) [subsumption resolution 746,666]
748. 58 | 19 | ~43 | 54 [avatar split clause 747,665,469,229,707]
751. patient(alice) | calm(alice) | kind(alice) <- (19) [resolution 230,79]
766. ~generous(alice) | patient(alice) <- (58) [resolution 709,205]
768. patient(alice) <- (53, 58) [subsumption resolution 766,663]
769. $false <- (~43, 53, 58) [subsumption resolution 768,470]
770. 43 | ~53 | ~58 [avatar contradiction clause 769]
771. calm(alice) | kind(alice) <- (19, ~43) [subsumption resolution 751,470]
772. 58 | 54 | ~19 | 43 [avatar split clause 771,469,229,665,707]
784. patient(alice) | ~wise(alice) <- (54) [resolution 667,143]
785. ~wise(alice) <- (~43, 54) [subsumption resolution 784,470]
786. $false <- (~43, 54) [subsumption resolution 785,141]
787. 43 | ~54 [avatar contradiction clause 786]
788. $false [avatar sat refutation 668,697,723,724,726,743,745,748,770,772,787]
% SZS output end Proof for 4054471452395753171665897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or kind is both not humble and not happy.
If someone is not patient or not funny then mary is both calm and patient.
Everyone who is kind or not old is either happy or kind and vice versa.
If someone is not calm or brave then lucy is generous or not rich and vice versa.
If fred is both not wise and patient then paul is calm and vice versa.
If alice is patient or generous then someone is not generous and vice versa.
Everyone who is patient is either not wise or generous and vice versa.
Everyone who is not rich or humble is not old or not brave.
Everyone who is not generous is both strong and creative and vice versa.
If mary is either not happy or wise then fred is humble.
Everyone who is either wise or strong is either not rich or not old and vice versa.
If susan is either old or not wise then someone is either not brave or not rich.
If someone is not tall or quiet then someone is either not rich or patient and vice versa.
Everyone who is either not happy or not quiet is kind and vice versa.
Everyone who is quiet or not humble is not kind.
John is quiet.
Someone is either patient or not old.
Lucy is either not strong or patient.
Fred is not brave or patient.
Mary is not rich or not calm.
Someone is not patient or not kind.
Someone is not patient or not tall.
Someone is either rich or brave. | John is old. | contradiction | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
((?[X]:((~patient(X)|~funny(X))))=>((calm(mary)&patient(mary))))&
(![X]:((kind(X)|~old(X))<=>(happy(X)<~>kind(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((generous(lucy)|~rich(lucy))))&
(((~wise(fred)&patient(fred)))<=>(calm(paul)))&
(((patient(alice)|generous(alice)))<=>(?[X]:(~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>generous(X))))&
(![X]:((~rich(X)|humble(X))=>(~old(X)|~brave(X))))&
(![X]:(~generous(X)<=>(strong(X)&creative(X))))&
(((~happy(mary)<~>wise(mary)))=>(humble(fred)))&
(![X]:((wise(X)<~>strong(X))<=>(~rich(X)<~>~old(X))))&
(((old(susan)<~>~wise(susan)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((quiet(X)|~humble(X))=>~kind(X)))&
(quiet(john))&
(?[X]:((patient(X)<~>~old(X))))&
((~strong(lucy)<~>patient(lucy)))&
((~brave(fred)|patient(fred)))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>brave(X)))) | old(john) | [
"p2",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 642344724204902409919785
% SZS output start Proof for 642344724204902409919785
3. ! [X0] : ((~old(X0) | kind(X0)) <=> (happy(X0) <~> kind(X0))) [input p2]
14. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | quiet(X0)) => ~kind(X0)) [input p14]
16. quiet(john) [input p15]
24. old(john) [input hypothesis]
33. ! [X0] : (~kind(X0) | (humble(X0) & ~quiet(X0))) [ennf transformation 15]
35. ! [X0] : (((~old(X0) | kind(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) & (((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (old(X0) & ~kind(X0)))) [nnf transformation 3]
36. ! [X0] : ((~old(X0) | kind(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) & (((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (old(X0) & ~kind(X0)))) [flattening 35]
62. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ~kind(X0)) & (kind(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 14]
82. ~kind(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 36]
84. ~old(X0) | kind(X0) | kind(X0) | ~happy(X0) [cnf transformation 36]
125. ~quiet(X0) | kind(X0) | happy(X0) [cnf transformation 62]
128. quiet(X0) | happy(X0) | ~kind(X0) [cnf transformation 62]
129. ~kind(X0) | ~quiet(X0) [cnf transformation 33]
131. quiet(john) [cnf transformation 16]
142. old(john) [cnf transformation 24]
143. ~happy(X0) | ~kind(X0) [duplicate literal removal 82]
144. ~old(X0) | kind(X0) | ~happy(X0) [duplicate literal removal 84]
285. ~kind(X0) | quiet(X0) [subsumption resolution 128,143]
286. ~kind(X0) [subsumption resolution 129,285]
377. kind(john) | happy(john) [resolution 125,131]
380. happy(john) [subsumption resolution 377,286]
381. kind(john) | ~happy(john) [resolution 144,142]
384. ~happy(john) [subsumption resolution 381,286]
385. $false [subsumption resolution 384,380]
% SZS output end Proof for 642344724204902409919785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not funny or creative and vice versa. Everyone who is curious or tall is not brave. Everyone who is old is creative or not humble and vice versa. If someone is brave then lucy is not wise and vice versa. If someone is both happy and wise then susan is both kind and not brave. Everyone who is both wise and not funny is calm or not patient. Everyone who is both not creative and old is not kind. Everyone who is not quiet is quiet. Everyone who is both not wise and old is wise or rich. If someone is not curious or not generous then alice is brave and vice versa. If susan is not old or not kind then someone is both creative and not wise. If someone is both not brave and not happy then someone is not patient. Everyone who is not kind is both not tall and curious. Everyone who is either not old or strong is both not happy and creative and vice versa. Everyone who is both not tall and funny is both kind and not tall and vice versa. Everyone who is humble or kind is both curious and calm. Mary is both not brave and calm. Someone is quiet or curious. Someone is either not brave or not generous. Lucy is funny. Fred is either not old or curious. Alice is either not creative or old. Someone is either not rich or curious. | Susan is not generous. | contradiction | (![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((?[X]:(brave(X)))<=>(~wise(lucy)))&
((?[X]:((happy(X)&wise(X))))=>((kind(susan)&~brave(susan))))&
(![X]:((wise(X)&~funny(X))=>(calm(X)|~patient(X))))&
(![X]:((~creative(X)&old(X))=>~kind(X)))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~wise(X)&old(X))=>(wise(X)|rich(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>(brave(alice)))&
(((~old(susan)|~kind(susan)))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~tall(X)&curious(X))))&
(![X]:((~old(X)<~>strong(X))<=>(~happy(X)&creative(X))))&
(![X]:((~tall(X)&funny(X))<=>(kind(X)&~tall(X))))&
(![X]:((humble(X)|kind(X))=>(curious(X)&calm(X))))&
((~brave(mary)&calm(mary)))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(funny(lucy))&
((~old(fred)<~>curious(fred)))&
((~creative(alice)<~>old(alice)))&
(?[X]:((~rich(X)<~>curious(X)))) | ~generous(susan) | [
"p1",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7935754947835991265646675
% SZS output start Proof for 7935754947835991265646675
2. ! [X0] : ((tall(X0) | curious(X0)) => ~brave(X0)) [input p1]
10. ? [X0] : (~generous(X0) | ~curious(X0)) <=> brave(alice) [input p9]
13. ! [X0] : (~kind(X0) => (curious(X0) & ~tall(X0))) [input p12]
16. ! [X0] : ((kind(X0) | humble(X0)) => (calm(X0) & curious(X0))) [input p15]
24. ~generous(susan) [input hypothesis]
30. ! [X0] : ((kind(X0) | humble(X0)) => curious(X0)) [pure predicate removal 16]
32. ! [X0] : (~brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 2]
39. ! [X0] : ((curious(X0) & ~tall(X0)) | kind(X0)) [ennf transformation 13]
40. ! [X0] : (curious(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 30]
48. (? [X0] : (~generous(X0) | ~curious(X0)) | ~brave(alice)) & (brave(alice) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 10]
49. (? [X0] : (~generous(X0) | ~curious(X0)) | ~brave(alice)) & (brave(alice) | ! [X1] : (generous(X1) & curious(X1))) [rectify 48]
50. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK1) | ~curious(sK1)) [choice axiom]
51. ((~generous(sK1) | ~curious(sK1)) | ~brave(alice)) & (brave(alice) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 49,50]
70. ~brave(X0) | ~curious(X0) [cnf transformation 32]
82. brave(alice) | generous(X1) [cnf transformation 51]
89. curious(X0) | kind(X0) [cnf transformation 39]
101. curious(X0) | ~kind(X0) [cnf transformation 40]
112. ~generous(susan) [cnf transformation 24]
141. 7 <=> brave(alice) [avatar definition]
142. brave(alice) <- (7) [avatar component clause 141]
154. 10 <=> ! [X1] : generous(X1) [avatar definition]
155. generous(X1) <- (10) [avatar component clause 154]
156. 10 | 7 [avatar split clause 82,141,154]
158. 11 <=> ! [X1] : curious(X1) [avatar definition]
159. curious(X1) <- (11) [avatar component clause 158]
180. curious(X0) [subsumption resolution 101,89]
181. 11 [avatar split clause 180,158]
226. ~curious(alice) <- (7) [resolution 70,142]
230. $false <- (7, 11) [subsumption resolution 226,159]
231. ~7 | ~11 [avatar contradiction clause 230]
234. $false <- (10) [resolution 155,112]
237. ~10 [avatar contradiction clause 234]
238. $false [avatar sat refutation 156,181,231,237]
% SZS output end Proof for 7935754947835991265646675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and quiet is patient or not generous. If susan is both not calm and kind then lucy is both not funny and not humble. If someone is not tall then someone is rich or quiet and vice versa. Everyone who is not funny is curious. Everyone who is brave or wise is either quiet or not funny. If someone is both not curious and kind then lucy is either old or funny. If someone is tall then someone is funny or not happy and vice versa. If someone is either not creative or brave then someone is both not tall and calm and vice versa. If john is both not calm and brave then mary is old or curious. If john is both not humble and humble then someone is old or happy. Everyone who is brave is either not patient or not tall and vice versa. If someone is both tall and old then fred is either patient or not curious and vice versa. Everyone who is not tall or not quiet is not rich and vice versa. Everyone who is both creative and not creative is kind and vice versa. Everyone who is both humble and generous is either not tall or not funny and vice versa. Everyone who is humble or not kind is either not strong or not quiet. John is rich. Alice is not creative. John is both not humble and not old. Someone is both not curious and wise. Someone is either calm or not kind. Someone is not quiet. Susan is tall or not tall. John is happy. | John is funny. | entailment | (![X]:((~quiet(X)&quiet(X))=>(patient(X)|~generous(X))))&
(((~calm(susan)&kind(susan)))=>((~funny(lucy)&~humble(lucy))))&
((?[X]:(~tall(X)))<=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:(~funny(X)=>curious(X)))&
(![X]:((brave(X)|wise(X))=>(quiet(X)<~>~funny(X))))&
((?[X]:((~curious(X)&kind(X))))=>((old(lucy)<~>funny(lucy))))&
((?[X]:(tall(X)))<=>(?[X]:((funny(X)|~happy(X)))))&
((?[X]:((~creative(X)<~>brave(X))))<=>(?[X]:((~tall(X)&calm(X)))))&
(((~calm(john)&brave(john)))=>((old(mary)|curious(mary))))&
(((~humble(john)&humble(john)))=>(?[X]:((old(X)|happy(X)))))&
(![X]:(brave(X)<=>(~patient(X)<~>~tall(X))))&
((?[X]:((tall(X)&old(X))))<=>((patient(fred)<~>~curious(fred))))&
(![X]:((~tall(X)|~quiet(X))<=>~rich(X)))&
(![X]:((creative(X)&~creative(X))<=>kind(X)))&
(![X]:((humble(X)&generous(X))<=>(~tall(X)<~>~funny(X))))&
(![X]:((humble(X)|~kind(X))=>(~strong(X)<~>~quiet(X))))&
(rich(john))&
(~creative(alice))&
((~humble(john)&~old(john)))&
(?[X]:((~curious(X)&wise(X))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:(~quiet(X)))&
((tall(susan)|~tall(susan)))&
(happy(john)) | funny(john) | [
"p12",
"p14",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3078487991071284968803694
% SZS output start Proof for 3078487991071284968803694
13. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> ~rich(X0)) [input p12]
15. ! [X0] : ((generous(X0) & humble(X0)) <=> (~tall(X0) <~> ~funny(X0))) [input p14]
17. rich(john) [input p16]
19. ~old(john) & ~humble(john) [input p18]
25. ~funny(john) [input hypothesis]
65. ! [X0] : (((~quiet(X0) | ~tall(X0)) | rich(X0)) & (~rich(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 13]
66. ! [X0] : ((~quiet(X0) | ~tall(X0) | rich(X0)) & (~rich(X0) | (quiet(X0) & tall(X0)))) [flattening 65]
69. ! [X0] : (((generous(X0) & humble(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~generous(X0) | ~humble(X0)))) [nnf transformation 15]
70. ! [X0] : (((generous(X0) & humble(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~generous(X0) | ~humble(X0))) [flattening 69]
113. ~rich(X0) | tall(X0) [cnf transformation 66]
122. ~tall(X0) | humble(X0) | funny(X0) [cnf transformation 70]
129. rich(john) [cnf transformation 17]
131. ~humble(john) [cnf transformation 19]
140. ~funny(john) [cnf transformation 25]
301. tall(john) [resolution 113,129]
402. humble(john) | funny(john) [resolution 122,301]
406. funny(john) [subsumption resolution 402,131]
407. $false [subsumption resolution 406,140]
% SZS output end Proof for 3078487991071284968803694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not old is both rich and quiet.
Everyone who is not funny or not quiet is either funny or not old and vice versa.
If john is not strong or not old then someone is not rich or quiet and vice versa.
If someone is calm or rich then lucy is either not old or brave and vice versa.
If someone is either not humble or not funny then susan is both quiet and not old and vice versa.
If someone is both happy and not funny then someone is tall or quiet and vice versa.
If someone is either generous or creative then someone is both not curious and quiet.
If someone is patient then lucy is either not happy or not curious and vice versa.
If mary is either not strong or strong then fred is not funny and vice versa.
Everyone who is both not wise and old is either not curious or not rich and vice versa.
If someone is funny or not calm then mary is both creative and not generous and vice versa.
Everyone who is either funny or brave is either kind or not brave.
If someone is old or not wise then lucy is both curious and not generous and vice versa.
If susan is both patient and not brave then susan is humble or not old.
Everyone who is humble is generous or not tall.
Everyone who is both not old and not quiet is both kind and not calm and vice versa.
Lucy is not patient.
Someone is both not kind and not wise.
Mary is quiet.
Fred is either creative or not humble.
Someone is both not generous and kind. | Fred is not tall. | neutral | (![X]:((~wise(X)|~old(X))=>(rich(X)&quiet(X))))&
(![X]:((~funny(X)|~quiet(X))<=>(funny(X)<~>~old(X))))&
(((~strong(john)|~old(john)))<=>(?[X]:((~rich(X)|quiet(X)))))&
((?[X]:((calm(X)|rich(X))))<=>((~old(lucy)<~>brave(lucy))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((quiet(susan)&~old(susan))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
((?[X]:((generous(X)<~>creative(X))))=>(?[X]:((~curious(X)&quiet(X)))))&
((?[X]:(patient(X)))<=>((~happy(lucy)<~>~curious(lucy))))&
(((~strong(mary)<~>strong(mary)))<=>(~funny(fred)))&
(![X]:((~wise(X)&old(X))<=>(~curious(X)<~>~rich(X))))&
((?[X]:((funny(X)|~calm(X))))<=>((creative(mary)&~generous(mary))))&
(![X]:((funny(X)<~>brave(X))=>(kind(X)<~>~brave(X))))&
((?[X]:((old(X)|~wise(X))))<=>((curious(lucy)&~generous(lucy))))&
(((patient(susan)&~brave(susan)))=>((humble(susan)|~old(susan))))&
(![X]:(humble(X)=>(generous(X)|~tall(X))))&
(![X]:((~old(X)&~quiet(X))<=>(kind(X)&~calm(X))))&
(~patient(lucy))&
(?[X]:((~kind(X)&~wise(X))))&
(quiet(mary))&
((creative(fred)<~>~humble(fred)))&
(?[X]:((~generous(X)&kind(X)))) | ~tall(fred) | [] | null | 0 |
Everyone who is strong or funny is either not funny or not rich. If someone is both generous and not brave then someone is both not generous and tall. If john is not kind then fred is kind or not quiet. Everyone who is both curious and not strong is either patient or not quiet. If someone is both not strong and tall then someone is both not old and creative. If someone is happy or not humble then john is not funny and vice versa. If lucy is not calm or quiet then someone is old. If fred is not brave then fred is both not strong and brave. Everyone who is either not strong or not wise is both not rich and calm and vice versa. If john is not creative then susan is happy or not patient. If paul is both kind and funny then someone is either not curious or quiet and vice versa. Everyone who is both generous and not rich is either not brave or rich and vice versa. Everyone who is either wise or strong is not funny. If someone is brave then mary is not kind or not quiet. Everyone who is both creative and not calm is both not wise and not creative. If someone is both not curious and not calm then someone is either generous or not curious. Mary is humble. Lucy is kind. John is generous. Lucy is both not humble and old. Paul is either not old or rich. Paul is both not happy and rich. Someone is tall or not funny. Alice is both not tall and happy. | Alice is happy. | entailment | (![X]:((strong(X)|funny(X))=>(~funny(X)<~>~rich(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((~generous(X)&tall(X)))))&
((~kind(john))=>((kind(fred)|~quiet(fred))))&
(![X]:((curious(X)&~strong(X))=>(patient(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:((happy(X)|~humble(X))))<=>(~funny(john)))&
(((~calm(lucy)|quiet(lucy)))=>(?[X]:(old(X))))&
((~brave(fred))=>((~strong(fred)&brave(fred))))&
(![X]:((~strong(X)<~>~wise(X))<=>(~rich(X)&calm(X))))&
((~creative(john))=>((happy(susan)|~patient(susan))))&
(((kind(paul)&funny(paul)))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((wise(X)<~>strong(X))=>~funny(X)))&
((?[X]:(brave(X)))=>((~kind(mary)|~quiet(mary))))&
(![X]:((creative(X)&~calm(X))=>(~wise(X)&~creative(X))))&
((?[X]:((~curious(X)&~calm(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(humble(mary))&
(kind(lucy))&
(generous(john))&
((~humble(lucy)&old(lucy)))&
((~old(paul)<~>rich(paul)))&
((~happy(paul)&rich(paul)))&
(?[X]:((tall(X)|~funny(X))))&
((~tall(alice)&happy(alice))) | happy(alice) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4546815046142381489495705
% SZS output start Proof for 4546815046142381489495705
24. happy(alice) & ~tall(alice) [input p23]
25. ~happy(alice) [input hypothesis]
132. happy(alice) [cnf transformation 24]
133. ~happy(alice) [cnf transformation 25]
300. $false [subsumption resolution 133,132]
% SZS output end Proof for 4546815046142381489495705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
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