premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is either happy or not curious is creative or not strong.
Everyone who is calm or not curious is happy.
Everyone who is either patient or not patient is either not patient or not brave and vice versa.
If someone is not old then someone is either generous or not curious.
Everyone who is either not patient or not rich is both funny and not funny.
If someone is both strong and humble then someone is both wise and happy and vice versa.
If someone is either creative or funny then someone is both not creative and not funny.
If someone is not wise then john is not quiet or not patient.
Everyone who is not happy or generous is both funny and not rich.
Everyone who is not brave or funny is both not kind and calm.
If paul is either not strong or kind then someone is creative or not wise and vice versa.
If someone is happy then susan is both wise and old and vice versa.
Everyone who is not old is either not creative or wise and vice versa.
Everyone who is calm or old is not funny or not wise.
Everyone who is both not quiet and happy is either brave or quiet and vice versa.
Everyone who is both not quiet and tall is both patient and not rich.
Lucy is either kind or not patient.
Someone is either quiet or wise.
Someone is not patient or strong.
Mary is either not old or not generous.
Mary is either brave or not calm.
Someone is generous or quiet. | Susan is rich. | contradiction | (![X]:((happy(X)<~>~curious(X))=>(creative(X)|~strong(X))))&
(![X]:((calm(X)|~curious(X))=>happy(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>(funny(X)&~funny(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((creative(X)<~>funny(X))))=>(?[X]:((~creative(X)&~funny(X)))))&
((?[X]:(~wise(X)))=>((~quiet(john)|~patient(john))))&
(![X]:((~happy(X)|generous(X))=>(funny(X)&~rich(X))))&
(![X]:((~brave(X)|funny(X))=>(~kind(X)&calm(X))))&
(((~strong(paul)<~>kind(paul)))<=>(?[X]:((creative(X)|~wise(X)))))&
((?[X]:(happy(X)))<=>((wise(susan)&old(susan))))&
(![X]:(~old(X)<=>(~creative(X)<~>wise(X))))&
(![X]:((calm(X)|old(X))=>(~funny(X)|~wise(X))))&
(![X]:((~quiet(X)&happy(X))<=>(brave(X)<~>quiet(X))))&
(![X]:((~quiet(X)&tall(X))=>(patient(X)&~rich(X))))&
((kind(lucy)<~>~patient(lucy)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((~patient(X)|strong(X))))&
((~old(mary)<~>~generous(mary)))&
((brave(mary)<~>~calm(mary)))&
(?[X]:((generous(X)|quiet(X)))) | rich(susan) | [
"p1",
"p2",
"p4",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7503696487986386552831199
% SZS output start Proof for 7503696487986386552831199
2. ! [X0] : ((~curious(X0) | calm(X0)) => happy(X0)) [input p1]
3. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (~patient(X0) <~> ~brave(X0))) [input p2]
5. ! [X0] : ((~patient(X0) <~> ~rich(X0)) => (~funny(X0) & funny(X0))) [input p4]
9. ! [X0] : ((generous(X0) | ~happy(X0)) => (~rich(X0) & funny(X0))) [input p8]
10. ! [X0] : ((funny(X0) | ~brave(X0)) => (calm(X0) & ~kind(X0))) [input p9]
15. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (brave(X0) <~> quiet(X0))) [input p14]
23. rich(susan) [input hypothesis]
30. ! [X0] : (happy(X0) | (curious(X0) & ~calm(X0))) [ennf transformation 2]
32. ! [X0] : ((~funny(X0) & funny(X0)) | (~patient(X0) <=> ~rich(X0))) [ennf transformation 5]
36. ! [X0] : ((~rich(X0) & funny(X0)) | (~generous(X0) & happy(X0))) [ennf transformation 9]
37. ! [X0] : ((calm(X0) & ~kind(X0)) | (~funny(X0) & brave(X0))) [ennf transformation 10]
41. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 3]
46. ! [X0] : ((~funny(X0) & funny(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) [nnf transformation 32]
66. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~happy(X0) | quiet(X0)))) [nnf transformation 15]
67. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ~happy(X0) | quiet(X0))) [flattening 66]
80. ~calm(X0) | happy(X0) [cnf transformation 30]
82. ~brave(X0) | ~patient(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 41]
92. funny(X0) | ~rich(X0) | patient(X0) [cnf transformation 46]
94. ~funny(X0) | ~rich(X0) | patient(X0) [cnf transformation 46]
105. funny(X0) | happy(X0) [cnf transformation 36]
112. ~funny(X0) | calm(X0) [cnf transformation 37]
128. quiet(X0) | brave(X0) | ~happy(X0) | quiet(X0) [cnf transformation 67]
131. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 67]
144. rich(susan) [cnf transformation 23]
145. quiet(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 128]
146. ~quiet(X0) | brave(X0) [duplicate literal removal 131]
147. ~brave(X0) | ~patient(X0) [duplicate literal removal 82]
169. ~rich(X0) | patient(X0) [subsumption resolution 92,94]
270. ~happy(X0) | brave(X0) [subsumption resolution 145,146]
327. calm(X0) | happy(X0) [resolution 112,105]
329. happy(X0) [subsumption resolution 327,80]
336. patient(susan) [resolution 169,144]
349. brave(X0) [resolution 270,329]
361. ~patient(X0) [resolution 349,147]
362. $false [resolution 361,336]
% SZS output end Proof for 7503696487986386552831199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or calm is happy and vice versa. Everyone who is either not patient or brave is creative and vice versa. If someone is not generous or not wise then lucy is both quiet and not quiet and vice versa. Everyone who is either not strong or creative is either not humble or not creative and vice versa. If john is both funny and kind then someone is brave and vice versa. If lucy is not strong or patient then paul is humble or wise and vice versa. If lucy is either not old or not creative then someone is kind and vice versa. Everyone who is either not humble or quiet is not humble or not brave and vice versa. Everyone who is quiet or not wise is either calm or humble and vice versa. Everyone who is not patient is both kind and not funny and vice versa. If someone is not quiet or not wise then someone is either tall or old and vice versa. Everyone who is not rich is both tall and generous. Everyone who is either not quiet or kind is either wise or not strong. Everyone who is happy is not strong or tall and vice versa. If someone is either creative or calm then someone is not strong. Fred is happy or funny. Paul is either happy or not happy. Someone is either happy or not patient. Alice is not wise or not strong. Susan is both not brave and not creative. Someone is not tall. Alice is rich or strong. | Alice is kind. | entailment | (![X]:((kind(X)|calm(X))<=>happy(X)))&
(![X]:((~patient(X)<~>brave(X))<=>creative(X)))&
((?[X]:((~generous(X)|~wise(X))))<=>((quiet(lucy)&~quiet(lucy))))&
(![X]:((~strong(X)<~>creative(X))<=>(~humble(X)<~>~creative(X))))&
(((funny(john)&kind(john)))<=>(?[X]:(brave(X))))&
(((~strong(lucy)|patient(lucy)))<=>((humble(paul)|wise(paul))))&
(((~old(lucy)<~>~creative(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~humble(X)|~brave(X))))&
(![X]:((quiet(X)|~wise(X))<=>(calm(X)<~>humble(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
((?[X]:((~quiet(X)|~wise(X))))<=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(wise(X)<~>~strong(X))))&
(![X]:(happy(X)<=>(~strong(X)|tall(X))))&
((?[X]:((creative(X)<~>calm(X))))=>(?[X]:(~strong(X))))&
((happy(fred)|funny(fred)))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((happy(X)<~>~patient(X))))&
((~wise(alice)|~strong(alice)))&
((~brave(susan)&~creative(susan)))&
(?[X]:(~tall(X)))&
((rich(alice)|strong(alice))) | kind(alice) | [
"p0",
"p2",
"p7",
"p8",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5172511045861358648209410
% SZS output start Proof for 5172511045861358648209410
1. ! [X0] : ((calm(X0) | kind(X0)) <=> happy(X0)) [input p0]
3. ? [X0] : (~wise(X0) | ~generous(X0)) <=> (~quiet(lucy) & quiet(lucy)) [input p2]
8. ! [X0] : ((~humble(X0) <~> quiet(X0)) <=> (~brave(X0) | ~humble(X0))) [input p7]
9. ! [X0] : ((~wise(X0) | quiet(X0)) <=> (calm(X0) <~> humble(X0))) [input p8]
13. ! [X0] : ((~quiet(X0) <~> kind(X0)) => (wise(X0) <~> ~strong(X0))) [input p12]
14. ! [X0] : (happy(X0) <=> (tall(X0) | ~strong(X0))) [input p13]
19. ~strong(alice) | ~wise(alice) [input p18]
23. ~kind(alice) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> ~strong(X0)) | (~quiet(X0) <=> kind(X0))) [ennf transformation 13]
30. ! [X0] : (((calm(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (~calm(X0) & ~kind(X0)))) [nnf transformation 1]
31. ! [X0] : ((calm(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (~calm(X0) & ~kind(X0)))) [flattening 30]
33. (? [X0] : (~wise(X0) | ~generous(X0)) | (quiet(lucy) | ~quiet(lucy))) & ((~quiet(lucy) & quiet(lucy)) | ! [X0] : (wise(X0) & generous(X0))) [nnf transformation 3]
34. (? [X0] : (~wise(X0) | ~generous(X0)) | quiet(lucy) | ~quiet(lucy)) & ((~quiet(lucy) & quiet(lucy)) | ! [X0] : (wise(X0) & generous(X0))) [flattening 33]
35. (? [X0] : (~wise(X0) | ~generous(X0)) | quiet(lucy) | ~quiet(lucy)) & ((~quiet(lucy) & quiet(lucy)) | ! [X1] : (wise(X1) & generous(X1))) [rectify 34]
36. ? [X0] : (~wise(X0) | ~generous(X0)) => (~wise(sK0) | ~generous(sK0)) [choice axiom]
37. ((~wise(sK0) | ~generous(sK0)) | quiet(lucy) | ~quiet(lucy)) & ((~quiet(lucy) & quiet(lucy)) | ! [X1] : (wise(X1) & generous(X1))) [skolemisation 35,36]
50. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (brave(X0) & humble(X0))) & ((~brave(X0) | ~humble(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [nnf transformation 8]
51. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (brave(X0) & humble(X0))) & (~brave(X0) | ~humble(X0) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [flattening 50]
52. ! [X0] : (((~wise(X0) | quiet(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (wise(X0) & ~quiet(X0)))) [nnf transformation 9]
53. ! [X0] : ((~wise(X0) | quiet(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (wise(X0) & ~quiet(X0)))) [flattening 52]
61. ! [X0] : (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) [nnf transformation 28]
62. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~happy(X0))) [nnf transformation 14]
63. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~happy(X0))) [flattening 62]
76. ~happy(X0) | kind(X0) | calm(X0) [cnf transformation 31]
82. quiet(lucy) | wise(X1) [cnf transformation 37]
84. ~quiet(lucy) | wise(X1) [cnf transformation 37]
109. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 51]
113. ~humble(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 53]
128. ~wise(X0) | strong(X0) | kind(X0) | quiet(X0) [cnf transformation 61]
131. strong(X0) | happy(X0) [cnf transformation 63]
140. ~strong(alice) | ~wise(alice) [cnf transformation 19]
144. ~kind(alice) [cnf transformation 23]
146. ~quiet(X0) | humble(X0) [duplicate literal removal 109]
152. 1 <=> ! [X1] : wise(X1) [avatar definition]
153. wise(X1) <- (1) [avatar component clause 152]
155. 2 <=> quiet(lucy) [avatar definition]
158. 1 | ~2 [avatar split clause 84,155,152]
163. 1 | 2 [avatar split clause 82,155,152]
226. ~quiet(X0) | ~calm(X0) [subsumption resolution 113,146]
290. 30 <=> wise(alice) [avatar definition]
292. ~wise(alice) <- (~30) [avatar component clause 290]
294. 31 <=> strong(alice) [avatar definition]
296. ~strong(alice) <- (~31) [avatar component clause 294]
297. ~30 | ~31 [avatar split clause 140,294,290]
298. $false <- (1, ~30) [resolution 292,153]
299. ~1 | 30 [avatar contradiction clause 298]
309. happy(alice) <- (~31) [resolution 131,296]
314. kind(alice) | calm(alice) <- (~31) [resolution 76,309]
337. calm(alice) <- (~31) [subsumption resolution 314,144]
499. strong(X0) | kind(X0) | quiet(X0) <- (1) [resolution 128,153]
535. kind(alice) | quiet(alice) <- (1, ~31) [resolution 499,296]
540. quiet(alice) <- (1, ~31) [subsumption resolution 535,144]
543. ~calm(alice) <- (1, ~31) [resolution 540,226]
546. $false <- (1, ~31) [subsumption resolution 543,337]
547. ~1 | 31 [avatar contradiction clause 546]
550. $false [avatar sat refutation 158,163,297,299,547]
% SZS output end Proof for 5172511045861358648209410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or humble is both not happy and wise.
Everyone who is happy or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Everyone who is kind is either kind or not rich.
Everyone who is either brave or not old is both not wise and not calm.
If paul is patient or rich then someone is both not quiet and kind.
Everyone who is either humble or funny is wise and vice versa.
If someone is either not patient or creative then someone is rich or not creative.
John is both not wise and not rich.
Someone is both not brave and not rich.
Paul is not strong or patient.
Someone is creative or patient.
Alice is either not happy or creative.
Lucy is both curious and not funny.
Susan is old.
Alice is not wise. | John is not curious. | entailment | (![X]:((rich(X)|humble(X))=>(~happy(X)&wise(X))))&
(![X]:((happy(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
(![X]:(kind(X)=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~old(X))=>(~wise(X)&~calm(X))))&
(((patient(paul)|rich(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((~wise(john)&~rich(john)))&
(?[X]:((~brave(X)&~rich(X))))&
((~strong(paul)|patient(paul)))&
(?[X]:((creative(X)|patient(X))))&
((~happy(alice)<~>creative(alice)))&
((curious(lucy)&~funny(lucy)))&
(old(susan))&
(~wise(alice)) | ~curious(john) | [
"p1",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8835516032619938450888
% SZS output start Proof for 8835516032619938450888
2. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~patient(X0) <~> ~curious(X0))) [input p1]
7. ! [X0] : (wise(X0) <=> (generous(X0) | ~patient(X0))) [input p6]
17. ~rich(john) & ~wise(john) [input p16]
25. curious(john) [input hypothesis]
40. ! [X0] : (((~rich(X0) | happy(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | happy(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [flattening 40]
50. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ~wise(X0))) [nnf transformation 7]
51. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ~wise(X0))) [flattening 50]
79. ~curious(X0) | ~patient(X0) | rich(X0) [cnf transformation 41]
95. patient(X0) | wise(X0) [cnf transformation 51]
120. ~wise(john) [cnf transformation 17]
121. ~rich(john) [cnf transformation 17]
132. curious(john) [cnf transformation 25]
137. 1 <=> patient(john) [avatar definition]
138. ~patient(john) <- (~1) [avatar component clause 137]
139. patient(john) <- (1) [avatar component clause 137]
274. wise(john) <- (~1) [resolution 95,138]
276. $false <- (~1) [subsumption resolution 274,120]
277. 1 [avatar contradiction clause 276]
316. ~patient(john) | rich(john) [resolution 79,132]
323. rich(john) <- (1) [subsumption resolution 316,139]
324. $false <- (1) [subsumption resolution 323,121]
325. ~1 [avatar contradiction clause 324]
326. $false [avatar sat refutation 277,325]
% SZS output end Proof for 8835516032619938450888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and vice versa. Everyone who is not humble or brave is either not funny or not brave. Everyone who is old or kind is funny and vice versa. Everyone who is both rich and not tall is not funny or kind and vice versa. Everyone who is both not old and rich is both not rich and not curious. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Everyone who is not curious or brave is not patient or not generous. If mary is rich then someone is not patient or happy and vice versa. Someone is not calm. Someone is not strong or not funny. Alice is either creative or wise. Someone is either not curious or kind. Lucy is humble or strong. Someone is old. | Mary is rich. | entailment | (![X]:((~kind(X)&kind(X))<=>creative(X)))&
(![X]:((~humble(X)|brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((old(X)|kind(X))<=>funny(X)))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
((rich(mary))<=>(?[X]:((~patient(X)|happy(X)))))&
(?[X]:(~calm(X)))&
(?[X]:((~strong(X)|~funny(X))))&
((creative(alice)<~>wise(alice)))&
(?[X]:((~curious(X)<~>kind(X))))&
((humble(lucy)|strong(lucy)))&
(?[X]:(old(X))) | rich(mary) | [
"p0",
"p2",
"p3",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4026349809050727277291805
% SZS output start Proof for 4026349809050727277291805
1. ! [X0] : ((kind(X0) & ~kind(X0)) <=> creative(X0)) [input p0]
3. ! [X0] : ((kind(X0) | old(X0)) <=> funny(X0)) [input p2]
4. ! [X0] : ((~tall(X0) & rich(X0)) <=> (kind(X0) | ~funny(X0))) [input p3]
5. ! [X0] : ((rich(X0) & ~old(X0)) => (~curious(X0) & ~rich(X0))) [input p4]
12. ? [X0] : (curious(X0) & ~funny(X0)) <=> (~happy(lucy) & ~creative(lucy)) [input p11]
14. rich(mary) <=> ? [X0] : (happy(X0) | ~patient(X0)) [input p13]
21. ~rich(mary) [input hypothesis]
24. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~rich(X0) | old(X0))) [ennf transformation 5]
25. ! [X0] : ((~curious(X0) & ~rich(X0)) | ~rich(X0) | old(X0)) [flattening 24]
33. ! [X0] : (((kind(X0) & ~kind(X0)) | ~creative(X0)) & (creative(X0) | (~kind(X0) | kind(X0)))) [nnf transformation 1]
34. ! [X0] : (((kind(X0) & ~kind(X0)) | ~creative(X0)) & (creative(X0) | ~kind(X0) | kind(X0))) [flattening 33]
36. ! [X0] : (((kind(X0) | old(X0)) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 3]
37. ! [X0] : ((kind(X0) | old(X0) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~old(X0)))) [flattening 36]
38. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | (tall(X0) | ~rich(X0)))) [nnf transformation 4]
39. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | tall(X0) | ~rich(X0))) [flattening 38]
48. (? [X0] : (curious(X0) & ~funny(X0)) | (happy(lucy) | creative(lucy))) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [nnf transformation 12]
49. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [flattening 48]
50. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [rectify 49]
51. ? [X0] : (curious(X0) & ~funny(X0)) => (curious(sK0) & ~funny(sK0)) [choice axiom]
52. ((curious(sK0) & ~funny(sK0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [skolemisation 50,51]
53. (rich(mary) | ! [X0] : (~happy(X0) & patient(X0))) & (? [X0] : (happy(X0) | ~patient(X0)) | ~rich(mary)) [nnf transformation 14]
54. (rich(mary) | ! [X0] : (~happy(X0) & patient(X0))) & (? [X1] : (happy(X1) | ~patient(X1)) | ~rich(mary)) [rectify 53]
55. ? [X1] : (happy(X1) | ~patient(X1)) => (happy(sK1) | ~patient(sK1)) [choice axiom]
56. (rich(mary) | ! [X0] : (~happy(X0) & patient(X0))) & ((happy(sK1) | ~patient(sK1)) | ~rich(mary)) [skolemisation 54,55]
68. ~kind(X0) | ~creative(X0) [cnf transformation 34]
69. ~creative(X0) | kind(X0) [cnf transformation 34]
74. ~old(X0) | funny(X0) [cnf transformation 37]
78. rich(X0) | funny(X0) [cnf transformation 39]
82. ~rich(X0) | ~rich(X0) | old(X0) [cnf transformation 25]
105. ~funny(sK0) | happy(lucy) | creative(lucy) [cnf transformation 52]
111. rich(mary) | ~happy(X0) [cnf transformation 56]
120. ~rich(mary) [cnf transformation 21]
123. ~rich(X0) | old(X0) [duplicate literal removal 82]
125. ~creative(X0) [subsumption resolution 68,69]
145. 3 <=> happy(lucy) [avatar definition]
147. happy(lucy) <- (3) [avatar component clause 145]
153. ~funny(sK0) | happy(lucy) [subsumption resolution 105,125]
155. 5 <=> funny(sK0) [avatar definition]
157. ~funny(sK0) <- (~5) [avatar component clause 155]
158. 3 | ~5 [avatar split clause 153,155,145]
165. 7 <=> ! [X0] : ~happy(X0) [avatar definition]
166. ~happy(X0) <- (7) [avatar component clause 165]
168. 8 <=> rich(mary) [avatar definition]
171. 7 | 8 [avatar split clause 111,168,165]
214. ~8 [avatar split clause 120,168]
222. old(X0) | funny(X0) [resolution 123,78]
223. funny(X0) [subsumption resolution 222,74]
224. $false <- (~5) [resolution 223,157]
227. 5 [avatar contradiction clause 224]
228. $false <- (3, 7) [subsumption resolution 147,166]
229. ~3 | ~7 [avatar contradiction clause 228]
230. $false [avatar sat refutation 158,171,214,227,229]
% SZS output end Proof for 4026349809050727277291805
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not generous then john is either quiet or old.
If someone is either brave or tall then paul is either not rich or not patient and vice versa.
If someone is funny then someone is either not happy or rich and vice versa.
Everyone who is not kind is creative or not patient and vice versa.
Everyone who is both brave and curious is both not quiet and generous and vice versa.
If paul is both happy and funny then mary is not funny and vice versa.
Everyone who is either not old or generous is both calm and generous and vice versa.
Everyone who is either not patient or funny is not humble.
If paul is both curious and not kind then someone is not brave.
If someone is not patient then someone is both not brave and not old and vice versa.
If someone is both funny and not brave then paul is both kind and humble.
Everyone who is not strong is either creative or not strong and vice versa.
Everyone who is both strong and old is tall.
Everyone who is strong or not kind is either not funny or not tall and vice versa.
Everyone who is both not strong and tall is happy or kind and vice versa.
Everyone who is not quiet is not tall or generous and vice versa.
Susan is both happy and not strong.
Someone is either not quiet or tall.
Someone is not rich.
Susan is old.
Paul is not old.
Alice is both old and curious.
Paul is curious or not generous. | Alice is not humble. | entailment | ((?[X]:((generous(X)|~generous(X))))=>((quiet(john)<~>old(john))))&
((?[X]:((brave(X)<~>tall(X))))<=>((~rich(paul)<~>~patient(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(creative(X)|~patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~quiet(X)&generous(X))))&
(((happy(paul)&funny(paul)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>generous(X))<=>(calm(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>~humble(X)))&
(((curious(paul)&~kind(paul)))=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((?[X]:((funny(X)&~brave(X))))=>((kind(paul)&humble(paul))))&
(![X]:(~strong(X)<=>(creative(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))=>tall(X)))&
(![X]:((strong(X)|~kind(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~strong(X)&tall(X))<=>(happy(X)|kind(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|generous(X))))&
((happy(susan)&~strong(susan)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~rich(X)))&
(old(susan))&
(~old(paul))&
((old(alice)&curious(alice)))&
((curious(paul)|~generous(paul))) | ~humble(alice) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6055852932966073497923489
% SZS output start Proof for 6055852932966073497923489
4. ! [X0] : (~kind(X0) <=> (~patient(X0) | creative(X0))) [input p3]
5. ! [X0] : ((curious(X0) & brave(X0)) <=> (generous(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~old(X0) <~> generous(X0)) <=> (generous(X0) & calm(X0))) [input p6]
8. ! [X0] : ((~patient(X0) <~> funny(X0)) => ~humble(X0)) [input p7]
10. ? [X0] : ~patient(X0) <=> ? [X0] : (~old(X0) & ~brave(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (creative(X0) <~> ~strong(X0))) [input p11]
14. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p13]
15. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (kind(X0) | happy(X0))) [input p14]
16. ! [X0] : (~quiet(X0) <=> (generous(X0) | ~tall(X0))) [input p15]
24. humble(alice) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : (~old(X1) & ~brave(X1)) [rectify 10]
28. ! [X0] : (~humble(X0) | (~patient(X0) <=> funny(X0))) [ennf transformation 8]
44. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | kind(X0))) [nnf transformation 4]
45. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | kind(X0))) [flattening 44]
46. ! [X0] : (((curious(X0) & brave(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((curious(X0) & brave(X0)) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [flattening 50]
52. ! [X0] : (~humble(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) [nnf transformation 28]
55. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X1] : (~old(X1) & ~brave(X1)) | ! [X0] : patient(X0)) [nnf transformation 26]
56. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X2] : (~old(X2) & ~brave(X2)) | ! [X3] : patient(X3)) [rectify 55]
57. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
58. ? [X2] : (~old(X2) & ~brave(X2)) => (~old(sK5) & ~brave(sK5)) [choice axiom]
59. (~patient(sK4) | ! [X1] : (old(X1) | brave(X1))) & ((~old(sK5) & ~brave(sK5)) | ! [X3] : patient(X3)) [skolemisation 56,58,57]
60. ! [X0] : ((~strong(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | strong(X0))) [nnf transformation 12]
61. ! [X0] : (((~kind(X0) | strong(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : ((~kind(X0) | strong(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [flattening 61]
63. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & ((kind(X0) | happy(X0)) | (~tall(X0) | strong(X0)))) [nnf transformation 15]
64. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & (kind(X0) | happy(X0) | ~tall(X0) | strong(X0))) [flattening 63]
65. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | quiet(X0))) [flattening 65]
88. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 45]
93. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
100. generous(X0) | generous(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
107. ~brave(sK5) | patient(X3) [cnf transformation 59]
108. ~old(sK5) | patient(X3) [cnf transformation 59]
113. strong(X0) | ~creative(X0) | strong(X0) [cnf transformation 60]
114. ~strong(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 60]
120. kind(X0) | funny(X0) | tall(X0) [cnf transformation 62]
121. ~kind(X0) | strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 62]
125. ~strong(X0) | ~kind(X0) [cnf transformation 64]
127. ~kind(X0) | tall(X0) [cnf transformation 64]
130. ~quiet(X0) | ~generous(X0) [cnf transformation 66]
141. humble(alice) [cnf transformation 24]
142. strong(X0) | ~creative(X0) [duplicate literal removal 113]
143. ~strong(X0) | ~creative(X0) [duplicate literal removal 114]
144. old(X0) | generous(X0) [duplicate literal removal 100]
256. 25 <=> ! [X3] : patient(X3) [avatar definition]
257. patient(X3) <- (25) [avatar component clause 256]
259. 26 <=> old(sK5) [avatar definition]
261. ~old(sK5) <- (~26) [avatar component clause 259]
262. 25 | ~26 [avatar split clause 108,259,256]
264. 27 <=> brave(sK5) [avatar definition]
266. ~brave(sK5) <- (~27) [avatar component clause 264]
267. 25 | ~27 [avatar split clause 107,264,256]
277. ~creative(X0) [subsumption resolution 142,143]
294. generous(sK5) <- (~26) [resolution 144,261]
328. brave(sK5) | quiet(sK5) <- (~26) [resolution 93,294]
331. quiet(sK5) <- (~26, ~27) [subsumption resolution 328,266]
380. ~patient(alice) | ~funny(alice) [resolution 105,141]
403. funny(X0) | tall(X0) | tall(X0) [resolution 120,127]
405. funny(X0) | tall(X0) [duplicate literal removal 403]
437. ~generous(sK5) <- (~26, ~27) [resolution 331,130]
439. $false <- (~26, ~27) [subsumption resolution 437,294]
440. 26 | 27 [avatar contradiction clause 439]
452. creative(X0) | kind(X0) <- (25) [resolution 257,88]
454. kind(X0) <- (25) [subsumption resolution 452,277]
458. strong(X1) | ~tall(X1) | funny(X1) <- (25) [resolution 454,121]
462. strong(X1) | funny(X1) <- (25) [subsumption resolution 458,405]
526. funny(X4) | ~kind(X4) <- (25) [resolution 462,125]
530. funny(X4) <- (25) [subsumption resolution 526,454]
539. ~funny(alice) <- (25) [subsumption resolution 380,257]
540. $false <- (25) [subsumption resolution 539,530]
541. ~25 [avatar contradiction clause 540]
544. $false [avatar sat refutation 262,267,440,541]
% SZS output end Proof for 6055852932966073497923489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and strong is not rich or not curious.
Everyone who is both brave and strong is both patient and not humble and vice versa.
If john is either humble or quiet then alice is both creative and not old and vice versa.
Everyone who is either brave or not patient is old or wise.
Everyone who is patient is not strong or not brave and vice versa.
Everyone who is both wise and happy is not old or kind and vice versa.
Everyone who is either not old or not curious is not wise or not funny and vice versa.
If someone is either not strong or not funny then alice is not kind or humble and vice versa.
Everyone who is either not funny or not generous is both funny and brave.
If lucy is not curious or old then someone is brave or not brave and vice versa.
Everyone who is either not happy or tall is both kind and not funny and vice versa.
If mary is not calm then someone is either not patient or curious and vice versa.
Everyone who is rich or funny is not quiet or old and vice versa.
Everyone who is either wise or quiet is both humble and rich and vice versa.
If alice is calm or rich then fred is not humble or curious and vice versa.
Everyone who is generous or not happy is both tall and wise and vice versa.
John is creative or rich.
Someone is either quiet or kind.
Lucy is not calm or patient.
Someone is both funny and not kind.
Someone is strong.
John is not curious or old.
Paul is strong or not calm. | Fred is patient. | entailment | (![X]:((~generous(X)&strong(X))=>(~rich(X)|~curious(X))))&
(![X]:((brave(X)&strong(X))<=>(patient(X)&~humble(X))))&
(((humble(john)<~>quiet(john)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
((creative(john)|rich(john)))&
(?[X]:((quiet(X)<~>kind(X))))&
((~calm(lucy)|patient(lucy)))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:(strong(X)))&
((~curious(john)|old(john)))&
((strong(paul)|~calm(paul))) | patient(fred) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3014958950706384404658235
% SZS output start Proof for 3014958950706384404658235
2. ! [X0] : ((strong(X0) & brave(X0)) <=> (~humble(X0) & patient(X0))) [input p1]
5. ! [X0] : (patient(X0) <=> (~brave(X0) | ~strong(X0))) [input p4]
24. ~patient(fred) [input hypothesis]
30. ! [X0] : (((strong(X0) & brave(X0)) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 2]
31. ! [X0] : (((strong(X0) & brave(X0)) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | ~strong(X0) | ~brave(X0))) [flattening 30]
35. ! [X0] : ((patient(X0) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | ~patient(X0))) [nnf transformation 5]
36. ! [X0] : ((patient(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | ~patient(X0))) [flattening 35]
74. patient(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 31]
86. ~brave(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 36]
87. patient(X0) | strong(X0) [cnf transformation 36]
88. patient(X0) | brave(X0) [cnf transformation 36]
152. ~patient(fred) [cnf transformation 24]
176. ~brave(X0) | ~strong(X0) [subsumption resolution 86,74]
313. strong(fred) [resolution 87,152]
315. brave(fred) [resolution 88,152]
317. ~strong(fred) [resolution 176,315]
319. $false [subsumption resolution 317,313]
% SZS output end Proof for 3014958950706384404658235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not calm or not old then paul is not generous or tall.
Everyone who is both happy and quiet is strong or not funny and vice versa.
Everyone who is both not wise and strong is not brave and vice versa.
Everyone who is either not creative or creative is either rich or not strong.
If john is tall then someone is either not happy or not humble and vice versa.
If someone is both humble and not patient then mary is both strong and funny.
If alice is both creative and not patient then someone is wise.
Everyone who is not brave is calm and vice versa.
Everyone who is both not calm and not generous is either quiet or calm and vice versa.
Everyone who is tall is funny or not tall and vice versa.
Everyone who is either not humble or kind is generous or patient.
If someone is both brave and humble then paul is tall or not rich and vice versa.
If fred is not brave or not quiet then someone is both not wise and not funny and vice versa.
Everyone who is either not tall or curious is not patient.
Everyone who is not tall is not wise and vice versa.
Someone is either happy or old.
Someone is either rich or not patient.
Someone is patient.
Someone is both strong and happy.
Susan is strong.
Fred is either not creative or not generous. | Paul is not brave. | contradiction | (((~calm(fred)|~old(fred)))=>((~generous(paul)|tall(paul))))&
(![X]:((happy(X)&quiet(X))<=>(strong(X)|~funny(X))))&
(![X]:((~wise(X)&strong(X))<=>~brave(X)))&
(![X]:((~creative(X)<~>creative(X))=>(rich(X)<~>~strong(X))))&
((tall(john))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
((?[X]:((humble(X)&~patient(X))))=>((strong(mary)&funny(mary))))&
(((creative(alice)&~patient(alice)))=>(?[X]:(wise(X))))&
(![X]:(~brave(X)<=>calm(X)))&
(![X]:((~calm(X)&~generous(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(tall(X)<=>(funny(X)|~tall(X))))&
(![X]:((~humble(X)<~>kind(X))=>(generous(X)|patient(X))))&
((?[X]:((brave(X)&humble(X))))<=>((tall(paul)|~rich(paul))))&
(((~brave(fred)|~quiet(fred)))<=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((~tall(X)<~>curious(X))=>~patient(X)))&
(![X]:(~tall(X)<=>~wise(X)))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((strong(X)&happy(X))))&
(strong(susan))&
((~creative(fred)<~>~generous(fred))) | ~brave(paul) | [
"p2",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 11482336777071562747308
% SZS output start Proof for 11482336777071562747308
3. ! [X0] : ((strong(X0) & ~wise(X0)) <=> ~brave(X0)) [input p2]
10. ! [X0] : (tall(X0) <=> (~tall(X0) | funny(X0))) [input p9]
15. ! [X0] : (~tall(X0) <=> ~wise(X0)) [input p14]
22. ~brave(paul) [input hypothesis]
34. ! [X0] : (((strong(X0) & ~wise(X0)) | brave(X0)) & (~brave(X0) | (~strong(X0) | wise(X0)))) [nnf transformation 3]
35. ! [X0] : (((strong(X0) & ~wise(X0)) | brave(X0)) & (~brave(X0) | ~strong(X0) | wise(X0))) [flattening 34]
46. ! [X0] : ((tall(X0) | (tall(X0) & ~funny(X0))) & ((~tall(X0) | funny(X0)) | ~tall(X0))) [nnf transformation 10]
47. ! [X0] : ((tall(X0) | (tall(X0) & ~funny(X0))) & (~tall(X0) | funny(X0) | ~tall(X0))) [flattening 46]
60. ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 15]
80. ~wise(X0) | brave(X0) [cnf transformation 35]
103. tall(X0) | tall(X0) [cnf transformation 47]
119. ~tall(X0) | wise(X0) [cnf transformation 60]
130. ~brave(paul) [cnf transformation 22]
132. tall(X0) [duplicate literal removal 103]
230. wise(X0) [subsumption resolution 119,132]
267. brave(X0) [resolution 80,230]
268. $false [resolution 267,130]
% SZS output end Proof for 11482336777071562747308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or creative is both curious and happy and vice versa. Everyone who is kind or not old is either not wise or not generous. If someone is creative then paul is either not wise or patient. Everyone who is either humble or not quiet is both happy and not rich. If john is both not patient and not calm then someone is both old and kind. If alice is not calm then someone is both happy and not tall. If someone is strong or calm then paul is both quiet and rich. If someone is either calm or not strong then fred is both not curious and not kind. If someone is happy then paul is either humble or not wise and vice versa. If someone is not wise then alice is both not patient and quiet. If someone is not humble then someone is both generous and not brave. Everyone who is both calm and brave is both not patient and not humble and vice versa. Everyone who is not generous or humble is happy or wise and vice versa. Everyone who is both not wise and not happy is either patient or curious and vice versa. Everyone who is not strong is not humble or humble and vice versa. Everyone who is both not happy and not curious is both calm and brave. Alice is not quiet or not rich. Fred is both old and curious. Lucy is both not old and creative. Someone is not strong. John is happy or generous. Fred is not patient. Someone is not patient or not funny. Someone is not rich or rich. | Paul is wise. | contradiction | (![X]:((~funny(X)|creative(X))<=>(curious(X)&happy(X))))&
(![X]:((kind(X)|~old(X))=>(~wise(X)<~>~generous(X))))&
((?[X]:(creative(X)))=>((~wise(paul)<~>patient(paul))))&
(![X]:((humble(X)<~>~quiet(X))=>(happy(X)&~rich(X))))&
(((~patient(john)&~calm(john)))=>(?[X]:((old(X)&kind(X)))))&
((~calm(alice))=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((strong(X)|calm(X))))=>((quiet(paul)&rich(paul))))&
((?[X]:((calm(X)<~>~strong(X))))=>((~curious(fred)&~kind(fred))))&
((?[X]:(happy(X)))<=>((humble(paul)<~>~wise(paul))))&
((?[X]:(~wise(X)))=>((~patient(alice)&quiet(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((calm(X)&brave(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~generous(X)|humble(X))<=>(happy(X)|wise(X))))&
(![X]:((~wise(X)&~happy(X))<=>(patient(X)<~>curious(X))))&
(![X]:(~strong(X)<=>(~humble(X)|humble(X))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)&brave(X))))&
((~quiet(alice)|~rich(alice)))&
((old(fred)&curious(fred)))&
((~old(lucy)&creative(lucy)))&
(?[X]:(~strong(X)))&
((happy(john)|generous(john)))&
(~patient(fred))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((~rich(X)|rich(X)))) | wise(paul) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p17",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8479612294620397929137076
% SZS output start Proof for 8479612294620397929137076
1. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (happy(X0) & curious(X0))) [input p0]
4. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => (~rich(X0) & happy(X0))) [input p3]
7. ? [X0] : (calm(X0) | strong(X0)) => (rich(paul) & quiet(paul)) [input p6]
8. ? [X0] : (calm(X0) <~> ~strong(X0)) => (~kind(fred) & ~curious(fred)) [input p7]
9. ? [X0] : happy(X0) <=> (humble(paul) <~> ~wise(paul)) [input p8]
18. curious(fred) & old(fred) [input p17]
19. creative(lucy) & ~old(lucy) [input p18]
20. ? [X0] : ~strong(X0) [input p19]
25. wise(paul) [input hypothesis]
30. ! [X0] : ((~rich(X0) & happy(X0)) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 4]
34. (rich(paul) & quiet(paul)) | ! [X0] : (~calm(X0) & ~strong(X0)) [ennf transformation 7]
35. (~kind(fred) & ~curious(fred)) | ! [X0] : (calm(X0) <=> ~strong(X0)) [ennf transformation 8]
40. ! [X0] : (((creative(X0) | ~funny(X0)) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | ~funny(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [flattening 40]
44. ! [X0] : ((~rich(X0) & happy(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 30]
49. (~kind(fred) & ~curious(fred)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 35]
50. (? [X0] : happy(X0) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X0] : ~happy(X0)) [nnf transformation 9]
51. (? [X0] : happy(X0) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X1] : ~happy(X1)) [rectify 50]
52. ? [X0] : happy(X0) => happy(sK2) [choice axiom]
53. (happy(sK2) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X1] : ~happy(X1)) [skolemisation 51,52]
65. ? [X0] : ~strong(X0) => ~strong(sK4) [choice axiom]
66. ~strong(sK4) [skolemisation 20,65]
74. ~creative(X0) | happy(X0) [cnf transformation 41]
84. ~rich(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 44]
90. quiet(paul) | ~calm(X0) [cnf transformation 34]
92. rich(paul) | ~calm(X0) [cnf transformation 34]
94. ~curious(fred) | calm(X0) | strong(X0) [cnf transformation 49]
97. ~wise(paul) | humble(paul) | ~happy(X1) [cnf transformation 53]
126. curious(fred) [cnf transformation 18]
128. creative(lucy) [cnf transformation 19]
129. ~strong(sK4) [cnf transformation 66]
134. wise(paul) [cnf transformation 25]
139. 2 <=> wise(paul) [avatar definition]
176. 10 <=> ! [X0] : ~calm(X0) [avatar definition]
177. ~calm(X0) <- (10) [avatar component clause 176]
179. 11 <=> rich(paul) [avatar definition]
181. rich(paul) <- (11) [avatar component clause 179]
182. 10 | 11 [avatar split clause 92,179,176]
188. 13 <=> quiet(paul) [avatar definition]
190. quiet(paul) <- (13) [avatar component clause 188]
191. 10 | 13 [avatar split clause 90,188,176]
194. 14 <=> ! [X0] : (calm(X0) | strong(X0)) [avatar definition]
195. strong(X0) | calm(X0) <- (14) [avatar component clause 194]
206. 17 <=> curious(fred) [avatar definition]
209. 14 | ~17 [avatar split clause 94,206,194]
212. 18 <=> humble(paul) [avatar definition]
222. 20 <=> ! [X1] : ~happy(X1) [avatar definition]
223. ~happy(X1) <- (20) [avatar component clause 222]
225. 20 | 18 | ~2 [avatar split clause 97,139,212,222]
259. 17 [avatar split clause 126,206]
278. 2 [avatar split clause 134,139]
282. happy(lucy) [resolution 74,128]
283. calm(sK4) <- (14) [resolution 195,129]
286. $false <- (10, 14) [subsumption resolution 283,177]
287. ~10 | ~14 [avatar contradiction clause 286]
303. ~quiet(paul) | ~humble(paul) <- (11) [resolution 84,181]
304. ~humble(paul) <- (11, 13) [subsumption resolution 303,190]
307. ~18 | ~11 | ~13 [avatar split clause 304,188,179,212]
315. $false <- (20) [resolution 223,282]
320. ~20 [avatar contradiction clause 315]
322. $false [avatar sat refutation 182,191,209,225,259,278,287,307,320]
% SZS output end Proof for 8479612294620397929137076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not patient is either curious or not patient. Everyone who is rich is both rich and not strong. Everyone who is not strong is not curious or not brave and vice versa. Everyone who is either not funny or old is both tall and patient. Everyone who is generous is not funny and vice versa. If someone is not patient then someone is old and vice versa. Everyone who is both not brave and not kind is either creative or kind and vice versa. If someone is patient then someone is either not quiet or quiet. Everyone who is either kind or brave is both brave and curious. Everyone who is either brave or not old is either not funny or not rich. Everyone who is both humble and not funny is both not curious and brave and vice versa. Everyone who is happy or quiet is generous or not creative and vice versa. If someone is humble then lucy is either not kind or creative. Everyone who is either not happy or not funny is both kind and not generous and vice versa. Everyone who is both not tall and generous is quiet or happy and vice versa. Everyone who is either quiet or brave is both not generous and happy and vice versa. Someone is rich. Someone is not rich or not calm. Someone is not happy. Someone is not tall or curious. | Lucy is not rich. | contradiction | (![X]:((~brave(X)|~patient(X))=>(curious(X)<~>~patient(X))))&
(![X]:(rich(X)=>(rich(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(![X]:(generous(X)<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&curious(X))))&
(![X]:((brave(X)<~>~old(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))<=>(~curious(X)&brave(X))))&
(![X]:((happy(X)|quiet(X))<=>(generous(X)|~creative(X))))&
((?[X]:(humble(X)))=>((~kind(lucy)<~>creative(lucy))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)&~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(quiet(X)|happy(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~generous(X)&happy(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)|curious(X)))) | ~rich(lucy) | [
"p3",
"p4",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 390560000421807314539302
% SZS output start Proof for 390560000421807314539302
4. ! [X0] : ((~funny(X0) <~> old(X0)) => (patient(X0) & tall(X0))) [input p3]
5. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p4]
9. ! [X0] : ((kind(X0) <~> brave(X0)) => (curious(X0) & brave(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> ~old(X0)) => (~funny(X0) <~> ~rich(X0))) [input p9]
12. ! [X0] : ((quiet(X0) | happy(X0)) <=> (~creative(X0) | generous(X0))) [input p11]
14. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> (~generous(X0) & kind(X0))) [input p13]
15. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (happy(X0) | quiet(X0))) [input p14]
16. ! [X0] : ((quiet(X0) <~> brave(X0)) <=> (happy(X0) & ~generous(X0))) [input p15]
21. ~rich(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) & tall(X0)) | (~funny(X0) <=> old(X0))) [ennf transformation 4]
32. ! [X0] : ((curious(X0) & brave(X0)) | (kind(X0) <=> brave(X0))) [ennf transformation 9]
33. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (brave(X0) <=> ~old(X0))) [ennf transformation 10]
36. ! [X0] : ((patient(X0) & tall(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) [nnf transformation 30]
37. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((curious(X0) & brave(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 32]
50. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) [nnf transformation 33]
53. ! [X0] : (((quiet(X0) | happy(X0)) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | (~quiet(X0) & ~happy(X0)))) [nnf transformation 12]
54. ! [X0] : ((quiet(X0) | happy(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | (~quiet(X0) & ~happy(X0)))) [flattening 53]
56. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 14]
57. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [flattening 56]
58. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 15]
59. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~generous(X0) | tall(X0))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [flattening 60]
75. tall(X0) | old(X0) | funny(X0) [cnf transformation 36]
79. ~generous(X0) | ~funny(X0) [cnf transformation 37]
80. generous(X0) | funny(X0) [cnf transformation 37]
91. brave(X0) | brave(X0) | ~kind(X0) [cnf transformation 49]
97. ~old(X0) | funny(X0) | rich(X0) | ~brave(X0) [cnf transformation 50]
104. ~quiet(X0) | generous(X0) | ~creative(X0) [cnf transformation 54]
105. ~generous(X0) | happy(X0) | quiet(X0) [cnf transformation 54]
106. happy(X0) | quiet(X0) | creative(X0) [cnf transformation 54]
109. ~funny(X0) | kind(X0) | happy(X0) [cnf transformation 57]
112. ~generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 57]
116. ~quiet(X0) | ~tall(X0) [cnf transformation 59]
118. ~quiet(X0) | generous(X0) [cnf transformation 59]
119. generous(X0) | ~happy(X0) [cnf transformation 59]
122. happy(X0) | brave(X0) | ~quiet(X0) [cnf transformation 61]
123. happy(X0) | quiet(X0) | ~brave(X0) [cnf transformation 61]
129. ~rich(lucy) [cnf transformation 21]
130. ~kind(X0) | brave(X0) [duplicate literal removal 91]
164. ~happy(X0) | ~generous(X0) [subsumption resolution 112,79]
165. ~happy(X0) [subsumption resolution 119,164]
166. ~brave(X0) | quiet(X0) [subsumption resolution 123,165]
167. ~quiet(X0) | brave(X0) [subsumption resolution 122,165]
220. happy(X0) | quiet(X0) | funny(X0) [resolution 105,80]
221. quiet(X0) | funny(X0) [subsumption resolution 220,165]
223. funny(X1) | brave(X1) [resolution 221,167]
228. quiet(X2) | creative(X2) [resolution 106,165]
231. creative(X2) | generous(X2) [resolution 228,118]
268. brave(X1) | kind(X1) | happy(X1) [resolution 223,109]
272. brave(X1) | kind(X1) [subsumption resolution 268,165]
273. brave(X1) [subsumption resolution 272,130]
277. quiet(X2) [resolution 273,166]
284. generous(X0) | ~creative(X0) [resolution 277,104]
287. ~tall(X3) [resolution 277,116]
288. generous(X0) [subsumption resolution 284,231]
308. old(X0) | funny(X0) [resolution 287,75]
347. ~funny(X2) [resolution 288,79]
363. funny(X0) | funny(X0) | rich(X0) | ~brave(X0) [resolution 308,97]
367. funny(X0) | rich(X0) | ~brave(X0) [duplicate literal removal 363]
368. rich(X0) | ~brave(X0) [subsumption resolution 367,347]
369. rich(X0) [subsumption resolution 368,273]
370. $false [resolution 369,129]
% SZS output end Proof for 390560000421807314539302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or generous then mary is both creative and not strong and vice versa. If someone is either quiet or not tall then susan is not humble and vice versa. If someone is either not brave or not quiet then someone is either wise or rich and vice versa. Everyone who is either not wise or brave is not generous. If someone is kind or not old then someone is either funny or calm and vice versa. If lucy is either old or not strong then someone is either not old or generous. If someone is both quiet and not old then mary is curious and vice versa. If fred is either not creative or old then someone is patient or old and vice versa. Everyone who is curious or rich is not strong or not curious. Everyone who is either humble or curious is not humble and vice versa. If susan is generous then alice is both not creative and calm and vice versa. If susan is not brave then someone is both strong and tall. Everyone who is not quiet or not patient is either quiet or not happy. Everyone who is not curious or brave is both not creative and not happy. Everyone who is both strong and not kind is either not calm or not brave. Everyone who is either kind or not quiet is strong or rich and vice versa. John is either not tall or not patient. John is creative. Someone is funny. Someone is not kind or curious. Lucy is both not quiet and old. Paul is either tall or not humble. Someone is not old. | Fred is strong. | contradiction | ((?[X]:((strong(X)<~>generous(X))))<=>((creative(mary)&~strong(mary))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~humble(susan)))&
((?[X]:((~brave(X)<~>~quiet(X))))<=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>brave(X))=>~generous(X)))&
((?[X]:((kind(X)|~old(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
(((old(lucy)<~>~strong(lucy)))=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>(curious(mary)))&
(((~creative(fred)<~>old(fred)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((curious(X)|rich(X))=>(~strong(X)|~curious(X))))&
(![X]:((humble(X)<~>curious(X))<=>~humble(X)))&
((generous(susan))<=>((~creative(alice)&calm(alice))))&
((~brave(susan))=>(?[X]:((strong(X)&tall(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((~curious(X)|brave(X))=>(~creative(X)&~happy(X))))&
(![X]:((strong(X)&~kind(X))=>(~calm(X)<~>~brave(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(strong(X)|rich(X))))&
((~tall(john)<~>~patient(john)))&
(creative(john))&
(?[X]:(funny(X)))&
(?[X]:((~kind(X)|curious(X))))&
((~quiet(lucy)&old(lucy)))&
((tall(paul)<~>~humble(paul)))&
(?[X]:(~old(X))) | strong(fred) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8649920817983800986984260
% SZS output start Proof for 8649920817983800986984260
9. ! [X0] : ((rich(X0) | curious(X0)) => (~curious(X0) | ~strong(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> curious(X0)) <=> ~humble(X0)) [input p9]
24. strong(fred) [input hypothesis]
29. ! [X0] : ((~curious(X0) | ~strong(X0)) | (~rich(X0) & ~curious(X0))) [ennf transformation 9]
30. ! [X0] : (~curious(X0) | ~strong(X0) | (~rich(X0) & ~curious(X0))) [flattening 29]
67. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | humble(X0)) & (~humble(X0) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 10]
123. ~curious(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 30]
125. ~humble(X0) | curious(X0) | ~humble(X0) [cnf transformation 67]
127. curious(X0) | humble(X0) | humble(X0) [cnf transformation 67]
160. strong(fred) [cnf transformation 24]
162. ~humble(X0) | curious(X0) [duplicate literal removal 125]
163. curious(X0) | humble(X0) [duplicate literal removal 127]
164. ~curious(X0) | ~strong(X0) [duplicate literal removal 123]
351. curious(X0) [subsumption resolution 162,163]
407. ~strong(X1) [resolution 164,351]
408. $false [resolution 407,160]
% SZS output end Proof for 8649920817983800986984260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not brave is either not generous or not happy.
Everyone who is both not calm and not humble is both generous and not kind and vice versa.
Everyone who is both not rich and old is not humble.
Everyone who is both patient and not old is either not funny or funny and vice versa.
Everyone who is happy is not curious and vice versa.
Everyone who is curious or not brave is either patient or calm and vice versa.
Everyone who is not calm is curious and vice versa.
If someone is not generous or not tall then lucy is not funny or not curious and vice versa.
Everyone who is both not strong and old is both not tall and humble.
Everyone who is both not tall and not brave is not curious.
If lucy is not brave then alice is patient or not curious.
If someone is curious or rich then someone is both creative and strong.
If someone is humble or happy then alice is old or not patient and vice versa.
Everyone who is either not curious or not kind is not humble or not creative.
If fred is tall then someone is both not strong and creative.
John is strong or tall.
Someone is either not happy or not quiet.
Someone is tall.
John is brave.
Someone is generous or not calm.
John is either quiet or creative.
Mary is not patient or not tall. | Mary is kind. | contradiction | (![X]:((creative(X)&~brave(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~calm(X)&~humble(X))<=>(generous(X)&~kind(X))))&
(![X]:((~rich(X)&old(X))=>~humble(X)))&
(![X]:((patient(X)&~old(X))<=>(~funny(X)<~>funny(X))))&
(![X]:(happy(X)<=>~curious(X)))&
(![X]:((curious(X)|~brave(X))<=>(patient(X)<~>calm(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((?[X]:((~generous(X)|~tall(X))))<=>((~funny(lucy)|~curious(lucy))))&
(![X]:((~strong(X)&old(X))=>(~tall(X)&humble(X))))&
(![X]:((~tall(X)&~brave(X))=>~curious(X)))&
((~brave(lucy))=>((patient(alice)|~curious(alice))))&
((?[X]:((curious(X)|rich(X))))=>(?[X]:((creative(X)&strong(X)))))&
((?[X]:((humble(X)|happy(X))))<=>((old(alice)|~patient(alice))))&
(![X]:((~curious(X)<~>~kind(X))=>(~humble(X)|~creative(X))))&
((tall(fred))=>(?[X]:((~strong(X)&creative(X)))))&
((strong(john)|tall(john)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:(tall(X)))&
(brave(john))&
(?[X]:((generous(X)|~calm(X))))&
((quiet(john)<~>creative(john)))&
((~patient(mary)|~tall(mary))) | kind(mary) | [
"p1",
"p3",
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2055724506858955805997055
% SZS output start Proof for 2055724506858955805997055
2. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> (~kind(X0) & generous(X0))) [input p1]
4. ! [X0] : ((~old(X0) & patient(X0)) <=> (~funny(X0) <~> funny(X0))) [input p3]
5. ! [X0] : (happy(X0) <=> ~curious(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | curious(X0)) <=> (patient(X0) <~> calm(X0))) [input p5]
13. ? [X0] : (happy(X0) | humble(X0)) <=> (~patient(alice) | old(alice)) [input p12]
23. kind(mary) [input hypothesis]
40. ! [X0] : (((~humble(X0) & ~calm(X0)) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | (humble(X0) | calm(X0)))) [nnf transformation 2]
41. ! [X0] : (((~humble(X0) & ~calm(X0)) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | humble(X0) | calm(X0))) [flattening 40]
42. ! [X0] : (((~old(X0) & patient(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (old(X0) | ~patient(X0)))) [nnf transformation 4]
43. ! [X0] : (((~old(X0) & patient(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | old(X0) | ~patient(X0))) [flattening 42]
44. ! [X0] : ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0))) [nnf transformation 5]
45. ! [X0] : (((~brave(X0) | curious(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | (brave(X0) & ~curious(X0)))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | curious(X0) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | (brave(X0) & ~curious(X0)))) [flattening 45]
56. (? [X0] : (happy(X0) | humble(X0)) | (patient(alice) & ~old(alice))) & ((~patient(alice) | old(alice)) | ! [X0] : (~happy(X0) & ~humble(X0))) [nnf transformation 13]
57. (? [X0] : (happy(X0) | humble(X0)) | (patient(alice) & ~old(alice))) & (~patient(alice) | old(alice) | ! [X0] : (~happy(X0) & ~humble(X0))) [flattening 56]
58. (? [X0] : (happy(X0) | humble(X0)) | (patient(alice) & ~old(alice))) & (~patient(alice) | old(alice) | ! [X1] : (~happy(X1) & ~humble(X1))) [rectify 57]
59. ? [X0] : (happy(X0) | humble(X0)) => (happy(sK2) | humble(sK2)) [choice axiom]
60. ((happy(sK2) | humble(sK2)) | (patient(alice) & ~old(alice))) & (~patient(alice) | old(alice) | ! [X1] : (~happy(X1) & ~humble(X1))) [skolemisation 58,59]
75. ~kind(X0) | humble(X0) | calm(X0) [cnf transformation 41]
81. patient(X0) | funny(X0) | funny(X0) [cnf transformation 43]
82. patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 43]
83. ~old(X0) | funny(X0) | funny(X0) [cnf transformation 43]
84. ~old(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 43]
86. curious(X0) | happy(X0) [cnf transformation 44]
89. ~calm(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 46]
107. ~patient(alice) | old(alice) | ~humble(X1) [cnf transformation 60]
108. ~patient(alice) | old(alice) | ~happy(X1) [cnf transformation 60]
124. kind(mary) [cnf transformation 23]
125. patient(X0) | funny(X0) [duplicate literal removal 81]
126. ~funny(X0) | patient(X0) [duplicate literal removal 82]
127. ~old(X0) | funny(X0) [duplicate literal removal 83]
128. ~funny(X0) | ~old(X0) [duplicate literal removal 84]
129. ~old(X0) [subsumption resolution 127,128]
130. patient(X0) [subsumption resolution 125,126]
133. ~curious(X0) | ~calm(X0) [subsumption resolution 89,130]
178. old(alice) | ~happy(X1) [subsumption resolution 108,130]
179. ~happy(X1) [subsumption resolution 178,129]
180. old(alice) | ~humble(X1) [subsumption resolution 107,130]
181. ~humble(X1) [subsumption resolution 180,129]
236. ~calm(X1) | happy(X1) [resolution 133,86]
238. ~calm(X1) [subsumption resolution 236,179]
244. humble(mary) | calm(mary) [resolution 75,124]
245. calm(mary) [subsumption resolution 244,181]
246. $false [subsumption resolution 245,238]
% SZS output end Proof for 2055724506858955805997055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is rich then someone is not happy and vice versa.
If someone is kind or old then susan is not kind or funny.
If someone is generous then someone is quiet or wise.
If alice is either not happy or not patient then someone is either not brave or quiet.
Everyone who is not old or not quiet is both kind and not curious and vice versa.
Everyone who is either calm or not calm is both curious and quiet and vice versa.
Everyone who is both not brave and patient is quiet.
Everyone who is kind or humble is not old or not tall and vice versa.
Everyone who is humble or quiet is not rich and vice versa.
Everyone who is old or not old is either not wise or calm.
Everyone who is brave is both old and calm.
If someone is both quiet and rich then someone is both creative and not humble.
If paul is both quiet and not tall then paul is not happy or calm.
If john is not rich then lucy is not quiet or not humble.
If someone is either old or not tall then mary is either not generous or not old.
Someone is tall or calm.
Someone is both not tall and generous.
Mary is both not wise and not patient.
Susan is brave or happy.
Someone is either rich or not strong. | Alice is not creative. | neutral | ((rich(john))<=>(?[X]:(~happy(X))))&
((?[X]:((kind(X)|old(X))))=>((~kind(susan)|funny(susan))))&
((?[X]:(generous(X)))=>(?[X]:((quiet(X)|wise(X)))))&
(((~happy(alice)<~>~patient(alice)))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:((~old(X)|~quiet(X))<=>(kind(X)&~curious(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(curious(X)&quiet(X))))&
(![X]:((~brave(X)&patient(X))=>quiet(X)))&
(![X]:((kind(X)|humble(X))<=>(~old(X)|~tall(X))))&
(![X]:((humble(X)|quiet(X))<=>~rich(X)))&
(![X]:((old(X)|~old(X))=>(~wise(X)<~>calm(X))))&
(![X]:(brave(X)=>(old(X)&calm(X))))&
((?[X]:((quiet(X)&rich(X))))=>(?[X]:((creative(X)&~humble(X)))))&
(((quiet(paul)&~tall(paul)))=>((~happy(paul)|calm(paul))))&
((~rich(john))=>((~quiet(lucy)|~humble(lucy))))&
((?[X]:((old(X)<~>~tall(X))))=>((~generous(mary)<~>~old(mary))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((~tall(X)&generous(X))))&
((~wise(mary)&~patient(mary)))&
((brave(susan)|happy(susan)))&
(?[X]:((rich(X)<~>~strong(X)))) | ~creative(alice) | [] | null | 0 |
If mary is either old or not brave then fred is kind or strong and vice versa.
Everyone who is both not curious and rich is not tall and vice versa.
Everyone who is humble or wise is both generous and not strong.
Everyone who is not tall is not happy and vice versa.
If someone is both not brave and not tall then john is both patient and not wise and vice versa.
Everyone who is both curious and patient is both creative and generous.
Everyone who is either brave or strong is not old.
If someone is either not strong or not humble then susan is not patient and vice versa.
If john is either old or funny then alice is happy or humble.
If someone is either generous or not wise then alice is happy or not quiet and vice versa.
If someone is strong then someone is either rich or patient.
Everyone who is quiet or wise is either creative or calm and vice versa.
Everyone who is not tall is not creative.
If someone is curious or not kind then someone is not strong.
Everyone who is calm or happy is happy or tall and vice versa.
If someone is either not generous or wise then mary is not happy.
Someone is happy.
Susan is both not funny and strong.
Paul is either not calm or happy.
Lucy is not funny or not curious.
Someone is both not rich and tall.
Alice is not funny.
Someone is either not calm or not humble.
Someone is both not calm and not tall. | Mary is not calm. | entailment | (((old(mary)<~>~brave(mary)))<=>((kind(fred)|strong(fred))))&
(![X]:((~curious(X)&rich(X))<=>~tall(X)))&
(![X]:((humble(X)|wise(X))=>(generous(X)&~strong(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~tall(X))))<=>((patient(john)&~wise(john))))&
(![X]:((curious(X)&patient(X))=>(creative(X)&generous(X))))&
(![X]:((brave(X)<~>strong(X))=>~old(X)))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(~patient(susan)))&
(((old(john)<~>funny(john)))=>((happy(alice)|humble(alice))))&
((?[X]:((generous(X)<~>~wise(X))))<=>((happy(alice)|~quiet(alice))))&
((?[X]:(strong(X)))=>(?[X]:((rich(X)<~>patient(X)))))&
(![X]:((quiet(X)|wise(X))<=>(creative(X)<~>calm(X))))&
(![X]:(~tall(X)=>~creative(X)))&
((?[X]:((curious(X)|~kind(X))))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|happy(X))<=>(happy(X)|tall(X))))&
((?[X]:((~generous(X)<~>wise(X))))=>(~happy(mary)))&
(?[X]:(happy(X)))&
((~funny(susan)&strong(susan)))&
((~calm(paul)<~>happy(paul)))&
((~funny(lucy)|~curious(lucy)))&
(?[X]:((~rich(X)&tall(X))))&
(~funny(alice))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:((~calm(X)&~tall(X)))) | ~calm(mary) | [
"p2",
"p3",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3649997562889306559824816
% SZS output start Proof for 3649997562889306559824816
3. ! [X0] : ((wise(X0) | humble(X0)) => (~strong(X0) & generous(X0))) [input p2]
4. ! [X0] : (~tall(X0) <=> ~happy(X0)) [input p3]
10. ? [X0] : (generous(X0) <~> ~wise(X0)) <=> (~quiet(alice) | happy(alice)) [input p9]
12. ! [X0] : ((wise(X0) | quiet(X0)) <=> (creative(X0) <~> calm(X0))) [input p11]
13. ! [X0] : (~tall(X0) => ~creative(X0)) [input p12]
15. ! [X0] : ((happy(X0) | calm(X0)) <=> (tall(X0) | happy(X0))) [input p14]
16. ? [X0] : (~generous(X0) <~> wise(X0)) => ~happy(mary) [input p15]
25. calm(mary) [input hypothesis]
28. ! [X0] : ((~strong(X0) & generous(X0)) | (~wise(X0) & ~humble(X0))) [ennf transformation 3]
35. ! [X0] : (~creative(X0) | tall(X0)) [ennf transformation 13]
37. ~happy(mary) | ! [X0] : (~generous(X0) <=> wise(X0)) [ennf transformation 16]
42. ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 4]
54. (? [X0] : ((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (quiet(alice) & ~happy(alice))) & ((~quiet(alice) | happy(alice)) | ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) [nnf transformation 10]
55. (? [X0] : ((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (quiet(alice) & ~happy(alice))) & (~quiet(alice) | happy(alice) | ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) [flattening 54]
56. (? [X0] : ((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (quiet(alice) & ~happy(alice))) & (~quiet(alice) | happy(alice) | ! [X1] : ((generous(X1) | wise(X1)) & (~wise(X1) | ~generous(X1)))) [rectify 55]
57. ? [X0] : ((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) => ((wise(sK2) | ~generous(sK2)) & (~wise(sK2) | generous(sK2))) [choice axiom]
58. (((wise(sK2) | ~generous(sK2)) & (~wise(sK2) | generous(sK2))) | (quiet(alice) & ~happy(alice))) & (~quiet(alice) | happy(alice) | ! [X1] : ((generous(X1) | wise(X1)) & (~wise(X1) | ~generous(X1)))) [skolemisation 56,57]
63. ! [X0] : (((wise(X0) | quiet(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (~wise(X0) & ~quiet(X0)))) [nnf transformation 12]
64. ! [X0] : ((wise(X0) | quiet(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (~wise(X0) & ~quiet(X0)))) [flattening 63]
68. ! [X0] : (((happy(X0) | calm(X0)) | (~tall(X0) & ~happy(X0))) & ((tall(X0) | happy(X0)) | (~happy(X0) & ~calm(X0)))) [nnf transformation 15]
69. ! [X0] : ((happy(X0) | calm(X0) | (~tall(X0) & ~happy(X0))) & (tall(X0) | happy(X0) | (~happy(X0) & ~calm(X0)))) [flattening 68]
70. ~happy(mary) | ! [X0] : ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))) [nnf transformation 37]
91. ~wise(X0) | generous(X0) [cnf transformation 28]
95. ~tall(X0) | happy(X0) [cnf transformation 42]
114. wise(sK2) | ~generous(sK2) | ~happy(alice) [cnf transformation 58]
115. wise(sK2) | ~generous(sK2) | quiet(alice) [cnf transformation 58]
118. ~quiet(X0) | creative(X0) | calm(X0) [cnf transformation 64]
124. ~creative(X0) | tall(X0) [cnf transformation 35]
127. tall(X0) | happy(X0) | ~calm(X0) [cnf transformation 69]
131. ~happy(mary) | wise(X0) | generous(X0) [cnf transformation 70]
132. ~happy(mary) | ~generous(X0) | ~wise(X0) [cnf transformation 70]
146. calm(mary) [cnf transformation 25]
224. 17 <=> happy(alice) [avatar definition]
225. ~happy(alice) <- (~17) [avatar component clause 224]
234. 19 <=> quiet(alice) [avatar definition]
236. quiet(alice) <- (19) [avatar component clause 234]
238. 20 <=> generous(sK2) [avatar definition]
240. ~generous(sK2) <- (~20) [avatar component clause 238]
242. 21 <=> wise(sK2) [avatar definition]
244. wise(sK2) <- (21) [avatar component clause 242]
245. 19 | ~20 | 21 [avatar split clause 115,242,238,234]
246. ~17 | ~20 | 21 [avatar split clause 114,242,238,224]
249. 22 <=> ! [X1] : generous(X1) [avatar definition]
250. generous(X1) <- (22) [avatar component clause 249]
254. 23 <=> ! [X1] : ~wise(X1) [avatar definition]
255. ~wise(X1) <- (23) [avatar component clause 254]
279. ~calm(X0) | happy(X0) [subsumption resolution 127,95]
280. ~happy(mary) | ~wise(X0) [subsumption resolution 132,91]
282. 29 <=> happy(mary) [avatar definition]
285. 23 | ~29 [avatar split clause 280,282,254]
286. ~happy(mary) | generous(X0) [subsumption resolution 131,91]
287. 22 | ~29 [avatar split clause 286,282,249]
329. happy(mary) [resolution 279,146]
333. 29 [avatar split clause 329,282]
334. $false <- (~20, 22) [resolution 250,240]
335. 20 | ~22 [avatar contradiction clause 334]
384. 44 <=> calm(alice) [avatar definition]
386. calm(alice) <- (44) [avatar component clause 384]
388. 45 <=> creative(alice) [avatar definition]
390. creative(alice) <- (45) [avatar component clause 388]
392. $false <- (21, 23) [subsumption resolution 244,255]
393. ~21 | ~23 [avatar contradiction clause 392]
394. creative(alice) | calm(alice) <- (19) [resolution 236,118]
395. happy(alice) <- (44) [resolution 386,279]
396. $false <- (~17, 44) [subsumption resolution 395,225]
397. 17 | ~44 [avatar contradiction clause 396]
398. 44 | 45 | ~19 [avatar split clause 394,234,388,384]
421. tall(alice) <- (45) [resolution 390,124]
440. happy(alice) <- (45) [resolution 421,95]
442. $false <- (~17, 45) [subsumption resolution 440,225]
443. 17 | ~45 [avatar contradiction clause 442]
444. $false [avatar sat refutation 245,246,285,287,333,335,393,397,398,443]
% SZS output end Proof for 3649997562889306559824816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not curious or wise then someone is creative or generous. If someone is curious then someone is either curious or not old. Everyone who is both old and kind is tall or calm. Everyone who is not humble is not humble or not brave and vice versa. Everyone who is either old or not brave is both not brave and old and vice versa. If john is both not calm and wise then someone is either tall or old. Everyone who is either funny or brave is generous or not happy and vice versa. If mary is either not humble or not rich then mary is either old or brave. Everyone who is curious is generous or humble. If susan is both happy and not strong then susan is not tall or kind. Everyone who is either not strong or not tall is not wise and vice versa. Everyone who is both patient and quiet is both calm and not kind and vice versa. Everyone who is either tall or kind is quiet and vice versa. Everyone who is either not quiet or not strong is both not curious and not tall. If john is both calm and not funny then mary is either not brave or calm. If paul is not kind then someone is happy or generous. Someone is funny or not old. Lucy is both quiet and not creative. Lucy is happy. Someone is both curious and not kind. Someone is either not quiet or not kind. Someone is either brave or curious. Someone is both not quiet and not funny. Susan is kind. | John is old. | contradiction | (((~curious(alice)<~>wise(alice)))=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:(curious(X)))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((old(X)&kind(X))=>(tall(X)|calm(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~brave(X))))&
(![X]:((old(X)<~>~brave(X))<=>(~brave(X)&old(X))))&
(((~calm(john)&wise(john)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((funny(X)<~>brave(X))<=>(generous(X)|~happy(X))))&
(((~humble(mary)<~>~rich(mary)))=>((old(mary)<~>brave(mary))))&
(![X]:(curious(X)=>(generous(X)|humble(X))))&
(((happy(susan)&~strong(susan)))=>((~tall(susan)|kind(susan))))&
(![X]:((~strong(X)<~>~tall(X))<=>~wise(X)))&
(![X]:((patient(X)&quiet(X))<=>(calm(X)&~kind(X))))&
(![X]:((tall(X)<~>kind(X))<=>quiet(X)))&
(![X]:((~quiet(X)<~>~strong(X))=>(~curious(X)&~tall(X))))&
(((calm(john)&~funny(john)))=>((~brave(mary)<~>calm(mary))))&
((~kind(paul))=>(?[X]:((happy(X)|generous(X)))))&
(?[X]:((funny(X)|~old(X))))&
((quiet(lucy)&~creative(lucy)))&
(happy(lucy))&
(?[X]:((curious(X)&~kind(X))))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(?[X]:((~quiet(X)&~funny(X))))&
(kind(susan)) | old(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3132246838305725946473378
% SZS output start Proof for 3132246838305725946473378
5. ! [X0] : ((old(X0) <~> ~brave(X0)) <=> (old(X0) & ~brave(X0))) [input p4]
25. old(john) [input hypothesis]
51. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | (~old(X0) | brave(X0))) & ((old(X0) & ~brave(X0)) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [nnf transformation 5]
52. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~old(X0) | brave(X0)) & ((old(X0) & ~brave(X0)) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [flattening 51]
87. ~brave(X0) | ~brave(X0) | ~old(X0) [cnf transformation 52]
90. old(X0) | old(X0) | brave(X0) [cnf transformation 52]
92. brave(X0) | ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 52]
139. old(john) [cnf transformation 25]
140. ~brave(X0) | ~old(X0) [duplicate literal removal 87]
141. old(X0) | brave(X0) [duplicate literal removal 90]
142. brave(X0) | ~old(X0) [duplicate literal removal 92]
174. brave(X0) [subsumption resolution 141,142]
175. ~old(X0) [subsumption resolution 140,174]
245. $false [subsumption resolution 139,175]
% SZS output end Proof for 3132246838305725946473378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not calm then someone is not patient or not old and vice versa.
Everyone who is patient is brave or not funny and vice versa.
Everyone who is either not brave or not patient is creative or not rich.
If someone is either happy or not creative then john is both patient and not rich and vice versa.
If someone is either not humble or not creative then someone is both strong and not strong.
Everyone who is not happy or not patient is both humble and creative.
If someone is brave then fred is either happy or kind and vice versa.
If someone is not generous or old then someone is rich or happy.
Everyone who is not kind or not strong is happy or not funny.
If someone is kind then paul is not quiet.
Everyone who is not rich is generous and vice versa.
Everyone who is either not funny or not patient is not strong or old and vice versa.
If susan is both wise and not strong then susan is wise or not rich.
If mary is either not creative or not strong then someone is both old and not curious.
Everyone who is both tall and creative is both old and not quiet.
Lucy is either not strong or curious.
Fred is not rich.
Paul is old.
Paul is humble.
Susan is both creative and calm.
Alice is both not brave and not creative.
Someone is both not generous and not humble.
Alice is tall. | Mary is happy. | neutral | ((?[X]:((tall(X)<~>~calm(X))))<=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(patient(X)<=>(brave(X)|~funny(X))))&
(![X]:((~brave(X)<~>~patient(X))=>(creative(X)|~rich(X))))&
((?[X]:((happy(X)<~>~creative(X))))<=>((patient(john)&~rich(john))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~happy(X)|~patient(X))=>(humble(X)&creative(X))))&
((?[X]:(brave(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)|~funny(X))))&
((?[X]:(kind(X)))=>(~quiet(paul)))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(~strong(X)|old(X))))&
(((wise(susan)&~strong(susan)))=>((wise(susan)|~rich(susan))))&
(((~creative(mary)<~>~strong(mary)))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)&creative(X))=>(old(X)&~quiet(X))))&
((~strong(lucy)<~>curious(lucy)))&
(~rich(fred))&
(old(paul))&
(humble(paul))&
((creative(susan)&calm(susan)))&
((~brave(alice)&~creative(alice)))&
(?[X]:((~generous(X)&~humble(X))))&
(tall(alice)) | happy(mary) | [] | null | 0 |
If fred is either not funny or wise then fred is both patient and not funny. If someone is funny or not patient then someone is both strong and not strong and vice versa. If someone is humble then alice is kind or generous. Everyone who is both quiet and strong is not tall or wise. Everyone who is brave or wise is either rich or strong and vice versa. Everyone who is patient or curious is not happy or not brave and vice versa. Everyone who is calm or not tall is either tall or calm. If john is funny then lucy is generous and vice versa. If someone is calm then john is not humble or not happy. If someone is not humble then susan is either not funny or not strong. Everyone who is either curious or not calm is both not brave and not creative. Everyone who is not calm is not brave and vice versa. If someone is strong then john is both strong and old. Everyone who is both not funny and not kind is both humble and creative and vice versa. If someone is both not brave and not curious then alice is tall or old. Fred is not humble or humble. Someone is not creative or not funny. Paul is old. Someone is not curious or not patient. Someone is not curious. Someone is either happy or not patient. John is tall or calm. Mary is brave or not quiet. | Susan is not calm. | neutral | (((~funny(fred)<~>wise(fred)))=>((patient(fred)&~funny(fred))))&
((?[X]:((funny(X)|~patient(X))))<=>(?[X]:((strong(X)&~strong(X)))))&
((?[X]:(humble(X)))=>((kind(alice)|generous(alice))))&
(![X]:((quiet(X)&strong(X))=>(~tall(X)|wise(X))))&
(![X]:((brave(X)|wise(X))<=>(rich(X)<~>strong(X))))&
(![X]:((patient(X)|curious(X))<=>(~happy(X)|~brave(X))))&
(![X]:((calm(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((funny(john))<=>(generous(lucy)))&
((?[X]:(calm(X)))=>((~humble(john)|~happy(john))))&
((?[X]:(~humble(X)))=>((~funny(susan)<~>~strong(susan))))&
(![X]:((curious(X)<~>~calm(X))=>(~brave(X)&~creative(X))))&
(![X]:(~calm(X)<=>~brave(X)))&
((?[X]:(strong(X)))=>((strong(john)&old(john))))&
(![X]:((~funny(X)&~kind(X))<=>(humble(X)&creative(X))))&
((?[X]:((~brave(X)&~curious(X))))=>((tall(alice)|old(alice))))&
((~humble(fred)|humble(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(old(paul))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~patient(X))))&
((tall(john)|calm(john)))&
((brave(mary)|~quiet(mary))) | ~calm(susan) | [] | null | 0 |
Everyone who is both wise and not kind is either not humble or creative and vice versa. Everyone who is both not kind and humble is either not rich or not quiet and vice versa. Everyone who is not tall is not wise and vice versa. If someone is both brave and not brave then lucy is both not quiet and strong and vice versa. If lucy is curious then someone is happy and vice versa. Everyone who is either rich or not happy is either brave or not funny. Everyone who is happy is funny or creative and vice versa. Everyone who is either patient or brave is both not kind and patient. Everyone who is humble or not quiet is not wise. Everyone who is not tall or not brave is both rich and old and vice versa. If someone is not funny then someone is happy and vice versa. Everyone who is either tall or curious is not old and vice versa. Everyone who is humble is both calm and not quiet. Everyone who is humble or not funny is not brave or not happy and vice versa. If someone is rich or not humble then someone is either curious or generous. If fred is both not patient and not quiet then someone is patient and vice versa. Fred is either old or strong. Fred is either strong or curious. Someone is both not wise and kind. Someone is both not patient and not calm. | Fred is not generous. | neutral | (![X]:((wise(X)&~kind(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~kind(X)&humble(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:(~tall(X)<=>~wise(X)))&
((?[X]:((brave(X)&~brave(X))))<=>((~quiet(lucy)&strong(lucy))))&
((curious(lucy))<=>(?[X]:(happy(X))))&
(![X]:((rich(X)<~>~happy(X))=>(brave(X)<~>~funny(X))))&
(![X]:(happy(X)<=>(funny(X)|creative(X))))&
(![X]:((patient(X)<~>brave(X))=>(~kind(X)&patient(X))))&
(![X]:((humble(X)|~quiet(X))=>~wise(X)))&
(![X]:((~tall(X)|~brave(X))<=>(rich(X)&old(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(happy(X))))&
(![X]:((tall(X)<~>curious(X))<=>~old(X)))&
(![X]:(humble(X)=>(calm(X)&~quiet(X))))&
(![X]:((humble(X)|~funny(X))<=>(~brave(X)|~happy(X))))&
((?[X]:((rich(X)|~humble(X))))=>(?[X]:((curious(X)<~>generous(X)))))&
(((~patient(fred)&~quiet(fred)))<=>(?[X]:(patient(X))))&
((old(fred)<~>strong(fred)))&
((strong(fred)<~>curious(fred)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~patient(X)&~calm(X)))) | ~generous(fred) | [] | null | 0 |
If someone is either calm or strong then john is both strong and not tall and vice versa. If someone is either old or not rich then someone is creative. If someone is either not brave or creative then someone is brave. Everyone who is either not quiet or not happy is either quiet or strong and vice versa. If someone is both brave and not happy then someone is both patient and tall and vice versa. Everyone who is either old or humble is either patient or not quiet. Everyone who is not calm or generous is both wise and not old. Everyone who is either humble or generous is both not wise and generous and vice versa. Everyone who is kind is not rich and vice versa. Everyone who is creative or strong is not brave or not old and vice versa. If someone is kind or not kind then someone is not happy or tall and vice versa. Everyone who is not rich is both curious and not curious. If lucy is either strong or not rich then someone is strong or not curious. Everyone who is kind or old is either not calm or calm. If someone is both tall and kind then fred is old and vice versa. If someone is calm or happy then lucy is either not tall or calm and vice versa. Someone is both strong and not creative. Someone is curious or not tall. Someone is not creative. Someone is both not tall and calm. Lucy is both not wise and not generous. Someone is either tall or curious. Someone is funny. John is humble or happy. | John is not rich. | contradiction | ((?[X]:((calm(X)<~>strong(X))))<=>((strong(john)&~tall(john))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(quiet(X)<~>strong(X))))&
((?[X]:((brave(X)&~happy(X))))<=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((old(X)<~>humble(X))=>(patient(X)<~>~quiet(X))))&
(![X]:((~calm(X)|generous(X))=>(wise(X)&~old(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~wise(X)&generous(X))))&
(![X]:(kind(X)<=>~rich(X)))&
(![X]:((creative(X)|strong(X))<=>(~brave(X)|~old(X))))&
((?[X]:((kind(X)|~kind(X))))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:(~rich(X)=>(curious(X)&~curious(X))))&
(((strong(lucy)<~>~rich(lucy)))=>(?[X]:((strong(X)|~curious(X)))))&
(![X]:((kind(X)|old(X))=>(~calm(X)<~>calm(X))))&
((?[X]:((tall(X)&kind(X))))<=>(old(fred)))&
((?[X]:((calm(X)|happy(X))))<=>((~tall(lucy)<~>calm(lucy))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)&calm(X))))&
((~wise(lucy)&~generous(lucy)))&
(?[X]:((tall(X)<~>curious(X))))&
(?[X]:(funny(X)))&
((humble(john)|happy(john))) | ~rich(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3503072355857849815172
% SZS output start Proof for 3503072355857849815172
12. ! [X0] : (~rich(X0) => (~curious(X0) & curious(X0))) [input p11]
25. ~rich(john) [input hypothesis]
35. ! [X0] : ((~curious(X0) & curious(X0)) | rich(X0)) [ennf transformation 12]
137. curious(X0) | rich(X0) [cnf transformation 35]
138. ~curious(X0) | rich(X0) [cnf transformation 35]
165. ~rich(john) [cnf transformation 25]
269. rich(X0) [subsumption resolution 137,138]
358. $false [subsumption resolution 165,269]
% SZS output end Proof for 3503072355857849815172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not tall then alice is both quiet and funny and vice versa.
If mary is generous or not wise then alice is either humble or brave.
Everyone who is creative or funny is not old or rich.
If someone is both not strong and creative then mary is both not wise and creative and vice versa.
If someone is either generous or not brave then someone is funny or rich.
Everyone who is both rich and not patient is quiet or brave and vice versa.
If lucy is either not calm or not curious then paul is either not strong or kind and vice versa.
If someone is not wise then paul is either strong or not old.
Everyone who is rich is both calm and wise and vice versa.
Everyone who is not generous or funny is patient or not strong and vice versa.
Everyone who is creative or not patient is either curious or not old and vice versa.
If fred is not generous or curious then alice is both not brave and not creative and vice versa.
If someone is either not happy or not humble then susan is either not quiet or quiet and vice versa.
Everyone who is either rich or not funny is both old and patient.
If someone is not strong or not humble then john is either old or rich.
Someone is both not brave and not rich.
John is tall.
Fred is either not quiet or calm.
Someone is happy or not generous.
Someone is both not funny and curious.
Someone is either not generous or not curious.
Paul is not calm.
Someone is both happy and strong. | Mary is not funny. | neutral | ((?[X]:((~humble(X)|~tall(X))))<=>((quiet(alice)&funny(alice))))&
(((generous(mary)|~wise(mary)))=>((humble(alice)<~>brave(alice))))&
(![X]:((creative(X)|funny(X))=>(~old(X)|rich(X))))&
((?[X]:((~strong(X)&creative(X))))<=>((~wise(mary)&creative(mary))))&
((?[X]:((generous(X)<~>~brave(X))))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((rich(X)&~patient(X))<=>(quiet(X)|brave(X))))&
(((~calm(lucy)<~>~curious(lucy)))<=>((~strong(paul)<~>kind(paul))))&
((?[X]:(~wise(X)))=>((strong(paul)<~>~old(paul))))&
(![X]:(rich(X)<=>(calm(X)&wise(X))))&
(![X]:((~generous(X)|funny(X))<=>(patient(X)|~strong(X))))&
(![X]:((creative(X)|~patient(X))<=>(curious(X)<~>~old(X))))&
(((~generous(fred)|curious(fred)))<=>((~brave(alice)&~creative(alice))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((~quiet(susan)<~>quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(old(X)&patient(X))))&
((?[X]:((~strong(X)|~humble(X))))=>((old(john)<~>rich(john))))&
(?[X]:((~brave(X)&~rich(X))))&
(tall(john))&
((~quiet(fred)<~>calm(fred)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:((~generous(X)<~>~curious(X))))&
(~calm(paul))&
(?[X]:((happy(X)&strong(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is strong is either not tall or not quiet and vice versa.
If someone is either not brave or not generous then someone is both not brave and brave and vice versa.
Everyone who is either not kind or creative is not funny or not quiet.
If someone is both calm and quiet then alice is either generous or quiet and vice versa.
Everyone who is both not strong and funny is both generous and strong and vice versa.
Everyone who is both creative and wise is brave.
If someone is both not creative and patient then someone is either not kind or patient and vice versa.
Everyone who is either patient or quiet is kind or not quiet and vice versa.
If someone is either not wise or patient then lucy is both not happy and not brave and vice versa.
If susan is both kind and not quiet then someone is either humble or not wise and vice versa.
If mary is generous or wise then mary is both not kind and not creative and vice versa.
Everyone who is either not humble or quiet is both funny and not tall.
Everyone who is patient or not creative is not curious and vice versa.
If mary is not strong or not quiet then alice is not funny or not curious and vice versa.
If someone is generous then john is brave.
Everyone who is either not tall or not funny is not kind.
Someone is both not rich and not quiet.
Lucy is either not patient or strong.
Someone is wise.
Susan is not wise.
Someone is calm or not tall.
Paul is not humble or not calm.
Paul is both happy and not kind.
Someone is either generous or not curious. | Susan is patient. | entailment | (![X]:(strong(X)<=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~brave(X)<~>~generous(X))))<=>(?[X]:((~brave(X)&brave(X)))))&
(![X]:((~kind(X)<~>creative(X))=>(~funny(X)|~quiet(X))))&
((?[X]:((calm(X)&quiet(X))))<=>((generous(alice)<~>quiet(alice))))&
(![X]:((~strong(X)&funny(X))<=>(generous(X)&strong(X))))&
(![X]:((creative(X)&wise(X))=>brave(X)))&
((?[X]:((~creative(X)&patient(X))))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(kind(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>patient(X))))<=>((~happy(lucy)&~brave(lucy))))&
(((kind(susan)&~quiet(susan)))<=>(?[X]:((humble(X)<~>~wise(X)))))&
(((generous(mary)|wise(mary)))<=>((~kind(mary)&~creative(mary))))&
(![X]:((~humble(X)<~>quiet(X))=>(funny(X)&~tall(X))))&
(![X]:((patient(X)|~creative(X))<=>~curious(X)))&
(((~strong(mary)|~quiet(mary)))<=>((~funny(alice)|~curious(alice))))&
((?[X]:(generous(X)))=>(brave(john)))&
(![X]:((~tall(X)<~>~funny(X))=>~kind(X)))&
(?[X]:((~rich(X)&~quiet(X))))&
((~patient(lucy)<~>strong(lucy)))&
(?[X]:(wise(X)))&
(~wise(susan))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul)))&
(?[X]:((generous(X)<~>~curious(X)))) | patient(susan) | [
"p7",
"p9",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6732304760438734037503899
% SZS output start Proof for 6732304760438734037503899
8. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (~quiet(X0) | kind(X0))) [input p7]
10. (~quiet(susan) & kind(susan)) <=> ? [X0] : (humble(X0) <~> ~wise(X0)) [input p9]
12. ! [X0] : ((~humble(X0) <~> quiet(X0)) => (~tall(X0) & funny(X0))) [input p11]
16. ! [X0] : ((~tall(X0) <~> ~funny(X0)) => ~kind(X0)) [input p15]
20. ~wise(susan) [input p19]
25. ~patient(susan) [input hypothesis]
33. ! [X0] : ((~tall(X0) & funny(X0)) | (~humble(X0) <=> quiet(X0))) [ennf transformation 12]
35. ! [X0] : (~kind(X0) | (~tall(X0) <=> ~funny(X0))) [ennf transformation 16]
54. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 8]
55. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 54]
61. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (quiet(susan) | ~kind(susan))) [nnf transformation 10]
62. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | quiet(susan) | ~kind(susan)) [flattening 61]
63. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X1] : ((wise(X1) | ~humble(X1)) & (~wise(X1) | humble(X1))) | quiet(susan) | ~kind(susan)) [rectify 62]
64. ? [X1] : ((wise(X1) | ~humble(X1)) & (~wise(X1) | humble(X1))) => ((wise(sK6) | ~humble(sK6)) & (~wise(sK6) | humble(sK6))) [choice axiom]
65. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(sK6) | ~humble(sK6)) & (~wise(sK6) | humble(sK6))) | quiet(susan) | ~kind(susan)) [skolemisation 63,64]
68. ! [X0] : ((~tall(X0) & funny(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) [nnf transformation 33]
73. ! [X0] : (~kind(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) [nnf transformation 35]
114. ~quiet(X0) | kind(X0) | patient(X0) | ~quiet(X0) [cnf transformation 55]
116. quiet(X0) | patient(X0) | quiet(X0) [cnf transformation 55]
130. ~quiet(susan) | humble(X0) | wise(X0) [cnf transformation 65]
137. ~humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 68]
139. ~humble(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 68]
148. ~funny(X0) | ~kind(X0) | tall(X0) [cnf transformation 73]
154. ~wise(susan) [cnf transformation 20]
161. ~patient(susan) [cnf transformation 25]
162. ~quiet(X0) | kind(X0) | patient(X0) [duplicate literal removal 114]
163. patient(X0) | quiet(X0) [duplicate literal removal 116]
214. 11 <=> ! [X1] : (patient(X1) | kind(X1)) [avatar definition]
215. patient(X1) | kind(X1) <- (11) [avatar component clause 214]
236. kind(X0) | patient(X0) [subsumption resolution 162,163]
237. 11 [avatar split clause 236,214]
267. 22 <=> ! [X0] : (humble(X0) | wise(X0)) [avatar definition]
268. humble(X0) | wise(X0) <- (22) [avatar component clause 267]
270. 23 <=> quiet(susan) [avatar definition]
271. quiet(susan) <- (23) [avatar component clause 270]
273. 22 | ~23 [avatar split clause 130,270,267]
279. 25 <=> kind(susan) [avatar definition]
281. kind(susan) <- (25) [avatar component clause 279]
383. quiet(susan) [resolution 163,161]
388. 23 [avatar split clause 383,270]
392. kind(susan) <- (11) [resolution 215,161]
400. 25 | ~11 [avatar split clause 392,214,279]
432. 49 <=> tall(susan) [avatar definition]
500. ~quiet(X1) | funny(X1) | wise(X1) <- (22) [resolution 137,268]
503. ~quiet(X1) | ~tall(X1) | wise(X1) <- (22) [resolution 139,268]
570. funny(susan) | wise(susan) <- (22, 23) [resolution 500,271]
580. funny(susan) <- (22, 23) [subsumption resolution 570,154]
597. ~tall(susan) | wise(susan) <- (22, 23) [resolution 503,271]
647. ~kind(susan) | tall(susan) <- (22, 23) [resolution 580,148]
651. tall(susan) <- (22, 23, 25) [subsumption resolution 647,281]
655. 49 | ~22 | ~23 | ~25 [avatar split clause 651,279,270,267,432]
656. ~tall(susan) <- (22, 23) [subsumption resolution 597,154]
657. ~49 | ~22 | ~23 [avatar split clause 656,270,267,432]
659. $false [avatar sat refutation 237,273,388,400,655,657]
% SZS output end Proof for 6732304760438734037503899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both humble and patient then someone is wise.
If lucy is not humble then fred is either not kind or generous.
Everyone who is not calm or not happy is not creative or tall.
Everyone who is not curious is both patient and not strong and vice versa.
If fred is funny then someone is either patient or humble.
If lucy is both happy and not quiet then someone is both happy and calm.
If someone is both rich and old then lucy is either kind or curious.
Everyone who is both rich and not generous is happy.
Everyone who is either not kind or happy is both calm and not kind and vice versa.
Everyone who is not rich or wise is both curious and not tall and vice versa.
Everyone who is both patient and creative is both not rich and wise and vice versa.
Everyone who is either rich or brave is not curious or quiet.
If john is wise then paul is both not rich and funny.
If alice is not old then lucy is both not creative and kind and vice versa.
If someone is humble then susan is either rich or not wise.
Everyone who is both funny and strong is rich or not strong and vice versa.
Lucy is generous.
John is not funny.
Paul is not brave.
Someone is either not strong or kind.
Someone is old or not creative.
Fred is both not patient and not creative. | Alice is not creative. | neutral | (((humble(paul)&patient(paul)))=>(?[X]:(wise(X))))&
((~humble(lucy))=>((~kind(fred)<~>generous(fred))))&
(![X]:((~calm(X)|~happy(X))=>(~creative(X)|tall(X))))&
(![X]:(~curious(X)<=>(patient(X)&~strong(X))))&
((funny(fred))=>(?[X]:((patient(X)<~>humble(X)))))&
(((happy(lucy)&~quiet(lucy)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:((rich(X)&old(X))))=>((kind(lucy)<~>curious(lucy))))&
(![X]:((rich(X)&~generous(X))=>happy(X)))&
(![X]:((~kind(X)<~>happy(X))<=>(calm(X)&~kind(X))))&
(![X]:((~rich(X)|wise(X))<=>(curious(X)&~tall(X))))&
(![X]:((patient(X)&creative(X))<=>(~rich(X)&wise(X))))&
(![X]:((rich(X)<~>brave(X))=>(~curious(X)|quiet(X))))&
((wise(john))=>((~rich(paul)&funny(paul))))&
((~old(alice))<=>((~creative(lucy)&kind(lucy))))&
((?[X]:(humble(X)))=>((rich(susan)<~>~wise(susan))))&
(![X]:((funny(X)&strong(X))<=>(rich(X)|~strong(X))))&
(generous(lucy))&
(~funny(john))&
(~brave(paul))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((old(X)|~creative(X))))&
((~patient(fred)&~creative(fred))) | ~creative(alice) | [] | null | 0 |
If mary is not happy or brave then mary is rich.
Everyone who is humble or kind is not calm.
Everyone who is not kind or wise is both curious and funny.
Everyone who is either funny or not funny is either not wise or brave.
Everyone who is humble or quiet is not humble or happy.
Everyone who is not generous is not rich or not old and vice versa.
Everyone who is either rich or brave is not humble or not rich.
Everyone who is creative or old is happy.
Everyone who is creative or not kind is either patient or not rich.
Everyone who is both calm and not curious is brave or not rich and vice versa.
If someone is both curious and happy then lucy is both not humble and rich and vice versa.
Everyone who is either not quiet or generous is not funny.
Everyone who is either old or funny is both not funny and funny.
If someone is either humble or quiet then mary is both not curious and not quiet.
If someone is kind then lucy is quiet and vice versa.
Everyone who is patient or humble is curious or not strong and vice versa.
John is either calm or not happy.
Someone is creative or not tall.
Mary is calm or tall.
Someone is either tall or not humble.
John is both not generous and tall.
Alice is brave or generous.
Someone is brave or funny. | Alice is not funny. | contradiction | (((~happy(mary)|brave(mary)))=>(rich(mary)))&
(![X]:((humble(X)|kind(X))=>~calm(X)))&
(![X]:((~kind(X)|wise(X))=>(curious(X)&funny(X))))&
(![X]:((funny(X)<~>~funny(X))=>(~wise(X)<~>brave(X))))&
(![X]:((humble(X)|quiet(X))=>(~humble(X)|happy(X))))&
(![X]:(~generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((rich(X)<~>brave(X))=>(~humble(X)|~rich(X))))&
(![X]:((creative(X)|old(X))=>happy(X)))&
(![X]:((creative(X)|~kind(X))=>(patient(X)<~>~rich(X))))&
(![X]:((calm(X)&~curious(X))<=>(brave(X)|~rich(X))))&
((?[X]:((curious(X)&happy(X))))<=>((~humble(lucy)&rich(lucy))))&
(![X]:((~quiet(X)<~>generous(X))=>~funny(X)))&
(![X]:((old(X)<~>funny(X))=>(~funny(X)&funny(X))))&
((?[X]:((humble(X)<~>quiet(X))))=>((~curious(mary)&~quiet(mary))))&
((?[X]:(kind(X)))<=>(quiet(lucy)))&
(![X]:((patient(X)|humble(X))<=>(curious(X)|~strong(X))))&
((calm(john)<~>~happy(john)))&
(?[X]:((creative(X)|~tall(X))))&
((calm(mary)|tall(mary)))&
(?[X]:((tall(X)<~>~humble(X))))&
((~generous(john)&tall(john)))&
((brave(alice)|generous(alice)))&
(?[X]:((brave(X)|funny(X)))) | ~funny(alice) | [
"p1",
"p2",
"p5",
"p9",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 124949074463708376438343
% SZS output start Proof for 124949074463708376438343
2. ! [X0] : ((kind(X0) | humble(X0)) => ~calm(X0)) [input p1]
3. ! [X0] : ((wise(X0) | ~kind(X0)) => (funny(X0) & curious(X0))) [input p2]
6. ! [X0] : (~generous(X0) <=> (~old(X0) | ~rich(X0))) [input p5]
10. ! [X0] : ((~curious(X0) & calm(X0)) <=> (~rich(X0) | brave(X0))) [input p9]
13. ! [X0] : ((old(X0) <~> funny(X0)) => (funny(X0) & ~funny(X0))) [input p12]
22. generous(alice) | brave(alice) [input p21]
24. ~funny(alice) [input hypothesis]
26. ! [X0] : (~calm(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 2]
27. ! [X0] : ((funny(X0) & curious(X0)) | (~wise(X0) & kind(X0))) [ennf transformation 3]
36. ! [X0] : ((funny(X0) & ~funny(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 13]
39. ! [X0] : ((~generous(X0) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | generous(X0))) [nnf transformation 6]
40. ! [X0] : ((~generous(X0) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | generous(X0))) [flattening 39]
43. ! [X0] : (((~curious(X0) & calm(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 10]
44. ! [X0] : (((~curious(X0) & calm(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | curious(X0) | ~calm(X0))) [flattening 43]
51. ! [X0] : ((funny(X0) & ~funny(X0)) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 36]
70. ~calm(X0) | ~kind(X0) [cnf transformation 26]
73. funny(X0) | kind(X0) [cnf transformation 27]
83. ~generous(X0) | old(X0) [cnf transformation 40]
93. ~brave(X0) | calm(X0) [cnf transformation 44]
105. funny(X0) | funny(X0) | ~old(X0) [cnf transformation 51]
125. generous(alice) | brave(alice) [cnf transformation 22]
127. ~funny(alice) [cnf transformation 24]
129. ~old(X0) | funny(X0) [duplicate literal removal 105]
246. 24 <=> brave(alice) [avatar definition]
248. brave(alice) <- (24) [avatar component clause 246]
250. 25 <=> generous(alice) [avatar definition]
252. generous(alice) <- (25) [avatar component clause 250]
253. 24 | 25 [avatar split clause 125,250,246]
260. kind(alice) [resolution 73,127]
261. calm(alice) <- (24) [resolution 93,248]
265. ~kind(alice) <- (24) [resolution 261,70]
267. $false <- (24) [subsumption resolution 265,260]
268. ~24 [avatar contradiction clause 267]
269. old(alice) <- (25) [resolution 252,83]
282. funny(alice) <- (25) [resolution 129,269]
283. $false <- (25) [subsumption resolution 282,127]
284. ~25 [avatar contradiction clause 283]
285. $false [avatar sat refutation 253,268,284]
% SZS output end Proof for 124949074463708376438343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is quiet. Everyone who is generous or not funny is not quiet or not kind and vice versa. Everyone who is patient or not wise is tall or not wise and vice versa. Everyone who is either kind or generous is either not old or tall and vice versa. Everyone who is not wise is either not patient or strong. If susan is old then someone is either funny or not brave and vice versa. Everyone who is not curious is both generous and not happy and vice versa. Everyone who is tall is happy or not tall. If someone is both not patient and not kind then someone is both calm and old and vice versa. If mary is both not creative and wise then someone is not old or not creative and vice versa. Everyone who is not strong or quiet is patient and vice versa. If john is not rich then someone is old. Everyone who is not tall or not rich is tall and vice versa. Everyone who is not quiet or strong is either not curious or not old. If susan is not tall then alice is calm. Everyone who is either not brave or wise is both kind and not tall. Someone is quiet. Someone is either not wise or curious. Someone is either generous or old. Someone is either not creative or wise. Someone is either not old or not humble. John is generous. | Mary is not patient. | contradiction | (![X]:(funny(X)=>quiet(X)))&
(![X]:((generous(X)|~funny(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((patient(X)|~wise(X))<=>(tall(X)|~wise(X))))&
(![X]:((kind(X)<~>generous(X))<=>(~old(X)<~>tall(X))))&
(![X]:(~wise(X)=>(~patient(X)<~>strong(X))))&
((old(susan))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:(~curious(X)<=>(generous(X)&~happy(X))))&
(![X]:(tall(X)=>(happy(X)|~tall(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((calm(X)&old(X)))))&
(((~creative(mary)&wise(mary)))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((~strong(X)|quiet(X))<=>patient(X)))&
((~rich(john))=>(?[X]:(old(X))))&
(![X]:((~tall(X)|~rich(X))<=>tall(X)))&
(![X]:((~quiet(X)|strong(X))=>(~curious(X)<~>~old(X))))&
((~tall(susan))=>(calm(alice)))&
(![X]:((~brave(X)<~>wise(X))=>(kind(X)&~tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(generous(john)) | ~patient(mary) | [
"p2",
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1582265831351629508772112
% SZS output start Proof for 1582265831351629508772112
3. ! [X0] : ((~wise(X0) | patient(X0)) <=> (~wise(X0) | tall(X0))) [input p2]
5. ! [X0] : (~wise(X0) => (~patient(X0) <~> strong(X0))) [input p4]
11. ! [X0] : ((quiet(X0) | ~strong(X0)) <=> patient(X0)) [input p10]
13. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> tall(X0)) [input p12]
23. ~patient(mary) [input hypothesis]
26. ! [X0] : ((~patient(X0) <~> strong(X0)) | wise(X0)) [ennf transformation 5]
35. ! [X0] : (((~wise(X0) | patient(X0)) | (wise(X0) & ~tall(X0))) & ((~wise(X0) | tall(X0)) | (wise(X0) & ~patient(X0)))) [nnf transformation 3]
36. ! [X0] : ((~wise(X0) | patient(X0) | (wise(X0) & ~tall(X0))) & (~wise(X0) | tall(X0) | (wise(X0) & ~patient(X0)))) [flattening 35]
38. ! [X0] : (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | wise(X0)) [nnf transformation 26]
55. ! [X0] : (((quiet(X0) | ~strong(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & strong(X0)))) [nnf transformation 11]
56. ! [X0] : ((quiet(X0) | ~strong(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & strong(X0)))) [flattening 55]
59. ! [X0] : (((~rich(X0) | ~tall(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) & tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~rich(X0) | ~tall(X0) | ~tall(X0)) & (tall(X0) | (rich(X0) & tall(X0)))) [flattening 59]
84. ~tall(X0) | patient(X0) | ~wise(X0) [cnf transformation 36]
95. ~strong(X0) | patient(X0) | wise(X0) [cnf transformation 38]
113. strong(X0) | patient(X0) [cnf transformation 56]
117. tall(X0) | tall(X0) [cnf transformation 60]
139. ~patient(mary) [cnf transformation 23]
140. tall(X0) [duplicate literal removal 117]
317. patient(X0) | ~wise(X0) [resolution 84,140]
330. patient(X0) | wise(X0) | patient(X0) [resolution 95,113]
331. patient(X0) | wise(X0) [duplicate literal removal 330]
332. patient(X0) [subsumption resolution 331,317]
333. $false [resolution 332,139]
% SZS output end Proof for 1582265831351629508772112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not tall then fred is both not kind and tall.
If paul is both not creative and not strong then john is not generous and vice versa.
Everyone who is both humble and not tall is both humble and kind and vice versa.
Everyone who is both happy and not calm is not humble.
Everyone who is both not kind and quiet is either patient or not quiet.
Everyone who is quiet is not strong or humble.
If someone is funny then alice is either funny or not rich and vice versa.
Everyone who is brave is both not happy and generous.
Everyone who is creative or not patient is wise or kind.
If someone is not quiet or strong then john is not creative or not calm.
If someone is both quiet and calm then susan is funny or not kind.
Everyone who is happy or not wise is both strong and not generous.
If someone is both funny and not brave then susan is quiet and vice versa.
If someone is not creative or tall then someone is both not tall and not calm and vice versa.
Everyone who is not curious is not kind or rich and vice versa.
If someone is wise then someone is tall and vice versa.
Someone is either funny or not kind.
Someone is kind or not wise.
Someone is either not kind or happy.
Someone is both not patient and humble.
Lucy is tall.
Susan is quiet.
John is both happy and kind.
Someone is not rich. | John is not brave. | entailment | ((?[X]:((~curious(X)|~tall(X))))=>((~kind(fred)&tall(fred))))&
(((~creative(paul)&~strong(paul)))<=>(~generous(john)))&
(![X]:((humble(X)&~tall(X))<=>(humble(X)&kind(X))))&
(![X]:((happy(X)&~calm(X))=>~humble(X)))&
(![X]:((~kind(X)&quiet(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(quiet(X)=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((funny(alice)<~>~rich(alice))))&
(![X]:(brave(X)=>(~happy(X)&generous(X))))&
(![X]:((creative(X)|~patient(X))=>(wise(X)|kind(X))))&
((?[X]:((~quiet(X)|strong(X))))=>((~creative(john)|~calm(john))))&
((?[X]:((quiet(X)&calm(X))))=>((funny(susan)|~kind(susan))))&
(![X]:((happy(X)|~wise(X))=>(strong(X)&~generous(X))))&
((?[X]:((funny(X)&~brave(X))))<=>(quiet(susan)))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
((?[X]:(wise(X)))<=>(?[X]:(tall(X))))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~patient(X)&humble(X))))&
(tall(lucy))&
(quiet(susan))&
((happy(john)&kind(john)))&
(?[X]:(~rich(X))) | ~brave(john) | [
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7261101631012015108878874
% SZS output start Proof for 7261101631012015108878874
8. ! [X0] : (brave(X0) => (generous(X0) & ~happy(X0))) [input p7]
23. kind(john) & happy(john) [input p22]
25. brave(john) [input hypothesis]
36. ! [X0] : ((generous(X0) & ~happy(X0)) | ~brave(X0)) [ennf transformation 8]
99. ~brave(X0) | ~happy(X0) [cnf transformation 36]
131. happy(john) [cnf transformation 23]
134. brave(john) [cnf transformation 25]
313. ~happy(john) [resolution 99,134]
314. $false [subsumption resolution 313,131]
% SZS output end Proof for 7261101631012015108878874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then susan is not funny.
If mary is patient then someone is not calm and vice versa.
If john is either not happy or rich then someone is old or not strong and vice versa.
Everyone who is not quiet or not happy is both not funny and rich and vice versa.
Everyone who is either not quiet or calm is both kind and not brave and vice versa.
Everyone who is either old or not strong is both patient and not happy and vice versa.
Everyone who is both not curious and rich is not strong.
Everyone who is both not calm and not quiet is both calm and not creative.
Everyone who is both not calm and curious is not funny or not quiet and vice versa.
If someone is not creative or strong then fred is quiet or humble.
If mary is either humble or happy then someone is not happy or humble and vice versa.
Everyone who is either quiet or tall is either not tall or brave and vice versa.
Everyone who is not curious or not calm is both not quiet and old and vice versa.
Everyone who is quiet or not rich is both quiet and not wise.
If someone is calm or brave then someone is both not brave and humble.
Everyone who is either creative or not tall is both not rich and funny.
Lucy is creative.
Susan is either generous or not quiet.
Susan is not rich or old.
Mary is not kind or not tall.
Fred is both not rich and generous.
Mary is not rich.
Susan is humble or not humble. | Mary is patient. | contradiction | ((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&old(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
((?[X]:((calm(X)|brave(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((creative(X)<~>~tall(X))=>(~rich(X)&funny(X))))&
(creative(lucy))&
((generous(susan)<~>~quiet(susan)))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary)))&
((~rich(fred)&generous(fred)))&
(~rich(mary))&
((humble(susan)|~humble(susan))) | patient(mary) | [
"p1",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2975416357288736494812194
% SZS output start Proof for 2975416357288736494812194
2. patient(mary) <=> ? [X0] : ~calm(X0) [input p1]
8. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p7]
9. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p8]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (old(X0) & ~quiet(X0))) [input p12]
24. patient(mary) [input hypothesis]
30. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 8]
31. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 30]
37. (patient(mary) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ~patient(mary)) [nnf transformation 2]
38. (patient(mary) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ~patient(mary)) [rectify 37]
39. ? [X1] : ~calm(X1) => ~calm(sK0) [choice axiom]
40. (patient(mary) | ! [X0] : calm(X0)) & (~calm(sK0) | ~patient(mary)) [skolemisation 38,39]
51. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 51]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 13]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [flattening 58]
66. ~calm(sK0) | ~patient(mary) [cnf transformation 40]
92. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 31]
96. ~calm(X0) | quiet(X0) [cnf transformation 52]
116. ~quiet(X0) | calm(X0) [cnf transformation 59]
139. patient(mary) [cnf transformation 24]
144. calm(X0) | quiet(X0) [duplicate literal removal 92]
154. 3 <=> ! [X0] : calm(X0) [avatar definition]
155. calm(X0) <- (3) [avatar component clause 154]
157. 4 <=> patient(mary) [avatar definition]
162. 5 <=> calm(sK0) [avatar definition]
164. ~calm(sK0) <- (~5) [avatar component clause 162]
165. ~4 | ~5 [avatar split clause 66,162,157]
194. quiet(X0) [subsumption resolution 96,144]
227. calm(X0) [subsumption resolution 116,194]
228. 3 [avatar split clause 227,154]
257. 4 [avatar split clause 139,157]
260. $false <- (3, ~5) [subsumption resolution 164,155]
261. ~3 | 5 [avatar contradiction clause 260]
262. $false [avatar sat refutation 165,228,257,261]
% SZS output end Proof for 2975416357288736494812194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not old then paul is both funny and generous and vice versa.
Everyone who is both not quiet and quiet is not creative or generous and vice versa.
If paul is both calm and not quiet then lucy is both not curious and happy.
Everyone who is both not calm and funny is both not patient and not generous.
Everyone who is not calm is not funny or not tall.
If someone is generous or not creative then someone is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Everyone who is both not quiet and funny is humble or happy and vice versa.
If someone is both not funny and not curious then someone is not humble and vice versa.
If alice is not tall or humble then susan is not patient or not creative.
Everyone who is either creative or not quiet is not kind or not old.
If someone is funny or not patient then fred is not patient or generous and vice versa.
Everyone who is not kind is not creative and vice versa.
Everyone who is both wise and not creative is either not humble or old.
If someone is not tall then someone is either rich or generous.
Someone is tall or funny.
John is not quiet.
Someone is funny.
Someone is either rich or not rich.
Someone is either brave or calm.
Susan is not happy.
Paul is both not happy and funny.
Fred is strong. | John is not tall. | contradiction | ((?[X]:((humble(X)&~old(X))))<=>((funny(paul)&generous(paul))))&
(![X]:((~quiet(X)&quiet(X))<=>(~creative(X)|generous(X))))&
(((calm(paul)&~quiet(paul)))=>((~curious(lucy)&happy(lucy))))&
(![X]:((~calm(X)&funny(X))=>(~patient(X)&~generous(X))))&
(![X]:(~calm(X)=>(~funny(X)|~tall(X))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(![X]:((~quiet(X)&funny(X))<=>(humble(X)|happy(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(((~tall(alice)|humble(alice)))=>((~patient(susan)|~creative(susan))))&
(![X]:((creative(X)<~>~quiet(X))=>(~kind(X)|~old(X))))&
((?[X]:((funny(X)|~patient(X))))<=>((~patient(fred)|generous(fred))))&
(![X]:(~kind(X)<=>~creative(X)))&
(![X]:((wise(X)&~creative(X))=>(~humble(X)<~>old(X))))&
((?[X]:(~tall(X)))=>(?[X]:((rich(X)<~>generous(X)))))&
(?[X]:((tall(X)|funny(X))))&
(~quiet(john))&
(?[X]:(funny(X)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(~happy(susan))&
((~happy(paul)&funny(paul)))&
(strong(fred)) | ~tall(john) | [
"p1",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2214742251329535404355047
% SZS output start Proof for 2214742251329535404355047
2. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (generous(X0) | ~creative(X0))) [input p1]
6. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X0] : (~creative(X0) | rich(X0)) [input p5]
16. ? [X0] : ~tall(X0) => ? [X0] : (rich(X0) <~> generous(X0)) [input p15]
25. ~tall(john) [input hypothesis]
26. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X1] : (~creative(X1) | rich(X1)) [rectify 6]
28. ? [X0] : ~tall(X0) => ? [X1] : (rich(X1) <~> generous(X1)) [rectify 16]
43. ? [X1] : (rich(X1) <~> generous(X1)) | ! [X0] : tall(X0) [ennf transformation 28]
49. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 2]
50. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | ~quiet(X0) | quiet(X0))) [flattening 49]
51. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (creative(X1) & ~rich(X1))) & (? [X1] : (~creative(X1) | rich(X1)) | ! [X0] : (creative(X0) & ~generous(X0))) [nnf transformation 26]
52. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (creative(X1) & ~rich(X1))) & (? [X2] : (~creative(X2) | rich(X2)) | ! [X3] : (creative(X3) & ~generous(X3))) [rectify 51]
53. ? [X0] : (~creative(X0) | generous(X0)) => (~creative(sK1) | generous(sK1)) [choice axiom]
54. ? [X2] : (~creative(X2) | rich(X2)) => (~creative(sK2) | rich(sK2)) [choice axiom]
55. ((~creative(sK1) | generous(sK1)) | ! [X1] : (creative(X1) & ~rich(X1))) & ((~creative(sK2) | rich(sK2)) | ! [X3] : (creative(X3) & ~generous(X3))) [skolemisation 52,54,53]
72. ? [X1] : ((~generous(X1) | ~rich(X1)) & (generous(X1) | rich(X1))) | ! [X0] : tall(X0) [nnf transformation 43]
73. ? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ! [X1] : tall(X1) [rectify 72]
74. ? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) => ((~generous(sK6) | ~rich(sK6)) & (generous(sK6) | rich(sK6))) [choice axiom]
75. ((~generous(sK6) | ~rich(sK6)) & (generous(sK6) | rich(sK6))) | ! [X1] : tall(X1) [skolemisation 73,74]
91. ~quiet(X0) | creative(X0) [cnf transformation 50]
92. ~quiet(X0) | ~generous(X0) [cnf transformation 50]
93. quiet(X0) | creative(X0) [cnf transformation 50]
94. quiet(X0) | ~generous(X0) [cnf transformation 50]
102. ~creative(sK1) | generous(sK1) | ~rich(X1) [cnf transformation 55]
131. generous(sK6) | rich(sK6) | tall(X1) [cnf transformation 75]
144. ~tall(john) [cnf transformation 25]
170. ~generous(X0) [subsumption resolution 92,94]
171. creative(X0) [subsumption resolution 91,93]
190. generous(sK1) | ~rich(X1) [subsumption resolution 102,171]
191. ~rich(X1) [subsumption resolution 190,170]
249. rich(sK6) | tall(X1) [subsumption resolution 131,170]
250. tall(X1) [subsumption resolution 249,191]
262. $false [subsumption resolution 144,250]
% SZS output end Proof for 2214742251329535404355047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or generous is either quiet or not humble and vice versa. If alice is not kind then someone is both kind and creative. If lucy is rich then alice is funny and vice versa. Everyone who is both not quiet and generous is not curious and vice versa. If paul is both calm and funny then someone is not brave or not happy. If someone is strong then alice is either wise or not tall and vice versa. Everyone who is either quiet or brave is creative and vice versa. Everyone who is either not tall or not patient is not generous or not creative. If mary is either not curious or generous then someone is creative and vice versa. Everyone who is both not brave and patient is brave or humble and vice versa. If someone is either patient or not brave then paul is both not strong and not tall. If someone is not curious or not happy then lucy is calm or funny and vice versa. Everyone who is both creative and patient is both not old and generous and vice versa. If susan is kind then mary is either not kind or not calm and vice versa. Everyone who is not funny is brave or strong. If lucy is funny or not wise then mary is not rich and vice versa. Someone is either happy or kind. Susan is both quiet and calm. John is patient or old. Someone is wise or curious. Someone is either old or not humble. Lucy is not calm. Someone is either not old or not strong. Someone is generous. | Mary is quiet. | entailment | (![X]:((rich(X)<~>generous(X))<=>(quiet(X)<~>~humble(X))))&
((~kind(alice))=>(?[X]:((kind(X)&creative(X)))))&
((rich(lucy))<=>(funny(alice)))&
(![X]:((~quiet(X)&generous(X))<=>~curious(X)))&
(((calm(paul)&funny(paul)))=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:(strong(X)))<=>((wise(alice)<~>~tall(alice))))&
(![X]:((quiet(X)<~>brave(X))<=>creative(X)))&
(![X]:((~tall(X)<~>~patient(X))=>(~generous(X)|~creative(X))))&
(((~curious(mary)<~>generous(mary)))<=>(?[X]:(creative(X))))&
(![X]:((~brave(X)&patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((patient(X)<~>~brave(X))))=>((~strong(paul)&~tall(paul))))&
((?[X]:((~curious(X)|~happy(X))))<=>((calm(lucy)|funny(lucy))))&
(![X]:((creative(X)&patient(X))<=>(~old(X)&generous(X))))&
((kind(susan))<=>((~kind(mary)<~>~calm(mary))))&
(![X]:(~funny(X)=>(brave(X)|strong(X))))&
(((funny(lucy)|~wise(lucy)))<=>(~rich(mary)))&
(?[X]:((happy(X)<~>kind(X))))&
((quiet(susan)&calm(susan)))&
((patient(john)|old(john)))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(~calm(lucy))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:(generous(X))) | quiet(mary) | [
"p3",
"p6",
"p8",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 98230033338856907544633
% SZS output start Proof for 98230033338856907544633
4. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> ~curious(X0)) [input p3]
7. ! [X0] : ((quiet(X0) <~> brave(X0)) <=> creative(X0)) [input p6]
9. (~curious(mary) <~> generous(mary)) <=> ? [X0] : creative(X0) [input p8]
10. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p9]
18. calm(susan) & quiet(susan) [input p17]
25. ~quiet(mary) [input hypothesis]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | curious(X0)) & (~curious(X0) | (~generous(X0) | quiet(X0)))) [nnf transformation 4]
39. ! [X0] : (((generous(X0) & ~quiet(X0)) | curious(X0)) & (~curious(X0) | ~generous(X0) | quiet(X0))) [flattening 38]
46. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~creative(X0)) & (creative(X0) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [nnf transformation 7]
48. (((~generous(mary) | curious(mary)) & (generous(mary) | ~curious(mary))) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | ((~curious(mary) | ~generous(mary)) & (generous(mary) | curious(mary)))) [nnf transformation 9]
49. (((~generous(mary) | curious(mary)) & (generous(mary) | ~curious(mary))) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | ((~curious(mary) | ~generous(mary)) & (generous(mary) | curious(mary)))) [rectify 48]
50. ? [X1] : creative(X1) => creative(sK3) [choice axiom]
51. (((~generous(mary) | curious(mary)) & (generous(mary) | ~curious(mary))) | ! [X0] : ~creative(X0)) & (creative(sK3) | ((~curious(mary) | ~generous(mary)) & (generous(mary) | curious(mary)))) [skolemisation 49,50]
52. ! [X0] : (((patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 10]
53. ! [X0] : (((patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | ~patient(X0) | brave(X0))) [flattening 52]
90. ~curious(X0) | ~generous(X0) | quiet(X0) [cnf transformation 39]
92. curious(X0) | generous(X0) [cnf transformation 39]
98. ~quiet(X0) | brave(X0) | creative(X0) [cnf transformation 46]
106. generous(mary) | ~curious(mary) | ~creative(X0) [cnf transformation 51]
107. ~generous(mary) | curious(mary) | ~creative(X0) [cnf transformation 51]
109. ~brave(X0) | ~brave(X0) [cnf transformation 53]
135. quiet(susan) [cnf transformation 18]
145. ~quiet(mary) [cnf transformation 25]
147. ~brave(X0) [duplicate literal removal 109]
208. curious(mary) | ~creative(X0) [subsumption resolution 107,92]
210. 14 <=> ! [X0] : ~creative(X0) [avatar definition]
211. ~creative(X0) <- (14) [avatar component clause 210]
213. 15 <=> curious(mary) [avatar definition]
215. curious(mary) <- (15) [avatar component clause 213]
216. 14 | 15 [avatar split clause 208,213,210]
217. generous(mary) | ~creative(X0) [subsumption resolution 106,92]
219. 16 <=> generous(mary) [avatar definition]
222. 14 | 16 [avatar split clause 217,219,210]
357. ~generous(mary) | quiet(mary) <- (15) [resolution 90,215]
360. brave(susan) | creative(susan) [resolution 98,135]
361. creative(susan) [subsumption resolution 360,147]
362. $false <- (14) [subsumption resolution 361,211]
363. ~14 [avatar contradiction clause 362]
364. ~generous(mary) <- (15) [subsumption resolution 357,145]
365. ~16 | ~15 [avatar split clause 364,213,219]
366. $false [avatar sat refutation 216,222,363,365]
% SZS output end Proof for 98230033338856907544633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both curious and not happy then someone is funny and vice versa. Everyone who is both quiet and not brave is not humble and vice versa. Everyone who is either old or not tall is both not kind and not brave and vice versa. Everyone who is either not rich or quiet is both funny and not generous. If someone is not brave then paul is both patient and funny and vice versa. If someone is humble then someone is either calm or not kind and vice versa. Everyone who is not happy or not old is either not old or kind. If someone is wise or humble then someone is both not strong and patient and vice versa. If alice is both not funny and calm then fred is both not humble and not creative. Everyone who is not tall is curious and vice versa. Everyone who is not generous is not brave. Everyone who is both quiet and not creative is either kind or rich. Everyone who is both strong and not calm is old or not funny. If susan is both not rich and old then someone is both not patient and curious. Everyone who is both not tall and brave is both not brave and not wise. Everyone who is either not wise or not calm is quiet or curious and vice versa. Alice is not funny or not happy. Someone is either strong or not tall. Susan is not happy or happy. Alice is either not funny or not brave. Paul is both patient and curious. Susan is both funny and quiet. Someone is either not brave or not old. | Paul is not tall. | entailment | (((curious(fred)&~happy(fred)))<=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&~brave(X))<=>~humble(X)))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(funny(X)&~generous(X))))&
((?[X]:(~brave(X)))<=>((patient(paul)&funny(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~happy(X)|~old(X))=>(~old(X)<~>kind(X))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~strong(X)&patient(X)))))&
(((~funny(alice)&calm(alice)))=>((~humble(fred)&~creative(fred))))&
(![X]:(~tall(X)<=>curious(X)))&
(![X]:(~generous(X)=>~brave(X)))&
(![X]:((quiet(X)&~creative(X))=>(kind(X)<~>rich(X))))&
(![X]:((strong(X)&~calm(X))=>(old(X)|~funny(X))))&
(((~rich(susan)&old(susan)))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~tall(X)&brave(X))=>(~brave(X)&~wise(X))))&
(![X]:((~wise(X)<~>~calm(X))<=>(quiet(X)|curious(X))))&
((~funny(alice)|~happy(alice)))&
(?[X]:((strong(X)<~>~tall(X))))&
((~happy(susan)|happy(susan)))&
((~funny(alice)<~>~brave(alice)))&
((patient(paul)&curious(paul)))&
((funny(susan)&quiet(susan)))&
(?[X]:((~brave(X)<~>~old(X)))) | ~tall(paul) | [
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 113651375021558620676796
% SZS output start Proof for 113651375021558620676796
10. ! [X0] : (~tall(X0) <=> curious(X0)) [input p9]
21. curious(paul) & patient(paul) [input p20]
24. tall(paul) [input hypothesis]
66. ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 10]
114. ~tall(X0) | ~curious(X0) [cnf transformation 66]
136. curious(paul) [cnf transformation 21]
141. tall(paul) [cnf transformation 24]
302. ~curious(paul) [resolution 114,141]
304. $false [subsumption resolution 302,136]
% SZS output end Proof for 113651375021558620676796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not strong then paul is both not old and not patient. Everyone who is either not strong or not tall is either not calm or not strong. Everyone who is strong is either not old or humble. Everyone who is not creative or not humble is both not old and not tall. If someone is not brave or not strong then fred is patient or tall. Everyone who is either wise or strong is not calm and vice versa. Everyone who is either strong or not strong is both not creative and curious and vice versa. If paul is not generous or tall then paul is not happy or not quiet and vice versa. Everyone who is funny is not funny or not calm and vice versa. Everyone who is not brave is creative or tall and vice versa. Everyone who is funny is both happy and not quiet and vice versa. Everyone who is both not rich and creative is either humble or not funny and vice versa. If paul is not wise then someone is both not humble and not tall. Everyone who is both generous and brave is both not calm and rich and vice versa. If someone is rich then someone is both happy and funny and vice versa. Fred is either tall or not wise. Susan is not tall. Lucy is either rich or not humble. Someone is both not quiet and not wise. Someone is not wise or patient. | Paul is not generous. | entailment | ((?[X]:((quiet(X)&~strong(X))))=>((~old(paul)&~patient(paul))))&
(![X]:((~strong(X)<~>~tall(X))=>(~calm(X)<~>~strong(X))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~wise(X)|patient(X)))) | ~generous(paul) | [
"p3",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3733891482179899241111109
% SZS output start Proof for 3733891482179899241111109
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
8. (tall(paul) | ~generous(paul)) <=> (~quiet(paul) | ~happy(paul)) [input p7]
9. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~quiet(X0) & happy(X0))) [input p10]
21. generous(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
33. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 7]
34. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 33]
35. ((tall(paul) | ~generous(paul)) | (quiet(paul) & happy(paul))) & ((~quiet(paul) | ~happy(paul)) | (~tall(paul) & generous(paul))) [nnf transformation 8]
36. (tall(paul) | ~generous(paul) | (quiet(paul) & happy(paul))) & (~quiet(paul) | ~happy(paul) | (~tall(paul) & generous(paul))) [flattening 35]
37. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
38. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 37]
41. ! [X0] : ((funny(X0) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 11]
42. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [flattening 41]
70. ~tall(X0) | creative(X0) [cnf transformation 26]
78. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 34]
79. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 34]
87. tall(paul) | ~generous(paul) | quiet(paul) [cnf transformation 36]
89. funny(X0) | funny(X0) [cnf transformation 38]
95. ~quiet(X0) | ~funny(X0) [cnf transformation 42]
120. generous(paul) [cnf transformation 21]
122. funny(X0) [duplicate literal removal 89]
123. ~creative(X0) | ~strong(X0) [duplicate literal removal 78]
124. ~creative(X0) | strong(X0) [duplicate literal removal 79]
159. ~creative(X0) [subsumption resolution 123,124]
161. 8 <=> quiet(paul) [avatar definition]
163. quiet(paul) <- (8) [avatar component clause 161]
165. 9 <=> generous(paul) [avatar definition]
169. 10 <=> tall(paul) [avatar definition]
171. tall(paul) <- (10) [avatar component clause 169]
172. 8 | ~9 | 10 [avatar split clause 87,169,165,161]
182. ~quiet(X0) [subsumption resolution 95,122]
215. 9 [avatar split clause 120,165]
218. creative(paul) <- (10) [resolution 70,171]
219. $false <- (10) [subsumption resolution 218,159]
220. ~10 [avatar contradiction clause 219]
221. $false <- (8) [subsumption resolution 163,182]
222. ~8 [avatar contradiction clause 221]
223. $false [avatar sat refutation 172,215,220,222]
% SZS output end Proof for 3733891482179899241111109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not calm is not patient or calm and vice versa.
If paul is either strong or funny then lucy is funny and vice versa.
Everyone who is either calm or not wise is not wise and vice versa.
Everyone who is tall is either rich or tall.
Everyone who is both funny and not tall is either funny or not creative and vice versa.
Everyone who is both not curious and creative is both strong and not patient.
If someone is not funny then john is both not funny and not rich.
Everyone who is either brave or curious is both kind and not patient and vice versa.
If alice is strong then lucy is calm or strong and vice versa.
Everyone who is either not happy or not strong is both not humble and not quiet and vice versa.
Everyone who is not humble is both humble and not quiet.
If mary is quiet then susan is not generous or old and vice versa.
Everyone who is happy is either funny or not tall and vice versa.
If someone is not strong then fred is strong or rich and vice versa.
Everyone who is both not old and not wise is either not happy or curious.
If someone is either tall or curious then paul is old or brave.
Alice is patient.
Someone is generous or calm.
Fred is wise or not tall.
Lucy is either brave or not funny.
Someone is both patient and not calm.
Fred is not funny.
Alice is funny or old. | Alice is not brave. | contradiction | (![X]:((~tall(X)<~>~calm(X))<=>(~patient(X)|calm(X))))&
(((strong(paul)<~>funny(paul)))<=>(funny(lucy)))&
(![X]:((calm(X)<~>~wise(X))<=>~wise(X)))&
(![X]:(tall(X)=>(rich(X)<~>tall(X))))&
(![X]:((funny(X)&~tall(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((~curious(X)&creative(X))=>(strong(X)&~patient(X))))&
((?[X]:(~funny(X)))=>((~funny(john)&~rich(john))))&
(![X]:((brave(X)<~>curious(X))<=>(kind(X)&~patient(X))))&
((strong(alice))<=>((calm(lucy)|strong(lucy))))&
(![X]:((~happy(X)<~>~strong(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(~humble(X)=>(humble(X)&~quiet(X))))&
((quiet(mary))<=>((~generous(susan)|old(susan))))&
(![X]:(happy(X)<=>(funny(X)<~>~tall(X))))&
((?[X]:(~strong(X)))<=>((strong(fred)|rich(fred))))&
(![X]:((~old(X)&~wise(X))=>(~happy(X)<~>curious(X))))&
((?[X]:((tall(X)<~>curious(X))))=>((old(paul)|brave(paul))))&
(patient(alice))&
(?[X]:((generous(X)|calm(X))))&
((wise(fred)|~tall(fred)))&
((brave(lucy)<~>~funny(lucy)))&
(?[X]:((patient(X)&~calm(X))))&
(~funny(fred))&
((funny(alice)|old(alice))) | ~brave(alice) | [
"p0",
"p4",
"p5",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 686870873026847126484385
% SZS output start Proof for 686870873026847126484385
1. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (calm(X0) | ~patient(X0))) [input p0]
5. ! [X0] : ((~tall(X0) & funny(X0)) <=> (funny(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((creative(X0) & ~curious(X0)) => (~patient(X0) & strong(X0))) [input p5]
8. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (~patient(X0) & kind(X0))) [input p7]
17. patient(alice) [input p16]
24. ~brave(alice) [input hypothesis]
26. ! [X0] : ((~patient(X0) & strong(X0)) | (~creative(X0) | curious(X0))) [ennf transformation 6]
27. ! [X0] : ((~patient(X0) & strong(X0)) | ~creative(X0) | curious(X0)) [flattening 26]
34. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | (~calm(X0) & patient(X0))) & ((calm(X0) | ~patient(X0)) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [nnf transformation 1]
35. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | (~calm(X0) & patient(X0))) & (calm(X0) | ~patient(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [flattening 34]
39. ! [X0] : (((~tall(X0) & funny(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (tall(X0) | ~funny(X0)))) [nnf transformation 5]
40. ! [X0] : (((~tall(X0) & funny(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | tall(X0) | ~funny(X0))) [flattening 39]
41. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 8]
42. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [flattening 41]
63. calm(X0) | ~patient(X0) | ~tall(X0) | calm(X0) [cnf transformation 35]
65. ~calm(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 35]
79. creative(X0) | ~funny(X0) | tall(X0) | ~funny(X0) [cnf transformation 40]
81. funny(X0) | funny(X0) | creative(X0) [cnf transformation 40]
85. ~creative(X0) | ~patient(X0) | curious(X0) [cnf transformation 27]
91. ~curious(X0) | brave(X0) | ~patient(X0) [cnf transformation 42]
119. patient(alice) [cnf transformation 17]
128. ~brave(alice) [cnf transformation 24]
130. creative(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 79]
131. creative(X0) | funny(X0) [duplicate literal removal 81]
135. calm(X0) | ~patient(X0) | ~tall(X0) [duplicate literal removal 63]
136. ~calm(X0) | ~tall(X0) [duplicate literal removal 65]
137. ~patient(X0) | ~tall(X0) [subsumption resolution 135,136]
155. creative(X0) | tall(X0) [subsumption resolution 130,131]
263. ~patient(X0) | curious(X0) | tall(X0) [resolution 85,155]
265. ~patient(X0) | curious(X0) [subsumption resolution 263,137]
266. curious(alice) [resolution 265,119]
282. brave(alice) | ~patient(alice) [resolution 91,266]
284. ~patient(alice) [subsumption resolution 282,128]
285. $false [subsumption resolution 284,119]
% SZS output end Proof for 686870873026847126484385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and humble is tall or brave. Everyone who is wise or not curious is either curious or wise and vice versa. If john is patient then someone is both not happy and generous. Everyone who is old is either not wise or not tall and vice versa. If john is both wise and generous then someone is not rich and vice versa. If someone is not brave or not strong then someone is either not happy or not funny and vice versa. If susan is not patient then alice is strong or curious and vice versa. Everyone who is not rich or not creative is rich or not calm. Everyone who is happy is not brave and vice versa. Everyone who is both not humble and rich is either not quiet or not creative and vice versa. Everyone who is either not calm or happy is either curious or happy. If susan is both creative and happy then someone is either not brave or humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. John is not generous or generous. Lucy is either wise or generous. Someone is either not wise or not rich. Someone is funny. Paul is both patient and rich. Someone is not tall. Lucy is not strong or creative. | Lucy is rich. | neutral | (![X]:((patient(X)&humble(X))=>(tall(X)|brave(X))))&
(![X]:((wise(X)|~curious(X))<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(((wise(john)&generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~patient(susan))<=>((strong(alice)|curious(alice))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
((~generous(john)|generous(john)))&
((wise(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
((patient(paul)&rich(paul)))&
(?[X]:(~tall(X)))&
((~strong(lucy)|creative(lucy))) | rich(lucy) | [] | null | 0 |
Everyone who is not patient or wise is both old and not rich. Everyone who is not humble or quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Someone is funny or not calm. Someone is funny. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Alice is not calm. | Alice is wise. | contradiction | (![X]:((~patient(X)|wise(X))=>(old(X)&~rich(X))))&
(![X]:((~humble(X)|quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | wise(alice) | [
"p0",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6059307162802049596434626
% SZS output start Proof for 6059307162802049596434626
1. ! [X0] : ((wise(X0) | ~patient(X0)) => (~rich(X0) & old(X0))) [input p0]
12. ! [X0] : ((humble(X0) | brave(X0)) <=> ~old(X0)) [input p11]
16. ! [X0] : (calm(X0) <=> (~brave(X0) | ~humble(X0))) [input p15]
23. ~calm(alice) [input p22]
24. wise(alice) [input hypothesis]
27. ! [X0] : ((~rich(X0) & old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 1]
58. ! [X0] : (((humble(X0) | brave(X0)) | old(X0)) & (~old(X0) | (~humble(X0) & ~brave(X0)))) [nnf transformation 12]
59. ! [X0] : ((humble(X0) | brave(X0) | old(X0)) & (~old(X0) | (~humble(X0) & ~brave(X0)))) [flattening 58]
68. ! [X0] : ((calm(X0) | (brave(X0) & humble(X0))) & ((~brave(X0) | ~humble(X0)) | ~calm(X0))) [nnf transformation 16]
69. ! [X0] : ((calm(X0) | (brave(X0) & humble(X0))) & (~brave(X0) | ~humble(X0) | ~calm(X0))) [flattening 68]
81. ~wise(X0) | old(X0) [cnf transformation 27]
119. ~humble(X0) | ~old(X0) [cnf transformation 59]
133. calm(X0) | humble(X0) [cnf transformation 69]
142. ~calm(alice) [cnf transformation 23]
143. wise(alice) [cnf transformation 24]
296. old(alice) [resolution 81,143]
300. humble(alice) [resolution 133,142]
304. ~old(alice) [resolution 300,119]
305. $false [subsumption resolution 304,296]
% SZS output end Proof for 6059307162802049596434626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not humble or not strong then someone is either wise or happy and vice versa. Everyone who is either kind or not strong is tall and vice versa. Everyone who is kind or rich is not strong or calm. If fred is creative then someone is not funny and vice versa. Everyone who is both not brave and patient is brave and vice versa. If someone is both patient and brave then fred is not quiet. Everyone who is funny or not calm is patient and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Fred is old. Lucy is not wise or calm. Susan is rich. Someone is both humble and rich. | Susan is not generous. | entailment | (((~humble(mary)|~strong(mary)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>tall(X)))&
(![X]:((kind(X)|rich(X))=>(~strong(X)|calm(X))))&
((creative(fred))<=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&patient(X))<=>brave(X)))&
((?[X]:((patient(X)&brave(X))))=>(~quiet(fred)))&
(![X]:((funny(X)|~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(old(fred))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(?[X]:((humble(X)&rich(X)))) | ~generous(susan) | [
"p1",
"p4",
"p6",
"p8",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 600062360579902528631117
% SZS output start Proof for 600062360579902528631117
2. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> tall(X0)) [input p1]
5. ! [X0] : ((patient(X0) & ~brave(X0)) <=> brave(X0)) [input p4]
7. ! [X0] : ((~calm(X0) | funny(X0)) <=> patient(X0)) [input p6]
9. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p8]
10. ? [X0] : (~humble(X0) & ~creative(X0)) <=> (~kind(susan) <~> generous(susan)) [input p9]
11. ! [X0] : ((creative(X0) <~> ~wise(X0)) <=> (~brave(X0) | ~calm(X0))) [input p10]
14. ! [X0] : (~strong(X0) <=> (funny(X0) & ~brave(X0))) [input p13]
15. ! [X0] : ((quiet(X0) | calm(X0)) <=> (wise(X0) & ~funny(X0))) [input p14]
20. generous(susan) [input hypothesis]
21. ! [X0] : ((old(X0) | generous(X0)) => tall(X0)) [pure predicate removal 9]
27. ! [X0] : (tall(X0) | (~old(X0) & ~generous(X0))) [ennf transformation 21]
35. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ~tall(X0)) & (tall(X0) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 2]
40. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 5]
41. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~patient(X0) | brave(X0))) [flattening 40]
42. ! [X0] : (((~calm(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (calm(X0) & ~funny(X0)))) [nnf transformation 7]
43. ! [X0] : ((~calm(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (calm(X0) & ~funny(X0)))) [flattening 42]
45. (? [X0] : (~humble(X0) & ~creative(X0)) | ((~kind(susan) | ~generous(susan)) & (generous(susan) | kind(susan)))) & (((~generous(susan) | kind(susan)) & (generous(susan) | ~kind(susan))) | ! [X0] : (humble(X0) | creative(X0))) [nnf transformation 10]
46. (? [X0] : (~humble(X0) & ~creative(X0)) | ((~kind(susan) | ~generous(susan)) & (generous(susan) | kind(susan)))) & (((~generous(susan) | kind(susan)) & (generous(susan) | ~kind(susan))) | ! [X1] : (humble(X1) | creative(X1))) [rectify 45]
47. ? [X0] : (~humble(X0) & ~creative(X0)) => (~humble(sK2) & ~creative(sK2)) [choice axiom]
48. ((~humble(sK2) & ~creative(sK2)) | ((~kind(susan) | ~generous(susan)) & (generous(susan) | kind(susan)))) & (((~generous(susan) | kind(susan)) & (generous(susan) | ~kind(susan))) | ! [X1] : (humble(X1) | creative(X1))) [skolemisation 46,47]
49. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [nnf transformation 11]
50. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [flattening 49]
53. ! [X0] : ((~strong(X0) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | strong(X0))) [nnf transformation 14]
54. ! [X0] : ((~strong(X0) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | strong(X0))) [flattening 53]
55. ! [X0] : (((quiet(X0) | calm(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 15]
56. ! [X0] : ((quiet(X0) | calm(X0) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 55]
67. ~tall(X0) | kind(X0) | ~strong(X0) [cnf transformation 35]
73. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 41]
74. ~brave(X0) | ~brave(X0) [cnf transformation 41]
77. patient(X0) | ~funny(X0) [cnf transformation 43]
78. patient(X0) | calm(X0) [cnf transformation 43]
82. ~generous(X0) | tall(X0) [cnf transformation 27]
87. ~creative(sK2) | ~kind(susan) | ~generous(susan) [cnf transformation 48]
93. ~wise(X0) | creative(X0) | brave(X0) [cnf transformation 50]
101. funny(X0) | strong(X0) [cnf transformation 54]
105. wise(X0) | ~calm(X0) [cnf transformation 56]
113. generous(susan) [cnf transformation 20]
114. brave(X0) | ~patient(X0) [duplicate literal removal 73]
115. ~brave(X0) [duplicate literal removal 74]
157. ~patient(X0) [subsumption resolution 114,115]
158. calm(X0) [subsumption resolution 78,157]
159. ~funny(X0) [subsumption resolution 77,157]
162. 10 <=> generous(susan) [avatar definition]
163. generous(susan) <- (10) [avatar component clause 162]
166. 11 <=> kind(susan) [avatar definition]
168. ~kind(susan) <- (~11) [avatar component clause 166]
176. 13 <=> creative(sK2) [avatar definition]
178. ~creative(sK2) <- (~13) [avatar component clause 176]
179. ~10 | ~11 | ~13 [avatar split clause 87,176,166,162]
187. ~wise(X0) | creative(X0) [subsumption resolution 93,115]
203. strong(X0) [subsumption resolution 101,159]
204. wise(X0) [subsumption resolution 105,158]
206. 10 [avatar split clause 113,162]
214. tall(susan) <- (10) [resolution 82,163]
219. creative(X0) [resolution 187,204]
220. $false <- (~13) [resolution 219,178]
222. 13 [avatar contradiction clause 220]
225. kind(susan) | ~strong(susan) <- (10) [resolution 67,214]
229. ~strong(susan) <- (10, ~11) [subsumption resolution 225,168]
230. $false <- (10, ~11) [subsumption resolution 229,203]
231. ~10 | 11 [avatar contradiction clause 230]
233. $false [avatar sat refutation 179,206,222,231]
% SZS output end Proof for 600062360579902528631117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not curious.
If someone is either not patient or not funny then paul is not generous.
Everyone who is old is both funny and quiet and vice versa.
Everyone who is not quiet is old.
If lucy is either not wise or quiet then alice is rich and vice versa.
If john is either not tall or funny then someone is not strong or strong.
If someone is both brave and humble then alice is both calm and strong and vice versa.
Everyone who is both not wise and not old is both strong and generous and vice versa.
If someone is wise then someone is either calm or old.
Everyone who is either kind or funny is both not funny and not patient.
Everyone who is either strong or patient is either not generous or old.
If someone is not old or not quiet then paul is either not creative or not generous and vice versa.
If alice is either strong or old then fred is both not rich and rich.
Everyone who is patient is both quiet and not generous.
If someone is both funny and tall then someone is not old and vice versa.
Everyone who is old is both quiet and happy and vice versa.
Alice is both curious and rich.
Someone is either not wise or not happy.
Someone is both generous and wise.
Someone is both not generous and not calm.
Fred is both funny and not brave.
Someone is either not kind or wise.
Mary is either not humble or not brave. | Paul is not strong. | neutral | (![X]:(~creative(X)=>~curious(X)))&
((?[X]:((~patient(X)<~>~funny(X))))=>(~generous(paul)))&
(![X]:(old(X)<=>(funny(X)&quiet(X))))&
(![X]:(~quiet(X)=>old(X)))&
(((~wise(lucy)<~>quiet(lucy)))<=>(rich(alice)))&
(((~tall(john)<~>funny(john)))=>(?[X]:((~strong(X)|strong(X)))))&
((?[X]:((brave(X)&humble(X))))<=>((calm(alice)&strong(alice))))&
(![X]:((~wise(X)&~old(X))<=>(strong(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((calm(X)<~>old(X)))))&
(![X]:((kind(X)<~>funny(X))=>(~funny(X)&~patient(X))))&
(![X]:((strong(X)<~>patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~creative(paul)<~>~generous(paul))))&
(((strong(alice)<~>old(alice)))=>((~rich(fred)&rich(fred))))&
(![X]:(patient(X)=>(quiet(X)&~generous(X))))&
((?[X]:((funny(X)&tall(X))))<=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>(quiet(X)&happy(X))))&
((curious(alice)&rich(alice)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((generous(X)&wise(X))))&
(?[X]:((~generous(X)&~calm(X))))&
((funny(fred)&~brave(fred)))&
(?[X]:((~kind(X)<~>wise(X))))&
((~humble(mary)<~>~brave(mary))) | ~strong(paul) | [] | null | 0 |
Everyone who is either wise or calm is wise and vice versa.
If alice is not rich or not generous then susan is either old or not creative 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.
If fred is either not happy or not kind then someone is both humble and not generous and vice versa.
Everyone who is curious is wise.
Everyone who is both not quiet and not kind is not tall or not strong and vice versa.
Everyone who is both not patient and generous is either not patient or generous.
If someone is either tall or old then alice is strong.
Everyone who is generous or kind is not humble or not quiet and vice versa.
Everyone who is both kind and not brave is both rich and not funny and vice versa.
Everyone who is either not rich or curious is calm.
Paul is not creative or not patient.
Someone is not creative or funny.
Someone is either rich or old.
Someone is funny or not generous.
Alice is not rich or not wise.
Someone is old.
Someone is not quiet or creative. | Paul is old. | neutral | (![X]:((wise(X)<~>calm(X))<=>wise(X)))&
(((~rich(alice)|~generous(alice)))<=>((old(susan)<~>~creative(susan))))&
(![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))))&
(((~happy(fred)<~>~kind(fred)))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((~quiet(X)&~kind(X))<=>(~tall(X)|~strong(X))))&
(![X]:((~patient(X)&generous(X))=>(~patient(X)<~>generous(X))))&
((?[X]:((tall(X)<~>old(X))))=>(strong(alice)))&
(![X]:((generous(X)|kind(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((kind(X)&~brave(X))<=>(rich(X)&~funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>calm(X)))&
((~creative(paul)|~patient(paul)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~rich(alice)|~wise(alice)))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)|creative(X)))) | old(paul) | [] | null | 0 |
Everyone who is brave or not happy is both not generous and not humble. Everyone who is not rich or not tall is either wise or not strong. Everyone who is old or tall is funny or not curious. If mary is not brave or not creative then someone is not patient or funny. If lucy is strong or creative then alice is either not happy or brave. Everyone who is curious or calm is both quiet and brave. If lucy is wise then someone is either rich or old and vice versa. If someone is curious or humble then john is humble and vice versa. If someone is not happy then someone is both rich and not curious and vice versa. If someone is either tall or not rich then someone is both not creative and not curious and vice versa. Everyone who is not humble or not brave is tall and vice versa. Everyone who is either patient or not calm is quiet and vice versa. Everyone who is both not calm and kind is both not generous and humble. If someone is both quiet and not generous then someone is not rich. If paul is not happy then someone is quiet and vice versa. Everyone who is not rich is both generous and rich and vice versa. Someone is not brave or old. Someone is both patient and humble. Fred is both not curious and funny. John is funny. Alice is either quiet or old. Someone is old. Paul is either humble or not calm. Susan is either generous or not calm. | Paul is humble. | contradiction | (![X]:((brave(X)|~happy(X))=>(~generous(X)&~humble(X))))&
(![X]:((~rich(X)|~tall(X))=>(wise(X)<~>~strong(X))))&
(![X]:((old(X)|tall(X))=>(funny(X)|~curious(X))))&
(((~brave(mary)|~creative(mary)))=>(?[X]:((~patient(X)|funny(X)))))&
(((strong(lucy)|creative(lucy)))=>((~happy(alice)<~>brave(alice))))&
(![X]:((curious(X)|calm(X))=>(quiet(X)&brave(X))))&
((wise(lucy))<=>(?[X]:((rich(X)<~>old(X)))))&
((?[X]:((curious(X)|humble(X))))<=>(humble(john)))&
((?[X]:(~happy(X)))<=>(?[X]:((rich(X)&~curious(X)))))&
((?[X]:((tall(X)<~>~rich(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
(![X]:((~humble(X)|~brave(X))<=>tall(X)))&
(![X]:((patient(X)<~>~calm(X))<=>quiet(X)))&
(![X]:((~calm(X)&kind(X))=>(~generous(X)&humble(X))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:(~rich(X))))&
((~happy(paul))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>(generous(X)&rich(X))))&
(?[X]:((~brave(X)|old(X))))&
(?[X]:((patient(X)&humble(X))))&
((~curious(fred)&funny(fred)))&
(funny(john))&
((quiet(alice)<~>old(alice)))&
(?[X]:(old(X)))&
((humble(paul)<~>~calm(paul)))&
((generous(susan)<~>~calm(susan))) | humble(paul) | [
"p0",
"p5",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7978109350727587707989718
% SZS output start Proof for 7978109350727587707989718
1. ! [X0] : ((~happy(X0) | brave(X0)) => (~humble(X0) & ~generous(X0))) [input p0]
6. ! [X0] : ((calm(X0) | curious(X0)) => (brave(X0) & quiet(X0))) [input p5]
15. ~happy(paul) <=> ? [X0] : quiet(X0) [input p14]
23. humble(paul) <~> ~calm(paul) [input p22]
25. humble(paul) [input hypothesis]
34. ! [X0] : ((~humble(X0) & ~generous(X0)) | (happy(X0) & ~brave(X0))) [ennf transformation 1]
37. ! [X0] : ((brave(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) [ennf transformation 6]
65. (~happy(paul) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | happy(paul)) [nnf transformation 15]
66. (~happy(paul) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | happy(paul)) [rectify 65]
67. ? [X1] : quiet(X1) => quiet(sK7) [choice axiom]
68. (~happy(paul) | ! [X0] : ~quiet(X0)) & (quiet(sK7) | happy(paul)) [skolemisation 66,67]
78. (calm(paul) | ~humble(paul)) & (~calm(paul) | humble(paul)) [nnf transformation 23]
83. ~humble(X0) | happy(X0) [cnf transformation 34]
93. ~calm(X0) | quiet(X0) [cnf transformation 37]
121. ~happy(paul) | ~quiet(X0) [cnf transformation 68]
133. calm(paul) | ~humble(paul) [cnf transformation 78]
136. humble(paul) [cnf transformation 25]
265. 29 <=> ! [X0] : ~quiet(X0) [avatar definition]
266. ~quiet(X0) <- (29) [avatar component clause 265]
268. 30 <=> happy(paul) [avatar definition]
271. 29 | ~30 [avatar split clause 121,268,265]
297. 36 <=> humble(paul) [avatar definition]
298. humble(paul) <- (36) [avatar component clause 297]
301. 37 <=> calm(paul) [avatar definition]
303. calm(paul) <- (37) [avatar component clause 301]
304. ~36 | 37 [avatar split clause 133,301,297]
316. 36 [avatar split clause 136,297]
338. happy(paul) <- (36) [resolution 83,298]
341. 30 | ~36 [avatar split clause 338,297,268]
349. quiet(paul) <- (37) [resolution 93,303]
350. $false <- (29, 37) [subsumption resolution 349,266]
351. ~29 | ~37 [avatar contradiction clause 350]
352. $false [avatar sat refutation 271,304,316,341,351]
% SZS output end Proof for 7978109350727587707989718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and rich is either not rich or quiet.
If someone is either kind or not strong then paul is wise or not curious and vice versa.
Everyone who is either not wise or not quiet is old.
If fred is not patient then alice is both generous and not creative and vice versa.
If someone is not brave or happy then someone is not patient and vice versa.
Everyone who is calm or patient is curious or not rich.
If someone is not strong or wise then someone is not humble and vice versa.
Everyone who is not generous is not patient and vice versa.
Everyone who is old is both patient and not humble and vice versa.
Everyone who is creative or funny is not generous.
Everyone who is wise or not brave is calm.
Everyone who is not wise is not quiet.
Everyone who is both not old and not funny is either wise or not old and vice versa.
If someone is not humble then someone is either not happy or tall and vice versa.
If someone is funny or not wise then alice is rich or old and vice versa.
Everyone who is both patient and not funny is either funny or tall.
Someone is both wise and kind.
Fred is not kind or old.
Someone is curious or not curious.
Alice is calm or tall.
Someone is both funny and quiet.
Someone is funny.
Susan is not wise.
Paul is tall or not strong. | Susan is not calm. | neutral | (![X]:((quiet(X)&rich(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>((wise(paul)|~curious(paul))))&
(![X]:((~wise(X)<~>~quiet(X))=>old(X)))&
((~patient(fred))<=>((generous(alice)&~creative(alice))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|patient(X))=>(curious(X)|~rich(X))))&
((?[X]:((~strong(X)|wise(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:(old(X)<=>(patient(X)&~humble(X))))&
(![X]:((creative(X)|funny(X))=>~generous(X)))&
(![X]:((wise(X)|~brave(X))=>calm(X)))&
(![X]:(~wise(X)=>~quiet(X)))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)<~>~old(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~happy(X)<~>tall(X)))))&
((?[X]:((funny(X)|~wise(X))))<=>((rich(alice)|old(alice))))&
(![X]:((patient(X)&~funny(X))=>(funny(X)<~>tall(X))))&
(?[X]:((wise(X)&kind(X))))&
((~kind(fred)|old(fred)))&
(?[X]:((curious(X)|~curious(X))))&
((calm(alice)|tall(alice)))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:(funny(X)))&
(~wise(susan))&
((tall(paul)|~strong(paul))) | ~calm(susan) | [] | null | 0 |
If mary is not strong or not old then someone is not quiet and vice versa.
Everyone who is wise or kind is curious and vice versa.
If someone is both calm and tall then someone is both patient and not strong and vice versa.
If someone is funny or not brave then fred is not rich or strong and vice versa.
Everyone who is either not curious or funny is happy or generous and vice versa.
Everyone who is generous is strong or creative and vice versa.
Everyone who is not calm is both generous and calm and vice versa.
Everyone who is both brave and not humble is either not quiet or wise.
Everyone who is not curious is not rich or not quiet.
If someone is either not tall or not wise then paul is not tall or kind and vice versa.
If someone is both not old and not kind then fred is not quiet and vice versa.
If someone is rich or old then someone is either old or not rich.
If someone is both not strong and not brave then mary is both creative and not curious and vice versa.
If someone is old then lucy is either calm or humble and vice versa.
Everyone who is either not curious or quiet is old and vice versa.
Everyone who is not curious or kind is not wise or not creative and vice versa.
Someone is either wise or not brave.
Someone is humble.
Someone is brave or not generous.
Someone is either strong or rich.
Someone is either not humble or funny.
Someone is both rich and not quiet. | Mary is brave. | entailment | (((~strong(mary)|~old(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)|kind(X))<=>curious(X)))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
((?[X]:((funny(X)|~brave(X))))<=>((~rich(fred)|strong(fred))))&
(![X]:((~curious(X)<~>funny(X))<=>(happy(X)|generous(X))))&
(![X]:(generous(X)<=>(strong(X)|creative(X))))&
(![X]:(~calm(X)<=>(generous(X)&calm(X))))&
(![X]:((brave(X)&~humble(X))=>(~quiet(X)<~>wise(X))))&
(![X]:(~curious(X)=>(~rich(X)|~quiet(X))))&
((?[X]:((~tall(X)<~>~wise(X))))<=>((~tall(paul)|kind(paul))))&
((?[X]:((~old(X)&~kind(X))))<=>(~quiet(fred)))&
((?[X]:((rich(X)|old(X))))=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~strong(X)&~brave(X))))<=>((creative(mary)&~curious(mary))))&
((?[X]:(old(X)))<=>((calm(lucy)<~>humble(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>old(X)))&
(![X]:((~curious(X)|kind(X))<=>(~wise(X)|~creative(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((rich(X)&~quiet(X)))) | brave(mary) | [
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1523795376589359032155522
% SZS output start Proof for 1523795376589359032155522
6. ! [X0] : (generous(X0) <=> (creative(X0) | strong(X0))) [input p5]
7. ! [X0] : (~calm(X0) <=> (calm(X0) & generous(X0))) [input p6]
13. ? [X0] : (~brave(X0) & ~strong(X0)) <=> (~curious(mary) & creative(mary)) [input p12]
23. ~brave(mary) [input hypothesis]
50. ! [X0] : ((generous(X0) | (~creative(X0) & ~strong(X0))) & ((creative(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 6]
51. ! [X0] : ((generous(X0) | (~creative(X0) & ~strong(X0))) & (creative(X0) | strong(X0) | ~generous(X0))) [flattening 50]
52. ! [X0] : ((~calm(X0) | (~calm(X0) | ~generous(X0))) & ((calm(X0) & generous(X0)) | calm(X0))) [nnf transformation 7]
53. ! [X0] : ((~calm(X0) | ~calm(X0) | ~generous(X0)) & ((calm(X0) & generous(X0)) | calm(X0))) [flattening 52]
68. (? [X0] : (~brave(X0) & ~strong(X0)) | (curious(mary) | ~creative(mary))) & ((~curious(mary) & creative(mary)) | ! [X0] : (brave(X0) | strong(X0))) [nnf transformation 13]
69. (? [X0] : (~brave(X0) & ~strong(X0)) | curious(mary) | ~creative(mary)) & ((~curious(mary) & creative(mary)) | ! [X0] : (brave(X0) | strong(X0))) [flattening 68]
70. (? [X0] : (~brave(X0) & ~strong(X0)) | curious(mary) | ~creative(mary)) & ((~curious(mary) & creative(mary)) | ! [X1] : (brave(X1) | strong(X1))) [rectify 69]
71. ? [X0] : (~brave(X0) & ~strong(X0)) => (~brave(sK7) & ~strong(sK7)) [choice axiom]
72. ((~brave(sK7) & ~strong(sK7)) | curious(mary) | ~creative(mary)) & ((~curious(mary) & creative(mary)) | ! [X1] : (brave(X1) | strong(X1))) [skolemisation 70,71]
116. ~strong(X0) | generous(X0) [cnf transformation 51]
117. ~creative(X0) | generous(X0) [cnf transformation 51]
119. calm(X0) | calm(X0) [cnf transformation 53]
120. ~calm(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 53]
137. creative(mary) | brave(X1) | strong(X1) [cnf transformation 72]
163. ~brave(mary) [cnf transformation 23]
164. calm(X0) [duplicate literal removal 119]
165. ~generous(X0) | ~calm(X0) [duplicate literal removal 120]
170. 2 <=> strong(mary) [avatar definition]
171. strong(mary) <- (2) [avatar component clause 170]
301. 31 <=> creative(mary) [avatar definition]
302. creative(mary) <- (31) [avatar component clause 301]
319. 35 <=> ! [X1] : (brave(X1) | strong(X1)) [avatar definition]
320. brave(X1) | strong(X1) <- (35) [avatar component clause 319]
322. 35 | 31 [avatar split clause 137,301,319]
378. generous(mary) <- (31) [resolution 117,302]
380. ~calm(mary) <- (31) [resolution 165,378]
383. $false <- (31) [subsumption resolution 380,164]
384. ~31 [avatar contradiction clause 383]
388. strong(mary) <- (35) [resolution 320,163]
396. 2 | ~35 [avatar split clause 388,319,170]
397. generous(mary) <- (2) [resolution 171,116]
400. ~calm(mary) <- (2) [resolution 397,165]
401. $false <- (2) [subsumption resolution 400,164]
402. ~2 [avatar contradiction clause 401]
403. $false [avatar sat refutation 322,384,396,402]
% SZS output end Proof for 1523795376589359032155522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both patient and quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Everyone who is either patient or calm is either wise or not strong.
Everyone who is wise or generous is both not old and strong and vice versa.
Everyone who is both kind and tall is both kind and not tall.
Everyone who is curious is not patient.
Everyone who is both creative and not kind is not patient.
If someone is both rich and tall then mary is both not tall and tall and vice versa.
Everyone who is either not quiet or strong is either not curious or not tall.
Everyone who is not old or not wise is both humble and not rich.
If lucy is not tall then fred is either brave or strong and vice versa.
Someone is not old or not brave.
John is either brave or calm.
Someone is rich or tall.
Mary is either kind or not happy.
Alice is old or not wise.
Someone is not kind or not funny. | Alice is not calm. | contradiction | (![X]:((~wise(X)|curious(X))<=>(patient(X)&quiet(X))))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(![X]:((patient(X)<~>calm(X))=>(wise(X)<~>~strong(X))))&
(![X]:((wise(X)|generous(X))<=>(~old(X)&strong(X))))&
(![X]:((kind(X)&tall(X))=>(kind(X)&~tall(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((creative(X)&~kind(X))=>~patient(X)))&
((?[X]:((rich(X)&tall(X))))<=>((~tall(mary)&tall(mary))))&
(![X]:((~quiet(X)<~>strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~old(X)|~wise(X))=>(humble(X)&~rich(X))))&
((~tall(lucy))<=>((brave(fred)<~>strong(fred))))&
(?[X]:((~old(X)|~brave(X))))&
((brave(john)<~>calm(john)))&
(?[X]:((rich(X)|tall(X))))&
((kind(mary)<~>~happy(mary)))&
((old(alice)|~wise(alice)))&
(?[X]:((~kind(X)|~funny(X)))) | ~calm(alice) | [
"p0",
"p2",
"p8",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 837403948658865653318603
% SZS output start Proof for 837403948658865653318603
1. ! [X0] : ((curious(X0) | ~wise(X0)) <=> (quiet(X0) & patient(X0))) [input p0]
3. ! [X0] : ((~calm(X0) <~> patient(X0)) <=> humble(X0)) [input p2]
9. ! [X0] : ((generous(X0) | wise(X0)) <=> (strong(X0) & ~old(X0))) [input p8]
15. ! [X0] : ((~wise(X0) | ~old(X0)) => (~rich(X0) & humble(X0))) [input p14]
21. ~wise(alice) | old(alice) [input p20]
23. ~calm(alice) [input hypothesis]
24. ! [X0] : (humble(X0) => (~calm(X0) <~> patient(X0))) [unused predicate definition removal 3]
25. ! [X0] : ((~calm(X0) <~> patient(X0)) | ~humble(X0)) [ennf transformation 24]
34. ! [X0] : ((~rich(X0) & humble(X0)) | (wise(X0) & old(X0))) [ennf transformation 15]
35. ! [X0] : (((curious(X0) | ~wise(X0)) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((curious(X0) | ~wise(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [flattening 35]
38. ! [X0] : (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | ~humble(X0)) [nnf transformation 25]
47. ! [X0] : (((generous(X0) | wise(X0)) | (~strong(X0) | old(X0))) & ((strong(X0) & ~old(X0)) | (~generous(X0) & ~wise(X0)))) [nnf transformation 9]
48. ! [X0] : ((generous(X0) | wise(X0) | ~strong(X0) | old(X0)) & ((strong(X0) & ~old(X0)) | (~generous(X0) & ~wise(X0)))) [flattening 47]
64. patient(X0) | wise(X0) [cnf transformation 36]
78. ~humble(X0) | calm(X0) | ~patient(X0) [cnf transformation 38]
94. ~old(X0) | ~wise(X0) [cnf transformation 48]
112. humble(X0) | wise(X0) [cnf transformation 34]
125. ~wise(alice) | old(alice) [cnf transformation 21]
127. ~calm(alice) [cnf transformation 23]
252. ~wise(alice) [subsumption resolution 125,94]
281. calm(X0) | ~patient(X0) | wise(X0) [resolution 78,112]
283. calm(X0) | wise(X0) [subsumption resolution 281,64]
405. wise(alice) [resolution 283,127]
406. $false [subsumption resolution 405,252]
% SZS output end Proof for 837403948658865653318603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not humble and humble then someone is not calm and vice versa. Everyone who is both not brave and strong is either generous or not old. Everyone who is either strong or not brave is either not calm or happy and vice versa. Everyone who is both quiet and not creative is creative. Everyone who is both not humble and wise is both brave and patient. If alice is not happy then lucy is either rich or not brave and vice versa. If susan is both strong and not quiet then someone is brave or not kind and vice versa. If someone is either generous or tall then john is both not kind and not wise and vice versa. Everyone who is either calm or creative is either wise or old and vice versa. If mary is both not wise and not old then someone is not tall. Everyone who is either calm or generous is either not wise or not happy and vice versa. Everyone who is not wise or not patient is either funny or kind. If someone is either not calm or not tall then susan is both old and brave. If someone is not curious then someone is calm or funny and vice versa. Everyone who is old or strong is not strong and vice versa. Everyone who is both funny and happy is either kind or not rich and vice versa. Alice is calm or not brave. Someone is either not wise or not strong. Paul is both tall and not patient. Someone is either old or not funny. Mary is not rich or curious. Someone is not creative or not brave. | Susan is not creative. | contradiction | (((~humble(john)&humble(john)))<=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)&strong(X))=>(generous(X)<~>~old(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))=>creative(X)))&
(![X]:((~humble(X)&wise(X))=>(brave(X)&patient(X))))&
((~happy(alice))<=>((rich(lucy)<~>~brave(lucy))))&
(((strong(susan)&~quiet(susan)))<=>(?[X]:((brave(X)|~kind(X)))))&
((?[X]:((generous(X)<~>tall(X))))<=>((~kind(john)&~wise(john))))&
(![X]:((calm(X)<~>creative(X))<=>(wise(X)<~>old(X))))&
(((~wise(mary)&~old(mary)))=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((~wise(X)|~patient(X))=>(funny(X)<~>kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>((old(susan)&brave(susan))))&
((?[X]:(~curious(X)))<=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((old(X)|strong(X))<=>~strong(X)))&
(![X]:((funny(X)&happy(X))<=>(kind(X)<~>~rich(X))))&
((calm(alice)|~brave(alice)))&
(?[X]:((~wise(X)<~>~strong(X))))&
((tall(paul)&~patient(paul)))&
(?[X]:((old(X)<~>~funny(X))))&
((~rich(mary)|curious(mary)))&
(?[X]:((~creative(X)|~brave(X)))) | ~creative(susan) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8162304771301038935521768
% SZS output start Proof for 8162304771301038935521768
1. (humble(john) & ~humble(john)) <=> ? [X0] : ~calm(X0) [input p0]
3. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (~calm(X0) <~> happy(X0))) [input p2]
7. (~quiet(susan) & strong(susan)) <=> ? [X0] : (~kind(X0) | brave(X0)) [input p6]
8. ? [X0] : (generous(X0) <~> tall(X0)) <=> (~wise(john) & ~kind(john)) [input p7]
9. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (wise(X0) <~> old(X0))) [input p8]
11. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (~wise(X0) <~> ~happy(X0))) [input p10]
13. ? [X0] : (~calm(X0) <~> ~tall(X0)) => (brave(susan) & old(susan)) [input p12]
15. ! [X0] : ((strong(X0) | old(X0)) <=> ~strong(X0)) [input p14]
23. ~creative(susan) [input hypothesis]
34. (brave(susan) & old(susan)) | ! [X0] : (~calm(X0) <=> ~tall(X0)) [ennf transformation 13]
35. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | (~humble(john) | humble(john))) [nnf transformation 1]
36. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ~humble(john) | humble(john)) [flattening 35]
37. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ~humble(john) | humble(john)) [rectify 36]
38. ? [X1] : ~calm(X1) => ~calm(sK0) [choice axiom]
39. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (~calm(sK0) | ~humble(john) | humble(john)) [skolemisation 37,38]
41. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 3]
43. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X0] : (~kind(X0) | brave(X0)) | (quiet(susan) | ~strong(susan))) [nnf transformation 7]
44. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X0] : (~kind(X0) | brave(X0)) | quiet(susan) | ~strong(susan)) [flattening 43]
45. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X1] : (~kind(X1) | brave(X1)) | quiet(susan) | ~strong(susan)) [rectify 44]
46. ? [X1] : (~kind(X1) | brave(X1)) => (~kind(sK1) | brave(sK1)) [choice axiom]
47. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & ((~kind(sK1) | brave(sK1)) | quiet(susan) | ~strong(susan)) [skolemisation 45,46]
48. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (wise(john) | kind(john))) & ((~wise(john) & ~kind(john)) | ! [X0] : ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) [nnf transformation 8]
49. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X0] : ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) [flattening 48]
50. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X1] : ((generous(X1) | ~tall(X1)) & (tall(X1) | ~generous(X1)))) [rectify 49]
51. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) => ((~tall(sK2) | ~generous(sK2)) & (tall(sK2) | generous(sK2))) [choice axiom]
52. (((~tall(sK2) | ~generous(sK2)) & (tall(sK2) | generous(sK2))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X1] : ((generous(X1) | ~tall(X1)) & (tall(X1) | ~generous(X1)))) [skolemisation 50,51]
53. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 11]
58. (brave(susan) & old(susan)) | ! [X0] : ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))) [nnf transformation 34]
64. ! [X0] : (((strong(X0) | old(X0)) | strong(X0)) & (~strong(X0) | (~strong(X0) & ~old(X0)))) [nnf transformation 15]
65. ! [X0] : ((strong(X0) | old(X0) | strong(X0)) & (~strong(X0) | (~strong(X0) & ~old(X0)))) [flattening 64]
77. ~humble(john) | calm(X0) [cnf transformation 39]
78. humble(john) | calm(X0) [cnf transformation 39]
82. ~calm(X0) | happy(X0) | strong(X0) | brave(X0) [cnf transformation 41]
97. strong(susan) | ~brave(X0) [cnf transformation 47]
98. strong(susan) | kind(X0) [cnf transformation 47]
102. ~kind(john) | generous(X1) | ~tall(X1) [cnf transformation 52]
109. ~wise(X0) | ~old(X0) | creative(X0) | ~calm(X0) [cnf transformation 53]
122. ~happy(X0) | ~calm(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
131. brave(susan) | ~calm(X0) | tall(X0) [cnf transformation 58]
136. ~strong(X0) | ~strong(X0) [cnf transformation 65]
137. strong(X0) | old(X0) | strong(X0) [cnf transformation 65]
153. ~creative(susan) [cnf transformation 23]
154. ~strong(X0) [duplicate literal removal 136]
155. old(X0) | strong(X0) [duplicate literal removal 137]
158. 1 <=> ! [X0] : calm(X0) [avatar definition]
159. calm(X0) <- (1) [avatar component clause 158]
161. 2 <=> humble(john) [avatar definition]
164. 1 | 2 [avatar split clause 78,161,158]
165. 1 | ~2 [avatar split clause 77,161,158]
183. 6 <=> ! [X0] : kind(X0) [avatar definition]
184. kind(X0) <- (6) [avatar component clause 183]
191. 8 <=> ! [X0] : ~brave(X0) [avatar definition]
192. ~brave(X0) <- (8) [avatar component clause 191]
195. 9 <=> strong(susan) [avatar definition]
197. strong(susan) <- (9) [avatar component clause 195]
198. 6 | 9 [avatar split clause 98,195,183]
199. 8 | 9 [avatar split clause 97,195,191]
210. 12 <=> kind(john) [avatar definition]
211. ~kind(john) <- (~12) [avatar component clause 210]
228. 16 <=> ! [X1] : (generous(X1) | ~tall(X1)) [avatar definition]
229. ~tall(X1) | generous(X1) <- (16) [avatar component clause 228]
235. 16 | ~12 [avatar split clause 102,210,228]
251. 21 <=> ! [X0] : (~calm(X0) | tall(X0)) [avatar definition]
252. ~calm(X0) | tall(X0) <- (21) [avatar component clause 251]
254. 22 <=> brave(susan) [avatar definition]
256. brave(susan) <- (22) [avatar component clause 254]
257. 21 | 22 [avatar split clause 131,254,251]
336. $false <- (9) [subsumption resolution 197,154]
337. ~9 [avatar contradiction clause 336]
338. $false <- (6, ~12) [resolution 211,184]
339. ~6 | 12 [avatar contradiction clause 338]
404. happy(X0) | strong(X0) | brave(X0) <- (1) [resolution 82,159]
405. happy(X0) | brave(X0) <- (1) [subsumption resolution 404,154]
406. happy(X0) <- (1, 8) [subsumption resolution 405,192]
584. ~calm(X0) | ~generous(X0) | wise(X0) <- (1, 8) [resolution 122,406]
585. ~generous(X0) | wise(X0) <- (1, 8) [subsumption resolution 584,159]
611. $false <- (8, 22) [subsumption resolution 256,192]
612. ~8 | ~22 [avatar contradiction clause 611]
613. tall(X0) <- (1, 21) [subsumption resolution 252,159]
645. generous(X1) <- (1, 16, 21) [resolution 613,229]
698. wise(X0) <- (1, 8, 16, 21) [resolution 585,645]
708. ~old(X2) | creative(X2) | ~calm(X2) <- (1, 8, 16, 21) [resolution 698,109]
717. ~old(X2) | creative(X2) <- (1, 8, 16, 21) [subsumption resolution 708,159]
729. creative(X0) | strong(X0) <- (1, 8, 16, 21) [resolution 717,155]
737. creative(X0) <- (1, 8, 16, 21) [subsumption resolution 729,154]
740. $false <- (1, 8, 16, 21) [resolution 737,153]
743. ~1 | ~8 | ~16 | ~21 [avatar contradiction clause 740]
744. $false [avatar sat refutation 164,165,198,199,235,257,337,339,612,743]
% SZS output end Proof for 8162304771301038935521768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not tall and not calm is not brave or not humble. If fred is both quiet and creative then alice is not rich and vice versa. If someone is happy or not generous then someone is patient and vice versa. Everyone who is not kind or not brave is rich or not tall. Everyone who is funny or humble is rich or curious and vice versa. Everyone who is not generous is brave or creative. Everyone who is not tall or not funny is not kind or kind and vice versa. If fred is either not tall or funny then mary is not patient or curious. If mary is either not kind or not old then john is either not kind or not rich. Everyone who is not creative or quiet is creative. Everyone who is brave is either humble or not patient. Everyone who is either old or not funny is not curious. Everyone who is both not rich and not wise is not kind and vice versa. If john is not calm then fred is either happy or not generous and vice versa. Everyone who is not funny is not calm or not kind and vice versa. Everyone who is rich is not creative. Someone is either brave or not tall. Lucy is either patient or not calm. Alice is curious or generous. John is both not humble and not old. Someone is either quiet or not quiet. Lucy is not strong or not patient. John is not kind. Lucy is not generous. | Mary is creative. | entailment | (![X]:((~tall(X)&~calm(X))=>(~brave(X)|~humble(X))))&
(((quiet(fred)&creative(fred)))<=>(~rich(alice)))&
((?[X]:((happy(X)|~generous(X))))<=>(?[X]:(patient(X))))&
(![X]:((~kind(X)|~brave(X))=>(rich(X)|~tall(X))))&
(![X]:((funny(X)|humble(X))<=>(rich(X)|curious(X))))&
(![X]:(~generous(X)=>(brave(X)|creative(X))))&
(![X]:((~tall(X)|~funny(X))<=>(~kind(X)|kind(X))))&
(((~tall(fred)<~>funny(fred)))=>((~patient(mary)|curious(mary))))&
(((~kind(mary)<~>~old(mary)))=>((~kind(john)<~>~rich(john))))&
(![X]:((~creative(X)|quiet(X))=>creative(X)))&
(![X]:(brave(X)=>(humble(X)<~>~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~rich(X)&~wise(X))<=>~kind(X)))&
((~calm(john))<=>((happy(fred)<~>~generous(fred))))&
(![X]:(~funny(X)<=>(~calm(X)|~kind(X))))&
(![X]:(rich(X)=>~creative(X)))&
(?[X]:((brave(X)<~>~tall(X))))&
((patient(lucy)<~>~calm(lucy)))&
((curious(alice)|generous(alice)))&
((~humble(john)&~old(john)))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((~strong(lucy)|~patient(lucy)))&
(~kind(john))&
(~generous(lucy)) | creative(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6632929358715379174682235
% SZS output start Proof for 6632929358715379174682235
10. ! [X0] : ((quiet(X0) | ~creative(X0)) => creative(X0)) [input p9]
25. ~creative(mary) [input hypothesis]
37. ! [X0] : (creative(X0) | (~quiet(X0) & creative(X0))) [ennf transformation 10]
92. creative(X0) | creative(X0) [cnf transformation 37]
120. ~creative(mary) [cnf transformation 25]
121. creative(X0) [duplicate literal removal 92]
246. $false [subsumption resolution 120,121]
% SZS output end Proof for 6632929358715379174682235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and brave is either brave or not curious.
Everyone who is both tall and curious is not happy.
If someone is both happy and not brave then someone is not creative or humble.
If someone is both rich and old then someone is both not kind and tall and vice versa.
If paul is not curious then mary is not brave and vice versa.
If someone is either old or patient then someone is both not kind and not wise.
If paul is happy then paul is tall or humble.
If fred is either not tall or not patient then mary is rich or calm.
If alice is both not calm and not kind then someone is either generous or happy and vice versa.
If someone is not curious then someone is not patient or not brave.
Everyone who is both not brave and patient is either not wise or not brave.
Everyone who is not strong is both not rich and not old and vice versa.
If someone is not generous or not quiet then someone is both not creative and not funny and vice versa.
Everyone who is not generous is both generous and not quiet and vice versa.
Everyone who is both kind and humble is not creative and vice versa.
If lucy is either not curious or not old then fred is patient or not strong.
Fred is both not humble and curious.
Alice is both kind and not brave.
Someone is either not curious or wise.
Someone is both curious and not rich.
Alice is not curious or not creative.
Mary is either creative or rich.
Paul is brave or quiet. | Fred is not quiet. | contradiction | (![X]:((happy(X)&brave(X))=>(brave(X)<~>~curious(X))))&
(![X]:((tall(X)&curious(X))=>~happy(X)))&
((?[X]:((happy(X)&~brave(X))))=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:((~kind(X)&tall(X)))))&
((~curious(paul))<=>(~brave(mary)))&
((?[X]:((old(X)<~>patient(X))))=>(?[X]:((~kind(X)&~wise(X)))))&
((happy(paul))=>((tall(paul)|humble(paul))))&
(((~tall(fred)<~>~patient(fred)))=>((rich(mary)|calm(mary))))&
(((~calm(alice)&~kind(alice)))<=>(?[X]:((generous(X)<~>happy(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((~brave(X)&patient(X))=>(~wise(X)<~>~brave(X))))&
(![X]:(~strong(X)<=>(~rich(X)&~old(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:(~generous(X)<=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)&humble(X))<=>~creative(X)))&
(((~curious(lucy)<~>~old(lucy)))=>((patient(fred)|~strong(fred))))&
((~humble(fred)&curious(fred)))&
((kind(alice)&~brave(alice)))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((curious(X)&~rich(X))))&
((~curious(alice)|~creative(alice)))&
((creative(mary)<~>rich(mary)))&
((brave(paul)|quiet(paul))) | ~quiet(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8505495965326539966228966
% SZS output start Proof for 8505495965326539966228966
14. ! [X0] : (~generous(X0) <=> (~quiet(X0) & generous(X0))) [input p13]
24. ~quiet(fred) [input hypothesis]
76. ! [X0] : ((~generous(X0) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | generous(X0))) [nnf transformation 14]
77. ! [X0] : ((~generous(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | generous(X0))) [flattening 76]
120. generous(X0) | generous(X0) [cnf transformation 77]
122. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 77]
140. ~quiet(fred) [cnf transformation 24]
141. generous(X0) [duplicate literal removal 120]
142. ~generous(X0) | quiet(X0) [duplicate literal removal 122]
295. 35 <=> ! [X3] : quiet(X3) [avatar definition]
296. quiet(X3) <- (35) [avatar component clause 295]
303. 37 <=> ! [X3] : generous(X3) [avatar definition]
304. generous(X3) <- (37) [avatar component clause 303]
312. 37 [avatar split clause 141,303]
368. quiet(X0) <- (37) [resolution 142,304]
369. 35 | ~37 [avatar split clause 368,303,295]
370. $false <- (35) [resolution 296,140]
374. ~35 [avatar contradiction clause 370]
375. $false [avatar sat refutation 312,369,374]
% SZS output end Proof for 8505495965326539966228966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and happy then someone is not brave and vice versa. If someone is either creative or brave then lucy is both not quiet and tall and vice versa. If someone is calm or not tall then john is both brave and tall and vice versa. Everyone who is rich or not old is both not curious and not wise and vice versa. Everyone who is both not kind and not strong is either kind or not funny. Everyone who is not happy is brave. Everyone who is happy is not humble and vice versa. Everyone who is both not wise and generous is not calm. Everyone who is brave or rich is not patient or happy and vice versa. If someone is kind then paul is both not funny and not strong and vice versa. If lucy is calm or kind then someone is old or creative. Everyone who is strong or kind is not kind or not generous and vice versa. Everyone who is not wise is either not curious or not creative. Everyone who is both not curious and wise is not wise or not funny and vice versa. If someone is quiet or not kind then lucy is not generous or not wise and vice versa. Everyone who is either not strong or not patient is either not wise or not humble. Someone is either strong or calm. Mary is humble. Someone is both curious and not rich. Someone is both happy and curious. John is happy. Someone is not humble. Mary is creative or funny. | Paul is happy. | neutral | ((?[X]:((rich(X)&happy(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~quiet(lucy)&tall(lucy))))&
((?[X]:((calm(X)|~tall(X))))<=>((brave(john)&tall(john))))&
(![X]:((rich(X)|~old(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~kind(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((~wise(X)&generous(X))=>~calm(X)))&
(![X]:((brave(X)|rich(X))<=>(~patient(X)|happy(X))))&
((?[X]:(kind(X)))<=>((~funny(paul)&~strong(paul))))&
(((calm(lucy)|kind(lucy)))=>(?[X]:((old(X)|creative(X)))))&
(![X]:((strong(X)|kind(X))<=>(~kind(X)|~generous(X))))&
(![X]:(~wise(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((~curious(X)&wise(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~generous(lucy)|~wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))=>(~wise(X)<~>~humble(X))))&
(?[X]:((strong(X)<~>calm(X))))&
(humble(mary))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((happy(X)&curious(X))))&
(happy(john))&
(?[X]:(~humble(X)))&
((creative(mary)|funny(mary))) | happy(paul) | [] | null | 0 |
If someone is both brave and not tall then someone is either not quiet or not rich and vice versa.
If someone is either not curious or not rich then mary is generous and vice versa.
Everyone who is not kind or rich is patient and vice versa.
Everyone who is either not strong or not creative is both generous and not old and vice versa.
Everyone who is quiet or funny is humble or kind.
If someone is not wise then someone is either creative or not creative and vice versa.
If someone is not strong or patient then lucy is either not calm or generous and vice versa.
Everyone who is both happy and rich is both not quiet and humble.
If someone is tall or calm then mary is brave and vice versa.
Everyone who is wise or not kind is both wise and not tall and vice versa.
If alice is not strong or not brave then alice is not generous and vice versa.
If someone is patient or rich then john is not happy or not quiet.
If lucy is either quiet or kind then fred is not funny or not brave.
If someone is both not wise and not happy then someone is both happy and tall.
Everyone who is tall is not kind or not funny and vice versa.
If fred is either happy or tall then mary is not funny and vice versa.
Lucy is quiet or old.
Susan is either not old or not generous.
Fred is both tall and generous.
Someone is not happy or not generous.
Someone is either rich or not quiet.
John is not strong.
Susan is not tall or wise.
Someone is either happy or not brave. | John is not brave. | neutral | ((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
((?[X]:((~curious(X)<~>~rich(X))))<=>(generous(mary)))&
(![X]:((~kind(X)|rich(X))<=>patient(X)))&
(![X]:((~strong(X)<~>~creative(X))<=>(generous(X)&~old(X))))&
(![X]:((quiet(X)|funny(X))=>(humble(X)|kind(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
((?[X]:((~strong(X)|patient(X))))<=>((~calm(lucy)<~>generous(lucy))))&
(![X]:((happy(X)&rich(X))=>(~quiet(X)&humble(X))))&
((?[X]:((tall(X)|calm(X))))<=>(brave(mary)))&
(![X]:((wise(X)|~kind(X))<=>(wise(X)&~tall(X))))&
(((~strong(alice)|~brave(alice)))<=>(~generous(alice)))&
((?[X]:((patient(X)|rich(X))))=>((~happy(john)|~quiet(john))))&
(((quiet(lucy)<~>kind(lucy)))=>((~funny(fred)|~brave(fred))))&
((?[X]:((~wise(X)&~happy(X))))=>(?[X]:((happy(X)&tall(X)))))&
(![X]:(tall(X)<=>(~kind(X)|~funny(X))))&
(((happy(fred)<~>tall(fred)))<=>(~funny(mary)))&
((quiet(lucy)|old(lucy)))&
((~old(susan)<~>~generous(susan)))&
((tall(fred)&generous(fred)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
(~strong(john))&
((~tall(susan)|wise(susan)))&
(?[X]:((happy(X)<~>~brave(X)))) | ~brave(john) | [] | null | 0 |
Everyone who is either happy or quiet is rich or not brave.
If lucy is both quiet and funny then alice is not kind and vice versa.
If someone is not humble then lucy is not tall and vice versa.
If paul is patient then john is either rich or not funny.
If someone is not generous or calm then mary is both not wise and not brave.
If someone is either not rich or not calm then paul is both not happy and wise and vice versa.
Everyone who is not humble is brave and vice versa.
Everyone who is tall is patient and vice versa.
If someone is either not humble or funny then susan is either not rich or patient.
If someone is both not tall and humble then someone is not brave and vice versa.
Everyone who is generous or humble is kind and vice versa.
If lucy is not generous or brave then susan is both creative and brave and vice versa.
Everyone who is kind or generous is happy or not tall and vice versa.
Everyone who is curious is strong or happy.
Everyone who is both happy and not generous is funny.
If alice is not generous then mary is strong or humble and vice versa.
Someone is rich.
Lucy is both not brave and not strong.
Someone is curious.
Someone is funny.
John is curious.
Someone is curious or not funny.
Fred is both curious and happy.
Alice is not humble. | Lucy is not brave. | entailment | (![X]:((happy(X)<~>quiet(X))=>(rich(X)|~brave(X))))&
(((quiet(lucy)&funny(lucy)))<=>(~kind(alice)))&
((?[X]:(~humble(X)))<=>(~tall(lucy)))&
((patient(paul))=>((rich(john)<~>~funny(john))))&
((?[X]:((~generous(X)|calm(X))))=>((~wise(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~calm(X))))<=>((~happy(paul)&wise(paul))))&
(![X]:(~humble(X)<=>brave(X)))&
(![X]:(tall(X)<=>patient(X)))&
((?[X]:((~humble(X)<~>funny(X))))=>((~rich(susan)<~>patient(susan))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((generous(X)|humble(X))<=>kind(X)))&
(((~generous(lucy)|brave(lucy)))<=>((creative(susan)&brave(susan))))&
(![X]:((kind(X)|generous(X))<=>(happy(X)|~tall(X))))&
(![X]:(curious(X)=>(strong(X)|happy(X))))&
(![X]:((happy(X)&~generous(X))=>funny(X)))&
((~generous(alice))<=>((strong(mary)|humble(mary))))&
(?[X]:(rich(X)))&
((~brave(lucy)&~strong(lucy)))&
(?[X]:(curious(X)))&
(?[X]:(funny(X)))&
(curious(john))&
(?[X]:((curious(X)|~funny(X))))&
((curious(fred)&happy(fred)))&
(~humble(alice)) | ~brave(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6633207681792545934283893
% SZS output start Proof for 6633207681792545934283893
18. ~strong(lucy) & ~brave(lucy) [input p17]
25. brave(lucy) [input hypothesis]
121. ~brave(lucy) [cnf transformation 18]
130. brave(lucy) [cnf transformation 25]
271. 32 <=> brave(lucy) [avatar definition]
296. ~32 [avatar split clause 121,271]
306. 32 [avatar split clause 130,271]
307. $false [avatar sat refutation 296,306]
% SZS output end Proof for 6633207681792545934283893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is humble and vice versa.
Everyone who is quiet is either not rich or brave.
If mary is not creative or rich then someone is either rich or not happy.
Everyone who is both funny and not strong is strong or happy and vice versa.
If paul is wise or brave then someone is either not tall or not curious.
If someone is either not calm or creative then someone is both rich and not humble and vice versa.
If someone is both patient and generous then someone is not kind and vice versa.
Everyone who is either not calm or not humble is not brave.
Everyone who is wise or not strong is both creative and tall and vice versa.
Everyone who is not tall is not funny or wise and vice versa.
Everyone who is either happy or not generous is not funny or old and vice versa.
Everyone who is not creative is not generous or not curious.
Everyone who is not brave is brave or not generous and vice versa.
If someone is brave or patient then alice is either not humble or not funny and vice versa.
If someone is tall then someone is not humble.
If lucy is generous then someone is creative or funny.
Paul is funny.
Mary is not rich.
Susan is not wise.
Susan is both creative and rich.
Alice is either calm or creative. | Alice is funny. | entailment | (![X]:(patient(X)<=>humble(X)))&
(![X]:(quiet(X)=>(~rich(X)<~>brave(X))))&
(((~creative(mary)|rich(mary)))=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((funny(X)&~strong(X))<=>(strong(X)|happy(X))))&
(((wise(paul)|brave(paul)))=>(?[X]:((~tall(X)<~>~curious(X)))))&
((?[X]:((~calm(X)<~>creative(X))))<=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~calm(X)<~>~humble(X))=>~brave(X)))&
(![X]:((wise(X)|~strong(X))<=>(creative(X)&tall(X))))&
(![X]:(~tall(X)<=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~funny(X)|old(X))))&
(![X]:(~creative(X)=>(~generous(X)|~curious(X))))&
(![X]:(~brave(X)<=>(brave(X)|~generous(X))))&
((?[X]:((brave(X)|patient(X))))<=>((~humble(alice)<~>~funny(alice))))&
((?[X]:(tall(X)))=>(?[X]:(~humble(X))))&
((generous(lucy))=>(?[X]:((creative(X)|funny(X)))))&
(funny(paul))&
(~rich(mary))&
(~wise(susan))&
((creative(susan)&rich(susan)))&
((calm(alice)<~>creative(alice))) | funny(alice) | [
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 31528037058829665589964
% SZS output start Proof for 31528037058829665589964
4. ! [X0] : ((~strong(X0) & funny(X0)) <=> (happy(X0) | strong(X0))) [input p3]
9. ! [X0] : ((~strong(X0) | wise(X0)) <=> (tall(X0) & creative(X0))) [input p8]
10. ! [X0] : (~tall(X0) <=> (wise(X0) | ~funny(X0))) [input p9]
22. ~funny(alice) [input hypothesis]
38. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | strong(X0) | ~funny(X0))) [flattening 38]
54. ! [X0] : (((~strong(X0) | wise(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 9]
55. ! [X0] : ((~strong(X0) | wise(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | (strong(X0) & ~wise(X0)))) [flattening 54]
56. ! [X0] : ((~tall(X0) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | tall(X0))) [nnf transformation 10]
57. ! [X0] : ((~tall(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | tall(X0))) [flattening 56]
81. ~strong(X0) | ~strong(X0) [cnf transformation 39]
101. tall(X0) | strong(X0) [cnf transformation 55]
104. ~tall(X0) | funny(X0) [cnf transformation 57]
131. ~funny(alice) [cnf transformation 22]
135. ~strong(X0) [duplicate literal removal 81]
229. tall(X0) [subsumption resolution 101,135]
232. funny(X0) [subsumption resolution 104,229]
254. $false [subsumption resolution 131,232]
% SZS output end Proof for 31528037058829665589964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or brave is either not curious or brave.
Everyone who is both old and not funny is either not creative or old.
If someone is either not patient or not quiet then susan is not patient.
Everyone who is both not curious and wise is happy or strong and vice versa.
Everyone who is either not kind or not old is both not quiet and not rich and vice versa.
If mary is not brave or kind then mary is not tall or not generous and vice versa.
Everyone who is either humble or not kind is both calm and not curious.
If john is not creative then fred is happy or creative.
Everyone who is both curious and not curious is either old or humble and vice versa.
If mary is both tall and not patient then someone is old or humble and vice versa.
If fred is both calm and not calm then mary is either funny or not curious and vice versa.
If susan is strong then mary is either not creative or strong and vice versa.
If fred is both not rich and strong then someone is both not quiet and brave.
If mary is both not happy and funny then lucy is both not generous and humble and vice versa.
Everyone who is not curious is not tall or calm and vice versa.
If mary is happy or calm then someone is either generous or strong and vice versa.
Someone is not wise or curious.
Someone is either funny or wise.
Alice is either tall or curious.
Someone is either funny or generous.
Alice is either not generous or not creative.
Someone is either rich or not old.
Someone is generous or not creative. | John is creative. | neutral | (![X]:((~calm(X)<~>brave(X))=>(~curious(X)<~>brave(X))))&
(![X]:((old(X)&~funny(X))=>(~creative(X)<~>old(X))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(~patient(susan)))&
(![X]:((~curious(X)&wise(X))<=>(happy(X)|strong(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(~quiet(X)&~rich(X))))&
(((~brave(mary)|kind(mary)))<=>((~tall(mary)|~generous(mary))))&
(![X]:((humble(X)<~>~kind(X))=>(calm(X)&~curious(X))))&
((~creative(john))=>((happy(fred)|creative(fred))))&
(![X]:((curious(X)&~curious(X))<=>(old(X)<~>humble(X))))&
(((tall(mary)&~patient(mary)))<=>(?[X]:((old(X)|humble(X)))))&
(((calm(fred)&~calm(fred)))<=>((funny(mary)<~>~curious(mary))))&
((strong(susan))<=>((~creative(mary)<~>strong(mary))))&
(((~rich(fred)&strong(fred)))=>(?[X]:((~quiet(X)&brave(X)))))&
(((~happy(mary)&funny(mary)))<=>((~generous(lucy)&humble(lucy))))&
(![X]:(~curious(X)<=>(~tall(X)|calm(X))))&
(((happy(mary)|calm(mary)))<=>(?[X]:((generous(X)<~>strong(X)))))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((funny(X)<~>wise(X))))&
((tall(alice)<~>curious(alice)))&
(?[X]:((funny(X)<~>generous(X))))&
((~generous(alice)<~>~creative(alice)))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((generous(X)|~creative(X)))) | creative(john) | [] | null | 0 |
If lucy is both wise and kind then fred is not kind or not curious.
If someone is calm then someone is both not funny and curious.
Everyone who is quiet or not creative is not kind or calm.
Everyone who is not old is both generous and calm.
If someone is not curious or not humble then paul is either patient or not quiet.
Everyone who is both not humble and not generous is either not rich or not old and vice versa.
If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa.
If someone is generous or tall then alice is strong and vice versa.
Everyone who is not happy is brave or humble.
Everyone who is not happy or not funny is both creative and quiet.
If someone is not creative or quiet then someone is both wise and not wise.
Everyone who is not patient is both not kind and happy and vice versa.
If someone is either brave or wise then susan is both brave and not strong and vice versa.
If someone is either kind or happy then someone is both not kind and not creative and vice versa.
Everyone who is not wise or humble is creative or not strong and vice versa.
Someone is curious or happy.
Someone is humble.
Mary is either quiet or happy.
John is either not tall or wise. | Paul is quiet. | contradiction | (((wise(lucy)&kind(lucy)))=>((~kind(fred)|~curious(fred))))&
((?[X]:(calm(X)))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:((quiet(X)|~creative(X))=>(~kind(X)|calm(X))))&
(![X]:(~old(X)=>(generous(X)&calm(X))))&
((?[X]:((~curious(X)|~humble(X))))=>((patient(paul)<~>~quiet(paul))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((brave(susan)&~strong(susan))))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((~wise(X)|humble(X))<=>(creative(X)|~strong(X))))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:(humble(X)))&
((quiet(mary)<~>happy(mary)))&
((~tall(john)<~>wise(john))) | quiet(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6659787520830908605223371
% SZS output start Proof for 6659787520830908605223371
11. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p10]
20. quiet(paul) [input hypothesis]
23. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 11]
35. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 23]
51. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 35]
52. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK4) & wise(sK4)) [choice axiom]
53. (~wise(sK4) & wise(sK4)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 51,52]
104. wise(sK4) | ~quiet(X1) [cnf transformation 53]
106. ~wise(sK4) | ~quiet(X1) [cnf transformation 53]
132. quiet(paul) [cnf transformation 20]
171. 10 <=> quiet(paul) [avatar definition]
173. quiet(paul) <- (10) [avatar component clause 171]
231. 23 <=> ! [X1] : ~quiet(X1) [avatar definition]
232. ~quiet(X1) <- (23) [avatar component clause 231]
234. 24 <=> wise(sK4) [avatar definition]
237. 23 | ~24 [avatar split clause 106,234,231]
242. 23 | 24 [avatar split clause 104,234,231]
331. 10 [avatar split clause 132,171]
332. $false <- (10, 23) [subsumption resolution 173,232]
333. ~10 | ~23 [avatar contradiction clause 332]
334. $false [avatar sat refutation 237,242,331,333]
% SZS output end Proof for 6659787520830908605223371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or kind then someone is either old or calm.
Everyone who is not generous is old.
Everyone who is not kind or kind is not happy and vice versa.
If paul is humble or happy then john is old or not patient and vice versa.
Everyone who is either not kind or not old is both not kind and tall and vice versa.
Everyone who is not happy is both not humble and quiet.
Everyone who is both not strong and rich is not rich.
If paul is either tall or not generous then alice is generous or not funny.
If someone is creative or tall then john is both not wise and not happy and vice versa.
If someone is both curious and quiet then fred is not old or not kind.
If someone is kind or not strong then someone is not brave.
If someone is not old then john is either not wise or not strong.
If someone is both patient and quiet then someone is either not creative or calm and vice versa.
Everyone who is not old is rich.
If someone is either humble or calm then someone is rich.
Paul is either creative or rich.
Someone is not funny or patient.
Someone is not quiet or curious.
Someone is funny.
Someone is either tall or generous. | Alice is kind. | neutral | ((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:((old(X)<~>calm(X)))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((~kind(X)|kind(X))<=>~happy(X)))&
(((humble(paul)|happy(paul)))<=>((old(john)|~patient(john))))&
(![X]:((~kind(X)<~>~old(X))<=>(~kind(X)&tall(X))))&
(![X]:(~happy(X)=>(~humble(X)&quiet(X))))&
(![X]:((~strong(X)&rich(X))=>~rich(X)))&
(((tall(paul)<~>~generous(paul)))=>((generous(alice)|~funny(alice))))&
((?[X]:((creative(X)|tall(X))))<=>((~wise(john)&~happy(john))))&
((?[X]:((curious(X)&quiet(X))))=>((~old(fred)|~kind(fred))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:(~brave(X))))&
((?[X]:(~old(X)))=>((~wise(john)<~>~strong(john))))&
((?[X]:((patient(X)&quiet(X))))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((humble(X)<~>calm(X))))=>(?[X]:(rich(X))))&
((creative(paul)<~>rich(paul)))&
(?[X]:((~funny(X)|patient(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((tall(X)<~>generous(X)))) | kind(alice) | [] | null | 0 |
If someone is not wise then someone is happy or not brave.
If mary is not brave or not wise then someone is quiet.
If fred is not creative then someone is either not curious or humble.
If alice is not patient or happy then someone is not rich and vice versa.
Everyone who is wise or not curious is either wise or brave and vice versa.
If someone is not rich then someone is either not strong or quiet.
If fred is not wise or calm then lucy is happy or wise and vice versa.
Everyone who is rich or humble is both curious and tall and vice versa.
Everyone who is both kind and patient is both not happy and funny and vice versa.
Everyone who is not brave or old is both brave and not strong and vice versa.
If john is both not creative and not tall then someone is either strong or quiet.
Everyone who is not humble is kind or curious.
Everyone who is patient or rich is not generous and vice versa.
Everyone who is not calm is both not happy and not old and vice versa.
If someone is both not strong and not creative then mary is either not curious or not quiet and vice versa.
Everyone who is either tall or old is not kind.
Someone is not strong or not funny.
Someone is either rich or quiet.
Someone is generous or not funny.
Someone is brave or not creative.
Someone is not rich or strong.
Susan is not kind or not generous. | Alice is not brave. | contradiction | ((?[X]:(~wise(X)))=>(?[X]:((happy(X)|~brave(X)))))&
(((~brave(mary)|~wise(mary)))=>(?[X]:(quiet(X))))&
((~creative(fred))=>(?[X]:((~curious(X)<~>humble(X)))))&
(((~patient(alice)|happy(alice)))<=>(?[X]:(~rich(X))))&
(![X]:((wise(X)|~curious(X))<=>(wise(X)<~>brave(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(((~wise(fred)|calm(fred)))<=>((happy(lucy)|wise(lucy))))&
(![X]:((rich(X)|humble(X))<=>(curious(X)&tall(X))))&
(![X]:((kind(X)&patient(X))<=>(~happy(X)&funny(X))))&
(![X]:((~brave(X)|old(X))<=>(brave(X)&~strong(X))))&
(((~creative(john)&~tall(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(kind(X)|curious(X))))&
(![X]:((patient(X)|rich(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~happy(X)&~old(X))))&
((?[X]:((~strong(X)&~creative(X))))<=>((~curious(mary)<~>~quiet(mary))))&
(![X]:((tall(X)<~>old(X))=>~kind(X)))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((rich(X)<~>quiet(X))))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:((~rich(X)|strong(X))))&
((~kind(susan)|~generous(susan))) | ~brave(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5577215819758615685399927
% SZS output start Proof for 5577215819758615685399927
10. ! [X0] : ((old(X0) | ~brave(X0)) <=> (~strong(X0) & brave(X0))) [input p9]
23. ~brave(alice) [input hypothesis]
60. ! [X0] : (((old(X0) | ~brave(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (~old(X0) & brave(X0)))) [nnf transformation 10]
61. ! [X0] : ((old(X0) | ~brave(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (~old(X0) & brave(X0)))) [flattening 60]
114. brave(X0) | brave(X0) [cnf transformation 61]
143. ~brave(alice) [cnf transformation 23]
144. brave(X0) [duplicate literal removal 114]
326. $false [subsumption resolution 143,144]
% SZS output end Proof for 5577215819758615685399927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not creative is not calm. If alice is both funny and not happy then john is either not tall or not humble. If someone is not rich then someone is strong or not wise. Everyone who is both curious and generous is not generous or not old and vice versa. If someone is not happy or not calm then fred is both not calm and wise and vice versa. Everyone who is generous is not wise. Everyone who is not creative is either not humble or rich. If mary is not wise or curious then mary is not wise. If alice is happy or not patient then mary is either not kind or curious and vice versa. Everyone who is either happy or not humble is strong. Everyone who is not funny is not rich. Everyone who is both not patient and not quiet is both not brave and not wise and vice versa. If someone is either not funny or not humble then paul is not old or not calm and vice versa. If someone is either not curious or rich then someone is generous or not patient. If someone is strong or wise then someone is both not tall and not brave and vice versa. Everyone who is not creative or wise is wise and vice versa. Someone is either not brave or not curious. Someone is both funny and brave. Someone is either not wise or strong. Someone is both not wise and happy. Paul is not quiet or curious. Susan is either not funny or kind. | John is not generous. | contradiction | (![X]:((~patient(X)<~>~creative(X))=>~calm(X)))&
(((funny(alice)&~happy(alice)))=>((~tall(john)<~>~humble(john))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((curious(X)&generous(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((~calm(fred)&wise(fred))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:(~creative(X)=>(~humble(X)<~>rich(X))))&
(((~wise(mary)|curious(mary)))=>(~wise(mary)))&
(((happy(alice)|~patient(alice)))<=>((~kind(mary)<~>curious(mary))))&
(![X]:((happy(X)<~>~humble(X))=>strong(X)))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>((~old(paul)|~calm(paul))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)|wise(X))<=>wise(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
(?[X]:((funny(X)&brave(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~quiet(paul)|curious(paul)))&
((~funny(susan)<~>kind(susan))) | ~generous(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8489502937068260828491317
% SZS output start Proof for 8489502937068260828491317
4. ! [X0] : ((generous(X0) & curious(X0)) <=> (~old(X0) | ~generous(X0))) [input p3]
23. ~generous(john) [input hypothesis]
42. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~generous(X0) | ~curious(X0))) [flattening 42]
90. generous(X0) | generous(X0) [cnf transformation 43]
142. ~generous(john) [cnf transformation 23]
144. generous(X0) [duplicate literal removal 90]
305. $false [subsumption resolution 142,144]
% SZS output end Proof for 8489502937068260828491317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or brave is creative. Everyone who is not calm or not creative is either strong or not tall. If someone is either kind or humble then paul is funny or not curious. Everyone who is humble is not old or strong and vice versa. Everyone who is both not calm and not creative is not quiet and vice versa. Everyone who is both creative and not generous is either not kind or not wise and vice versa. If someone is either rich or not quiet then alice is either tall or not quiet and vice versa. Everyone who is either not rich or calm is not creative or not generous. If john is either happy or not calm then someone is not curious or not wise. Everyone who is strong is both funny and creative and vice versa. Everyone who is both happy and quiet is funny or not humble and vice versa. If someone is both old and not tall then someone is generous and vice versa. If paul is both patient and not humble then alice is both strong and not tall. If someone is not strong or brave then lucy is not generous and vice versa. If lucy is either generous or not humble then someone is kind or creative and vice versa. Everyone who is both kind and not generous is either generous or not generous and vice versa. Someone is rich or not calm. Alice is not creative or not wise. Someone is not patient or creative. Someone is either not calm or not kind. Someone is humble or not quiet. Mary is not funny or curious. | Paul is tall. | neutral | (![X]:((rich(X)|brave(X))=>creative(X)))&
(![X]:((~calm(X)|~creative(X))=>(strong(X)<~>~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))=>((funny(paul)|~curious(paul))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~quiet(X)))&
(![X]:((creative(X)&~generous(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)|~generous(X))))&
(((happy(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~wise(X)))))&
(![X]:(strong(X)<=>(funny(X)&creative(X))))&
(![X]:((happy(X)&quiet(X))<=>(funny(X)|~humble(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)&~humble(paul)))=>((strong(alice)&~tall(alice))))&
((?[X]:((~strong(X)|brave(X))))<=>(~generous(lucy)))&
(((generous(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(?[X]:((rich(X)|~calm(X))))&
((~creative(alice)|~wise(alice)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|curious(mary))) | tall(paul) | [] | null | 0 |
Everyone who is either not calm or not wise is either tall or old.
If fred is not old or not happy then someone is either not calm or not strong and vice versa.
Everyone who is strong is either not old or humble.
Everyone who is not creative or not humble is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
If someone is rich then someone is both happy and funny and vice versa.
Fred is either tall or not wise.
Susan is not tall.
Lucy is either rich or not humble.
Someone is both not quiet and not wise.
Someone is not wise or patient. | Lucy is wise. | contradiction | (![X]:((~calm(X)<~>~wise(X))=>(tall(X)<~>old(X))))&
(((~old(fred)|~happy(fred)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~wise(X)|patient(X)))) | wise(lucy) | [
"p0",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 39390196325890793250942
% SZS output start Proof for 39390196325890793250942
1. ! [X0] : ((~calm(X0) <~> ~wise(X0)) => (tall(X0) <~> old(X0))) [input p0]
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
9. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p8]
21. wise(lucy) [input hypothesis]
25. ! [X0] : ((tall(X0) <~> old(X0)) | (~calm(X0) <=> ~wise(X0))) [ennf transformation 1]
27. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
29. ! [X0] : (((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [nnf transformation 25]
37. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 7]
38. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 37]
41. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
42. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 41]
62. ~wise(X0) | tall(X0) | old(X0) | calm(X0) [cnf transformation 29]
74. ~old(X0) | creative(X0) [cnf transformation 27]
76. ~tall(X0) | creative(X0) [cnf transformation 27]
82. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 38]
83. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 38]
92. ~calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
93. funny(X0) | funny(X0) [cnf transformation 42]
123. wise(lucy) [cnf transformation 21]
124. ~calm(X0) | ~funny(X0) [duplicate literal removal 92]
125. funny(X0) [duplicate literal removal 93]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 82]
127. ~creative(X0) | strong(X0) [duplicate literal removal 83]
159. ~creative(X0) [subsumption resolution 126,127]
180. ~calm(X0) [subsumption resolution 124,125]
237. tall(lucy) | old(lucy) | calm(lucy) [resolution 62,123]
238. tall(lucy) | old(lucy) [subsumption resolution 237,180]
240. 15 <=> old(lucy) [avatar definition]
242. old(lucy) <- (15) [avatar component clause 240]
244. 16 <=> tall(lucy) [avatar definition]
246. tall(lucy) <- (16) [avatar component clause 244]
247. 15 | 16 [avatar split clause 238,244,240]
249. creative(lucy) <- (15) [resolution 242,74]
252. $false <- (15) [subsumption resolution 249,159]
253. ~15 [avatar contradiction clause 252]
255. creative(lucy) <- (16) [resolution 246,76]
258. $false <- (16) [subsumption resolution 255,159]
259. ~16 [avatar contradiction clause 258]
260. $false [avatar sat refutation 247,253,259]
% SZS output end Proof for 39390196325890793250942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or tall then alice is happy or not quiet.
If someone is curious then someone is either not brave or not strong and vice versa.
Everyone who is both not rich and not funny is not creative or not humble and vice versa.
If lucy is both kind and calm then lucy is not happy and vice versa.
If susan is not generous or not calm then someone is not strong.
If someone is either not tall or brave then lucy is either happy or strong.
Everyone who is not calm is not curious.
Everyone who is both not brave and tall is either humble or rich and vice versa.
Everyone who is both not humble and not calm is both strong and tall.
Everyone who is patient is either quiet or not rich.
Everyone who is both not humble and tall is calm or not curious and vice versa.
If someone is humble then someone is strong.
Everyone who is creative or not tall is either not brave or not strong and vice versa.
If someone is either quiet or not wise then lucy is both not brave and not old and vice versa.
Everyone who is creative or not wise is either not wise or wise.
Everyone who is either not tall or not patient is not wise or not brave.
Someone is not curious or not patient.
Someone is quiet.
Susan is not generous.
Mary is not tall or not strong.
Alice is tall.
Alice is either old or funny.
Someone is both not calm and wise. | Mary is not creative. | contradiction | ((?[X]:((~tall(X)|tall(X))))=>((happy(alice)|~quiet(alice))))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((~rich(X)&~funny(X))<=>(~creative(X)|~humble(X))))&
(((kind(lucy)&calm(lucy)))<=>(~happy(lucy)))&
(((~generous(susan)|~calm(susan)))=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>brave(X))))=>((happy(lucy)<~>strong(lucy))))&
(![X]:(~calm(X)=>~curious(X)))&
(![X]:((~brave(X)&tall(X))<=>(humble(X)<~>rich(X))))&
(![X]:((~humble(X)&~calm(X))=>(strong(X)&tall(X))))&
(![X]:(patient(X)=>(quiet(X)<~>~rich(X))))&
(![X]:((~humble(X)&tall(X))<=>(calm(X)|~curious(X))))&
((?[X]:(humble(X)))=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~tall(X))<=>(~brave(X)<~>~strong(X))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>((~brave(lucy)&~old(lucy))))&
(![X]:((creative(X)|~wise(X))=>(~wise(X)<~>wise(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~wise(X)|~brave(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(quiet(X)))&
(~generous(susan))&
((~tall(mary)|~strong(mary)))&
(tall(alice))&
((old(alice)<~>funny(alice)))&
(?[X]:((~calm(X)&wise(X)))) | ~creative(mary) | [
"p2",
"p6",
"p7",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7141030125084044328702653
% SZS output start Proof for 7141030125084044328702653
3. ! [X0] : ((~funny(X0) & ~rich(X0)) <=> (~humble(X0) | ~creative(X0))) [input p2]
7. ! [X0] : (~calm(X0) => ~curious(X0)) [input p6]
8. ! [X0] : ((tall(X0) & ~brave(X0)) <=> (humble(X0) <~> rich(X0))) [input p7]
11. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (~curious(X0) | calm(X0))) [input p10]
13. ! [X0] : ((~tall(X0) | creative(X0)) <=> (~brave(X0) <~> ~strong(X0))) [input p12]
20. ~strong(mary) | ~tall(mary) [input p19]
24. ~creative(mary) [input hypothesis]
31. ! [X0] : (~curious(X0) | calm(X0)) [ennf transformation 7]
44. ! [X0] : (((~funny(X0) & ~rich(X0)) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | (funny(X0) | rich(X0)))) [nnf transformation 3]
45. ! [X0] : (((~funny(X0) & ~rich(X0)) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | funny(X0) | rich(X0))) [flattening 44]
51. ! [X0] : (((tall(X0) & ~brave(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | (~tall(X0) | brave(X0)))) [nnf transformation 8]
52. ! [X0] : (((tall(X0) & ~brave(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ~tall(X0) | brave(X0))) [flattening 51]
54. ! [X0] : (((tall(X0) & ~humble(X0)) | (curious(X0) & ~calm(X0))) & ((~curious(X0) | calm(X0)) | (~tall(X0) | humble(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & ~humble(X0)) | (curious(X0) & ~calm(X0))) & (~curious(X0) | calm(X0) | ~tall(X0) | humble(X0))) [flattening 54]
59. ! [X0] : (((~tall(X0) | creative(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (tall(X0) & ~creative(X0)))) [nnf transformation 13]
60. ! [X0] : ((~tall(X0) | creative(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (tall(X0) & ~creative(X0)))) [flattening 59]
83. ~rich(X0) | humble(X0) [cnf transformation 45]
95. ~curious(X0) | calm(X0) [cnf transformation 31]
96. rich(X0) | humble(X0) | ~tall(X0) | brave(X0) [cnf transformation 52]
107. ~calm(X0) | ~humble(X0) [cnf transformation 55]
108. ~humble(X0) | curious(X0) [cnf transformation 55]
109. ~calm(X0) | tall(X0) [cnf transformation 55]
110. curious(X0) | tall(X0) [cnf transformation 55]
117. ~brave(X0) | creative(X0) | ~tall(X0) | strong(X0) [cnf transformation 60]
133. ~strong(mary) | ~tall(mary) [cnf transformation 20]
139. ~creative(mary) [cnf transformation 24]
155. 4 <=> ! [X0] : tall(X0) [avatar definition]
156. tall(X0) <- (4) [avatar component clause 155]
227. ~tall(X0) | humble(X0) | brave(X0) [subsumption resolution 96,83]
275. 30 <=> tall(mary) [avatar definition]
277. ~tall(mary) <- (~30) [avatar component clause 275]
279. 31 <=> strong(mary) [avatar definition]
281. ~strong(mary) <- (~31) [avatar component clause 279]
282. ~30 | ~31 [avatar split clause 133,279,275]
295. tall(X0) | calm(X0) [resolution 110,95]
298. tall(X0) [subsumption resolution 295,109]
299. 4 [avatar split clause 298,155]
301. $false <- (4, ~30) [resolution 156,277]
302. ~4 | 30 [avatar contradiction clause 301]
322. humble(X0) | brave(X0) <- (4) [resolution 227,156]
416. brave(X3) | curious(X3) <- (4) [resolution 322,108]
476. curious(X0) | creative(X0) | ~tall(X0) | strong(X0) <- (4) [resolution 416,117]
481. creative(X0) | curious(X0) | strong(X0) <- (4) [subsumption resolution 476,156]
706. curious(mary) | strong(mary) <- (4) [resolution 481,139]
726. curious(mary) <- (4, ~31) [subsumption resolution 706,281]
741. calm(mary) <- (4, ~31) [resolution 726,95]
745. ~humble(mary) <- (4, ~31) [resolution 741,107]
746. brave(mary) <- (4, ~31) [resolution 745,322]
748. creative(mary) | ~tall(mary) | strong(mary) <- (4, ~31) [resolution 746,117]
758. ~tall(mary) | strong(mary) <- (4, ~31) [subsumption resolution 748,139]
759. strong(mary) <- (4, ~31) [subsumption resolution 758,156]
760. $false <- (4, ~31) [subsumption resolution 759,281]
761. ~4 | 31 [avatar contradiction clause 760]
762. $false [avatar sat refutation 282,299,302,761]
% SZS output end Proof for 7141030125084044328702653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is strong or not generous is humble.
Everyone who is not creative or not quiet is both not patient and tall.
Everyone who is both calm and not tall is either not calm or not strong.
Everyone who is funny is not patient or not humble and vice versa.
If alice is both tall and not brave then susan is not old or not quiet and vice versa.
If someone is creative or humble then paul is either not wise or not old and vice versa.
Everyone who is either strong or not humble is brave or not generous.
If someone is both calm and old then someone is either quiet or strong and vice versa.
Everyone who is both not calm and tall is not rich or strong.
If someone is either rich or not wise then someone is either not quiet or old and vice versa.
If someone is kind or generous then lucy is wise.
If someone is either humble or generous then someone is either happy or kind.
Everyone who is not kind is either wise or creative and vice versa.
Everyone who is either happy or not curious is brave or old.
Everyone who is both humble and not funny is not tall.
If someone is either humble or not old then john is both wise and rich and vice versa.
Lucy is not wise or tall.
Someone is quiet or not wise.
Someone is funny.
Alice is rich.
Someone is not wise or not brave.
Mary is not tall or quiet.
Someone is either not calm or creative.
Someone is either rich or not funny. | John is wise. | neutral | (![X]:((strong(X)|~generous(X))=>humble(X)))&
(![X]:((~creative(X)|~quiet(X))=>(~patient(X)&tall(X))))&
(![X]:((calm(X)&~tall(X))=>(~calm(X)<~>~strong(X))))&
(![X]:(funny(X)<=>(~patient(X)|~humble(X))))&
(((tall(alice)&~brave(alice)))<=>((~old(susan)|~quiet(susan))))&
((?[X]:((creative(X)|humble(X))))<=>((~wise(paul)<~>~old(paul))))&
(![X]:((strong(X)<~>~humble(X))=>(brave(X)|~generous(X))))&
((?[X]:((calm(X)&old(X))))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((~calm(X)&tall(X))=>(~rich(X)|strong(X))))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:((~quiet(X)<~>old(X)))))&
((?[X]:((kind(X)|generous(X))))=>(wise(lucy)))&
((?[X]:((humble(X)<~>generous(X))))=>(?[X]:((happy(X)<~>kind(X)))))&
(![X]:(~kind(X)<=>(wise(X)<~>creative(X))))&
(![X]:((happy(X)<~>~curious(X))=>(brave(X)|old(X))))&
(![X]:((humble(X)&~funny(X))=>~tall(X)))&
((?[X]:((humble(X)<~>~old(X))))<=>((wise(john)&rich(john))))&
((~wise(lucy)|tall(lucy)))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:(funny(X)))&
(rich(alice))&
(?[X]:((~wise(X)|~brave(X))))&
((~tall(mary)|quiet(mary)))&
(?[X]:((~calm(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~funny(X)))) | wise(john) | [] | null | 0 |
Everyone who is either not strong or not patient is happy.
If someone is either wise or not funny then alice is both not quiet and generous and vice versa.
Everyone who is wise is not quiet or not rich.
If mary is strong then susan is old.
If alice is humble or not old then someone is either kind or humble.
Everyone who is both humble and not generous is either not brave or patient and vice versa.
If susan is either not quiet or not generous then alice is either not humble or not tall and vice versa.
Everyone who is both not creative and not brave is either not creative or not brave and vice versa.
Everyone who is calm or not rich is old and vice versa.
If john is both quiet and generous then someone is rich and vice versa.
If someone is both not happy and wise then alice is patient and vice versa.
Everyone who is wise or creative is not humble or funny.
If someone is rich or not funny then someone is either old or not creative and vice versa.
Everyone who is both not curious and not wise is happy.
Everyone who is either calm or not patient is both not brave and creative.
Everyone who is both not humble and patient is either not kind or not brave.
Someone is either happy or not humble.
Someone is not funny or humble.
Someone is both not wise and not rich.
Someone is creative.
Alice is old or not generous.
Paul is both happy and not rich.
Fred is either wise or not brave. | John is not old. | contradiction | (![X]:((~strong(X)<~>~patient(X))=>happy(X)))&
((?[X]:((wise(X)<~>~funny(X))))<=>((~quiet(alice)&generous(alice))))&
(![X]:(wise(X)=>(~quiet(X)|~rich(X))))&
((strong(mary))=>(old(susan)))&
(((humble(alice)|~old(alice)))=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((humble(X)&~generous(X))<=>(~brave(X)<~>patient(X))))&
(((~quiet(susan)<~>~generous(susan)))<=>((~humble(alice)<~>~tall(alice))))&
(![X]:((~creative(X)&~brave(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:((calm(X)|~rich(X))<=>old(X)))&
(((quiet(john)&generous(john)))<=>(?[X]:(rich(X))))&
((?[X]:((~happy(X)&wise(X))))<=>(patient(alice)))&
(![X]:((wise(X)|creative(X))=>(~humble(X)|funny(X))))&
((?[X]:((rich(X)|~funny(X))))<=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:((~curious(X)&~wise(X))=>happy(X)))&
(![X]:((calm(X)<~>~patient(X))=>(~brave(X)&creative(X))))&
(![X]:((~humble(X)&patient(X))=>(~kind(X)<~>~brave(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~wise(X)&~rich(X))))&
(?[X]:(creative(X)))&
((old(alice)|~generous(alice)))&
((happy(paul)&~rich(paul)))&
((wise(fred)<~>~brave(fred))) | ~old(john) | [
"p5",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5980926487011109500783113
% SZS output start Proof for 5980926487011109500783113
6. ! [X0] : ((~generous(X0) & humble(X0)) <=> (~brave(X0) <~> patient(X0))) [input p5]
8. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> (~creative(X0) <~> ~brave(X0))) [input p7]
9. ! [X0] : ((~rich(X0) | calm(X0)) <=> old(X0)) [input p8]
10. (generous(john) & quiet(john)) <=> ? [X0] : rich(X0) [input p9]
15. ! [X0] : ((calm(X0) <~> ~patient(X0)) => (creative(X0) & ~brave(X0))) [input p14]
24. ~old(john) [input hypothesis]
34. ! [X0] : ((creative(X0) & ~brave(X0)) | (calm(X0) <=> ~patient(X0))) [ennf transformation 15]
46. ! [X0] : (((~generous(X0) & humble(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (generous(X0) | ~humble(X0)))) [nnf transformation 6]
47. ! [X0] : (((~generous(X0) & humble(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | generous(X0) | ~humble(X0))) [flattening 46]
49. ! [X0] : (((~brave(X0) & ~creative(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | (brave(X0) | creative(X0)))) [nnf transformation 8]
50. ! [X0] : (((~brave(X0) & ~creative(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | brave(X0) | creative(X0))) [flattening 49]
51. ! [X0] : (((~rich(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (rich(X0) & ~calm(X0)))) [nnf transformation 9]
52. ! [X0] : ((~rich(X0) | calm(X0) | ~old(X0)) & (old(X0) | (rich(X0) & ~calm(X0)))) [flattening 51]
53. ((generous(john) & quiet(john)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | (~generous(john) | ~quiet(john))) [nnf transformation 10]
54. ((generous(john) & quiet(john)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~generous(john) | ~quiet(john)) [flattening 53]
55. ((generous(john) & quiet(john)) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~generous(john) | ~quiet(john)) [rectify 54]
56. ? [X1] : rich(X1) => rich(sK2) [choice axiom]
57. ((generous(john) & quiet(john)) | ! [X0] : ~rich(X0)) & (rich(sK2) | ~generous(john) | ~quiet(john)) [skolemisation 55,56]
67. ! [X0] : ((creative(X0) & ~brave(X0)) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) [nnf transformation 34]
98. ~brave(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 47]
108. brave(X0) | creative(X0) | brave(X0) | creative(X0) [cnf transformation 50]
110. ~creative(X0) | ~creative(X0) | brave(X0) [cnf transformation 50]
111. ~brave(X0) | ~brave(X0) | creative(X0) [cnf transformation 50]
113. ~calm(X0) | old(X0) [cnf transformation 52]
114. old(X0) | rich(X0) [cnf transformation 52]
118. generous(john) | ~rich(X0) [cnf transformation 57]
131. ~brave(X0) | calm(X0) | patient(X0) [cnf transformation 67]
147. ~old(john) [cnf transformation 24]
148. brave(X0) | creative(X0) [duplicate literal removal 108]
149. ~creative(X0) | brave(X0) [duplicate literal removal 110]
150. ~brave(X0) | creative(X0) [duplicate literal removal 111]
228. creative(X0) [subsumption resolution 148,150]
230. 16 <=> ! [X0] : ~rich(X0) [avatar definition]
231. ~rich(X0) <- (16) [avatar component clause 230]
233. 17 <=> generous(john) [avatar definition]
235. generous(john) <- (17) [avatar component clause 233]
236. 16 | 17 [avatar split clause 118,233,230]
334. rich(john) [resolution 114,147]
336. $false <- (16) [subsumption resolution 334,231]
337. ~16 [avatar contradiction clause 336]
340. brave(X0) [resolution 149,228]
384. ~generous(X1) | ~patient(X1) [resolution 98,340]
385. ~patient(john) <- (17) [resolution 384,235]
398. calm(X1) | patient(X1) [resolution 131,340]
409. old(X1) | patient(X1) [resolution 398,113]
453. patient(john) [resolution 409,147]
455. $false <- (17) [subsumption resolution 453,385]
456. ~17 [avatar contradiction clause 455]
457. $false [avatar sat refutation 236,337,456]
% SZS output end Proof for 5980926487011109500783113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not creative or kind then alice is either generous or patient and vice versa.
Everyone who is either kind or not funny is either wise or not strong and vice versa.
Everyone who is kind or old is either not wise or not patient.
Everyone who is not rich is not curious and vice versa.
If susan is either generous or creative then someone is either not wise or not quiet.
Everyone who is not calm is not calm or generous and vice versa.
Everyone who is kind is not tall or not happy and vice versa.
If john is not generous or not quiet then someone is both not happy and wise and vice versa.
If susan is either creative or kind then someone is either old or generous.
If someone is both calm and not tall then fred is patient or not patient and vice versa.
Everyone who is either not patient or not strong is wise.
If mary is wise then susan is either kind or curious and vice versa.
Everyone who is not rich or creative is either not quiet or not strong.
If someone is either not wise or not funny then someone is generous and vice versa.
If john is either happy or creative then alice is either humble or not tall.
Everyone who is either not humble or not old is either humble or not happy and vice versa.
Someone is not curious or not wise.
Someone is quiet or old.
Someone is not happy.
Someone is not wise or not brave.
Someone is both not strong and not creative.
Someone is both not humble and patient.
Susan is either not curious or curious.
Someone is not quiet. | John is not strong. | neutral | (((~creative(john)<~>kind(john)))<=>((generous(alice)<~>patient(alice))))&
(![X]:((kind(X)<~>~funny(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((kind(X)|old(X))=>(~wise(X)<~>~patient(X))))&
(![X]:(~rich(X)<=>~curious(X)))&
(((generous(susan)<~>creative(susan)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(~calm(X)<=>(~calm(X)|generous(X))))&
(![X]:(kind(X)<=>(~tall(X)|~happy(X))))&
(((~generous(john)|~quiet(john)))<=>(?[X]:((~happy(X)&wise(X)))))&
(((creative(susan)<~>kind(susan)))=>(?[X]:((old(X)<~>generous(X)))))&
((?[X]:((calm(X)&~tall(X))))<=>((patient(fred)|~patient(fred))))&
(![X]:((~patient(X)<~>~strong(X))=>wise(X)))&
((wise(mary))<=>((kind(susan)<~>curious(susan))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)<~>~strong(X))))&
((?[X]:((~wise(X)<~>~funny(X))))<=>(?[X]:(generous(X))))&
(((happy(john)<~>creative(john)))=>((humble(alice)<~>~tall(alice))))&
(![X]:((~humble(X)<~>~old(X))<=>(humble(X)<~>~happy(X))))&
(?[X]:((~curious(X)|~wise(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)|~brave(X))))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~humble(X)&patient(X))))&
((~curious(susan)<~>curious(susan)))&
(?[X]:(~quiet(X))) | ~strong(john) | [] | null | 0 |
Everyone who is not calm is both wise and not rich. Everyone who is either not quiet or funny is patient. If mary is both not calm and not creative then alice is tall or not patient and vice versa. If someone is either not strong or not rich then mary is both not generous and not tall and vice versa. If someone is either brave or strong then someone is both not rich and not curious. If susan is either old or not funny then someone is rich or not kind and vice versa. If someone is both funny and strong then someone is old and vice versa. If someone is not tall then someone is humble. Everyone who is both not kind and quiet is funny and vice versa. Everyone who is either quiet or not happy is both not humble and not happy. Everyone who is either quiet or not humble is either brave or creative. Everyone who is wise or not curious is funny and vice versa. If john is both strong and not brave then someone is both tall and not calm and vice versa. If john is both humble and not generous then someone is not curious or funny and vice versa. If someone is not calm or brave then john is old. If mary is both patient and not quiet then mary is not brave or not patient and vice versa. Someone is not curious. Someone is both not strong and not humble. Someone is either brave or not tall. Someone is either not tall or wise. Someone is happy. Someone is not humble or wise. Someone is either strong or not creative. Someone is happy or not curious. | Mary is not patient. | contradiction | (![X]:(~calm(X)=>(wise(X)&~rich(X))))&
(![X]:((~quiet(X)<~>funny(X))=>patient(X)))&
(((~calm(mary)&~creative(mary)))<=>((tall(alice)|~patient(alice))))&
((?[X]:((~strong(X)<~>~rich(X))))<=>((~generous(mary)&~tall(mary))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~rich(X)&~curious(X)))))&
(((old(susan)<~>~funny(susan)))<=>(?[X]:((rich(X)|~kind(X)))))&
((?[X]:((funny(X)&strong(X))))<=>(?[X]:(old(X))))&
((?[X]:(~tall(X)))=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&quiet(X))<=>funny(X)))&
(![X]:((quiet(X)<~>~happy(X))=>(~humble(X)&~happy(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(brave(X)<~>creative(X))))&
(![X]:((wise(X)|~curious(X))<=>funny(X)))&
(((strong(john)&~brave(john)))<=>(?[X]:((tall(X)&~calm(X)))))&
(((humble(john)&~generous(john)))<=>(?[X]:((~curious(X)|funny(X)))))&
((?[X]:((~calm(X)|brave(X))))=>(old(john)))&
(((patient(mary)&~quiet(mary)))<=>((~brave(mary)|~patient(mary))))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:((~tall(X)<~>wise(X))))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
(?[X]:((happy(X)|~curious(X)))) | ~patient(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2507723795047861480265148
% SZS output start Proof for 2507723795047861480265148
16. (~quiet(mary) & patient(mary)) <=> (~patient(mary) | ~brave(mary)) [input p15]
25. ~patient(mary) [input hypothesis]
76. ((~quiet(mary) & patient(mary)) | (patient(mary) & brave(mary))) & ((~patient(mary) | ~brave(mary)) | (quiet(mary) | ~patient(mary))) [nnf transformation 16]
77. ((~quiet(mary) & patient(mary)) | (patient(mary) & brave(mary))) & (~patient(mary) | ~brave(mary) | quiet(mary) | ~patient(mary)) [flattening 76]
153. patient(mary) | patient(mary) [cnf transformation 77]
168. ~patient(mary) [cnf transformation 25]
170. patient(mary) [duplicate literal removal 153]
356. 41 <=> patient(mary) [avatar definition]
369. 41 [avatar split clause 170,356]
420. ~41 [avatar split clause 168,356]
421. $false [avatar sat refutation 369,420]
% SZS output end Proof for 2507723795047861480265148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or kind is either not patient or generous and vice versa.
Everyone who is not humble is curious or creative and vice versa.
If mary is both not wise and generous then susan is not kind.
Everyone who is not wise or kind is not humble and vice versa.
Everyone who is either curious or not generous is not tall.
Everyone who is both wise and not happy is not funny.
Everyone who is both patient and not funny is either not funny or strong.
If john is both patient and not patient then someone is wise and vice versa.
Everyone who is brave is not quiet or not patient.
Everyone who is strong or creative is both not old and happy.
Everyone who is both brave and not wise is either brave or funny and vice versa.
Everyone who is both quiet and not generous is generous or calm.
Everyone who is both humble and old is both rich and brave and vice versa.
If someone is not kind or not patient then lucy is either not rich or curious.
If alice is not funny or generous then lucy is both not creative and generous and vice versa.
Someone is either kind or humble.
Someone is not wise.
Someone is not generous.
Paul is either patient or funny.
Alice is not kind.
Someone is not happy or humble.
Someone is not funny. | Paul is not patient. | contradiction | (![X]:((patient(X)|kind(X))<=>(~patient(X)<~>generous(X))))&
(![X]:(~humble(X)<=>(curious(X)|creative(X))))&
(((~wise(mary)&generous(mary)))=>(~kind(susan)))&
(![X]:((~wise(X)|kind(X))<=>~humble(X)))&
(![X]:((curious(X)<~>~generous(X))=>~tall(X)))&
(![X]:((wise(X)&~happy(X))=>~funny(X)))&
(![X]:((patient(X)&~funny(X))=>(~funny(X)<~>strong(X))))&
(((patient(john)&~patient(john)))<=>(?[X]:(wise(X))))&
(![X]:(brave(X)=>(~quiet(X)|~patient(X))))&
(![X]:((strong(X)|creative(X))=>(~old(X)&happy(X))))&
(![X]:((brave(X)&~wise(X))<=>(brave(X)<~>funny(X))))&
(![X]:((quiet(X)&~generous(X))=>(generous(X)|calm(X))))&
(![X]:((humble(X)&old(X))<=>(rich(X)&brave(X))))&
((?[X]:((~kind(X)|~patient(X))))=>((~rich(lucy)<~>curious(lucy))))&
(((~funny(alice)|generous(alice)))<=>((~creative(lucy)&generous(lucy))))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~generous(X)))&
((patient(paul)<~>funny(paul)))&
(~kind(alice))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:(~funny(X))) | ~patient(paul) | [
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7871840636220417520946089
% SZS output start Proof for 7871840636220417520946089
8. (~patient(john) & patient(john)) <=> ? [X0] : wise(X0) [input p7]
11. ! [X0] : ((~wise(X0) & brave(X0)) <=> (brave(X0) <~> funny(X0))) [input p10]
19. patient(paul) <~> funny(paul) [input p18]
23. ~patient(paul) [input hypothesis]
42. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (patient(john) | ~patient(john))) [nnf transformation 8]
43. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | patient(john) | ~patient(john)) [flattening 42]
44. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | patient(john) | ~patient(john)) [rectify 43]
45. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
46. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (wise(sK0) | patient(john) | ~patient(john)) [skolemisation 44,45]
47. ! [X0] : (((~wise(X0) & brave(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (wise(X0) | ~brave(X0)))) [nnf transformation 11]
48. ! [X0] : (((~wise(X0) & brave(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | wise(X0) | ~brave(X0))) [flattening 47]
61. (~funny(paul) | ~patient(paul)) & (funny(paul) | patient(paul)) [nnf transformation 19]
83. patient(john) | ~wise(X0) [cnf transformation 46]
84. ~patient(john) | ~wise(X0) [cnf transformation 46]
90. ~funny(X0) | ~brave(X0) | wise(X0) | ~brave(X0) [cnf transformation 48]
92. brave(X0) | brave(X0) | ~funny(X0) [cnf transformation 48]
112. funny(paul) | patient(paul) [cnf transformation 61]
117. ~patient(paul) [cnf transformation 23]
118. ~funny(X0) | ~brave(X0) | wise(X0) [duplicate literal removal 90]
119. ~funny(X0) | brave(X0) [duplicate literal removal 92]
137. 4 <=> ! [X0] : ~wise(X0) [avatar definition]
138. ~wise(X0) <- (4) [avatar component clause 137]
140. 5 <=> patient(john) [avatar definition]
143. 4 | ~5 [avatar split clause 84,140,137]
144. 4 | 5 [avatar split clause 83,140,137]
145. ~funny(X0) | wise(X0) [subsumption resolution 118,119]
195. 16 <=> patient(paul) [avatar definition]
199. 17 <=> funny(paul) [avatar definition]
200. funny(paul) <- (17) [avatar component clause 199]
203. 16 | 17 [avatar split clause 112,199,195]
213. ~16 [avatar split clause 117,195]
215. wise(paul) <- (17) [resolution 145,200]
216. $false <- (4, 17) [subsumption resolution 215,138]
217. ~4 | ~17 [avatar contradiction clause 216]
218. $false [avatar sat refutation 143,144,203,213,217]
% SZS output end Proof for 7871840636220417520946089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is curious is not generous and vice versa. Everyone who is strong is either quiet or patient and vice versa. If someone is kind or not curious then john is not happy. Everyone who is either generous or not generous is not wise and vice versa. If someone is funny or old then john is calm and vice versa. Everyone who is not old is rich or not rich and vice versa. Everyone who is either not tall or calm is not quiet. If someone is funny then mary is both calm and not brave. If lucy is humble then john is kind. Everyone who is either not brave or not happy is patient and vice versa. If someone is both calm and strong then someone is either not generous or not curious and vice versa. Everyone who is not wise or not rich is quiet or calm. If susan is not happy or tall then someone is either calm or not calm. Everyone who is not creative or not patient is not generous and vice versa. Everyone who is both not quiet and not rich is not brave. Everyone who is either creative or not curious is not rich and vice versa. Someone is either brave or old. Someone is both not calm and kind. Lucy is either not funny or not old. Someone is either not strong or strong. Someone is both not quiet and creative. Someone is either not kind or humble. Susan is both not wise and happy. Someone is either not happy or not patient. | Mary is brave. | contradiction | (![X]:(curious(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(quiet(X)<~>patient(X))))&
((?[X]:((kind(X)|~curious(X))))=>(~happy(john)))&
(![X]:((generous(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((funny(X)|old(X))))<=>(calm(john)))&
(![X]:(~old(X)<=>(rich(X)|~rich(X))))&
(![X]:((~tall(X)<~>calm(X))=>~quiet(X)))&
((?[X]:(funny(X)))=>((calm(mary)&~brave(mary))))&
((humble(lucy))=>(kind(john)))&
(![X]:((~brave(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((calm(X)&strong(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((~wise(X)|~rich(X))=>(quiet(X)|calm(X))))&
(((~happy(susan)|tall(susan)))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~creative(X)|~patient(X))<=>~generous(X)))&
(![X]:((~quiet(X)&~rich(X))=>~brave(X)))&
(![X]:((creative(X)<~>~curious(X))<=>~rich(X)))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((~calm(X)&kind(X))))&
((~funny(lucy)<~>~old(lucy)))&
(?[X]:((~strong(X)<~>strong(X))))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~kind(X)<~>humble(X))))&
((~wise(susan)&happy(susan)))&
(?[X]:((~happy(X)<~>~patient(X)))) | brave(mary) | [
"p5",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1247908226454405727755412
% SZS output start Proof for 1247908226454405727755412
6. ! [X0] : (~old(X0) <=> (~rich(X0) | rich(X0))) [input p5]
8. ? [X0] : funny(X0) => (~brave(mary) & calm(mary)) [input p7]
19. ~funny(lucy) <~> ~old(lucy) [input p18]
25. brave(mary) [input hypothesis]
29. (~brave(mary) & calm(mary)) | ! [X0] : ~funny(X0) [ennf transformation 8]
43. ! [X0] : ((~old(X0) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | old(X0))) [nnf transformation 6]
44. ! [X0] : ((~old(X0) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | old(X0))) [flattening 43]
63. (old(lucy) | funny(lucy)) & (~old(lucy) | ~funny(lucy)) [nnf transformation 19]
91. ~old(X0) | ~rich(X0) [cnf transformation 44]
92. ~old(X0) | rich(X0) [cnf transformation 44]
96. ~brave(mary) | ~funny(X0) [cnf transformation 29]
127. old(lucy) | funny(lucy) [cnf transformation 63]
138. brave(mary) [cnf transformation 25]
168. 7 <=> ! [X1] : ~old(X1) [avatar definition]
169. ~old(X1) <- (7) [avatar component clause 168]
172. 8 <=> ! [X1] : ~funny(X1) [avatar definition]
173. ~funny(X1) <- (8) [avatar component clause 172]
175. ~old(X0) [subsumption resolution 91,92]
176. 7 [avatar split clause 175,168]
178. 9 <=> brave(mary) [avatar definition]
181. 8 | ~9 [avatar split clause 96,178,172]
227. 18 <=> funny(lucy) [avatar definition]
229. funny(lucy) <- (18) [avatar component clause 227]
231. 19 <=> old(lucy) [avatar definition]
233. old(lucy) <- (19) [avatar component clause 231]
234. 18 | 19 [avatar split clause 127,231,227]
256. 9 [avatar split clause 138,178]
257. $false <- (8, 18) [resolution 229,173]
258. ~8 | ~18 [avatar contradiction clause 257]
259. $false <- (7, 19) [subsumption resolution 233,169]
260. ~7 | ~19 [avatar contradiction clause 259]
261. $false [avatar sat refutation 176,181,234,256,258,260]
% SZS output end Proof for 1247908226454405727755412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not creative then alice is either not creative or not quiet and vice versa.
Everyone who is either not tall or brave is both not quiet and not rich.
If john is both old and not calm then someone is either kind or not curious and vice versa.
Everyone who is not funny or not curious is calm and vice versa.
Everyone who is both tall and humble is either calm or not tall and vice versa.
Everyone who is not brave or not humble is both curious and not strong and vice versa.
If lucy is not tall then paul is funny and vice versa.
If john is both not strong and patient then john is either not rich or patient.
If someone is either not happy or not calm then someone is not funny or not wise.
If susan is either not brave or not strong then mary is both not wise and wise and vice versa.
Everyone who is both generous and brave is either not brave or not calm and vice versa.
If someone is either patient or not curious then someone is both not tall and wise and vice versa.
Everyone who is not kind is either rich or not calm and vice versa.
Everyone who is not creative is both not curious and not old and vice versa.
If someone is quiet then john is not creative.
If john is patient then paul is not kind or not calm and vice versa.
Susan is both not calm and not rich.
Alice is both generous and patient.
Alice is not quiet or not calm.
Someone is either not old or generous.
Someone is not strong.
John is calm.
John is both quiet and patient.
Someone is old. | Susan is tall. | entailment | ((?[X]:((~humble(X)|~creative(X))))<=>((~creative(alice)<~>~quiet(alice))))&
(![X]:((~tall(X)<~>brave(X))=>(~quiet(X)&~rich(X))))&
(((old(john)&~calm(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)|~curious(X))<=>calm(X)))&
(![X]:((tall(X)&humble(X))<=>(calm(X)<~>~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(curious(X)&~strong(X))))&
((~tall(lucy))<=>(funny(paul)))&
(((~strong(john)&patient(john)))=>((~rich(john)<~>patient(john))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(((~brave(susan)<~>~strong(susan)))<=>((~wise(mary)&wise(mary))))&
(![X]:((generous(X)&brave(X))<=>(~brave(X)<~>~calm(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:(~kind(X)<=>(rich(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>(~curious(X)&~old(X))))&
((?[X]:(quiet(X)))=>(~creative(john)))&
((patient(john))<=>((~kind(paul)|~calm(paul))))&
((~calm(susan)&~rich(susan)))&
((generous(alice)&patient(alice)))&
((~quiet(alice)|~calm(alice)))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:(~strong(X)))&
(calm(john))&
((quiet(john)&patient(john)))&
(?[X]:(old(X))) | tall(susan) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2416128914068088835764188
% SZS output start Proof for 2416128914068088835764188
5. ! [X0] : ((humble(X0) & tall(X0)) <=> (calm(X0) <~> ~tall(X0))) [input p4]
17. ~rich(susan) & ~calm(susan) [input p16]
25. ~tall(susan) [input hypothesis]
45. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | (~humble(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | ~humble(X0) | ~tall(X0))) [flattening 45]
98. tall(X0) | calm(X0) | tall(X0) [cnf transformation 46]
141. ~calm(susan) [cnf transformation 17]
153. ~tall(susan) [cnf transformation 25]
158. calm(X0) | tall(X0) [duplicate literal removal 98]
350. tall(susan) [resolution 158,141]
353. $false [subsumption resolution 350,153]
% SZS output end Proof for 2416128914068088835764188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not brave is not quiet or humble.
Everyone who is curious is either tall or not generous.
If john is both not wise and wise then someone is either happy or not humble.
Everyone who is not patient is either not kind or not creative and vice versa.
If someone is both not wise and not rich then john is not tall.
Everyone who is either not strong or not quiet is both generous and not curious and vice versa.
Everyone who is both curious and not humble is either generous or patient and vice versa.
Everyone who is not happy or not rich is not calm or funny.
If someone is either not old or rich then someone is not kind or not curious and vice versa.
Everyone who is either not generous or not kind is both not humble and quiet.
Everyone who is humble or strong is either not wise or not kind and vice versa.
If alice is curious then someone is not old or generous and vice versa.
If alice is not tall then fred is not humble or curious and vice versa.
Everyone who is either not calm or curious is either quiet or curious.
Everyone who is not kind is wise and vice versa.
If susan is old then someone is patient or not happy.
John is either not rich or not quiet.
Alice is creative or not old.
Someone is both humble and wise.
Fred is either not calm or strong.
Someone is not calm or rich.
Someone is either not wise or not creative.
Someone is not curious or creative. | Susan is wise. | neutral | (![X]:((~funny(X)|~brave(X))=>(~quiet(X)|humble(X))))&
(![X]:(curious(X)=>(tall(X)<~>~generous(X))))&
(((~wise(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~patient(X)<=>(~kind(X)<~>~creative(X))))&
((?[X]:((~wise(X)&~rich(X))))=>(~tall(john)))&
(![X]:((~strong(X)<~>~quiet(X))<=>(generous(X)&~curious(X))))&
(![X]:((curious(X)&~humble(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~happy(X)|~rich(X))=>(~calm(X)|funny(X))))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:((~generous(X)<~>~kind(X))=>(~humble(X)&quiet(X))))&
(![X]:((humble(X)|strong(X))<=>(~wise(X)<~>~kind(X))))&
((curious(alice))<=>(?[X]:((~old(X)|generous(X)))))&
((~tall(alice))<=>((~humble(fred)|curious(fred))))&
(![X]:((~calm(X)<~>curious(X))=>(quiet(X)<~>curious(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((old(susan))=>(?[X]:((patient(X)|~happy(X)))))&
((~rich(john)<~>~quiet(john)))&
((creative(alice)|~old(alice)))&
(?[X]:((humble(X)&wise(X))))&
((~calm(fred)<~>strong(fred)))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((~curious(X)|creative(X)))) | wise(susan) | [] | null | 0 |
Everyone who is either not rich or patient is not curious or happy and vice versa. Everyone who is either generous or funny is patient and vice versa. Everyone who is not patient or happy is tall and vice versa. If alice is both not old and not tall then someone is either patient or humble and vice versa. Everyone who is both not happy and not calm is generous or brave. Everyone who is not calm or happy is either not creative or not quiet and vice versa. If someone is both old and not wise then someone is both not kind and not quiet. If someone is either not tall or patient then fred is both not kind and strong and vice versa. Everyone who is not rich is tall and vice versa. If someone is generous then someone is either not curious or not humble. If someone is strong then mary is not wise. If fred is both calm and creative then susan is either not strong or calm. If someone is both patient and not quiet then someone is creative and vice versa. If someone is both wise and not brave then lucy is both not patient and not funny and vice versa. If someone is humble then paul is both generous and not funny and vice versa. If someone is both curious and not strong then someone is not creative or wise. Fred is either not funny or not old. Alice is both not strong and kind. Lucy is either wise or not creative. Someone is old. Alice is creative or curious. Paul is not rich. Susan is both funny and strong. | Mary is humble. | contradiction | (![X]:((~rich(X)<~>patient(X))<=>(~curious(X)|happy(X))))&
(![X]:((generous(X)<~>funny(X))<=>patient(X)))&
(![X]:((~patient(X)|happy(X))<=>tall(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~happy(X)&~calm(X))=>(generous(X)|brave(X))))&
(![X]:((~calm(X)|happy(X))<=>(~creative(X)<~>~quiet(X))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:((~tall(X)<~>patient(X))))<=>((~kind(fred)&strong(fred))))&
(![X]:(~rich(X)<=>tall(X)))&
((?[X]:(generous(X)))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(((calm(fred)&creative(fred)))=>((~strong(susan)<~>calm(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:(creative(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((~patient(lucy)&~funny(lucy))))&
((?[X]:(humble(X)))<=>((generous(paul)&~funny(paul))))&
((?[X]:((curious(X)&~strong(X))))=>(?[X]:((~creative(X)|wise(X)))))&
((~funny(fred)<~>~old(fred)))&
((~strong(alice)&kind(alice)))&
((wise(lucy)<~>~creative(lucy)))&
(?[X]:(old(X)))&
((creative(alice)|curious(alice)))&
(~rich(paul))&
((funny(susan)&strong(susan))) | humble(mary) | [
"p0",
"p1",
"p2",
"p8",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8468650732517492748224439
% SZS output start Proof for 8468650732517492748224439
1. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (happy(X0) | ~curious(X0))) [input p0]
2. ! [X0] : ((generous(X0) <~> funny(X0)) <=> patient(X0)) [input p1]
3. ! [X0] : ((happy(X0) | ~patient(X0)) <=> tall(X0)) [input p2]
9. ! [X0] : (~rich(X0) <=> tall(X0)) [input p8]
15. ? [X0] : humble(X0) <=> (~funny(paul) & generous(paul)) [input p14]
22. ~rich(paul) [input p21]
24. humble(mary) [input hypothesis]
37. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [flattening 37]
39. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 2]
40. ! [X0] : (((happy(X0) | ~patient(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) & patient(X0)))) [nnf transformation 3]
41. ! [X0] : ((happy(X0) | ~patient(X0) | ~tall(X0)) & (tall(X0) | (~happy(X0) & patient(X0)))) [flattening 40]
57. ! [X0] : ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))) [nnf transformation 9]
73. (? [X0] : humble(X0) | (funny(paul) | ~generous(paul))) & ((~funny(paul) & generous(paul)) | ! [X0] : ~humble(X0)) [nnf transformation 15]
74. (? [X0] : humble(X0) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X0] : ~humble(X0)) [flattening 73]
75. (? [X0] : humble(X0) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X1] : ~humble(X1)) [rectify 74]
76. ? [X0] : humble(X0) => humble(sK7) [choice axiom]
77. (humble(sK7) | funny(paul) | ~generous(paul)) & ((~funny(paul) & generous(paul)) | ! [X1] : ~humble(X1)) [skolemisation 75,76]
90. ~happy(X0) | rich(X0) | ~patient(X0) [cnf transformation 38]
91. ~generous(X0) | funny(X0) | patient(X0) [cnf transformation 39]
97. ~tall(X0) | ~patient(X0) | happy(X0) [cnf transformation 41]
119. tall(X0) | rich(X0) [cnf transformation 57]
133. generous(paul) | ~humble(X1) [cnf transformation 77]
134. ~funny(paul) | ~humble(X1) [cnf transformation 77]
145. ~rich(paul) [cnf transformation 22]
148. humble(mary) [cnf transformation 24]
299. 34 <=> generous(paul) [avatar definition]
300. generous(paul) <- (34) [avatar component clause 299]
303. 35 <=> funny(paul) [avatar definition]
304. ~funny(paul) <- (~35) [avatar component clause 303]
312. 37 <=> ! [X1] : ~humble(X1) [avatar definition]
313. ~humble(X1) <- (37) [avatar component clause 312]
314. 37 | ~35 [avatar split clause 134,303,312]
315. 37 | 34 [avatar split clause 133,299,312]
402. funny(paul) | patient(paul) <- (34) [resolution 91,300]
403. patient(paul) <- (34, ~35) [subsumption resolution 402,304]
470. ~patient(X0) | happy(X0) | rich(X0) [resolution 97,119]
474. ~patient(X0) | rich(X0) [subsumption resolution 470,90]
701. rich(paul) <- (34, ~35) [resolution 474,403]
704. $false <- (34, ~35) [subsumption resolution 701,145]
705. ~34 | 35 [avatar contradiction clause 704]
706. $false <- (37) [resolution 313,148]
717. ~37 [avatar contradiction clause 706]
718. $false [avatar sat refutation 314,315,705,717]
% SZS output end Proof for 8468650732517492748224439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is quiet. If alice is happy then someone is calm or not wise and vice versa. If paul is not strong then lucy is not tall. Everyone who is creative is funny or old and vice versa. If someone is old or not happy then alice is both patient and strong and vice versa. If someone is either strong or humble then paul is both not creative and happy and vice versa. Everyone who is either not creative or generous is not wise and vice versa. Everyone who is not happy is not calm. If john is either not happy or wise then susan is either creative or not calm. Everyone who is both not rich and funny is happy or creative and vice versa. Everyone who is both not humble and not calm is funny and vice versa. If someone is both tall and not rich then alice is calm or not tall and vice versa. Everyone who is not patient or calm is calm and vice versa. Everyone who is both not quiet and not curious is old. If mary is either wise or brave then john is both curious and rich and vice versa. Everyone who is not old is funny and vice versa. Someone is either calm or not curious. Fred is kind. Someone is either not generous or generous. Someone is either brave or not quiet. Paul is either kind or patient. Someone is either not brave or rich. | Paul is humble. | contradiction | (![X]:(~tall(X)=>quiet(X)))&
((happy(alice))<=>(?[X]:((calm(X)|~wise(X)))))&
((~strong(paul))=>(~tall(lucy)))&
(![X]:(creative(X)<=>(funny(X)|old(X))))&
((?[X]:((old(X)|~happy(X))))<=>((patient(alice)&strong(alice))))&
((?[X]:((strong(X)<~>humble(X))))<=>((~creative(paul)&happy(paul))))&
(![X]:((~creative(X)<~>generous(X))<=>~wise(X)))&
(![X]:(~happy(X)=>~calm(X)))&
(((~happy(john)<~>wise(john)))=>((creative(susan)<~>~calm(susan))))&
(![X]:((~rich(X)&funny(X))<=>(happy(X)|creative(X))))&
(![X]:((~humble(X)&~calm(X))<=>funny(X)))&
((?[X]:((tall(X)&~rich(X))))<=>((calm(alice)|~tall(alice))))&
(![X]:((~patient(X)|calm(X))<=>calm(X)))&
(![X]:((~quiet(X)&~curious(X))=>old(X)))&
(((wise(mary)<~>brave(mary)))<=>((curious(john)&rich(john))))&
(![X]:(~old(X)<=>funny(X)))&
(?[X]:((calm(X)<~>~curious(X))))&
(kind(fred))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
((kind(paul)<~>patient(paul)))&
(?[X]:((~brave(X)<~>rich(X)))) | humble(paul) | [
"p3",
"p4",
"p5",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 320011988426272651994836
% SZS output start Proof for 320011988426272651994836
4. ! [X0] : (creative(X0) <=> (old(X0) | funny(X0))) [input p3]
5. ? [X0] : (~happy(X0) | old(X0)) <=> (strong(alice) & patient(alice)) [input p4]
6. ? [X0] : (strong(X0) <~> humble(X0)) <=> (happy(paul) & ~creative(paul)) [input p5]
10. ! [X0] : ((funny(X0) & ~rich(X0)) <=> (creative(X0) | happy(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> funny(X0)) [input p10]
16. ! [X0] : (~old(X0) <=> funny(X0)) [input p15]
23. humble(paul) [input hypothesis]
34. ! [X0] : ((creative(X0) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ~creative(X0))) [nnf transformation 4]
35. ! [X0] : ((creative(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ~creative(X0))) [flattening 34]
36. (? [X0] : (~happy(X0) | old(X0)) | (~strong(alice) | ~patient(alice))) & ((strong(alice) & patient(alice)) | ! [X0] : (happy(X0) & ~old(X0))) [nnf transformation 5]
37. (? [X0] : (~happy(X0) | old(X0)) | ~strong(alice) | ~patient(alice)) & ((strong(alice) & patient(alice)) | ! [X0] : (happy(X0) & ~old(X0))) [flattening 36]
38. (? [X0] : (~happy(X0) | old(X0)) | ~strong(alice) | ~patient(alice)) & ((strong(alice) & patient(alice)) | ! [X1] : (happy(X1) & ~old(X1))) [rectify 37]
39. ? [X0] : (~happy(X0) | old(X0)) => (~happy(sK1) | old(sK1)) [choice axiom]
40. ((~happy(sK1) | old(sK1)) | ~strong(alice) | ~patient(alice)) & ((strong(alice) & patient(alice)) | ! [X1] : (happy(X1) & ~old(X1))) [skolemisation 38,39]
41. (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | (~happy(paul) | creative(paul))) & ((happy(paul) & ~creative(paul)) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 6]
42. (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~happy(paul) | creative(paul)) & ((happy(paul) & ~creative(paul)) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [flattening 41]
43. (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~happy(paul) | creative(paul)) & ((happy(paul) & ~creative(paul)) | ! [X1] : ((strong(X1) | ~humble(X1)) & (humble(X1) | ~strong(X1)))) [rectify 42]
44. ? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) => ((~humble(sK2) | ~strong(sK2)) & (humble(sK2) | strong(sK2))) [choice axiom]
45. (((~humble(sK2) | ~strong(sK2)) & (humble(sK2) | strong(sK2))) | ~happy(paul) | creative(paul)) & ((happy(paul) & ~creative(paul)) | ! [X1] : ((strong(X1) | ~humble(X1)) & (humble(X1) | ~strong(X1)))) [skolemisation 43,44]
48. ! [X0] : (((funny(X0) & ~rich(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (~funny(X0) | rich(X0)))) [nnf transformation 10]
49. ! [X0] : (((funny(X0) & ~rich(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | ~funny(X0) | rich(X0))) [flattening 48]
50. ! [X0] : (((~calm(X0) & ~humble(X0)) | ~funny(X0)) & (funny(X0) | (calm(X0) | humble(X0)))) [nnf transformation 11]
51. ! [X0] : (((~calm(X0) & ~humble(X0)) | ~funny(X0)) & (funny(X0) | calm(X0) | humble(X0))) [flattening 50]
61. ! [X0] : ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))) [nnf transformation 16]
81. ~funny(X0) | creative(X0) [cnf transformation 35]
82. ~old(X0) | creative(X0) [cnf transformation 35]
86. strong(alice) | happy(X1) [cnf transformation 40]
88. ~creative(paul) | humble(X1) | ~strong(X1) [cnf transformation 45]
106. ~happy(X0) | funny(X0) [cnf transformation 49]
107. ~creative(X0) | funny(X0) [cnf transformation 49]
109. ~humble(X0) | ~funny(X0) [cnf transformation 51]
126. old(X0) | funny(X0) [cnf transformation 61]
139. humble(paul) [cnf transformation 23]
175. 9 <=> strong(alice) [avatar definition]
176. strong(alice) <- (9) [avatar component clause 175]
188. 12 <=> ! [X1] : happy(X1) [avatar definition]
189. happy(X1) <- (12) [avatar component clause 188]
190. 12 | 9 [avatar split clause 86,175,188]
198. 14 <=> creative(paul) [avatar definition]
199. ~creative(paul) <- (~14) [avatar component clause 198]
202. 15 <=> happy(paul) [avatar definition]
203. happy(paul) <- (15) [avatar component clause 202]
204. ~happy(paul) <- (~15) [avatar component clause 202]
220. 19 <=> ! [X1] : (humble(X1) | ~strong(X1)) [avatar definition]
221. ~strong(X1) | humble(X1) <- (19) [avatar component clause 220]
224. 19 | ~14 [avatar split clause 88,198,220]
333. funny(paul) <- (15) [resolution 106,203]
335. ~funny(paul) [resolution 109,139]
336. $false <- (15) [subsumption resolution 335,333]
337. ~15 [avatar contradiction clause 336]
341. funny(X0) | creative(X0) [resolution 126,82]
342. creative(X0) [subsumption resolution 341,81]
347. $false <- (~14) [resolution 342,199]
349. funny(X0) [resolution 342,107]
351. 14 [avatar contradiction clause 347]
354. humble(alice) <- (9, 19) [resolution 221,176]
361. ~funny(alice) <- (9, 19) [resolution 354,109]
364. $false <- (9, 19) [subsumption resolution 361,349]
365. ~9 | ~19 [avatar contradiction clause 364]
371. $false <- (12, ~15) [resolution 189,204]
376. ~12 | 15 [avatar contradiction clause 371]
377. $false [avatar sat refutation 190,224,337,351,365,376]
% SZS output end Proof for 320011988426272651994836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both not humble and not tall.
If someone is either patient or not brave then someone is both creative and wise and vice versa.
If someone is not strong or happy then mary is either not strong or old and vice versa.
If john is not rich or not funny then mary is both brave and not curious and vice versa.
If someone is either tall or not wise then paul is either not funny or not strong and vice versa.
If someone is both brave and not old then someone is not happy.
If fred is patient then fred is both brave and not kind.
Everyone who is both not creative and humble is not humble and vice versa.
Everyone who is not rich or rich is not old or not kind and vice versa.
Everyone who is not brave or not old is either old or not generous.
Everyone who is strong is old or not tall and vice versa.
Everyone who is calm is kind or happy and vice versa.
Everyone who is both not patient and not humble is either not generous or not old.
Everyone who is both strong and not rich is either not brave or kind.
Everyone who is curious is both happy and not brave and vice versa.
Everyone who is both quiet and not calm is either old or not tall.
John is either not creative or not strong.
Susan is either not happy or generous.
John is not kind or patient.
Alice is generous.
Fred is quiet or creative.
Fred is not strong or humble.
Someone is kind. | Alice is calm. | neutral | (![X]:(~rich(X)=>(~humble(X)&~tall(X))))&
((?[X]:((patient(X)<~>~brave(X))))<=>(?[X]:((creative(X)&wise(X)))))&
((?[X]:((~strong(X)|happy(X))))<=>((~strong(mary)<~>old(mary))))&
(((~rich(john)|~funny(john)))<=>((brave(mary)&~curious(mary))))&
((?[X]:((tall(X)<~>~wise(X))))<=>((~funny(paul)<~>~strong(paul))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:(~happy(X))))&
((patient(fred))=>((brave(fred)&~kind(fred))))&
(![X]:((~creative(X)&humble(X))<=>~humble(X)))&
(![X]:((~rich(X)|rich(X))<=>(~old(X)|~kind(X))))&
(![X]:((~brave(X)|~old(X))=>(old(X)<~>~generous(X))))&
(![X]:(strong(X)<=>(old(X)|~tall(X))))&
(![X]:(calm(X)<=>(kind(X)|happy(X))))&
(![X]:((~patient(X)&~humble(X))=>(~generous(X)<~>~old(X))))&
(![X]:((strong(X)&~rich(X))=>(~brave(X)<~>kind(X))))&
(![X]:(curious(X)<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)&~calm(X))=>(old(X)<~>~tall(X))))&
((~creative(john)<~>~strong(john)))&
((~happy(susan)<~>generous(susan)))&
((~kind(john)|patient(john)))&
(generous(alice))&
((quiet(fred)|creative(fred)))&
((~strong(fred)|humble(fred)))&
(?[X]:(kind(X))) | calm(alice) | [] | null | 0 |
Everyone who is calm or not rich is either quiet or not curious.
Everyone who is not kind is both not wise and not curious and vice versa.
Everyone who is either old or not happy is both not wise and kind.
Everyone who is happy is curious or not curious.
Everyone who is strong or not generous is both patient and not happy.
Everyone who is both not wise and generous is either patient or not kind and vice versa.
Everyone who is either kind or not kind is either not funny or not tall and vice versa.
If someone is strong or not curious then john is not kind.
Everyone who is either not patient or not rich is brave and vice versa.
Everyone who is not strong is not old or funny.
Everyone who is both not creative and not funny is quiet or not rich and vice versa.
If alice is not quiet then someone is both humble and kind.
If someone is either tall or rich then lucy is both not strong and patient.
Everyone who is either curious or not happy is both funny and old and vice versa.
If someone is either not tall or curious then someone is not humble.
Everyone who is not humble is both not generous and not rich and vice versa.
Paul is strong or not happy. | Paul is not generous. | contradiction | (![X]:((calm(X)|~rich(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~curious(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)&kind(X))))&
(![X]:(happy(X)=>(curious(X)|~curious(X))))&
(![X]:((strong(X)|~generous(X))=>(patient(X)&~happy(X))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~generous(X)&~rich(X))))&
((strong(paul)|~happy(paul))) | ~generous(paul) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 64618723427143458591679
% SZS output start Proof for 64618723427143458591679
2. ! [X0] : (~kind(X0) <=> (~curious(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (kind(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~generous(X0) | strong(X0)) => (~happy(X0) & patient(X0))) [input p4]
6. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
11. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> (~rich(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (old(X0) & funny(X0))) [input p13]
15. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : ~humble(X0) [input p14]
16. ! [X0] : (~humble(X0) <=> (~rich(X0) & ~generous(X0))) [input p15]
17. ~happy(paul) | strong(paul) [input p16]
18. ~generous(paul) [input hypothesis]
19. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : ~humble(X1) [rectify 15]
22. ! [X0] : ((kind(X0) & ~wise(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
25. ! [X0] : ((~happy(X0) & patient(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 5]
31. ? [X1] : ~humble(X1) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 19]
33. ! [X0] : ((~kind(X0) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [nnf transformation 2]
34. ! [X0] : ((~kind(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | kind(X0))) [flattening 33]
35. ! [X0] : ((kind(X0) & ~wise(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 22]
36. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~generous(X0) | wise(X0)))) [nnf transformation 6]
37. ! [X0] : (((generous(X0) & ~wise(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~generous(X0) | wise(X0))) [flattening 36]
38. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 7]
39. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (funny(X0) | creative(X0)))) [nnf transformation 11]
40. ! [X0] : (((~funny(X0) & ~creative(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | funny(X0) | creative(X0))) [flattening 39]
44. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 14]
45. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 44]
46. ? [X1] : ~humble(X1) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 31]
47. ? [X0] : ~humble(X0) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 46]
48. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
49. ~humble(sK1) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 47,48]
50. ! [X0] : ((~humble(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [nnf transformation 16]
51. ! [X0] : ((~humble(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | humble(X0))) [flattening 50]
55. ~curious(X0) | kind(X0) [cnf transformation 34]
59. ~happy(X0) | kind(X0) | ~old(X0) [cnf transformation 35]
60. happy(X0) | old(X0) | kind(X0) [cnf transformation 35]
63. patient(X0) | generous(X0) [cnf transformation 25]
64. ~strong(X0) | ~happy(X0) [cnf transformation 25]
65. ~happy(X0) | generous(X0) [cnf transformation 25]
70. generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
72. ~tall(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
73. ~tall(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 38]
87. ~funny(X0) | rich(X0) [cnf transformation 40]
95. funny(X0) | curious(X0) | happy(X0) [cnf transformation 45]
100. ~humble(sK1) | curious(X1) | tall(X1) [cnf transformation 49]
102. ~generous(X0) | humble(X0) [cnf transformation 51]
103. ~rich(X0) | humble(X0) [cnf transformation 51]
105. ~happy(paul) | strong(paul) [cnf transformation 17]
106. ~generous(paul) [cnf transformation 18]
107. ~tall(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 72]
108. ~tall(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 73]
111. ~kind(X0) | generous(X0) [subsumption resolution 70,63]
116. ~tall(X0) | ~funny(X0) [subsumption resolution 107,108]
165. 12 <=> humble(sK1) [avatar definition]
167. ~humble(sK1) <- (~12) [avatar component clause 165]
170. 13 <=> ! [X1] : (curious(X1) | tall(X1)) [avatar definition]
171. tall(X1) | curious(X1) <- (13) [avatar component clause 170]
172. 13 | ~12 [avatar split clause 100,165,170]
173. ~happy(paul) [subsumption resolution 105,64]
204. old(X2) | kind(X2) | generous(X2) [resolution 60,65]
207. 18 <=> kind(paul) [avatar definition]
208. ~kind(paul) <- (~18) [avatar component clause 207]
209. kind(paul) <- (18) [avatar component clause 207]
215. generous(X2) | old(X2) [subsumption resolution 204,111]
217. generous(paul) <- (18) [resolution 209,111]
223. 21 <=> curious(paul) [avatar definition]
224. ~curious(paul) <- (~21) [avatar component clause 223]
225. curious(paul) <- (21) [avatar component clause 223]
227. $false <- (18) [subsumption resolution 217,106]
228. ~18 [avatar contradiction clause 227]
240. happy(X0) | curious(X0) | rich(X0) [resolution 95,87]
268. humble(X0) | old(X0) [resolution 215,102]
336. curious(X2) | rich(X2) | kind(X2) | ~old(X2) [resolution 240,59]
344. ~old(X2) | kind(X2) | rich(X2) [subsumption resolution 336,55]
346. kind(paul) <- (21) [resolution 225,55]
352. $false <- (~18, 21) [subsumption resolution 346,208]
353. 18 | ~21 [avatar contradiction clause 352]
427. 44 <=> rich(sK1) [avatar definition]
429. rich(sK1) <- (44) [avatar component clause 427]
431. 45 <=> kind(sK1) [avatar definition]
433. kind(sK1) <- (45) [avatar component clause 431]
437. 46 <=> generous(sK1) [avatar definition]
439. generous(sK1) <- (46) [avatar component clause 437]
446. ~funny(X2) | curious(X2) <- (13) [resolution 171,116]
452. curious(X0) | curious(X0) | happy(X0) <- (13) [resolution 446,95]
455. happy(X0) | curious(X0) <- (13) [duplicate literal removal 452]
515. curious(paul) <- (13) [resolution 455,173]
521. $false <- (13, ~21) [subsumption resolution 515,224]
522. ~13 | 21 [avatar contradiction clause 521]
544. old(sK1) <- (~12) [resolution 167,268]
590. kind(sK1) | rich(sK1) <- (~12) [resolution 544,344]
612. humble(sK1) <- (44) [resolution 429,103]
622. $false <- (~12, 44) [subsumption resolution 612,167]
623. 12 | ~44 [avatar contradiction clause 622]
624. 44 | 45 | 12 [avatar split clause 590,165,431,427]
627. generous(sK1) <- (45) [resolution 433,111]
628. 46 | ~45 [avatar split clause 627,431,437]
629. humble(sK1) <- (46) [resolution 439,102]
630. $false <- (~12, 46) [subsumption resolution 629,167]
631. 12 | ~46 [avatar contradiction clause 630]
632. $false [avatar sat refutation 172,228,353,522,623,624,628,631]
% SZS output end Proof for 64618723427143458591679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not humble is not creative.
Everyone who is either brave or humble is rich.
Everyone who is not happy or not old is either not curious or brave.
Everyone who is both not generous and calm is humble and vice versa.
If someone is either patient or not patient then susan is not quiet or not old.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
If someone is both funny and creative then someone is not humble.
Everyone who is both kind and brave is not calm and vice versa.
Everyone who is not patient is either not strong or not tall and vice versa.
Someone is wise or creative.
Fred is not curious or curious.
John is both not strong and not kind.
Paul is not happy or not patient.
Someone is old or creative.
John is old.
Alice is either wise or patient. | Mary is calm. | entailment | (![X]:((kind(X)<~>~humble(X))=>~creative(X)))&
(![X]:((brave(X)<~>humble(X))=>rich(X)))&
(![X]:((~happy(X)|~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(~humble(X))))&
(![X]:((kind(X)&brave(X))<=>~calm(X)))&
(![X]:(~patient(X)<=>(~strong(X)<~>~tall(X))))&
(?[X]:((wise(X)|creative(X))))&
((~curious(fred)|curious(fred)))&
((~strong(john)&~kind(john)))&
((~happy(paul)|~patient(paul)))&
(?[X]:((old(X)|creative(X))))&
(old(john))&
((wise(alice)<~>patient(alice))) | calm(mary) | [
"p1",
"p3",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 487452236540524787819046
% SZS output start Proof for 487452236540524787819046
2. ! [X0] : ((brave(X0) <~> humble(X0)) => rich(X0)) [input p1]
4. ! [X0] : ((calm(X0) & ~generous(X0)) <=> humble(X0)) [input p3]
11. ? [X0] : (~rich(X0) | ~kind(X0)) => (patient(mary) & ~rich(mary)) [input p10]
15. ! [X0] : ((brave(X0) & kind(X0)) <=> ~calm(X0)) [input p14]
19. ~kind(john) & ~strong(john) [input p18]
24. ~calm(mary) [input hypothesis]
27. ! [X0] : (rich(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 2]
34. (patient(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & kind(X0)) [ennf transformation 11]
37. ! [X0] : (rich(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 27]
39. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | (~calm(X0) | generous(X0)))) [nnf transformation 4]
40. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | ~calm(X0) | generous(X0))) [flattening 39]
64. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~kind(X0)))) [nnf transformation 15]
65. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~kind(X0))) [flattening 64]
74. ~brave(X0) | humble(X0) | rich(X0) [cnf transformation 37]
82. ~humble(X0) | calm(X0) [cnf transformation 40]
107. ~rich(mary) | kind(X0) [cnf transformation 34]
123. calm(X0) | brave(X0) [cnf transformation 65]
131. ~kind(john) [cnf transformation 19]
137. ~calm(mary) [cnf transformation 24]
216. 16 <=> ! [X0] : kind(X0) [avatar definition]
217. kind(X0) <- (16) [avatar component clause 216]
220. 17 <=> rich(mary) [avatar definition]
222. ~rich(mary) <- (~17) [avatar component clause 220]
224. 16 | ~17 [avatar split clause 107,220,216]
297. brave(mary) [resolution 123,137]
318. humble(mary) | rich(mary) [resolution 74,297]
319. humble(mary) <- (~17) [subsumption resolution 318,222]
333. calm(mary) <- (~17) [resolution 319,82]
334. $false <- (~17) [subsumption resolution 333,137]
335. 17 [avatar contradiction clause 334]
342. $false <- (16) [resolution 217,131]
343. ~16 [avatar contradiction clause 342]
344. $false [avatar sat refutation 224,335,343]
% SZS output end Proof for 487452236540524787819046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not quiet is either kind or not curious.
If someone is old or not generous then someone is not happy or not kind and vice versa.
If mary is both wise and creative then alice is creative or happy and vice versa.
If paul is either wise or curious then john is not rich or not calm and vice versa.
If someone is not funny or not generous then alice is curious.
If john is either patient or not old then alice is either brave or not calm.
Everyone who is wise or not creative is not brave.
If someone is calm then someone is both not funny and tall and vice versa.
Everyone who is either wise or quiet is both not calm and not quiet and vice versa.
If someone is either not funny or not calm then someone is old or not wise.
If someone is curious or not quiet then mary is both not kind and not humble and vice versa.
Everyone who is not humble or not strong is generous.
Everyone who is either generous or funny is strong or calm and vice versa.
Everyone who is wise is both not patient and kind and vice versa.
If someone is kind then paul is not curious and vice versa.
If mary is not strong or curious then fred is not funny or creative and vice versa.
Susan is not generous.
Someone is not rich.
Someone is either creative or rich.
John is both not kind and not humble.
Fred is both strong and not kind.
Someone is kind.
Susan is calm.
Someone is both happy and not old. | Susan is not humble. | contradiction | (![X]:((~tall(X)&~quiet(X))=>(kind(X)<~>~curious(X))))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:((~happy(X)|~kind(X)))))&
(((wise(mary)&creative(mary)))<=>((creative(alice)|happy(alice))))&
(((wise(paul)<~>curious(paul)))<=>((~rich(john)|~calm(john))))&
((?[X]:((~funny(X)|~generous(X))))=>(curious(alice)))&
(((patient(john)<~>~old(john)))=>((brave(alice)<~>~calm(alice))))&
(![X]:((wise(X)|~creative(X))=>~brave(X)))&
((?[X]:(calm(X)))<=>(?[X]:((~funny(X)&tall(X)))))&
(![X]:((wise(X)<~>quiet(X))<=>(~calm(X)&~quiet(X))))&
((?[X]:((~funny(X)<~>~calm(X))))=>(?[X]:((old(X)|~wise(X)))))&
((?[X]:((curious(X)|~quiet(X))))<=>((~kind(mary)&~humble(mary))))&
(![X]:((~humble(X)|~strong(X))=>generous(X)))&
(![X]:((generous(X)<~>funny(X))<=>(strong(X)|calm(X))))&
(![X]:(wise(X)<=>(~patient(X)&kind(X))))&
((?[X]:(kind(X)))<=>(~curious(paul)))&
(((~strong(mary)|curious(mary)))<=>((~funny(fred)|creative(fred))))&
(~generous(susan))&
(?[X]:(~rich(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((~kind(john)&~humble(john)))&
((strong(fred)&~kind(fred)))&
(?[X]:(kind(X)))&
(calm(susan))&
(?[X]:((happy(X)&~old(X)))) | ~humble(susan) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 85196147063011802341967
% SZS output start Proof for 85196147063011802341967
12. ! [X0] : ((~strong(X0) | ~humble(X0)) => generous(X0)) [input p11]
17. ~generous(susan) [input p16]
25. ~humble(susan) [input hypothesis]
35. ! [X0] : (generous(X0) | (strong(X0) & humble(X0))) [ennf transformation 12]
123. humble(X0) | generous(X0) [cnf transformation 35]
140. ~generous(susan) [cnf transformation 17]
152. ~humble(susan) [cnf transformation 25]
367. generous(susan) [resolution 123,152]
369. $false [subsumption resolution 367,140]
% SZS output end Proof for 85196147063011802341967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is wise or not kind and vice versa.
Everyone who is both not patient and humble is not patient or old.
Everyone who is either calm or humble is either creative or rich.
If someone is old or creative then someone is both old and wise.
Everyone who is not happy or not quiet is happy and vice versa.
If someone is either not humble or patient then someone is not old or kind.
If paul is curious then someone is both creative and rich and vice versa.
Everyone who is creative or not old is either happy or humble and vice versa.
Everyone who is kind or tall is either rich or not kind and vice versa.
If susan is patient or funny then someone is not strong and vice versa.
Everyone who is both not calm and funny is calm.
Everyone who is not kind or curious is both strong and not rich.
If someone is not old then someone is either rich or brave and vice versa.
Everyone who is either not happy or not kind is not old or quiet.
Everyone who is both calm and not funny is not rich or not kind.
Someone is not generous.
Mary is either not patient or brave.
Paul is both happy and tall.
Alice is funny.
Someone is kind or curious.
Fred is either not tall or strong. | Mary is not old. | neutral | (![X]:(rich(X)<=>(wise(X)|~kind(X))))&
(![X]:((~patient(X)&humble(X))=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>humble(X))=>(creative(X)<~>rich(X))))&
((?[X]:((old(X)|creative(X))))=>(?[X]:((old(X)&wise(X)))))&
(![X]:((~happy(X)|~quiet(X))<=>happy(X)))&
((?[X]:((~humble(X)<~>patient(X))))=>(?[X]:((~old(X)|kind(X)))))&
((curious(paul))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((creative(X)|~old(X))<=>(happy(X)<~>humble(X))))&
(![X]:((kind(X)|tall(X))<=>(rich(X)<~>~kind(X))))&
(((patient(susan)|funny(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&funny(X))=>calm(X)))&
(![X]:((~kind(X)|curious(X))=>(strong(X)&~rich(X))))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(~old(X)|quiet(X))))&
(![X]:((calm(X)&~funny(X))=>(~rich(X)|~kind(X))))&
(?[X]:(~generous(X)))&
((~patient(mary)<~>brave(mary)))&
((happy(paul)&tall(paul)))&
(funny(alice))&
(?[X]:((kind(X)|curious(X))))&
((~tall(fred)<~>strong(fred))) | ~old(mary) | [] | null | 0 |
Everyone who is not old or wise is either not kind or not brave and vice versa.
If john is either creative or not old then mary is calm or not generous and vice versa.
Everyone who is either creative or not calm is either curious or not kind.
Everyone who is both not tall and not old is either not brave or brave and vice versa.
If someone is funny or not curious then fred is both funny and not curious and vice versa.
Everyone who is either rich or generous is both not old and kind.
If someone is kind then someone is either generous or not calm and vice versa.
If lucy is kind or funny then john is not creative or not wise and vice versa.
If susan is both quiet and old then someone is not rich or wise and vice versa.
Everyone who is happy is strong or rich and vice versa.
If paul is either not curious or not creative then someone is not generous.
If lucy is both kind and not happy then someone is both not curious and not funny and vice versa.
If lucy is creative then lucy is not funny or not humble.
Everyone who is either wise or old is old or not quiet and vice versa.
Everyone who is either tall or not creative is not happy or not quiet and vice versa.
Everyone who is happy is quiet and vice versa.
Paul is old or not old.
John is patient or not calm.
Someone is not strong.
Alice is not curious or tall.
John is both humble and not strong.
Paul is both calm and not generous. | Alice is not funny. | contradiction | (![X]:((~old(X)|wise(X))<=>(~kind(X)<~>~brave(X))))&
(((creative(john)<~>~old(john)))<=>((calm(mary)|~generous(mary))))&
(![X]:((creative(X)<~>~calm(X))=>(curious(X)<~>~kind(X))))&
(![X]:((~tall(X)&~old(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:((funny(X)|~curious(X))))<=>((funny(fred)&~curious(fred))))&
(![X]:((rich(X)<~>generous(X))=>(~old(X)&kind(X))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)<~>~calm(X)))))&
(((kind(lucy)|funny(lucy)))<=>((~creative(john)|~wise(john))))&
(((quiet(susan)&old(susan)))<=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:(happy(X)<=>(strong(X)|rich(X))))&
(((~curious(paul)<~>~creative(paul)))=>(?[X]:(~generous(X))))&
(((kind(lucy)&~happy(lucy)))<=>(?[X]:((~curious(X)&~funny(X)))))&
((creative(lucy))=>((~funny(lucy)|~humble(lucy))))&
(![X]:((wise(X)<~>old(X))<=>(old(X)|~quiet(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(~happy(X)|~quiet(X))))&
(![X]:(happy(X)<=>quiet(X)))&
((old(paul)|~old(paul)))&
((patient(john)|~calm(john)))&
(?[X]:(~strong(X)))&
((~curious(alice)|tall(alice)))&
((humble(john)&~strong(john)))&
((calm(paul)&~generous(paul))) | ~funny(alice) | [
"p3",
"p8",
"p9",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3457863043656457829232680
% SZS output start Proof for 3457863043656457829232680
4. ! [X0] : ((~old(X0) & ~tall(X0)) <=> (~brave(X0) <~> brave(X0))) [input p3]
9. (old(susan) & quiet(susan)) <=> ? [X0] : (wise(X0) | ~rich(X0)) [input p8]
10. ! [X0] : (happy(X0) <=> (rich(X0) | strong(X0))) [input p9]
12. (~happy(lucy) & kind(lucy)) <=> ? [X0] : (~funny(X0) & ~curious(X0)) [input p11]
20. tall(alice) | ~curious(alice) [input p19]
23. ~funny(alice) [input hypothesis]
36. ! [X0] : (((~old(X0) & ~tall(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (old(X0) | tall(X0)))) [nnf transformation 4]
37. ! [X0] : (((~old(X0) & ~tall(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | old(X0) | tall(X0))) [flattening 36]
51. ((old(susan) & quiet(susan)) | ! [X0] : (~wise(X0) & rich(X0))) & (? [X0] : (wise(X0) | ~rich(X0)) | (~old(susan) | ~quiet(susan))) [nnf transformation 9]
52. ((old(susan) & quiet(susan)) | ! [X0] : (~wise(X0) & rich(X0))) & (? [X0] : (wise(X0) | ~rich(X0)) | ~old(susan) | ~quiet(susan)) [flattening 51]
53. ((old(susan) & quiet(susan)) | ! [X0] : (~wise(X0) & rich(X0))) & (? [X1] : (wise(X1) | ~rich(X1)) | ~old(susan) | ~quiet(susan)) [rectify 52]
54. ? [X1] : (wise(X1) | ~rich(X1)) => (wise(sK3) | ~rich(sK3)) [choice axiom]
55. ((old(susan) & quiet(susan)) | ! [X0] : (~wise(X0) & rich(X0))) & ((wise(sK3) | ~rich(sK3)) | ~old(susan) | ~quiet(susan)) [skolemisation 53,54]
56. ! [X0] : ((happy(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | ~happy(X0))) [nnf transformation 10]
57. ! [X0] : ((happy(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | ~happy(X0))) [flattening 56]
61. ((~happy(lucy) & kind(lucy)) | ! [X0] : (funny(X0) | curious(X0))) & (? [X0] : (~funny(X0) & ~curious(X0)) | (happy(lucy) | ~kind(lucy))) [nnf transformation 12]
62. ((~happy(lucy) & kind(lucy)) | ! [X0] : (funny(X0) | curious(X0))) & (? [X0] : (~funny(X0) & ~curious(X0)) | happy(lucy) | ~kind(lucy)) [flattening 61]
63. ((~happy(lucy) & kind(lucy)) | ! [X0] : (funny(X0) | curious(X0))) & (? [X1] : (~funny(X1) & ~curious(X1)) | happy(lucy) | ~kind(lucy)) [rectify 62]
64. ? [X1] : (~funny(X1) & ~curious(X1)) => (~funny(sK5) & ~curious(sK5)) [choice axiom]
65. ((~happy(lucy) & kind(lucy)) | ! [X0] : (funny(X0) | curious(X0))) & ((~funny(sK5) & ~curious(sK5)) | happy(lucy) | ~kind(lucy)) [skolemisation 63,64]
91. ~tall(X0) | brave(X0) | brave(X0) [cnf transformation 37]
92. ~tall(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
93. ~old(X0) | brave(X0) | brave(X0) [cnf transformation 37]
94. ~old(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
115. old(susan) | rich(X0) [cnf transformation 55]
119. happy(X0) | ~rich(X0) [cnf transformation 57]
125. ~happy(lucy) | funny(X0) | curious(X0) [cnf transformation 65]
143. tall(alice) | ~curious(alice) [cnf transformation 20]
148. ~funny(alice) [cnf transformation 23]
151. ~tall(X0) | brave(X0) [duplicate literal removal 91]
152. ~tall(X0) | ~brave(X0) [duplicate literal removal 92]
153. ~old(X0) | brave(X0) [duplicate literal removal 93]
154. ~brave(X0) | ~old(X0) [duplicate literal removal 94]
177. ~old(X0) [subsumption resolution 153,154]
178. ~tall(X0) [subsumption resolution 151,152]
248. rich(X0) [subsumption resolution 115,177]
249. happy(X0) [subsumption resolution 119,248]
264. funny(X0) | curious(X0) [subsumption resolution 125,249]
279. ~curious(alice) [subsumption resolution 143,178]
286. curious(alice) [resolution 264,148]
288. $false [subsumption resolution 286,279]
% SZS output end Proof for 3457863043656457829232680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not humble is kind.
If someone is quiet then alice is both creative and not old and vice versa.
Everyone who is either brave or not patient is old or wise.
Everyone who is patient is not strong or not brave and vice versa.
Everyone who is both wise and happy is not old or kind and vice versa.
Everyone who is either not old or not curious is not wise or not funny and vice versa.
If someone is either not strong or not funny then alice is not kind or humble and vice versa.
Everyone who is either not funny or not generous is both funny and brave.
If lucy is not curious or old then someone is brave or not brave and vice versa.
Everyone who is either not happy or tall is both kind and not funny and vice versa.
If mary is not calm then someone is either not patient or curious and vice versa.
Everyone who is rich or funny is not quiet or old and vice versa.
Everyone who is either wise or quiet is both humble and rich and vice versa.
If alice is calm or rich then fred is not humble or curious and vice versa.
Everyone who is generous or not happy is both tall and wise and vice versa.
Everyone who is both not rich and creative is creative or funny.
Someone is both not patient and happy.
Someone is both not humble and not tall.
Susan is happy.
Lucy is both not tall and not brave.
Someone is either humble or not quiet.
Alice is both humble and not generous.
Alice is rich.
Someone is not calm or not curious. | Lucy is not happy. | contradiction | (![X]:((~generous(X)&~humble(X))=>kind(X)))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
(![X]:((~rich(X)&creative(X))=>(creative(X)|funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((~humble(X)&~tall(X))))&
(happy(susan))&
((~tall(lucy)&~brave(lucy)))&
(?[X]:((humble(X)<~>~quiet(X))))&
((humble(alice)&~generous(alice)))&
(rich(alice))&
(?[X]:((~calm(X)|~curious(X)))) | ~happy(lucy) | [
"p4",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4259188105101443576522870
% SZS output start Proof for 4259188105101443576522870
5. ! [X0] : ((happy(X0) & wise(X0)) <=> (kind(X0) | ~old(X0))) [input p4]
10. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (~funny(X0) & kind(X0))) [input p9]
20. ~brave(lucy) & ~tall(lucy) [input p19]
25. ~happy(lucy) [input hypothesis]
41. ! [X0] : (((happy(X0) & wise(X0)) | (~kind(X0) & old(X0))) & ((kind(X0) | ~old(X0)) | (~happy(X0) | ~wise(X0)))) [nnf transformation 5]
42. ! [X0] : (((happy(X0) & wise(X0)) | (~kind(X0) & old(X0))) & (kind(X0) | ~old(X0) | ~happy(X0) | ~wise(X0))) [flattening 41]
56. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 10]
57. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 56]
92. ~kind(X0) | happy(X0) [cnf transformation 42]
113. kind(X0) | tall(X0) | happy(X0) [cnf transformation 57]
148. ~tall(lucy) [cnf transformation 20]
156. ~happy(lucy) [cnf transformation 25]
223. tall(X0) | happy(X0) [subsumption resolution 113,92]
293. happy(lucy) [resolution 223,148]
294. $false [subsumption resolution 293,156]
% SZS output end Proof for 4259188105101443576522870
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not humble is either funny or not rich and vice versa.
Everyone who is wise is either not wise or not strong and vice versa.
Everyone who is either not tall or not rich is both not generous and not patient and vice versa.
If fred is either not funny or humble then someone is both not patient and quiet and vice versa.
If mary is not patient then paul is both not old and old.
Everyone who is both quiet and not humble is both not generous and old.
Everyone who is both creative and not brave is humble or not wise.
If someone is patient then someone is not brave or calm and vice versa.
Everyone who is strong or old is either strong or not curious and vice versa.
If john is not brave or creative then paul is old.
Everyone who is wise or patient is quiet or curious and vice versa.
If mary is either generous or calm then susan is quiet or calm and vice versa.
Everyone who is either tall or old is both kind and wise.
If someone is either quiet or funny then lucy is not strong and vice versa.
Everyone who is quiet is curious or rich and vice versa.
Everyone who is either tall or rich is both not strong and not generous and vice versa.
Someone is not calm or quiet.
Someone is either curious or humble.
John is either not humble or old.
Fred is either happy or not kind.
Someone is not generous.
Someone is both not funny and not calm.
Someone is both calm and not curious.
Fred is not quiet. | John is not humble. | contradiction | (![X]:((~curious(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
(![X]:(wise(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~generous(X)&~patient(X))))&
(((~funny(fred)<~>humble(fred)))<=>(?[X]:((~patient(X)&quiet(X)))))&
((~patient(mary))=>((~old(paul)&old(paul))))&
(![X]:((quiet(X)&~humble(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)&~brave(X))=>(humble(X)|~wise(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:((strong(X)|old(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(john)|creative(john)))=>(old(paul)))&
(![X]:((wise(X)|patient(X))<=>(quiet(X)|curious(X))))&
(((generous(mary)<~>calm(mary)))<=>((quiet(susan)|calm(susan))))&
(![X]:((tall(X)<~>old(X))=>(kind(X)&wise(X))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(~strong(lucy)))&
(![X]:(quiet(X)<=>(curious(X)|rich(X))))&
(![X]:((tall(X)<~>rich(X))<=>(~strong(X)&~generous(X))))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((~humble(john)<~>old(john)))&
((happy(fred)<~>~kind(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((calm(X)&~curious(X))))&
(~quiet(fred)) | ~humble(john) | [
"p1",
"p5",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3294719304664155984194841
% SZS output start Proof for 3294719304664155984194841
2. ! [X0] : (wise(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p1]
6. ! [X0] : ((~humble(X0) & quiet(X0)) => (old(X0) & ~generous(X0))) [input p5]
9. ! [X0] : ((old(X0) | strong(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p8]
15. ! [X0] : (quiet(X0) <=> (rich(X0) | curious(X0))) [input p14]
19. ~humble(john) <~> old(john) [input p18]
25. ~humble(john) [input hypothesis]
30. ! [X0] : ((old(X0) & ~generous(X0)) | (humble(X0) | ~quiet(X0))) [ennf transformation 6]
31. ! [X0] : ((old(X0) & ~generous(X0)) | humble(X0) | ~quiet(X0)) [flattening 30]
35. ! [X0] : ((wise(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~wise(X0))) [nnf transformation 2]
47. ! [X0] : (((old(X0) | strong(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (~old(X0) & ~strong(X0)))) [nnf transformation 9]
48. ! [X0] : ((old(X0) | strong(X0) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (~old(X0) & ~strong(X0)))) [flattening 47]
58. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 15]
59. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~quiet(X0))) [flattening 58]
67. (~old(john) | humble(john)) & (old(john) | ~humble(john)) [nnf transformation 19]
83. ~strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 35]
85. wise(X0) | ~strong(X0) | wise(X0) [cnf transformation 35]
102. ~quiet(X0) | humble(X0) | old(X0) [cnf transformation 31]
111. old(X0) | strong(X0) | strong(X0) | curious(X0) [cnf transformation 48]
132. ~curious(X0) | quiet(X0) [cnf transformation 59]
144. ~old(john) | humble(john) [cnf transformation 67]
153. ~humble(john) [cnf transformation 25]
155. old(X0) | strong(X0) | curious(X0) [duplicate literal removal 111]
156. ~strong(X0) | ~wise(X0) [duplicate literal removal 83]
157. ~strong(X0) | wise(X0) [duplicate literal removal 85]
158. ~strong(X0) [subsumption resolution 156,157]
218. old(X0) | curious(X0) [subsumption resolution 155,158]
281. 25 <=> humble(john) [avatar definition]
282. ~humble(john) <- (~25) [avatar component clause 281]
285. 26 <=> old(john) [avatar definition]
287. ~old(john) <- (~26) [avatar component clause 285]
288. 25 | ~26 [avatar split clause 144,285,281]
300. ~25 [avatar split clause 153,281]
302. curious(john) <- (~26) [resolution 218,287]
305. quiet(john) <- (~26) [resolution 302,132]
356. humble(john) | old(john) <- (~26) [resolution 102,305]
360. old(john) <- (~25, ~26) [subsumption resolution 356,282]
361. $false <- (~25, ~26) [subsumption resolution 360,287]
362. 25 | 26 [avatar contradiction clause 361]
374. $false [avatar sat refutation 288,300,362]
% SZS output end Proof for 3294719304664155984194841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not kind and not funny and vice versa. Everyone who is both not old and not quiet is either not tall or funny. If someone is tall or not curious then mary is not humble. Everyone who is calm or not brave is not funny and vice versa. Everyone who is quiet is curious and vice versa. If someone is not strong or humble then someone is both not happy and not quiet and vice versa. Everyone who is strong or not wise is either quiet or not generous. Everyone who is creative or not calm is either old or not old. Everyone who is humble is both not strong and not humble and vice versa. Everyone who is both old and strong is both funny and brave and vice versa. If someone is either wise or not rich then someone is both generous and not creative. Everyone who is not happy is not brave. If someone is either not creative or patient then someone is not humble and vice versa. If lucy is either not funny or wise then susan is either not patient or strong. If alice is not curious then susan is not creative or not humble. If someone is quiet or not tall then mary is calm. Someone is either not calm or not happy. Alice is either old or not funny. Susan is not happy or calm. Mary is either quiet or not calm. Someone is patient. Someone is not quiet or strong. Someone is both tall and strong. Someone is funny. | Susan is funny. | contradiction | (![X]:(~old(X)<=>(~kind(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))=>(~tall(X)<~>funny(X))))&
((?[X]:((tall(X)|~curious(X))))=>(~humble(mary)))&
(![X]:((calm(X)|~brave(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>curious(X)))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((strong(X)|~wise(X))=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)|~calm(X))=>(old(X)<~>~old(X))))&
(![X]:(humble(X)<=>(~strong(X)&~humble(X))))&
(![X]:((old(X)&strong(X))<=>(funny(X)&brave(X))))&
((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:(~happy(X)=>~brave(X)))&
((?[X]:((~creative(X)<~>patient(X))))<=>(?[X]:(~humble(X))))&
(((~funny(lucy)<~>wise(lucy)))=>((~patient(susan)<~>strong(susan))))&
((~curious(alice))=>((~creative(susan)|~humble(susan))))&
((?[X]:((quiet(X)|~tall(X))))=>(calm(mary)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((old(alice)<~>~funny(alice)))&
((~happy(susan)|calm(susan)))&
((quiet(mary)<~>~calm(mary)))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:(funny(X))) | funny(susan) | [
"p3",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7784127115170201627582698
% SZS output start Proof for 7784127115170201627582698
4. ! [X0] : ((~brave(X0) | calm(X0)) <=> ~funny(X0)) [input p3]
12. ! [X0] : (~happy(X0) => ~brave(X0)) [input p11]
19. calm(susan) | ~happy(susan) [input p18]
25. funny(susan) [input hypothesis]
35. ! [X0] : (~brave(X0) | happy(X0)) [ennf transformation 12]
43. ! [X0] : (((~brave(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (brave(X0) & ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : ((~brave(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (brave(X0) & ~calm(X0)))) [flattening 43]
87. ~calm(X0) | ~funny(X0) [cnf transformation 44]
88. ~funny(X0) | brave(X0) [cnf transformation 44]
116. ~brave(X0) | happy(X0) [cnf transformation 35]
132. calm(susan) | ~happy(susan) [cnf transformation 19]
140. funny(susan) [cnf transformation 25]
296. 35 <=> happy(susan) [avatar definition]
300. 36 <=> calm(susan) [avatar definition]
302. calm(susan) <- (36) [avatar component clause 300]
303. ~35 | 36 [avatar split clause 132,300,296]
323. brave(susan) [resolution 88,140]
326. happy(susan) [resolution 116,323]
329. 35 [avatar split clause 326,296]
330. ~funny(susan) <- (36) [resolution 302,87]
331. $false <- (36) [subsumption resolution 330,140]
332. ~36 [avatar contradiction clause 331]
333. $false [avatar sat refutation 303,329,332]
% SZS output end Proof for 7784127115170201627582698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or old then paul is both not strong and not generous and vice versa. Everyone who is both funny and patient is either strong or not wise and vice versa. If someone is not rich then john is creative or not calm and vice versa. If fred is calm then fred is brave. If paul is not patient or not funny then fred is happy and vice versa. If someone is creative or funny then susan is either wise or not brave. If someone is not creative then mary is both not funny and wise and vice versa. If someone is patient then mary is not brave. Everyone who is both calm and not quiet is both not curious and brave. If someone is either strong or kind then someone is both not happy and not curious and vice versa. Everyone who is curious or not brave is either not calm or tall and vice versa. If someone is either not creative or not calm then someone is either quiet or not curious and vice versa. If someone is rich then someone is strong and vice versa. If susan is patient then someone is curious or not curious and vice versa. If susan is either brave or not wise then john is not kind and vice versa. Everyone who is not quiet is not rich. Fred is either not kind or generous. John is not kind or not humble. Mary is patient. Paul is both kind and happy. Someone is either not funny or generous. John is either not humble or not curious. Someone is brave or not wise. Mary is either not rich or not brave. | Mary is brave. | contradiction | ((?[X]:((funny(X)|old(X))))<=>((~strong(paul)&~generous(paul))))&
(![X]:((funny(X)&patient(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:(~rich(X)))<=>((creative(john)|~calm(john))))&
((calm(fred))=>(brave(fred)))&
(((~patient(paul)|~funny(paul)))<=>(happy(fred)))&
((?[X]:((creative(X)|funny(X))))=>((wise(susan)<~>~brave(susan))))&
((?[X]:(~creative(X)))<=>((~funny(mary)&wise(mary))))&
((?[X]:(patient(X)))=>(~brave(mary)))&
(![X]:((calm(X)&~quiet(X))=>(~curious(X)&brave(X))))&
((?[X]:((strong(X)<~>kind(X))))<=>(?[X]:((~happy(X)&~curious(X)))))&
(![X]:((curious(X)|~brave(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:(rich(X)))<=>(?[X]:(strong(X))))&
((patient(susan))<=>(?[X]:((curious(X)|~curious(X)))))&
(((brave(susan)<~>~wise(susan)))<=>(~kind(john)))&
(![X]:(~quiet(X)=>~rich(X)))&
((~kind(fred)<~>generous(fred)))&
((~kind(john)|~humble(john)))&
(patient(mary))&
((kind(paul)&happy(paul)))&
(?[X]:((~funny(X)<~>generous(X))))&
((~humble(john)<~>~curious(john)))&
(?[X]:((brave(X)|~wise(X))))&
((~rich(mary)<~>~brave(mary))) | brave(mary) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9146924945923462664174160
% SZS output start Proof for 9146924945923462664174160
8. ? [X0] : patient(X0) => ~brave(mary) [input p7]
19. patient(mary) [input p18]
25. brave(mary) [input hypothesis]
31. ~brave(mary) | ! [X0] : ~patient(X0) [ennf transformation 8]
110. ~brave(mary) | ~patient(X0) [cnf transformation 31]
146. patient(mary) [cnf transformation 19]
156. brave(mary) [cnf transformation 25]
260. 23 <=> ! [X0] : ~patient(X0) [avatar definition]
261. ~patient(X0) <- (23) [avatar component clause 260]
263. 24 <=> brave(mary) [avatar definition]
266. 23 | ~24 [avatar split clause 110,263,260]
416. 24 [avatar split clause 156,263]
417. $false <- (23) [resolution 261,146]
418. ~23 [avatar contradiction clause 417]
419. $false [avatar sat refutation 266,416,418]
% SZS output end Proof for 9146924945923462664174160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or tall is both not tall and not kind.
If alice is not brave or old then john is both not creative and not funny.
If someone is not tall then someone is both old and rich.
If someone is both not old and not wise then lucy is both not tall and not calm and vice versa.
If john is either kind or not calm then susan is both not quiet and not creative.
Everyone who is not generous is not calm.
Everyone who is either not strong or strong is not kind and vice versa.
Everyone who is either brave or not funny is brave and vice versa.
If someone is not funny then someone is not calm.
If someone is either not curious or generous then paul is curious.
Everyone who is not wise or not creative is both not quiet and not happy and vice versa.
If lucy is both not funny and rich then someone is kind or not strong.
Everyone who is both not wise and curious is either kind or curious.
If alice is both patient and not tall then someone is either funny or not funny.
If someone is both funny and kind then mary is both not funny and not curious and vice versa.
If mary is either creative or not tall then mary is both quiet and not generous.
Someone is not quiet.
Fred is either old or calm.
Alice is both happy and not tall.
Alice is quiet.
Lucy is either not strong or not funny.
Susan is both not strong and happy.
Mary is both not patient and not kind. | Alice is funny. | entailment | (![X]:((~kind(X)<~>tall(X))=>(~tall(X)&~kind(X))))&
(((~brave(alice)|old(alice)))=>((~creative(john)&~funny(john))))&
((?[X]:(~tall(X)))=>(?[X]:((old(X)&rich(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>((~tall(lucy)&~calm(lucy))))&
(((kind(john)<~>~calm(john)))=>((~quiet(susan)&~creative(susan))))&
(![X]:(~generous(X)=>~calm(X)))&
(![X]:((~strong(X)<~>strong(X))<=>~kind(X)))&
(![X]:((brave(X)<~>~funny(X))<=>brave(X)))&
((?[X]:(~funny(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))=>(curious(paul)))&
(![X]:((~wise(X)|~creative(X))<=>(~quiet(X)&~happy(X))))&
(((~funny(lucy)&rich(lucy)))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(kind(X)<~>curious(X))))&
(((patient(alice)&~tall(alice)))=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((funny(X)&kind(X))))<=>((~funny(mary)&~curious(mary))))&
(((creative(mary)<~>~tall(mary)))=>((quiet(mary)&~generous(mary))))&
(?[X]:(~quiet(X)))&
((old(fred)<~>calm(fred)))&
((happy(alice)&~tall(alice)))&
(quiet(alice))&
((~strong(lucy)<~>~funny(lucy)))&
((~strong(susan)&happy(susan)))&
((~patient(mary)&~kind(mary))) | funny(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2851143726305425828191801
% SZS output start Proof for 2851143726305425828191801
8. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> brave(X0)) [input p7]
24. ~funny(alice) [input hypothesis]
52. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ~brave(X0)) & (brave(X0) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 8]
96. brave(X0) | brave(X0) | funny(X0) [cnf transformation 52]
98. funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
129. ~funny(alice) [cnf transformation 24]
131. brave(X0) | funny(X0) [duplicate literal removal 96]
132. funny(X0) | ~brave(X0) [duplicate literal removal 98]
214. funny(X0) [subsumption resolution 131,132]
259. $false [subsumption resolution 129,214]
% SZS output end Proof for 2851143726305425828191801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient is either patient or tall.
Everyone who is either creative or not brave is both wise and not humble and vice versa.
If someone is not quiet then someone is either not strong or generous.
If someone is either not humble or funny then mary is not strong or tall and vice versa.
Everyone who is funny or creative is both not strong and tall.
Everyone who is not brave or not patient is not funny.
Everyone who is happy or not tall is either not generous or generous and vice versa.
Everyone who is happy or brave is rich and vice versa.
Everyone who is curious or kind is both not old and not curious.
If paul is either strong or humble then lucy is not rich or curious.
If paul is generous or not kind then susan is creative and vice versa.
If someone is calm or kind then someone is patient or old and vice versa.
Everyone who is quiet or not funny is either not calm or curious.
If alice is both curious and not old then someone is not strong or happy and vice versa.
Everyone who is rich is not quiet or funny.
Someone is not creative.
Lucy is old or rich.
Someone is either not curious or wise.
Susan is not quiet.
Someone is either patient or not strong. | Susan is not rich. | contradiction | (![X]:(~patient(X)=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(wise(X)&~humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((~strong(mary)|tall(mary))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(((curious(alice)&~old(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
(?[X]:(~creative(X)))&
((old(lucy)|rich(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~quiet(susan))&
(?[X]:((patient(X)<~>~strong(X)))) | ~rich(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3036073842848329730824887
% SZS output start Proof for 3036073842848329730824887
2. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (~humble(X0) & wise(X0))) [input p1]
4. ? [X0] : (~humble(X0) <~> funny(X0)) <=> (tall(mary) | ~strong(mary)) [input p3]
5. ! [X0] : ((creative(X0) | funny(X0)) => (tall(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~brave(X0)) => ~funny(X0)) [input p5]
7. ! [X0] : ((~tall(X0) | happy(X0)) <=> (~generous(X0) <~> generous(X0))) [input p6]
8. ! [X0] : ((brave(X0) | happy(X0)) <=> rich(X0)) [input p7]
9. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p8]
14. (~old(alice) & curious(alice)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p13]
21. ~rich(susan) [input hypothesis]
26. ! [X0] : ((tall(X0) & ~strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 5]
27. ! [X0] : (~funny(X0) | (patient(X0) & brave(X0))) [ennf transformation 6]
28. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 9]
35. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 2]
36. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [flattening 35]
41. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & ((tall(mary) | ~strong(mary)) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 4]
42. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [flattening 41]
43. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [rectify 42]
44. ? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) => ((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) [choice axiom]
45. (((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [skolemisation 43,44]
46. ! [X0] : (((~tall(X0) | happy(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [nnf transformation 7]
47. ! [X0] : ((~tall(X0) | happy(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [flattening 46]
48. ! [X0] : (((brave(X0) | happy(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((brave(X0) | happy(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~happy(X0)))) [flattening 48]
59. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | (old(alice) | ~curious(alice))) [nnf transformation 14]
60. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | old(alice) | ~curious(alice)) [flattening 59]
61. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X1] : (happy(X1) | ~strong(X1)) | old(alice) | ~curious(alice)) [rectify 60]
62. ? [X1] : (happy(X1) | ~strong(X1)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
63. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & ((happy(sK4) | ~strong(sK4)) | old(alice) | ~curious(alice)) [skolemisation 61,62]
77. ~humble(X0) | creative(X0) | brave(X0) [cnf transformation 36]
82. tall(mary) | ~strong(mary) | funny(X1) | humble(X1) [cnf transformation 45]
89. ~strong(X0) | ~creative(X0) [cnf transformation 26]
92. ~funny(X0) | brave(X0) [cnf transformation 27]
98. ~tall(X0) | happy(X0) | generous(X0) | generous(X0) [cnf transformation 47]
99. ~tall(X0) | happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 47]
101. ~brave(X0) | rich(X0) [cnf transformation 49]
105. ~curious(X0) | ~curious(X0) [cnf transformation 28]
121. curious(alice) | strong(X0) [cnf transformation 63]
122. curious(alice) | ~happy(X0) [cnf transformation 63]
133. ~rich(susan) [cnf transformation 21]
134. ~curious(X0) [duplicate literal removal 105]
135. ~tall(X0) | happy(X0) | generous(X0) [duplicate literal removal 98]
136. ~generous(X0) | happy(X0) | ~tall(X0) [duplicate literal removal 99]
152. 4 <=> tall(mary) [avatar definition]
153. tall(mary) <- (4) [avatar component clause 152]
165. 7 <=> strong(mary) [avatar definition]
166. ~strong(mary) <- (~7) [avatar component clause 165]
176. 9 <=> ! [X1] : (funny(X1) | humble(X1)) [avatar definition]
177. funny(X1) | humble(X1) <- (9) [avatar component clause 176]
178. 9 | ~7 | 4 [avatar split clause 82,152,165,176]
179. ~tall(X0) | happy(X0) [subsumption resolution 135,136]
246. 24 <=> ! [X0] : ~happy(X0) [avatar definition]
247. ~happy(X0) <- (24) [avatar component clause 246]
254. 26 <=> ! [X0] : strong(X0) [avatar definition]
255. strong(X0) <- (26) [avatar component clause 254]
257. ~happy(X0) [subsumption resolution 122,134]
258. 24 [avatar split clause 257,246]
259. strong(X0) [subsumption resolution 121,134]
260. 26 [avatar split clause 259,254]
279. $false <- (~7, 26) [subsumption resolution 166,255]
280. 7 | ~26 [avatar contradiction clause 279]
285. ~creative(X0) <- (26) [resolution 89,255]
289. happy(mary) <- (4) [resolution 179,153]
291. $false <- (4, 24) [subsumption resolution 289,247]
292. ~4 | ~24 [avatar contradiction clause 291]
298. humble(X2) | brave(X2) <- (9) [resolution 177,92]
332. creative(X0) | brave(X0) | brave(X0) <- (9) [resolution 77,298]
334. creative(X0) | brave(X0) <- (9) [duplicate literal removal 332]
336. brave(X0) <- (9, 26) [subsumption resolution 334,285]
342. rich(X1) <- (9, 26) [resolution 336,101]
377. $false <- (9, 26) [resolution 342,133]
380. ~9 | ~26 [avatar contradiction clause 377]
381. $false [avatar sat refutation 178,258,260,280,292,380]
% SZS output end Proof for 3036073842848329730824887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not quiet or not old then someone is not generous or strong and vice versa. Everyone who is either not wise or tall is either not funny or patient and vice versa. If john is both not humble and not curious then john is brave. Everyone who is strong is both funny and wise and vice versa. If someone is brave or creative then someone is either not calm or strong. Everyone who is not strong or not creative is old. If mary is both wise and tall then someone is not quiet or not curious and vice versa. Everyone who is brave or strong is not happy or not tall. If lucy is old or brave then lucy is not kind. Everyone who is both not curious and not creative is either not patient or not brave and vice versa. If someone is not curious then someone is either brave or not wise and vice versa. Everyone who is not generous is either not old or tall. Everyone who is not strong is not funny or not rich and vice versa. If someone is not happy or rich then fred is either humble or not strong. Everyone who is both not wise and old is generous or brave and vice versa. Everyone who is not quiet is not kind. Lucy is either not calm or not generous. Susan is tall. Someone is patient. Someone is calm or not calm. Someone is not funny or not generous. Someone is either generous or not funny. Someone is either not wise or patient. Alice is either not curious or not brave. | Mary is old. | entailment | (((~quiet(mary)|~old(mary)))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((~wise(X)<~>tall(X))<=>(~funny(X)<~>patient(X))))&
(((~humble(john)&~curious(john)))=>(brave(john)))&
(![X]:(strong(X)<=>(funny(X)&wise(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~strong(X)|~creative(X))=>old(X)))&
(((wise(mary)&tall(mary)))<=>(?[X]:((~quiet(X)|~curious(X)))))&
(![X]:((brave(X)|strong(X))=>(~happy(X)|~tall(X))))&
(((old(lucy)|brave(lucy)))=>(~kind(lucy)))&
(![X]:((~curious(X)&~creative(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(~funny(X)|~rich(X))))&
((?[X]:((~happy(X)|rich(X))))=>((humble(fred)<~>~strong(fred))))&
(![X]:((~wise(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
((~calm(lucy)<~>~generous(lucy)))&
(tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
((~curious(alice)<~>~brave(alice))) | old(mary) | [
"p3",
"p5",
"p6",
"p9",
"p10",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 237495476755508270799330
% SZS output start Proof for 237495476755508270799330
4. ! [X0] : (strong(X0) <=> (wise(X0) & funny(X0))) [input p3]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) => old(X0)) [input p5]
7. (tall(mary) & wise(mary)) <=> ? [X0] : (~curious(X0) | ~quiet(X0)) [input p6]
10. ! [X0] : ((~creative(X0) & ~curious(X0)) <=> (~patient(X0) <~> ~brave(X0))) [input p9]
11. ? [X0] : ~curious(X0) <=> ? [X0] : (brave(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : (~generous(X0) => (~old(X0) <~> tall(X0))) [input p11]
15. ! [X0] : ((old(X0) & ~wise(X0)) <=> (brave(X0) | generous(X0))) [input p14]
23. ? [X0] : (~wise(X0) <~> patient(X0)) [input p22]
25. ~old(mary) [input hypothesis]
27. ? [X0] : ~curious(X0) <=> ? [X1] : (brave(X1) <~> ~wise(X1)) [rectify 11]
33. ! [X0] : (old(X0) | (creative(X0) & strong(X0))) [ennf transformation 6]
36. ! [X0] : ((~old(X0) <~> tall(X0)) | generous(X0)) [ennf transformation 12]
44. ! [X0] : ((strong(X0) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | ~strong(X0))) [nnf transformation 4]
45. ! [X0] : ((strong(X0) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | ~strong(X0))) [flattening 44]
50. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | (~tall(mary) | ~wise(mary))) [nnf transformation 7]
51. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | ~tall(mary) | ~wise(mary)) [flattening 50]
52. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X1] : (~curious(X1) | ~quiet(X1)) | ~tall(mary) | ~wise(mary)) [rectify 51]
53. ? [X1] : (~curious(X1) | ~quiet(X1)) => (~curious(sK2) | ~quiet(sK2)) [choice axiom]
54. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & ((~curious(sK2) | ~quiet(sK2)) | ~tall(mary) | ~wise(mary)) [skolemisation 52,53]
55. ! [X0] : (((~creative(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (creative(X0) | curious(X0)))) [nnf transformation 10]
56. ! [X0] : (((~creative(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | creative(X0) | curious(X0))) [flattening 55]
57. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X1] : ((wise(X1) | ~brave(X1)) & (~wise(X1) | brave(X1))) | ! [X0] : curious(X0)) [nnf transformation 27]
58. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) | ! [X3] : curious(X3)) [rectify 57]
59. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
60. ? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) => ((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) [choice axiom]
61. (~curious(sK3) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) | ! [X3] : curious(X3)) [skolemisation 58,60,59]
62. ! [X0] : (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | generous(X0)) [nnf transformation 36]
66. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 15]
67. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | wise(X0))) [flattening 66]
78. ? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) [nnf transformation 23]
79. ? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) => ((~patient(sK9) | wise(sK9)) & (patient(sK9) | ~wise(sK9))) [choice axiom]
80. (~patient(sK9) | wise(sK9)) & (patient(sK9) | ~wise(sK9)) [skolemisation 78,79]
96. ~strong(X0) | wise(X0) [cnf transformation 45]
102. strong(X0) | old(X0) [cnf transformation 33]
108. tall(mary) | curious(X0) [cnf transformation 54]
113. ~brave(X0) | ~curious(X0) | patient(X0) [cnf transformation 56]
114. ~curious(X0) | ~patient(X0) | brave(X0) [cnf transformation 56]
120. ~curious(sK3) | brave(X1) | wise(X1) [cnf transformation 61]
122. ~tall(X0) | old(X0) | generous(X0) [cnf transformation 62]
131. ~wise(X0) | ~generous(X0) [cnf transformation 67]
132. ~wise(X0) | ~brave(X0) [cnf transformation 67]
143. patient(sK9) | ~wise(sK9) [cnf transformation 80]
144. ~patient(sK9) | wise(sK9) [cnf transformation 80]
147. ~old(mary) [cnf transformation 25]
156. 3 <=> old(mary) [avatar definition]
158. ~old(mary) <- (~3) [avatar component clause 156]
206. 14 <=> ! [X0] : curious(X0) [avatar definition]
207. curious(X0) <- (14) [avatar component clause 206]
209. 15 <=> tall(mary) [avatar definition]
211. tall(mary) <- (15) [avatar component clause 209]
212. 14 | 15 [avatar split clause 108,209,206]
218. 17 <=> wise(mary) [avatar definition]
219. ~wise(mary) <- (~17) [avatar component clause 218]
220. wise(mary) <- (17) [avatar component clause 218]
233. 20 <=> ! [X1] : (brave(X1) | wise(X1)) [avatar definition]
234. brave(X1) | wise(X1) <- (20) [avatar component clause 233]
236. 21 <=> curious(sK3) [avatar definition]
238. ~curious(sK3) <- (~21) [avatar component clause 236]
239. 20 | ~21 [avatar split clause 120,236,233]
241. 22 <=> ! [X1] : (~wise(X1) | ~brave(X1)) [avatar definition]
242. ~brave(X1) | ~wise(X1) <- (22) [avatar component clause 241]
272. 22 [avatar split clause 132,241]
303. 35 <=> wise(sK9) [avatar definition]
304. ~wise(sK9) <- (~35) [avatar component clause 303]
305. wise(sK9) <- (35) [avatar component clause 303]
307. 36 <=> patient(sK9) [avatar definition]
308. patient(sK9) <- (36) [avatar component clause 307]
309. ~patient(sK9) <- (~36) [avatar component clause 307]
310. 35 | ~36 [avatar split clause 144,307,303]
311. ~35 | 36 [avatar split clause 143,307,303]
322. ~3 [avatar split clause 147,156]
323. $false <- (14, ~21) [resolution 238,207]
324. ~14 | 21 [avatar contradiction clause 323]
327. wise(X0) | old(X0) [resolution 102,96]
330. ~generous(mary) <- (17) [resolution 131,220]
386. ~patient(X0) | brave(X0) <- (14) [resolution 207,114]
401. wise(X0) | ~curious(X0) | patient(X0) <- (20) [resolution 234,113]
404. patient(X0) | wise(X0) <- (14, 20) [subsumption resolution 401,207]
408. old(mary) | generous(mary) <- (15) [resolution 122,211]
410. generous(mary) <- (~3, 15) [subsumption resolution 408,158]
411. $false <- (~3, 15, 17) [subsumption resolution 410,330]
412. 3 | ~15 | ~17 [avatar contradiction clause 411]
413. old(mary) <- (~17) [resolution 219,327]
414. $false <- (~3, ~17) [subsumption resolution 413,158]
415. 3 | 17 [avatar contradiction clause 414]
602. wise(sK9) <- (14, 20, ~36) [resolution 309,404]
603. $false <- (14, 20, ~35, ~36) [subsumption resolution 602,304]
604. ~14 | ~20 | 35 | 36 [avatar contradiction clause 603]
607. brave(sK9) <- (14, 36) [resolution 308,386]
626. ~wise(sK9) <- (14, 22, 36) [resolution 607,242]
628. $false <- (14, 22, 35, 36) [subsumption resolution 626,305]
629. ~14 | ~22 | ~35 | ~36 [avatar contradiction clause 628]
630. $false [avatar sat refutation 212,239,272,310,311,322,324,412,415,604,629]
% SZS output end Proof for 237495476755508270799330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not generous then someone is not strong or not brave. If fred is either not rich or not patient then someone is kind. If someone is not calm then alice is both not kind and not generous. If john is either strong or not happy then mary is both not wise and not curious and vice versa. Everyone who is curious or strong is either not brave or not old. Everyone who is not brave is either kind or happy and vice versa. If someone is happy then susan is both not quiet and not rich and vice versa. Everyone who is both not happy and brave is either wise or strong and vice versa. Everyone who is either not funny or not generous is quiet and vice versa. If alice is both curious and calm then paul is either patient or not quiet. Everyone who is calm is either not old or rich. Everyone who is not curious or rich is either not rich or tall. Everyone who is not wise or not patient is either kind or humble and vice versa. Everyone who is happy is either not curious or not old and vice versa. Everyone who is both not humble and happy is humble or curious and vice versa. Everyone who is not wise is not curious. Someone is not generous. Susan is not quiet. Lucy is both not patient and wise. Someone is not wise. Someone is rich. Someone is not brave. Mary is either not humble or strong. | Alice is not happy. | entailment | ((~generous(john))=>(?[X]:((~strong(X)|~brave(X)))))&
(((~rich(fred)<~>~patient(fred)))=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))=>((~kind(alice)&~generous(alice))))&
(((strong(john)<~>~happy(john)))<=>((~wise(mary)&~curious(mary))))&
(![X]:((curious(X)|strong(X))=>(~brave(X)<~>~old(X))))&
(![X]:(~brave(X)<=>(kind(X)<~>happy(X))))&
((?[X]:(happy(X)))<=>((~quiet(susan)&~rich(susan))))&
(![X]:((~happy(X)&brave(X))<=>(wise(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>quiet(X)))&
(((curious(alice)&calm(alice)))=>((patient(paul)<~>~quiet(paul))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(?[X]:(~generous(X)))&
(~quiet(susan))&
((~patient(lucy)&wise(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:(rich(X)))&
(?[X]:(~brave(X)))&
((~humble(mary)<~>strong(mary))) | ~happy(alice) | [
"p2",
"p4",
"p5",
"p7",
"p10",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4972737190399682240509636
% SZS output start Proof for 4972737190399682240509636
3. ? [X0] : ~calm(X0) => (~generous(alice) & ~kind(alice)) [input p2]
5. ! [X0] : ((strong(X0) | curious(X0)) => (~brave(X0) <~> ~old(X0))) [input p4]
6. ! [X0] : (~brave(X0) <=> (kind(X0) <~> happy(X0))) [input p5]
8. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (wise(X0) <~> strong(X0))) [input p7]
11. ! [X0] : (calm(X0) => (~old(X0) <~> rich(X0))) [input p10]
14. ! [X0] : (happy(X0) <=> (~curious(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p14]
16. ! [X0] : (~wise(X0) => ~curious(X0)) [input p15]
21. ? [X0] : rich(X0) [input p20]
24. happy(alice) [input hypothesis]
27. (~generous(alice) & ~kind(alice)) | ! [X0] : calm(X0) [ennf transformation 3]
28. ! [X0] : ((~brave(X0) <~> ~old(X0)) | (~strong(X0) & ~curious(X0))) [ennf transformation 5]
31. ! [X0] : ((~old(X0) <~> rich(X0)) | ~calm(X0)) [ennf transformation 11]
33. ! [X0] : (~curious(X0) | wise(X0)) [ennf transformation 16]
41. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (~strong(X0) & ~curious(X0))) [nnf transformation 28]
42. ! [X0] : ((~brave(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | brave(X0))) [nnf transformation 6]
48. ! [X0] : (((brave(X0) & ~happy(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) & (((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 8]
49. ! [X0] : (((brave(X0) & ~happy(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) & (((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | ~brave(X0) | happy(X0))) [flattening 48]
52. ! [X0] : (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | ~calm(X0)) [nnf transformation 31]
56. ! [X0] : ((happy(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 14]
57. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
58. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 57]
63. ? [X0] : rich(X0) => rich(sK5) [choice axiom]
64. rich(sK5) [skolemisation 21,63]
71. ~kind(alice) | calm(X0) [cnf transformation 27]
82. ~strong(X0) | brave(X0) | old(X0) [cnf transformation 41]
86. ~happy(X0) | kind(X0) | ~brave(X0) [cnf transformation 42]
92. ~wise(X0) | strong(X0) | ~happy(X0) [cnf transformation 49]
103. ~calm(X0) | old(X0) | ~rich(X0) [cnf transformation 52]
114. ~old(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 56]
116. ~old(X0) | happy(X0) | curious(X0) [cnf transformation 56]
118. curious(X0) | humble(X0) | ~happy(X0) | humble(X0) [cnf transformation 58]
119. ~humble(X0) | ~humble(X0) [cnf transformation 58]
122. ~curious(X0) | happy(X0) [cnf transformation 58]
123. ~curious(X0) | wise(X0) [cnf transformation 33]
129. rich(sK5) [cnf transformation 64]
133. happy(alice) [cnf transformation 24]
134. curious(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 118]
135. ~humble(X0) [duplicate literal removal 119]
165. 7 <=> ! [X0] : calm(X0) [avatar definition]
166. calm(X0) <- (7) [avatar component clause 165]
173. 9 <=> kind(alice) [avatar definition]
176. 7 | ~9 [avatar split clause 71,173,165]
218. 18 <=> curious(alice) [avatar definition]
219. curious(alice) <- (18) [avatar component clause 218]
235. ~happy(X0) | curious(X0) [subsumption resolution 134,135]
239. curious(alice) [resolution 235,133]
243. 18 [avatar split clause 239,218]
244. wise(alice) <- (18) [resolution 219,123]
251. 22 <=> old(alice) [avatar definition]
253. old(alice) <- (22) [avatar component clause 251]
255. 23 <=> brave(alice) [avatar definition]
257. brave(alice) <- (23) [avatar component clause 255]
275. 26 <=> strong(alice) [avatar definition]
276. strong(alice) <- (26) [avatar component clause 275]
317. kind(alice) | ~brave(alice) [resolution 86,133]
328. strong(alice) | ~happy(alice) <- (18) [resolution 92,244]
339. strong(alice) <- (18) [subsumption resolution 328,133]
340. 26 | ~18 [avatar split clause 339,218,275]
387. brave(alice) | old(alice) <- (26) [resolution 276,82]
415. ~curious(alice) | ~happy(alice) <- (22) [resolution 114,253]
417. ~happy(alice) <- (18, 22) [subsumption resolution 415,219]
418. $false <- (18, 22) [subsumption resolution 417,133]
419. ~18 | ~22 [avatar contradiction clause 418]
423. 22 | 23 | ~26 [avatar split clause 387,275,255,251]
429. kind(alice) <- (23) [subsumption resolution 317,257]
430. 9 | ~23 [avatar split clause 429,255,173]
432. ~rich(X0) | old(X0) <- (7) [resolution 166,103]
498. old(sK5) <- (7) [resolution 432,129]
515. happy(sK5) | curious(sK5) <- (7) [resolution 498,116]
516. ~curious(sK5) | ~happy(sK5) <- (7) [resolution 498,114]
520. curious(sK5) <- (7) [subsumption resolution 515,235]
521. ~happy(sK5) <- (7) [subsumption resolution 516,520]
627. happy(sK5) <- (7) [resolution 520,122]
628. $false <- (7) [subsumption resolution 627,521]
629. ~7 [avatar contradiction clause 628]
630. $false [avatar sat refutation 176,243,340,419,423,430,629]
% SZS output end Proof for 4972737190399682240509636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and quiet is both not tall and curious. Everyone who is rich or tall is not brave. Everyone who is generous is old and vice versa. Everyone who is not brave is not old or not happy. If someone is both not funny and old then someone is not curious. Everyone who is rich is either humble or wise. Everyone who is patient is not calm or humble and vice versa. If lucy is both creative and not creative then someone is both brave and not tall and vice versa. Everyone who is generous or not tall is both brave and not calm. Everyone who is both not happy and tall is not generous or humble and vice versa. If lucy is not creative then susan is curious. If mary is either not humble or not creative then someone is humble and vice versa. If someone is not funny or old then someone is either humble or not old. If someone is either humble or funny then mary is both not happy and not generous. Susan is not tall or wise. Someone is either not tall or not creative. Someone is not creative. Mary is not old or not curious. Susan is humble or rich. Paul is not humble. Alice is either strong or curious. Susan is both not humble and wise. | Susan is not quiet. | entailment | (![X]:((~happy(X)&quiet(X))=>(~tall(X)&curious(X))))&
(![X]:((rich(X)|tall(X))=>~brave(X)))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~brave(X)=>(~old(X)|~happy(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:(~curious(X))))&
(![X]:(rich(X)=>(humble(X)<~>wise(X))))&
(![X]:(patient(X)<=>(~calm(X)|humble(X))))&
(((creative(lucy)&~creative(lucy)))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~tall(X))=>(brave(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))<=>(~generous(X)|humble(X))))&
((~creative(lucy))=>(curious(susan)))&
(((~humble(mary)<~>~creative(mary)))<=>(?[X]:(humble(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:((humble(X)<~>funny(X))))=>((~happy(mary)&~generous(mary))))&
((~tall(susan)|wise(susan)))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~creative(X)))&
((~old(mary)|~curious(mary)))&
((humble(susan)|rich(susan)))&
(~humble(paul))&
((strong(alice)<~>curious(alice)))&
((~humble(susan)&wise(susan))) | ~quiet(susan) | [
"p0",
"p1",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3703466500955749642939855
% SZS output start Proof for 3703466500955749642939855
1. ! [X0] : ((quiet(X0) & ~happy(X0)) => (curious(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((tall(X0) | rich(X0)) => ~brave(X0)) [input p1]
8. (~creative(lucy) & creative(lucy)) <=> ? [X0] : (~tall(X0) & brave(X0)) [input p7]
9. ! [X0] : ((~tall(X0) | generous(X0)) => (~calm(X0) & brave(X0))) [input p8]
10. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (humble(X0) | ~generous(X0))) [input p9]
23. quiet(susan) [input hypothesis]
26. ! [X0] : ((~tall(X0) | generous(X0)) => brave(X0)) [pure predicate removal 9]
27. ! [X0] : ((curious(X0) & ~tall(X0)) | (~quiet(X0) | happy(X0))) [ennf transformation 1]
28. ! [X0] : ((curious(X0) & ~tall(X0)) | ~quiet(X0) | happy(X0)) [flattening 27]
29. ! [X0] : (~brave(X0) | (~tall(X0) & ~rich(X0))) [ennf transformation 2]
34. ! [X0] : (brave(X0) | (tall(X0) & ~generous(X0))) [ennf transformation 26]
43. ((~creative(lucy) & creative(lucy)) | ! [X0] : (tall(X0) | ~brave(X0))) & (? [X0] : (~tall(X0) & brave(X0)) | (creative(lucy) | ~creative(lucy))) [nnf transformation 8]
44. ((~creative(lucy) & creative(lucy)) | ! [X0] : (tall(X0) | ~brave(X0))) & (? [X0] : (~tall(X0) & brave(X0)) | creative(lucy) | ~creative(lucy)) [flattening 43]
45. ((~creative(lucy) & creative(lucy)) | ! [X0] : (tall(X0) | ~brave(X0))) & (? [X1] : (~tall(X1) & brave(X1)) | creative(lucy) | ~creative(lucy)) [rectify 44]
46. ? [X1] : (~tall(X1) & brave(X1)) => (~tall(sK1) & brave(sK1)) [choice axiom]
47. ((~creative(lucy) & creative(lucy)) | ! [X0] : (tall(X0) | ~brave(X0))) & ((~tall(sK1) & brave(sK1)) | creative(lucy) | ~creative(lucy)) [skolemisation 45,46]
48. ! [X0] : (((tall(X0) & ~happy(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((tall(X0) & ~happy(X0)) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | ~tall(X0) | happy(X0))) [flattening 48]
65. ~tall(X0) | ~quiet(X0) | happy(X0) [cnf transformation 28]
68. ~brave(X0) | ~tall(X0) [cnf transformation 29]
77. creative(lucy) | tall(X0) | ~brave(X0) [cnf transformation 47]
78. ~creative(lucy) | tall(X0) | ~brave(X0) [cnf transformation 47]
79. ~generous(X0) | brave(X0) [cnf transformation 34]
80. brave(X0) | tall(X0) [cnf transformation 34]
82. ~happy(X0) | generous(X0) [cnf transformation 49]
110. quiet(susan) [cnf transformation 23]
119. ~creative(lucy) | ~brave(X0) [subsumption resolution 78,68]
121. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
122. ~brave(X0) <- (3) [avatar component clause 121]
124. 4 <=> creative(lucy) [avatar definition]
127. 3 | ~4 [avatar split clause 119,124,121]
128. creative(lucy) | ~brave(X0) [subsumption resolution 77,68]
129. 3 | 4 [avatar split clause 128,124,121]
241. tall(X2) <- (3) [resolution 80,122]
247. ~quiet(X0) | happy(X0) <- (3) [resolution 65,241]
259. 30 <=> happy(susan) [avatar definition]
261. happy(susan) <- (30) [avatar component clause 259]
263. happy(susan) <- (3) [resolution 247,110]
264. 30 | ~3 [avatar split clause 263,121,259]
266. generous(susan) <- (30) [resolution 261,82]
268. brave(susan) <- (30) [resolution 266,79]
270. $false <- (3, 30) [subsumption resolution 268,122]
271. ~3 | ~30 [avatar contradiction clause 270]
272. $false [avatar sat refutation 127,129,264,271]
% SZS output end Proof for 3703466500955749642939855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and rich is both quiet and kind. Everyone who is funny is happy or not humble. If someone is either not rich or brave then someone is either not strong or generous and vice versa. Everyone who is both humble and not funny is either curious or not quiet. If mary is old or tall then lucy is either not generous or tall and vice versa. Everyone who is not happy or kind is creative or generous and vice versa. Everyone who is either not patient or brave is calm or happy. Everyone who is both not strong and curious is not brave and vice versa. Everyone who is quiet or old is rich or old and vice versa. Everyone who is both not wise and not humble is either not tall or not calm. If lucy is not brave or creative then someone is both rich and not calm. Everyone who is not funny or brave is both funny and not quiet. Everyone who is both happy and not happy is curious. Everyone who is not funny or humble is either wise or not humble and vice versa. If someone is brave then lucy is both curious and old. Everyone who is quiet is both not patient and patient and vice versa. Someone is not wise or generous. Someone is not calm or tall. Susan is quiet or not kind. Lucy is old or not calm. Lucy is both patient and strong. Paul is humble or not generous. | Paul is funny. | entailment | (![X]:((old(X)&rich(X))=>(quiet(X)&kind(X))))&
(![X]:(funny(X)=>(happy(X)|~humble(X))))&
((?[X]:((~rich(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((humble(X)&~funny(X))=>(curious(X)<~>~quiet(X))))&
(((old(mary)|tall(mary)))<=>((~generous(lucy)<~>tall(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(creative(X)|generous(X))))&
(![X]:((~patient(X)<~>brave(X))=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&curious(X))<=>~brave(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)|old(X))))&
(![X]:((~wise(X)&~humble(X))=>(~tall(X)<~>~calm(X))))&
(((~brave(lucy)|creative(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~funny(X)|brave(X))=>(funny(X)&~quiet(X))))&
(![X]:((happy(X)&~happy(X))=>curious(X)))&
(![X]:((~funny(X)|humble(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:(brave(X)))=>((curious(lucy)&old(lucy))))&
(![X]:(quiet(X)<=>(~patient(X)&patient(X))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((~calm(X)|tall(X))))&
((quiet(susan)|~kind(susan)))&
((old(lucy)|~calm(lucy)))&
((patient(lucy)&strong(lucy)))&
((humble(paul)|~generous(paul))) | funny(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5381061911510948178150764
% SZS output start Proof for 5381061911510948178150764
12. ! [X0] : ((brave(X0) | ~funny(X0)) => (~quiet(X0) & funny(X0))) [input p11]
23. ~funny(paul) [input hypothesis]
36. ! [X0] : ((~quiet(X0) & funny(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 12]
104. funny(X0) | funny(X0) [cnf transformation 36]
127. ~funny(paul) [cnf transformation 23]
130. funny(X0) [duplicate literal removal 104]
251. $false [subsumption resolution 127,130]
% SZS output end Proof for 5381061911510948178150764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not creative is both not quiet and not patient and vice versa. If john is not quiet then lucy is generous or not strong and vice versa. If fred is not patient or not kind then paul is tall and vice versa. Everyone who is not humble is either kind or not funny and vice versa. Everyone who is old or not humble is happy or kind. Everyone who is not generous is not strong and vice versa. Everyone who is rich is both tall and not curious. Everyone who is either not happy or not quiet is strong or old. Everyone who is humble is either curious or not humble and vice versa. Everyone who is wise or not strong is patient or not patient and vice versa. Everyone who is both quiet and kind is either wise or not patient and vice versa. Everyone who is both quiet and not tall is strong or generous. Everyone who is either not rich or curious is curious. If someone is not funny or humble then someone is both not happy and not kind and vice versa. If susan is not wise then someone is patient or calm. If someone is not curious then alice is either not creative or old. Alice is quiet. Someone is not rich. Someone is either not happy or not brave. Lucy is not calm or quiet. Paul is either humble or calm. John is not humble or not strong. Mary is not calm. Someone is not wise. | Alice is old. | neutral | (![X]:((tall(X)|~creative(X))<=>(~quiet(X)&~patient(X))))&
((~quiet(john))<=>((generous(lucy)|~strong(lucy))))&
(((~patient(fred)|~kind(fred)))<=>(tall(paul)))&
(![X]:(~humble(X)<=>(kind(X)<~>~funny(X))))&
(![X]:((old(X)|~humble(X))=>(happy(X)|kind(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:(rich(X)=>(tall(X)&~curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(strong(X)|old(X))))&
(![X]:(humble(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((wise(X)|~strong(X))<=>(patient(X)|~patient(X))))&
(![X]:((quiet(X)&kind(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((quiet(X)&~tall(X))=>(strong(X)|generous(X))))&
(![X]:((~rich(X)<~>curious(X))=>curious(X)))&
((?[X]:((~funny(X)|humble(X))))<=>(?[X]:((~happy(X)&~kind(X)))))&
((~wise(susan))=>(?[X]:((patient(X)|calm(X)))))&
((?[X]:(~curious(X)))=>((~creative(alice)<~>old(alice))))&
(quiet(alice))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)<~>~brave(X))))&
((~calm(lucy)|quiet(lucy)))&
((humble(paul)<~>calm(paul)))&
((~humble(john)|~strong(john)))&
(~calm(mary))&
(?[X]:(~wise(X))) | old(alice) | [] | null | 0 |
Everyone who is both brave and not curious is not humble or not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Everyone who is not wise or not old is not brave and vice versa.
Everyone who is either not kind or wise is not calm or old and vice versa.
Everyone who is both not creative and not curious is not happy or kind and vice versa.
If john is both curious and not funny then alice is wise and vice versa.
If someone is humble then someone is not quiet.
If someone is either not creative or not curious then alice is not quiet or calm.
Everyone who is not creative or generous is creative.
If someone is either not calm or not brave then fred is either not patient or not humble and vice versa.
Everyone who is generous is not funny or generous.
If someone is either quiet or not patient then someone is not happy and vice versa.
Everyone who is wise or not funny is generous or happy.
Someone is patient or kind.
Mary is not strong.
Someone is not strong.
Someone is either funny or not wise.
Someone is either not tall or not creative.
Someone is not curious. | Mary is not funny. | contradiction | (![X]:((brave(X)&~curious(X))=>(~humble(X)|~creative(X))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(![X]:((~wise(X)|~old(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|old(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~happy(X)|kind(X))))&
(((curious(john)&~funny(john)))<=>(wise(alice)))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>((~quiet(alice)|calm(alice))))&
(![X]:((~creative(X)|generous(X))=>creative(X)))&
((?[X]:((~calm(X)<~>~brave(X))))<=>((~patient(fred)<~>~humble(fred))))&
(![X]:(generous(X)=>(~funny(X)|generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))=>(generous(X)|happy(X))))&
(?[X]:((patient(X)|kind(X))))&
(~strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~curious(X))) | ~funny(mary) | [
"p2",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4474025312272706973599477
% SZS output start Proof for 4474025312272706973599477
3. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X0] : brave(X0) [input p2]
6. ! [X0] : ((~old(X0) | ~wise(X0)) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (old(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (kind(X0) | ~happy(X0))) [input p7]
12. ! [X0] : ((generous(X0) | ~creative(X0)) => creative(X0)) [input p11]
23. ~funny(mary) [input hypothesis]
24. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X1] : brave(X1) [rectify 3]
29. ? [X1] : brave(X1) | ! [X0] : (~creative(X0) | funny(X0)) [ennf transformation 24]
34. ! [X0] : (creative(X0) | (~generous(X0) & creative(X0))) [ennf transformation 12]
44. ? [X0] : brave(X0) | ! [X1] : (~creative(X1) | funny(X1)) [rectify 29]
45. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
46. brave(sK1) | ! [X1] : (~creative(X1) | funny(X1)) [skolemisation 44,45]
52. ! [X0] : (((~old(X0) | ~wise(X0)) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [nnf transformation 6]
53. ! [X0] : ((~old(X0) | ~wise(X0) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 54]
56. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 8]
57. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | curious(X0) | creative(X0))) [flattening 56]
91. brave(sK1) | ~creative(X1) | funny(X1) [cnf transformation 46]
99. ~brave(X0) | wise(X0) [cnf transformation 53]
100. ~brave(X0) | old(X0) [cnf transformation 53]
107. ~old(X0) | kind(X0) | ~wise(X0) [cnf transformation 55]
110. ~kind(X0) | ~creative(X0) [cnf transformation 57]
119. creative(X0) | creative(X0) [cnf transformation 34]
144. ~funny(mary) [cnf transformation 23]
145. creative(X0) [duplicate literal removal 119]
176. 7 <=> ! [X1] : (~creative(X1) | funny(X1)) [avatar definition]
177. ~creative(X1) | funny(X1) <- (7) [avatar component clause 176]
179. 8 <=> brave(sK1) [avatar definition]
181. brave(sK1) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 91,179,176]
327. funny(X1) <- (7) [subsumption resolution 177,145]
328. $false <- (7) [resolution 327,144]
333. ~7 [avatar contradiction clause 328]
334. wise(sK1) <- (8) [resolution 99,181]
335. old(sK1) <- (8) [resolution 100,181]
365. 43 <=> kind(sK1) [avatar definition]
367. kind(sK1) <- (43) [avatar component clause 365]
369. kind(sK1) | ~wise(sK1) <- (8) [resolution 107,335]
370. kind(sK1) <- (8) [subsumption resolution 369,334]
371. 43 | ~8 [avatar split clause 370,179,365]
376. ~creative(sK1) <- (43) [resolution 367,110]
377. $false <- (43) [subsumption resolution 376,145]
378. ~43 [avatar contradiction clause 377]
379. $false [avatar sat refutation 182,333,371,378]
% SZS output end Proof for 4474025312272706973599477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or curious is curious or humble and vice versa.
Everyone who is happy or humble is both not calm and not strong and vice versa.
If paul is both not creative and not rich then someone is not old.
If fred is patient or not creative then someone is either not old or not quiet.
If someone is both not humble and not kind then lucy is not curious.
If someone is not strong then someone is curious.
If paul is both not wise and creative then someone is both generous and not generous and vice versa.
Everyone who is either not humble or rich is either not wise or not generous.
If alice is both not brave and not generous then someone is not rich or not tall and vice versa.
Everyone who is either not calm or calm is both tall and strong and vice versa.
If mary is either not quiet or strong then someone is either kind or not strong and vice versa.
If someone is not strong or not old then someone is either kind or humble and vice versa.
Everyone who is both creative and not strong is both not old and not brave and vice versa.
If fred is both not funny and not brave then susan is both not generous and not rich and vice versa.
Everyone who is curious is old.
If susan is both patient and old then susan is generous and vice versa.
Someone is not quiet or not old.
Mary is not generous.
Alice is either happy or not patient.
Fred is either not creative or not generous.
Someone is patient or calm.
Someone is tall.
Someone is funny or old. | Lucy is not quiet. | neutral | (![X]:((happy(X)<~>curious(X))<=>(curious(X)|humble(X))))&
(![X]:((happy(X)|humble(X))<=>(~calm(X)&~strong(X))))&
(((~creative(paul)&~rich(paul)))=>(?[X]:(~old(X))))&
(((patient(fred)|~creative(fred)))=>(?[X]:((~old(X)<~>~quiet(X)))))&
((?[X]:((~humble(X)&~kind(X))))=>(~curious(lucy)))&
((?[X]:(~strong(X)))=>(?[X]:(curious(X))))&
(((~wise(paul)&creative(paul)))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(~wise(X)<~>~generous(X))))&
(((~brave(alice)&~generous(alice)))<=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(tall(X)&strong(X))))&
(((~quiet(mary)<~>strong(mary)))<=>(?[X]:((kind(X)<~>~strong(X)))))&
((?[X]:((~strong(X)|~old(X))))<=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((creative(X)&~strong(X))<=>(~old(X)&~brave(X))))&
(((~funny(fred)&~brave(fred)))<=>((~generous(susan)&~rich(susan))))&
(![X]:(curious(X)=>old(X)))&
(((patient(susan)&old(susan)))<=>(generous(susan)))&
(?[X]:((~quiet(X)|~old(X))))&
(~generous(mary))&
((happy(alice)<~>~patient(alice)))&
((~creative(fred)<~>~generous(fred)))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:(tall(X)))&
(?[X]:((funny(X)|old(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is either not funny or generous is either quiet or patient.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
If someone is old then lucy is happy or rich.
Everyone who is both happy and curious is strong.
If someone is rich then someone is both not brave and not kind.
Everyone who is not funny or not rich is not tall.
If lucy is not kind or strong then alice is old or not happy and vice versa.
Someone is curious or not brave.
Someone is humble or generous.
Fred is both not happy and rich.
Someone is kind or wise.
Someone is not calm or not generous. | Paul is not humble. | entailment | (![X]:((~funny(X)<~>generous(X))=>(quiet(X)<~>patient(X))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~funny(X)|~rich(X))=>~tall(X)))&
(((~kind(lucy)|strong(lucy)))<=>((old(alice)|~happy(alice))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((humble(X)|generous(X))))&
((~happy(fred)&rich(fred)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~calm(X)|~generous(X)))) | ~humble(paul) | [
"p4",
"p5",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 322319513966439588799587
% SZS output start Proof for 322319513966439588799587
5. ! [X0] : ((old(X0) <~> brave(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : old(X0) <=> (brave(alice) & ~happy(alice)) [input p5]
7. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p6]
9. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p9]
15. ! [X0] : ((~rich(X0) | ~funny(X0)) => ~tall(X0)) [input p14]
22. humble(paul) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 9]
34. ! [X0] : (~tall(X0) | (rich(X0) & funny(X0))) [ennf transformation 15]
44. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | tall(X0)) & (~tall(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 5]
45. (? [X0] : old(X0) | (~brave(alice) | happy(alice))) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [nnf transformation 6]
46. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [flattening 45]
47. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [rectify 46]
48. ? [X0] : old(X0) => old(sK1) [choice axiom]
49. (old(sK1) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 50]
53. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 10]
54. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 53]
85. ~tall(X0) | old(X0) | ~brave(X0) [cnf transformation 44]
86. tall(X0) | old(X0) | brave(X0) [cnf transformation 44]
87. ~brave(X0) | ~old(X0) | tall(X0) [cnf transformation 44]
89. brave(alice) | ~old(X1) [cnf transformation 49]
94. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 51]
103. ~brave(X0) | ~generous(X0) [cnf transformation 27]
104. ~brave(X0) | tall(X0) [cnf transformation 27]
105. quiet(X0) | quiet(X0) [cnf transformation 54]
108. ~humble(X0) | ~rich(X0) [cnf transformation 54]
119. ~tall(X0) | rich(X0) [cnf transformation 34]
129. humble(paul) [cnf transformation 22]
130. quiet(X0) [duplicate literal removal 105]
197. 14 <=> brave(alice) [avatar definition]
198. brave(alice) <- (14) [avatar component clause 197]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 14 [avatar split clause 89,197,206]
214. 18 <=> rich(paul) [avatar definition]
215. ~rich(paul) <- (~18) [avatar component clause 214]
223. 20 <=> humble(paul) [avatar definition]
224. humble(paul) <- (20) [avatar component clause 223]
256. 27 <=> old(alice) [avatar definition]
257. old(alice) <- (27) [avatar component clause 256]
289. 20 [avatar split clause 129,223]
295. tall(alice) <- (14) [resolution 104,198]
300. ~rich(paul) <- (20) [resolution 108,224]
302. ~18 | ~20 [avatar split clause 300,223,214]
312. old(alice) | ~brave(alice) <- (14) [resolution 85,295]
313. old(alice) <- (14) [subsumption resolution 312,198]
314. 27 | ~14 [avatar split clause 313,197,256]
320. old(X2) | brave(X2) | rich(X2) [resolution 86,119]
324. brave(X2) | rich(X2) <- (16) [subsumption resolution 320,207]
326. rich(X0) | tall(X0) <- (16) [resolution 324,104]
331. rich(X0) <- (16) [subsumption resolution 326,119]
335. $false <- (16, ~18) [resolution 331,215]
338. ~16 | 18 [avatar contradiction clause 335]
339. ~old(alice) | tall(alice) <- (14) [resolution 198,87]
341. ~generous(alice) <- (14) [resolution 198,103]
342. tall(alice) <- (14, 27) [subsumption resolution 339,257]
372. ~quiet(alice) | generous(alice) <- (14, 27) [resolution 94,342]
375. generous(alice) <- (14, 27) [subsumption resolution 372,130]
376. $false <- (14, 27) [subsumption resolution 375,341]
377. ~14 | ~27 [avatar contradiction clause 376]
378. $false [avatar sat refutation 208,289,302,314,338,377]
% SZS output end Proof for 322319513966439588799587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is either not funny or old.
Everyone who is happy or tall is either not curious or creative.
Everyone who is both tall and creative is not humble.
Everyone who is old or not wise is either not funny or patient.
If someone is creative or not curious then someone is both old and wise and vice versa.
If paul is rich then john is both not wise and old.
Everyone who is either strong or not tall is strong.
If paul is both not rich and not humble then mary is both not funny and not curious.
Everyone who is both creative and tall is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Someone is both patient and calm.
Paul is both funny and not old.
Someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise. | Paul is patient. | entailment | ((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((happy(X)|tall(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&creative(X))=>~humble(X)))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((old(X)&wise(X)))))&
((rich(paul))=>((~wise(john)&old(john))))&
(![X]:((strong(X)<~>~tall(X))=>strong(X)))&
(((~rich(paul)&~humble(paul)))=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&tall(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(?[X]:((patient(X)&calm(X))))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | patient(paul) | [
"p2",
"p3",
"p8",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4362775934619561897786237
% SZS output start Proof for 4362775934619561897786237
3. ! [X0] : ((creative(X0) & tall(X0)) => ~humble(X0)) [input p2]
4. ! [X0] : ((~wise(X0) | old(X0)) => (~funny(X0) <~> patient(X0))) [input p3]
9. ! [X0] : ((tall(X0) & creative(X0)) <=> wise(X0)) [input p8]
14. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p13]
18. ~old(paul) & funny(paul) [input p17]
23. ~patient(paul) [input hypothesis]
29. ! [X0] : (~humble(X0) | (~creative(X0) | ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 29]
31. ! [X0] : ((~funny(X0) <~> patient(X0)) | (wise(X0) & ~old(X0))) [ennf transformation 4]
46. ! [X0] : (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (wise(X0) & ~old(X0))) [nnf transformation 31]
53. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | ~tall(X0) | ~creative(X0))) [flattening 53]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
88. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 30]
90. ~funny(X0) | patient(X0) | wise(X0) [cnf transformation 46]
105. ~wise(X0) | creative(X0) [cnf transformation 54]
106. ~wise(X0) | tall(X0) [cnf transformation 54]
127. ~wise(X0) | humble(X0) [cnf transformation 67]
136. funny(paul) [cnf transformation 18]
144. ~patient(paul) [cnf transformation 23]
204. 14 <=> humble(paul) [avatar definition]
206. humble(paul) <- (14) [avatar component clause 204]
355. ~creative(paul) | ~tall(paul) <- (14) [resolution 88,206]
368. patient(paul) | wise(paul) [resolution 90,136]
372. wise(paul) [subsumption resolution 368,144]
401. humble(paul) [resolution 372,127]
403. tall(paul) [resolution 372,106]
404. creative(paul) [resolution 372,105]
409. ~tall(paul) <- (14) [subsumption resolution 355,404]
410. $false <- (14) [subsumption resolution 409,403]
411. ~14 [avatar contradiction clause 410]
426. 14 [avatar split clause 401,204]
427. $false [avatar sat refutation 411,426]
% SZS output end Proof for 4362775934619561897786237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and old then someone is either not humble or quiet and vice versa. Everyone who is not quiet is both not tall and rich and vice versa. Everyone who is not rich or not kind is either not calm or quiet and vice versa. Everyone who is generous is not happy or humble. Everyone who is kind or not strong is both not patient and humble and vice versa. Everyone who is wise is curious or generous. Everyone who is both rich and kind is both not curious and curious. Everyone who is both humble and not strong is not patient and vice versa. If fred is either old or kind then someone is both not calm and curious and vice versa. If john is humble or not creative then mary is not strong and vice versa. Everyone who is not calm is not happy or not tall and vice versa. Everyone who is brave is both not strong and brave. Everyone who is both not tall and generous is both not old and funny. If someone is both not curious and not happy then paul is both creative and not curious and vice versa. If someone is funny then someone is either not curious or quiet. If susan is both calm and kind then fred is not curious or old and vice versa. John is both brave and not funny. Someone is wise. Someone is either not wise or wise. Someone is humble or kind. Susan is not quiet. Someone is not generous or not curious. Lucy is either kind or not old. | John is calm. | contradiction | (((generous(susan)&old(susan)))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)&rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:(generous(X)=>(~happy(X)|humble(X))))&
(![X]:((kind(X)|~strong(X))<=>(~patient(X)&humble(X))))&
(![X]:(wise(X)=>(curious(X)|generous(X))))&
(![X]:((rich(X)&kind(X))=>(~curious(X)&curious(X))))&
(![X]:((humble(X)&~strong(X))<=>~patient(X)))&
(((old(fred)<~>kind(fred)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((humble(john)|~creative(john)))<=>(~strong(mary)))&
(![X]:(~calm(X)<=>(~happy(X)|~tall(X))))&
(![X]:(brave(X)=>(~strong(X)&brave(X))))&
(![X]:((~tall(X)&generous(X))=>(~old(X)&funny(X))))&
((?[X]:((~curious(X)&~happy(X))))<=>((creative(paul)&~curious(paul))))&
((?[X]:(funny(X)))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((calm(susan)&kind(susan)))<=>((~curious(fred)|old(fred))))&
((brave(john)&~funny(john)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((humble(X)|kind(X))))&
(~quiet(susan))&
(?[X]:((~generous(X)|~curious(X))))&
((kind(lucy)<~>~old(lucy))) | calm(john) | [
"p0",
"p1",
"p4",
"p10",
"p11",
"p12",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 809289610691576428283026
% SZS output start Proof for 809289610691576428283026
1. (old(susan) & generous(susan)) <=> ? [X0] : (~humble(X0) <~> quiet(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> (rich(X0) & ~tall(X0))) [input p1]
5. ! [X0] : ((~strong(X0) | kind(X0)) <=> (humble(X0) & ~patient(X0))) [input p4]
11. ! [X0] : (~calm(X0) <=> (~tall(X0) | ~happy(X0))) [input p10]
12. ! [X0] : (brave(X0) => (brave(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~tall(X0)) => (funny(X0) & ~old(X0))) [input p12]
17. ~funny(john) & brave(john) [input p16]
21. ~quiet(susan) [input p20]
24. calm(john) [input hypothesis]
32. ! [X0] : ((brave(X0) & ~strong(X0)) | ~brave(X0)) [ennf transformation 12]
33. ! [X0] : ((funny(X0) & ~old(X0)) | (~generous(X0) | tall(X0))) [ennf transformation 13]
34. ! [X0] : ((funny(X0) & ~old(X0)) | ~generous(X0) | tall(X0)) [flattening 33]
36. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X0] : ((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (~old(susan) | ~generous(susan))) [nnf transformation 1]
37. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X0] : ((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | ~old(susan) | ~generous(susan)) [flattening 36]
38. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X1] : ((~quiet(X1) | humble(X1)) & (quiet(X1) | ~humble(X1))) | ~old(susan) | ~generous(susan)) [rectify 37]
39. ? [X1] : ((~quiet(X1) | humble(X1)) & (quiet(X1) | ~humble(X1))) => ((~quiet(sK0) | humble(sK0)) & (quiet(sK0) | ~humble(sK0))) [choice axiom]
40. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (((~quiet(sK0) | humble(sK0)) & (quiet(sK0) | ~humble(sK0))) | ~old(susan) | ~generous(susan)) [skolemisation 38,39]
41. ! [X0] : ((~quiet(X0) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | quiet(X0))) [nnf transformation 2]
42. ! [X0] : ((~quiet(X0) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | quiet(X0))) [flattening 41]
45. ! [X0] : (((~strong(X0) | kind(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (strong(X0) & ~kind(X0)))) [nnf transformation 5]
46. ! [X0] : ((~strong(X0) | kind(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | (strong(X0) & ~kind(X0)))) [flattening 45]
55. ! [X0] : ((~calm(X0) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | calm(X0))) [nnf transformation 11]
56. ! [X0] : ((~calm(X0) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | calm(X0))) [flattening 55]
81. generous(susan) | ~humble(X0) | ~quiet(X0) [cnf transformation 40]
83. old(susan) | ~humble(X0) | ~quiet(X0) [cnf transformation 40]
84. ~tall(X0) | quiet(X0) [cnf transformation 42]
97. strong(X0) | humble(X0) [cnf transformation 46]
116. ~calm(X0) | tall(X0) [cnf transformation 56]
117. ~brave(X0) | ~strong(X0) [cnf transformation 32]
119. ~old(X0) | ~generous(X0) | tall(X0) [cnf transformation 34]
132. brave(john) [cnf transformation 17]
138. ~quiet(susan) [cnf transformation 21]
142. calm(john) [cnf transformation 24]
144. 1 <=> ! [X0] : (~humble(X0) | ~quiet(X0)) [avatar definition]
145. ~quiet(X0) | ~humble(X0) <- (1) [avatar component clause 144]
147. 2 <=> old(susan) [avatar definition]
149. old(susan) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 83,147,144]
156. 4 <=> generous(susan) [avatar definition]
158. generous(susan) <- (4) [avatar component clause 156]
159. 1 | 4 [avatar split clause 81,156,144]
204. 13 <=> humble(john) [avatar definition]
206. humble(john) <- (13) [avatar component clause 204]
292. tall(john) [resolution 116,142]
293. ~strong(john) [resolution 117,132]
294. quiet(john) [resolution 292,84]
297. humble(john) [resolution 293,97]
298. 13 [avatar split clause 297,204]
335. ~generous(susan) | tall(susan) <- (2) [resolution 119,149]
336. tall(susan) <- (2, 4) [subsumption resolution 335,158]
337. quiet(susan) <- (2, 4) [resolution 336,84]
338. $false <- (2, 4) [subsumption resolution 337,138]
339. ~2 | ~4 [avatar contradiction clause 338]
340. ~humble(john) <- (1) [resolution 145,294]
342. $false <- (1, 13) [subsumption resolution 340,206]
343. ~1 | ~13 [avatar contradiction clause 342]
345. $false [avatar sat refutation 150,159,298,339,343]
% SZS output end Proof for 809289610691576428283026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not calm and not creative then susan is tall and vice versa.
Everyone who is both curious and kind is patient or happy.
Everyone who is either quiet or humble is happy.
If someone is both quiet and not rich then mary is either patient or not quiet and vice versa.
If someone is either not strong or wise then susan is both not happy and generous.
Everyone who is not generous or not wise is both not happy and brave.
Everyone who is either generous or funny is both not rich and not curious and vice versa.
If someone is funny then someone is both strong and not creative.
Everyone who is either not rich or funny is both creative and not tall.
Everyone who is not kind or happy is not funny or not curious.
Everyone who is either tall or kind is not patient.
Everyone who is either kind or not humble is either kind or patient.
Everyone who is either not strong or old is both not patient and wise and vice versa.
Everyone who is humble is both kind and curious.
If alice is not funny then someone is both not funny and not rich and vice versa.
Everyone who is both generous and not brave is either happy or curious.
Someone is both happy and not curious.
John is not old or wise.
Someone is curious or not calm.
Susan is not creative or rich.
Alice is rich or not happy.
John is rich or not tall.
Someone is rich. | Mary is not humble. | entailment | ((?[X]:((~calm(X)&~creative(X))))<=>(tall(susan)))&
(![X]:((curious(X)&kind(X))=>(patient(X)|happy(X))))&
(![X]:((quiet(X)<~>humble(X))=>happy(X)))&
((?[X]:((quiet(X)&~rich(X))))<=>((patient(mary)<~>~quiet(mary))))&
((?[X]:((~strong(X)<~>wise(X))))=>((~happy(susan)&generous(susan))))&
(![X]:((~generous(X)|~wise(X))=>(~happy(X)&brave(X))))&
(![X]:((generous(X)<~>funny(X))<=>(~rich(X)&~curious(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(creative(X)&~tall(X))))&
(![X]:((~kind(X)|happy(X))=>(~funny(X)|~curious(X))))&
(![X]:((tall(X)<~>kind(X))=>~patient(X)))&
(![X]:((kind(X)<~>~humble(X))=>(kind(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~patient(X)&wise(X))))&
(![X]:(humble(X)=>(kind(X)&curious(X))))&
((~funny(alice))<=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:((generous(X)&~brave(X))=>(happy(X)<~>curious(X))))&
(?[X]:((happy(X)&~curious(X))))&
((~old(john)|wise(john)))&
(?[X]:((curious(X)|~calm(X))))&
((~creative(susan)|rich(susan)))&
((rich(alice)|~happy(alice)))&
((rich(john)|~tall(john)))&
(?[X]:(rich(X))) | ~humble(mary) | [
"p1",
"p5",
"p6",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1702633079104900595615590
% SZS output start Proof for 1702633079104900595615590
2. ! [X0] : ((kind(X0) & curious(X0)) => (happy(X0) | patient(X0))) [input p1]
6. ! [X0] : ((~wise(X0) | ~generous(X0)) => (brave(X0) & ~happy(X0))) [input p5]
7. ! [X0] : ((generous(X0) <~> funny(X0)) <=> (~curious(X0) & ~rich(X0))) [input p6]
10. ! [X0] : ((happy(X0) | ~kind(X0)) => (~curious(X0) | ~funny(X0))) [input p9]
12. ! [X0] : ((kind(X0) <~> ~humble(X0)) => (kind(X0) <~> patient(X0))) [input p11]
14. ! [X0] : (humble(X0) => (curious(X0) & kind(X0))) [input p13]
24. humble(mary) [input hypothesis]
26. ! [X0] : ((~wise(X0) | ~generous(X0)) => ~happy(X0)) [pure predicate removal 6]
28. ! [X0] : ((happy(X0) | patient(X0)) | (~kind(X0) | ~curious(X0))) [ennf transformation 2]
29. ! [X0] : (happy(X0) | patient(X0) | ~kind(X0) | ~curious(X0)) [flattening 28]
32. ! [X0] : (~happy(X0) | (wise(X0) & generous(X0))) [ennf transformation 26]
35. ! [X0] : ((~curious(X0) | ~funny(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 10]
36. ! [X0] : (~curious(X0) | ~funny(X0) | (~happy(X0) & kind(X0))) [flattening 35]
38. ! [X0] : ((kind(X0) <~> patient(X0)) | (kind(X0) <=> ~humble(X0))) [ennf transformation 12]
39. ! [X0] : ((curious(X0) & kind(X0)) | ~humble(X0)) [ennf transformation 14]
50. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [flattening 50]
57. ! [X0] : (((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) [nnf transformation 38]
73. ~kind(X0) | patient(X0) | happy(X0) | ~curious(X0) [cnf transformation 29]
86. ~happy(X0) | generous(X0) [cnf transformation 32]
90. ~generous(X0) | funny(X0) | ~curious(X0) [cnf transformation 51]
101. ~funny(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 36]
106. ~patient(X0) | ~kind(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 57]
114. ~humble(X0) | kind(X0) [cnf transformation 39]
115. ~humble(X0) | curious(X0) [cnf transformation 39]
127. humble(mary) [cnf transformation 24]
129. ~humble(X0) | ~kind(X0) | ~patient(X0) [duplicate literal removal 106]
153. 6 <=> patient(mary) [avatar definition]
154. ~patient(mary) <- (~6) [avatar component clause 153]
269. kind(mary) [resolution 114,127]
270. curious(mary) [resolution 115,127]
316. 34 <=> funny(mary) [avatar definition]
317. ~funny(mary) <- (~34) [avatar component clause 316]
318. funny(mary) <- (34) [avatar component clause 316]
395. ~curious(mary) | ~happy(mary) <- (34) [resolution 318,101]
401. ~happy(mary) <- (34) [subsumption resolution 395,270]
415. 47 <=> generous(mary) [avatar definition]
417. generous(mary) <- (47) [avatar component clause 415]
451. ~kind(mary) | ~patient(mary) [resolution 129,127]
454. ~patient(mary) [subsumption resolution 451,269]
458. ~6 [avatar split clause 454,153]
467. patient(mary) | happy(mary) | ~curious(mary) [resolution 73,269]
469. happy(mary) | ~curious(mary) <- (~6) [subsumption resolution 467,154]
470. ~curious(mary) <- (~6, 34) [subsumption resolution 469,401]
471. $false <- (~6, 34) [subsumption resolution 470,270]
472. 6 | ~34 [avatar contradiction clause 471]
476. happy(mary) <- (~6) [subsumption resolution 469,270]
496. generous(mary) <- (~6) [resolution 476,86]
615. funny(mary) | ~curious(mary) <- (47) [resolution 417,90]
617. ~curious(mary) <- (~34, 47) [subsumption resolution 615,317]
618. $false <- (~34, 47) [subsumption resolution 617,270]
619. 34 | ~47 [avatar contradiction clause 618]
623. 47 | 6 [avatar split clause 496,153,415]
624. $false [avatar sat refutation 458,472,619,623]
% SZS output end Proof for 1702633079104900595615590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is both kind and strong. Everyone who is either not brave or curious is both patient and brave. Everyone who is both happy and patient is not brave. Everyone who is brave or rich is not creative and vice versa. If alice is either not generous or not brave then someone is both wise and not brave and vice versa. If paul is brave or curious then lucy is not curious or quiet and vice versa. Everyone who is either not strong or rich is not rich or not calm. If someone is quiet then someone is both quiet and not happy. Everyone who is not happy is both old and not old. If fred is not humble then mary is either not quiet or not humble. If mary is wise then fred is kind and vice versa. Everyone who is humble or wise is either not brave or old and vice versa. Everyone who is generous or funny is both not funny and not quiet. If susan is kind or wise then someone is either generous or old and vice versa. Everyone who is both quiet and calm is both not happy and patient and vice versa. Paul is both not strong and not brave. Fred is not generous. John is curious. Lucy is both wise and not strong. Fred is both calm and patient. Someone is either happy or not strong. Susan is either tall or kind. | John is wise. | neutral | (![X]:(tall(X)=>(kind(X)&strong(X))))&
(![X]:((~brave(X)<~>curious(X))=>(patient(X)&brave(X))))&
(![X]:((happy(X)&patient(X))=>~brave(X)))&
(![X]:((brave(X)|rich(X))<=>~creative(X)))&
(((~generous(alice)<~>~brave(alice)))<=>(?[X]:((wise(X)&~brave(X)))))&
(((brave(paul)|curious(paul)))<=>((~curious(lucy)|quiet(lucy))))&
(![X]:((~strong(X)<~>rich(X))=>(~rich(X)|~calm(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
((~strong(paul)&~brave(paul)))&
(~generous(fred))&
(curious(john))&
((wise(lucy)&~strong(lucy)))&
((calm(fred)&patient(fred)))&
(?[X]:((happy(X)<~>~strong(X))))&
((tall(susan)<~>kind(susan))) | wise(john) | [] | null | 0 |
Everyone who is tall is kind or not strong.
If susan is both not brave and happy then someone is not curious.
If someone is either creative or not rich then paul is generous or wise and vice versa.
If susan is not curious then john is either not rich or generous and vice versa.
Everyone who is not funny or old is calm.
If john is either not calm or not creative then someone is either not brave or generous and vice versa.
If someone is old then alice is either not generous or not strong.
If john is both tall and not humble then someone is both strong and not tall and vice versa.
Everyone who is happy or not old is both quiet and not funny.
If someone is humble or not generous then someone is either not quiet or happy.
Everyone who is creative is either not happy or not old.
Everyone who is both wise and brave is both old and patient.
Everyone who is not old is either happy or not happy and vice versa.
If paul is either not generous or strong then lucy is kind.
Everyone who is tall is not kind.
Everyone who is either creative or old is not wise or humble and vice versa.
Someone is kind.
Someone is either patient or brave.
Someone is either generous or rich.
John is either quiet or strong.
Fred is either not calm or generous.
Lucy is not humble or not kind.
John is not curious.
Someone is not old. | John is not funny. | entailment | (![X]:(tall(X)=>(kind(X)|~strong(X))))&
(((~brave(susan)&happy(susan)))=>(?[X]:(~curious(X))))&
((?[X]:((creative(X)<~>~rich(X))))<=>((generous(paul)|wise(paul))))&
((~curious(susan))<=>((~rich(john)<~>generous(john))))&
(![X]:((~funny(X)|old(X))=>calm(X)))&
(((~calm(john)<~>~creative(john)))<=>(?[X]:((~brave(X)<~>generous(X)))))&
((?[X]:(old(X)))=>((~generous(alice)<~>~strong(alice))))&
(((tall(john)&~humble(john)))<=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((happy(X)|~old(X))=>(quiet(X)&~funny(X))))&
((?[X]:((humble(X)|~generous(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:(creative(X)=>(~happy(X)<~>~old(X))))&
(![X]:((wise(X)&brave(X))=>(old(X)&patient(X))))&
(![X]:(~old(X)<=>(happy(X)<~>~happy(X))))&
(((~generous(paul)<~>strong(paul)))=>(kind(lucy)))&
(![X]:(tall(X)=>~kind(X)))&
(![X]:((creative(X)<~>old(X))<=>(~wise(X)|humble(X))))&
(?[X]:(kind(X)))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((quiet(john)<~>strong(john)))&
((~calm(fred)<~>generous(fred)))&
((~humble(lucy)|~kind(lucy)))&
(~curious(john))&
(?[X]:(~old(X))) | ~funny(john) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 819226835521969305217282
% SZS output start Proof for 819226835521969305217282
9. ! [X0] : ((~old(X0) | happy(X0)) => (~funny(X0) & quiet(X0))) [input p8]
13. ! [X0] : (~old(X0) <=> (happy(X0) <~> ~happy(X0))) [input p12]
25. funny(john) [input hypothesis]
33. ! [X0] : ((~funny(X0) & quiet(X0)) | (old(X0) & ~happy(X0))) [ennf transformation 9]
63. ! [X0] : ((~old(X0) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | old(X0))) [nnf transformation 13]
110. ~funny(X0) | old(X0) [cnf transformation 33]
121. ~old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 63]
122. ~old(X0) | happy(X0) | happy(X0) [cnf transformation 63]
144. funny(john) [cnf transformation 25]
145. ~old(X0) | ~happy(X0) [duplicate literal removal 121]
146. ~old(X0) | happy(X0) [duplicate literal removal 122]
235. 19 <=> ! [X0] : ~old(X0) [avatar definition]
236. ~old(X0) <- (19) [avatar component clause 235]
286. ~old(X0) [subsumption resolution 145,146]
287. 19 [avatar split clause 286,235]
350. old(john) [resolution 110,144]
352. $false <- (19) [subsumption resolution 350,236]
353. ~19 [avatar contradiction clause 352]
356. $false [avatar sat refutation 287,353]
% SZS output end Proof for 819226835521969305217282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not strong is both not generous and not humble.
If someone is both not rich and not strong then mary is not calm.
If susan is both not rich and not creative then john is not brave or humble.
If someone is either old or not brave then john is brave and vice versa.
If someone is either not creative or kind then john is not wise or not calm and vice versa.
Everyone who is not humble is either tall or not funny and vice versa.
Everyone who is both not generous and not rich is not quiet and vice versa.
If someone is funny or patient then someone is both not strong and not generous and vice versa.
If alice is either not creative or not strong then fred is either not kind or not tall and vice versa.
If mary is either not quiet or not wise then john is either not funny or quiet.
Everyone who is rich is brave or creative.
Everyone who is kind or quiet is not quiet or curious.
Everyone who is both kind and patient is wise or not patient.
Everyone who is not humble is either happy or humble.
If susan is either strong or not happy then fred is both not happy and generous.
Everyone who is funny is not funny or not strong and vice versa.
Someone is both not rich and quiet.
Someone is not calm or not old.
Fred is both calm and humble.
Paul is either not tall or not generous.
Someone is either not creative or not kind.
Someone is curious.
Someone is either not curious or wise. | Paul is not kind. | neutral | (![X]:((patient(X)<~>~strong(X))=>(~generous(X)&~humble(X))))&
((?[X]:((~rich(X)&~strong(X))))=>(~calm(mary)))&
(((~rich(susan)&~creative(susan)))=>((~brave(john)|humble(john))))&
((?[X]:((old(X)<~>~brave(X))))<=>(brave(john)))&
((?[X]:((~creative(X)<~>kind(X))))<=>((~wise(john)|~calm(john))))&
(![X]:(~humble(X)<=>(tall(X)<~>~funny(X))))&
(![X]:((~generous(X)&~rich(X))<=>~quiet(X)))&
((?[X]:((funny(X)|patient(X))))<=>(?[X]:((~strong(X)&~generous(X)))))&
(((~creative(alice)<~>~strong(alice)))<=>((~kind(fred)<~>~tall(fred))))&
(((~quiet(mary)<~>~wise(mary)))=>((~funny(john)<~>quiet(john))))&
(![X]:(rich(X)=>(brave(X)|creative(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:((kind(X)&patient(X))=>(wise(X)|~patient(X))))&
(![X]:(~humble(X)=>(happy(X)<~>humble(X))))&
(((strong(susan)<~>~happy(susan)))=>((~happy(fred)&generous(fred))))&
(![X]:(funny(X)<=>(~funny(X)|~strong(X))))&
(?[X]:((~rich(X)&quiet(X))))&
(?[X]:((~calm(X)|~old(X))))&
((calm(fred)&humble(fred)))&
((~tall(paul)<~>~generous(paul)))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>wise(X)))) | ~kind(paul) | [] | null | 0 |
If paul is not quiet then mary is patient. Everyone who is both old and brave is rich and vice versa. If someone is creative then fred is generous and vice versa. If john is either rich or creative then alice is rich and vice versa. Everyone who is either not creative or not quiet is not humble or patient. If alice is happy or creative then someone is not happy and vice versa. Everyone who is generous or strong is either not creative or not generous and vice versa. Everyone who is calm is curious or not funny and vice versa. Everyone who is rich or funny is both strong and tall. If someone is both not rich and not calm then someone is both quiet and not strong and vice versa. If lucy is generous or not generous then lucy is both not old and humble and vice versa. Everyone who is kind is generous and vice versa. If fred is not funny then someone is both not old and old and vice versa. If susan is not quiet or tall then paul is not patient and vice versa. If mary is not quiet then someone is either tall or not funny and vice versa. If someone is not wise or not tall then someone is strong or creative. Someone is either not old or strong. Susan is patient or not generous. Lucy is both funny and not quiet. Fred is either not generous or generous. Someone is not humble. Someone is not old or not wise. Alice is not patient or not creative. Lucy is both curious and not quiet. | Lucy is not old. | entailment | ((~quiet(paul))=>(patient(mary)))&
(![X]:((old(X)&brave(X))<=>rich(X)))&
((?[X]:(creative(X)))<=>(generous(fred)))&
(((rich(john)<~>creative(john)))<=>(rich(alice)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~humble(X)|patient(X))))&
(((happy(alice)|creative(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((generous(X)|strong(X))<=>(~creative(X)<~>~generous(X))))&
(![X]:(calm(X)<=>(curious(X)|~funny(X))))&
(![X]:((rich(X)|funny(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(((generous(lucy)|~generous(lucy)))<=>((~old(lucy)&humble(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
((~funny(fred))<=>(?[X]:((~old(X)&old(X)))))&
(((~quiet(susan)|tall(susan)))<=>(~patient(paul)))&
((~quiet(mary))<=>(?[X]:((tall(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((strong(X)|creative(X)))))&
(?[X]:((~old(X)<~>strong(X))))&
((patient(susan)|~generous(susan)))&
((funny(lucy)&~quiet(lucy)))&
((~generous(fred)<~>generous(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((~old(X)|~wise(X))))&
((~patient(alice)|~creative(alice)))&
((curious(lucy)&~quiet(lucy))) | ~old(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1248210921816629854587284
% SZS output start Proof for 1248210921816629854587284
11. (~generous(lucy) | generous(lucy)) <=> (humble(lucy) & ~old(lucy)) [input p10]
25. old(lucy) [input hypothesis]
55. ((~generous(lucy) | generous(lucy)) | (~humble(lucy) | old(lucy))) & ((humble(lucy) & ~old(lucy)) | (generous(lucy) & ~generous(lucy))) [nnf transformation 11]
56. (~generous(lucy) | generous(lucy) | ~humble(lucy) | old(lucy)) & ((humble(lucy) & ~old(lucy)) | (generous(lucy) & ~generous(lucy))) [flattening 55]
110. ~old(lucy) | ~generous(lucy) [cnf transformation 56]
111. ~old(lucy) | generous(lucy) [cnf transformation 56]
139. old(lucy) [cnf transformation 25]
225. 19 <=> generous(lucy) [avatar definition]
235. 21 <=> old(lucy) [avatar definition]
238. 19 | ~21 [avatar split clause 111,235,225]
239. ~19 | ~21 [avatar split clause 110,235,225]
334. 21 [avatar split clause 139,235]
335. $false [avatar sat refutation 238,239,334]
% SZS output end Proof for 1248210921816629854587284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not creative is either quiet or rich and vice versa. If alice is both not patient and not old then someone 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. Paul is either not generous or not calm. Someone is either funny or not generous. Mary is both not humble and not calm. Paul is not happy or quiet. Fred is either not old or not brave. Someone is both rich and not curious. Fred is not humble or not creative. Someone is both not happy and not rich. | Alice is not creative. | entailment | (![X]:((~rich(X)|~creative(X))<=>(quiet(X)<~>rich(X))))&
(((~patient(alice)&~old(alice)))<=>(?[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))))&
((~generous(paul)<~>~calm(paul)))&
(?[X]:((funny(X)<~>~generous(X))))&
((~humble(mary)&~calm(mary)))&
((~happy(paul)|quiet(paul)))&
((~old(fred)<~>~brave(fred)))&
(?[X]:((rich(X)&~curious(X))))&
((~humble(fred)|~creative(fred)))&
(?[X]:((~happy(X)&~rich(X)))) | ~creative(alice) | [
"p1",
"p2",
"p5",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 518637546312793050158760
% SZS output start Proof for 518637546312793050158760
2. (~old(alice) & ~patient(alice)) <=> ? [X0] : (wise(X0) | old(X0)) [input p1]
3. ! [X0] : ((~creative(X0) | generous(X0)) => (~brave(X0) <~> wise(X0))) [input p2]
6. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p5]
9. ! [X0] : (creative(X0) <=> (~strong(X0) & patient(X0))) [input p8]
21. ~old(fred) <~> ~brave(fred) [input p20]
25. creative(alice) [input hypothesis]
27. ! [X0] : ((~brave(X0) <~> wise(X0)) | (creative(X0) & ~generous(X0))) [ennf transformation 3]
36. ((~old(alice) & ~patient(alice)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | (old(alice) | patient(alice))) [nnf transformation 2]
37. ((~old(alice) & ~patient(alice)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | old(alice) | patient(alice)) [flattening 36]
38. ((~old(alice) & ~patient(alice)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X1] : (wise(X1) | old(X1)) | old(alice) | patient(alice)) [rectify 37]
39. ? [X1] : (wise(X1) | old(X1)) => (wise(sK0) | old(sK0)) [choice axiom]
40. ((~old(alice) & ~patient(alice)) | ! [X0] : (~wise(X0) & ~old(X0))) & ((wise(sK0) | old(sK0)) | old(alice) | patient(alice)) [skolemisation 38,39]
41. ! [X0] : (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (creative(X0) & ~generous(X0))) [nnf transformation 27]
45. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (calm(X0) | ~wise(X0)))) [nnf transformation 6]
46. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | calm(X0) | ~wise(X0))) [flattening 45]
51. ! [X0] : ((creative(X0) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [nnf transformation 9]
52. ! [X0] : ((creative(X0) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [flattening 51]
64. (brave(fred) | old(fred)) & (~brave(fred) | ~old(fred)) [nnf transformation 21]
76. ~patient(alice) | ~old(X0) [cnf transformation 40]
77. ~patient(alice) | ~wise(X0) [cnf transformation 40]
81. ~brave(X0) | wise(X0) | creative(X0) [cnf transformation 41]
95. ~patient(X0) | wise(X0) | old(X0) [cnf transformation 46]
101. ~creative(X0) | patient(X0) [cnf transformation 52]
142. brave(fred) | old(fred) [cnf transformation 64]
148. creative(alice) [cnf transformation 25]
154. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
155. ~wise(X0) <- (1) [avatar component clause 154]
162. 3 <=> ! [X0] : ~old(X0) [avatar definition]
163. ~old(X0) <- (3) [avatar component clause 162]
166. 4 <=> patient(alice) [avatar definition]
169. 1 | ~4 [avatar split clause 77,166,154]
170. 3 | ~4 [avatar split clause 76,166,162]
267. 24 <=> old(fred) [avatar definition]
269. old(fred) <- (24) [avatar component clause 267]
271. 25 <=> brave(fred) [avatar definition]
273. brave(fred) <- (25) [avatar component clause 271]
274. 24 | 25 [avatar split clause 142,271,267]
281. 27 <=> creative(fred) [avatar definition]
282. creative(fred) <- (27) [avatar component clause 281]
287. patient(alice) [resolution 101,148]
290. 4 [avatar split clause 287,166]
292. $false <- (3, 24) [resolution 163,269]
293. ~3 | ~24 [avatar contradiction clause 292]
323. wise(fred) | creative(fred) <- (25) [resolution 81,273]
324. creative(fred) <- (1, 25) [subsumption resolution 323,155]
325. 27 | ~1 | ~25 [avatar split clause 324,271,154,281]
326. patient(fred) <- (27) [resolution 282,101]
341. wise(fred) | old(fred) <- (27) [resolution 95,326]
345. old(fred) <- (1, 27) [subsumption resolution 341,155]
346. $false <- (1, 3, 27) [subsumption resolution 345,163]
347. ~1 | ~3 | ~27 [avatar contradiction clause 346]
348. $false [avatar sat refutation 169,170,274,290,293,325,347]
% SZS output end Proof for 518637546312793050158760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both brave and not strong then fred is either curious or not tall. Everyone who is happy or not patient is both tall and not wise. Everyone who is not brave or generous is either not strong or patient and vice versa. Everyone who is not humble is not brave or generous and vice versa. Everyone who is both quiet and not wise is not generous and vice versa. If someone is not old or rich then paul is not humble. Everyone who is patient is either generous or not patient and vice versa. If someone is not patient or not tall then mary is both not quiet and calm. Everyone who is funny or patient is quiet and vice versa. If mary is either not strong or not kind then someone is both not tall and brave. Everyone who is both not old and kind is wise or kind and vice versa. Everyone who is wise is not strong. Everyone who is either strong or not quiet is both not funny and not kind and vice versa. Everyone who is either not patient or not quiet is either strong or funny. If mary is both not rich and calm then fred is either not calm or rich. If susan is either wise or generous then lucy is not happy and vice versa. Lucy is curious. John is both not rich and not calm. Fred is either not strong or not rich. Alice is creative or not tall. John is either not quiet or not creative. | Lucy is calm. | neutral | (((brave(fred)&~strong(fred)))=>((curious(fred)<~>~tall(fred))))&
(![X]:((happy(X)|~patient(X))=>(tall(X)&~wise(X))))&
(![X]:((~brave(X)|generous(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(~humble(X)<=>(~brave(X)|generous(X))))&
(![X]:((quiet(X)&~wise(X))<=>~generous(X)))&
((?[X]:((~old(X)|rich(X))))=>(~humble(paul)))&
(![X]:(patient(X)<=>(generous(X)<~>~patient(X))))&
((?[X]:((~patient(X)|~tall(X))))=>((~quiet(mary)&calm(mary))))&
(![X]:((funny(X)|patient(X))<=>quiet(X)))&
(((~strong(mary)<~>~kind(mary)))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((~old(X)&kind(X))<=>(wise(X)|kind(X))))&
(![X]:(wise(X)=>~strong(X)))&
(![X]:((strong(X)<~>~quiet(X))<=>(~funny(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))=>(strong(X)<~>funny(X))))&
(((~rich(mary)&calm(mary)))=>((~calm(fred)<~>rich(fred))))&
(((wise(susan)<~>generous(susan)))<=>(~happy(lucy)))&
(curious(lucy))&
((~rich(john)&~calm(john)))&
((~strong(fred)<~>~rich(fred)))&
((creative(alice)|~tall(alice)))&
((~quiet(john)<~>~creative(john))) | calm(lucy) | [] | null | 0 |
If someone is either not kind or strong then someone is not generous or not strong and vice versa. Everyone who is both humble and not creative is both not quiet and not generous and vice versa. Everyone who is either happy or strong is either not kind or not humble and vice versa. Everyone who is kind or not tall is either not wise or rich. If mary is not rich or wise then someone is either wise or not quiet and vice versa. Everyone who is quiet or creative is generous or wise and vice versa. If someone is quiet then someone is both not kind and creative. Everyone who is either not quiet or not brave is both humble and kind. Everyone who is not generous or brave is both tall and not quiet and vice versa. Everyone who is either old or quiet is either old or not curious. If lucy is not curious then someone is either kind or strong. If someone is both quiet and not strong then someone is quiet and vice versa. Everyone who is generous is brave and vice versa. If someone is either not humble or brave then someone is both old and patient. Everyone who is both creative and kind is humble or generous and vice versa. If paul is wise then mary is not creative. Susan is either strong or not brave. Lucy is either brave or not kind. Someone is calm. Alice is either not kind or funny. | Susan is not curious. | neutral | ((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((~generous(X)|~strong(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~quiet(X)&~generous(X))))&
(![X]:((happy(X)<~>strong(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((kind(X)|~tall(X))=>(~wise(X)<~>rich(X))))&
(((~rich(mary)|wise(mary)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((quiet(X)|creative(X))<=>(generous(X)|wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(humble(X)&kind(X))))&
(![X]:((~generous(X)|brave(X))<=>(tall(X)&~quiet(X))))&
(![X]:((old(X)<~>quiet(X))=>(old(X)<~>~curious(X))))&
((~curious(lucy))=>(?[X]:((kind(X)<~>strong(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((creative(X)&kind(X))<=>(humble(X)|generous(X))))&
((wise(paul))=>(~creative(mary)))&
((strong(susan)<~>~brave(susan)))&
((brave(lucy)<~>~kind(lucy)))&
(?[X]:(calm(X)))&
((~kind(alice)<~>funny(alice))) | ~curious(susan) | [] | null | 0 |
Everyone who is generous or not kind is both not curious and wise and vice versa.
Everyone who is either not happy or not creative is generous or kind and vice versa.
Everyone who is generous or happy is either not strong or not wise.
If mary is both generous and not creative then paul is both not tall and not creative and vice versa.
Everyone who is both not happy and not humble is not brave or rich and vice versa.
Everyone who is both strong and not old is both not humble and not kind.
If someone is wise or generous then someone is not humble and vice versa.
Everyone who is either humble or not strong is either not kind or not curious.
If paul is either not tall or funny then mary is old and vice versa.
If someone is both not happy and funny then someone is not creative or not humble and vice versa.
Everyone who is strong is not funny.
Everyone who is wise or calm is both not quiet and creative and vice versa.
If john is either not creative or not kind then fred is either humble or funny and vice versa.
Everyone who is not humble or happy is both not tall and quiet and vice versa.
If someone is either not kind or not generous then fred is both happy and not creative.
If someone is either not brave or not funny then someone is either not curious or not strong and vice versa.
Someone is either quiet or brave.
Someone is tall.
Fred is both not rich and not funny.
Someone is both not humble and not patient.
John is not quiet.
Alice is both wise and not tall.
Lucy is both not quiet and not wise. | Paul is brave. | neutral | (![X]:((generous(X)|~kind(X))<=>(~curious(X)&wise(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(generous(X)|kind(X))))&
(![X]:((generous(X)|happy(X))=>(~strong(X)<~>~wise(X))))&
(((generous(mary)&~creative(mary)))<=>((~tall(paul)&~creative(paul))))&
(![X]:((~happy(X)&~humble(X))<=>(~brave(X)|rich(X))))&
(![X]:((strong(X)&~old(X))=>(~humble(X)&~kind(X))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:(~humble(X))))&
(![X]:((humble(X)<~>~strong(X))=>(~kind(X)<~>~curious(X))))&
(((~tall(paul)<~>funny(paul)))<=>(old(mary)))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
(![X]:(strong(X)=>~funny(X)))&
(![X]:((wise(X)|calm(X))<=>(~quiet(X)&creative(X))))&
(((~creative(john)<~>~kind(john)))<=>((humble(fred)<~>funny(fred))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~generous(X))))=>((happy(fred)&~creative(fred))))&
((?[X]:((~brave(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
(?[X]:((quiet(X)<~>brave(X))))&
(?[X]:(tall(X)))&
((~rich(fred)&~funny(fred)))&
(?[X]:((~humble(X)&~patient(X))))&
(~quiet(john))&
((wise(alice)&~tall(alice)))&
((~quiet(lucy)&~wise(lucy))) | brave(paul) | [] | null | 0 |
Everyone who is both curious and strong is either curious or not strong and vice versa.
If someone is not quiet then john is either not strong or not wise.
Everyone who is generous is both not creative and not calm.
If paul is either tall or not wise then someone is both not funny and quiet and vice versa.
If someone is either not humble or not generous then someone is either strong or not happy and vice versa.
If paul is either not creative or not kind then someone is tall and vice versa.
If someone is strong or not strong then someone is both not rich and not quiet and vice versa.
If susan is strong then mary is either not calm or not kind.
If mary is happy or not strong then someone is generous.
If mary is either humble or not kind then mary is not tall or patient.
Everyone who is rich or calm is either kind or not patient and vice versa.
Everyone who is not quiet or not rich is old or not kind and vice versa.
Everyone who is curious or not strong is not quiet or not generous.
If someone is either not creative or generous then someone is happy or not strong and vice versa.
Everyone who is either not curious or not humble is both not brave and not humble.
Everyone who is not brave or not humble is not humble or not happy.
Someone is both humble and not tall.
Someone is not old.
Someone is not creative.
Someone is both not tall and creative.
Someone is either not creative or not tall.
Susan is both brave and not funny.
Alice is not brave.
Susan is brave or not wise. | Susan is brave. | entailment | (![X]:((curious(X)&strong(X))<=>(curious(X)<~>~strong(X))))&
((?[X]:(~quiet(X)))=>((~strong(john)<~>~wise(john))))&
(![X]:(generous(X)=>(~creative(X)&~calm(X))))&
(((tall(paul)<~>~wise(paul)))<=>(?[X]:((~funny(X)&quiet(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(((~creative(paul)<~>~kind(paul)))<=>(?[X]:(tall(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((strong(susan))=>((~calm(mary)<~>~kind(mary))))&
(((happy(mary)|~strong(mary)))=>(?[X]:(generous(X))))&
(((humble(mary)<~>~kind(mary)))=>((~tall(mary)|patient(mary))))&
(![X]:((rich(X)|calm(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(old(X)|~kind(X))))&
(![X]:((curious(X)|~strong(X))=>(~quiet(X)|~generous(X))))&
((?[X]:((~creative(X)<~>generous(X))))<=>(?[X]:((happy(X)|~strong(X)))))&
(![X]:((~curious(X)<~>~humble(X))=>(~brave(X)&~humble(X))))&
(![X]:((~brave(X)|~humble(X))=>(~humble(X)|~happy(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:(~old(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)&creative(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
((brave(susan)&~funny(susan)))&
(~brave(alice))&
((brave(susan)|~wise(susan))) | brave(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 213087337501645863981724
% SZS output start Proof for 213087337501645863981724
22. ~funny(susan) & brave(susan) [input p21]
25. ~brave(susan) [input hypothesis]
157. brave(susan) [cnf transformation 22]
161. ~brave(susan) [cnf transformation 25]
361. $false [subsumption resolution 161,157]
% SZS output end Proof for 213087337501645863981724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not kind is both rich and tall.
Everyone who is patient or not humble is not rich.
If someone is quiet or curious then someone is patient or happy.
If someone is either tall or patient then mary is either not funny or not tall and vice versa.
If someone is both funny and brave then mary is either happy or wise.
If fred is either not curious or kind then someone is either not calm or humble.
Everyone who is not happy is either not quiet or tall.
Everyone who is patient or wise is both happy and strong and vice versa.
Everyone who is both brave and creative is both not happy and not tall and vice versa.
Everyone who is happy is both happy and not tall.
If lucy is either not quiet or not creative then someone is both not generous and not wise and vice versa.
If someone is not patient then someone is not wise or humble.
If lucy is either old or not patient then someone is tall and vice versa.
If john is not funny or quiet then john is either not happy or not generous.
Everyone who is either quiet or creative is either humble or brave.
If john is either not creative or patient then someone is both not kind and not quiet and vice versa.
Fred is not patient.
Susan is not curious.
Paul is either not quiet or creative.
Someone is both not quiet and funny.
Someone is both funny and tall.
Susan is both not quiet and generous.
Someone is not funny or not generous.
John is patient or tall. | Susan is wise. | contradiction | (![X]:((strong(X)|~kind(X))=>(rich(X)&tall(X))))&
(![X]:((patient(X)|~humble(X))=>~rich(X)))&
((?[X]:((quiet(X)|curious(X))))=>(?[X]:((patient(X)|happy(X)))))&
((?[X]:((tall(X)<~>patient(X))))<=>((~funny(mary)<~>~tall(mary))))&
((?[X]:((funny(X)&brave(X))))=>((happy(mary)<~>wise(mary))))&
(((~curious(fred)<~>kind(fred)))=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:(~happy(X)=>(~quiet(X)<~>tall(X))))&
(![X]:((patient(X)|wise(X))<=>(happy(X)&strong(X))))&
(![X]:((brave(X)&creative(X))<=>(~happy(X)&~tall(X))))&
(![X]:(happy(X)=>(happy(X)&~tall(X))))&
(((~quiet(lucy)<~>~creative(lucy)))<=>(?[X]:((~generous(X)&~wise(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~wise(X)|humble(X)))))&
(((old(lucy)<~>~patient(lucy)))<=>(?[X]:(tall(X))))&
(((~funny(john)|quiet(john)))=>((~happy(john)<~>~generous(john))))&
(![X]:((quiet(X)<~>creative(X))=>(humble(X)<~>brave(X))))&
(((~creative(john)<~>patient(john)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(~patient(fred))&
(~curious(susan))&
((~quiet(paul)<~>creative(paul)))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:((funny(X)&tall(X))))&
((~quiet(susan)&generous(susan)))&
(?[X]:((~funny(X)|~generous(X))))&
((patient(john)|tall(john))) | wise(susan) | [
"p0",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8375396971145766330778158
% SZS output start Proof for 8375396971145766330778158
1. ! [X0] : ((~kind(X0) | strong(X0)) => (tall(X0) & rich(X0))) [input p0]
8. ! [X0] : ((wise(X0) | patient(X0)) <=> (strong(X0) & happy(X0))) [input p7]
10. ! [X0] : (happy(X0) => (~tall(X0) & happy(X0))) [input p9]
25. wise(susan) [input hypothesis]
28. ! [X0] : ((tall(X0) & rich(X0)) | (kind(X0) & ~strong(X0))) [ennf transformation 1]
34. ! [X0] : ((~tall(X0) & happy(X0)) | ~happy(X0)) [ennf transformation 10]
50. ! [X0] : (((wise(X0) | patient(X0)) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 8]
51. ! [X0] : ((wise(X0) | patient(X0) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | (~wise(X0) & ~patient(X0)))) [flattening 50]
80. ~strong(X0) | tall(X0) [cnf transformation 28]
103. ~wise(X0) | happy(X0) [cnf transformation 51]
105. ~wise(X0) | strong(X0) [cnf transformation 51]
112. ~happy(X0) | ~tall(X0) [cnf transformation 34]
150. wise(susan) [cnf transformation 25]
363. happy(susan) [resolution 103,150]
365. strong(susan) [resolution 105,150]
373. ~tall(susan) [resolution 112,363]
376. tall(susan) [resolution 365,80]
378. $false [subsumption resolution 376,373]
% SZS output end Proof for 8375396971145766330778158
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is humble or not old is not calm or happy.
Everyone who is both curious and not brave is either not funny or not strong and vice versa.
Everyone who is not calm or not generous is either not strong or not patient.
If someone is either not old or not curious then someone is both not kind and not curious.
Everyone who is either not happy or creative is either not kind or not generous.
Everyone who is both tall and not calm is tall or rich.
Everyone who is either wise or creative is either not kind or not generous and vice versa.
Everyone who is generous is both brave and old and vice versa.
If someone is either tall or not curious then someone is either strong or humble.
Everyone who is either not kind or not funny is funny and vice versa.
Everyone who is not quiet or not brave is both not wise and creative.
Everyone who is not quiet is not generous or not brave and vice versa.
Everyone who is both strong and humble is not strong or humble and vice versa.
If someone is funny then alice is either strong or creative and vice versa.
Everyone who is creative is either not patient or not kind.
Alice is old.
Alice is calm.
Someone is not quiet or not kind.
Fred is happy or not old.
Someone is both patient and brave.
Mary is happy or not funny. | Mary is not quiet. | contradiction | (![X]:((humble(X)|~old(X))=>(~calm(X)|happy(X))))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(old(alice))&
(calm(alice))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(fred)|~old(fred)))&
(?[X]:((patient(X)&brave(X))))&
((happy(mary)|~funny(mary))) | ~quiet(mary) | [
"p2",
"p7",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4152084191085044632669295
% SZS output start Proof for 4152084191085044632669295
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => (~strong(X0) <~> ~patient(X0))) [input p2]
8. ! [X0] : (generous(X0) <=> (old(X0) & brave(X0))) [input p7]
10. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
11. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p10]
12. ! [X0] : (~quiet(X0) <=> (~brave(X0) | ~generous(X0))) [input p11]
13. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p12]
15. ! [X0] : (creative(X0) => (~patient(X0) <~> ~kind(X0))) [input p14]
22. ~quiet(mary) [input hypothesis]
28. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (generous(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | ~creative(X0)) [ennf transformation 15]
36. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (generous(X0) & calm(X0))) [nnf transformation 28]
43. ! [X0] : ((generous(X0) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ~generous(X0))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ~generous(X0))) [flattening 43]
49. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 10]
50. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | quiet(X0))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | quiet(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 13]
53. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
58. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~creative(X0)) [nnf transformation 33]
72. ~patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 36]
91. ~generous(X0) | brave(X0) [cnf transformation 44]
99. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 49]
100. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
104. quiet(X0) | creative(X0) [cnf transformation 32]
106. ~brave(X0) | ~generous(X0) | quiet(X0) [cnf transformation 51]
111. strong(X0) | ~humble(X0) [cnf transformation 53]
112. strong(X0) | humble(X0) [cnf transformation 53]
119. kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 58]
127. ~quiet(mary) [cnf transformation 22]
130. funny(X0) | ~kind(X0) [duplicate literal removal 99]
131. ~kind(X0) | ~funny(X0) [duplicate literal removal 100]
168. ~kind(X0) [subsumption resolution 130,131]
169. ~generous(X0) | quiet(X0) [subsumption resolution 106,91]
170. strong(X0) [subsumption resolution 111,112]
186. ~creative(X0) | patient(X0) [subsumption resolution 119,168]
205. creative(mary) [resolution 104,127]
209. patient(mary) [resolution 186,205]
258. ~strong(mary) | generous(mary) [resolution 72,209]
261. generous(mary) [subsumption resolution 258,170]
292. quiet(mary) [resolution 261,169]
295. $false [subsumption resolution 292,127]
% SZS output end Proof for 4152084191085044632669295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not brave or creative then fred is both not humble and old.
Everyone who is not creative or quiet is not wise and vice versa.
Everyone who is both patient and not old is not kind and vice versa.
Everyone who is not strong or happy is both funny and not wise and vice versa.
If someone is both not generous and not brave then alice is not brave and vice versa.
Everyone who is not curious is either tall or old and vice versa.
If someone is either not calm or happy then alice is not quiet or not humble and vice versa.
Everyone who is funny or not patient is rich or not generous and vice versa.
If someone is generous then someone is not humble or creative.
Everyone who is not generous or not happy is not wise.
Everyone who is quiet is old or patient.
If fred is happy then susan is either funny or creative and vice versa.
If lucy is wise or quiet then paul is not brave.
Everyone who is both happy and not curious is both not humble and not kind.
If someone is humble or not funny then alice is either patient or rich and vice versa.
Everyone who is tall or not kind is both old and wise.
John is either creative or wise.
Someone is not humble or not old.
John is either not kind or not calm.
Paul is either not quiet or not creative.
Fred is not generous or not strong.
Alice is not patient or not rich.
Alice is not wise.
Alice is happy or humble. | Alice is not wise. | entailment | (((~brave(fred)|creative(fred)))=>((~humble(fred)&old(fred))))&
(![X]:((~creative(X)|quiet(X))<=>~wise(X)))&
(![X]:((patient(X)&~old(X))<=>~kind(X)))&
(![X]:((~strong(X)|happy(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~generous(X)&~brave(X))))<=>(~brave(alice)))&
(![X]:(~curious(X)<=>(tall(X)<~>old(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>((~quiet(alice)|~humble(alice))))&
(![X]:((funny(X)|~patient(X))<=>(rich(X)|~generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((~generous(X)|~happy(X))=>~wise(X)))&
(![X]:(quiet(X)=>(old(X)|patient(X))))&
((happy(fred))<=>((funny(susan)<~>creative(susan))))&
(((wise(lucy)|quiet(lucy)))=>(~brave(paul)))&
(![X]:((happy(X)&~curious(X))=>(~humble(X)&~kind(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((patient(alice)<~>rich(alice))))&
(![X]:((tall(X)|~kind(X))=>(old(X)&wise(X))))&
((creative(john)<~>wise(john)))&
(?[X]:((~humble(X)|~old(X))))&
((~kind(john)<~>~calm(john)))&
((~quiet(paul)<~>~creative(paul)))&
((~generous(fred)|~strong(fred)))&
((~patient(alice)|~rich(alice)))&
(~wise(alice))&
((happy(alice)|humble(alice))) | ~wise(alice) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8490590701620860553544898
% SZS output start Proof for 8490590701620860553544898
4. ! [X0] : ((happy(X0) | ~strong(X0)) <=> (~wise(X0) & funny(X0))) [input p3]
10. ! [X0] : ((~happy(X0) | ~generous(X0)) => ~wise(X0)) [input p9]
25. wise(alice) [input hypothesis]
31. ! [X0] : (~wise(X0) | (happy(X0) & generous(X0))) [ennf transformation 10]
42. ! [X0] : (((happy(X0) | ~strong(X0)) | (wise(X0) | ~funny(X0))) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [nnf transformation 4]
43. ! [X0] : ((happy(X0) | ~strong(X0) | wise(X0) | ~funny(X0)) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [flattening 42]
82. ~wise(X0) | ~happy(X0) [cnf transformation 43]
101. ~wise(X0) | happy(X0) [cnf transformation 31]
132. wise(alice) [cnf transformation 25]
211. ~wise(X0) [subsumption resolution 101,82]
303. $false [subsumption resolution 132,211]
% SZS output end Proof for 8490590701620860553544898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is not humble and vice versa. Everyone who is not brave is old. If fred is either creative or not wise then someone is not kind and vice versa. Everyone who is both brave and wise is both rich and tall. If someone is both not kind and tall then fred is old or curious. If lucy is not tall then someone is either not humble or kind and vice versa. Everyone who is either not strong or not tall is not quiet and vice versa. If alice is strong or not patient then someone is not happy. Everyone who is not tall or not old is not strong or not brave and vice versa. Everyone who is both rich and not happy is both not funny and not old and vice versa. If mary is either not quiet or generous then paul is both humble and not curious. If someone is humble or not curious then someone is both not generous and not brave and vice versa. Everyone who is not old or strong is both quiet and old. If fred is either not curious or happy then fred is not brave and vice versa. Everyone who is old is both creative and not funny and vice versa. Mary is either calm or patient. Someone is either not funny or wise. Someone is brave. Susan is not curious. John is generous. | Paul is quiet. | entailment | (![X]:(generous(X)<=>~humble(X)))&
(![X]:(~brave(X)=>old(X)))&
(((creative(fred)<~>~wise(fred)))<=>(?[X]:(~kind(X))))&
(![X]:((brave(X)&wise(X))=>(rich(X)&tall(X))))&
((?[X]:((~kind(X)&tall(X))))=>((old(fred)|curious(fred))))&
((~tall(lucy))<=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>~quiet(X)))&
(((strong(alice)|~patient(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~old(X))<=>(~strong(X)|~brave(X))))&
(![X]:((rich(X)&~happy(X))<=>(~funny(X)&~old(X))))&
(((~quiet(mary)<~>generous(mary)))=>((humble(paul)&~curious(paul))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((~old(X)|strong(X))=>(quiet(X)&old(X))))&
(((~curious(fred)<~>happy(fred)))<=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:((~funny(X)<~>wise(X))))&
(?[X]:(brave(X)))&
(~curious(susan))&
(generous(john)) | quiet(paul) | [
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2758343934705065736969125
% SZS output start Proof for 2758343934705065736969125
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (~brave(X0) | ~strong(X0))) [input p8]
13. ! [X0] : ((strong(X0) | ~old(X0)) => (old(X0) & quiet(X0))) [input p12]
21. ~quiet(paul) [input hypothesis]
30. ! [X0] : ((old(X0) & quiet(X0)) | (~strong(X0) & old(X0))) [ennf transformation 13]
40. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | quiet(X0)) & (~quiet(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 7]
43. ! [X0] : (((~old(X0) | ~tall(X0)) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | (old(X0) & tall(X0)))) [nnf transformation 9]
44. ! [X0] : ((~old(X0) | ~tall(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | (old(X0) & tall(X0)))) [flattening 43]
79. quiet(X0) | strong(X0) | tall(X0) [cnf transformation 40]
84. ~tall(X0) | ~old(X0) | strong(X0) [cnf transformation 44]
100. ~strong(X0) | quiet(X0) [cnf transformation 30]
101. old(X0) | old(X0) [cnf transformation 30]
117. ~quiet(paul) [cnf transformation 21]
118. old(X0) [duplicate literal removal 101]
269. strong(paul) | tall(paul) [resolution 79,117]
276. 31 <=> tall(paul) [avatar definition]
278. tall(paul) <- (31) [avatar component clause 276]
280. 32 <=> strong(paul) [avatar definition]
282. strong(paul) <- (32) [avatar component clause 280]
283. 31 | 32 [avatar split clause 269,280,276]
299. ~old(paul) | strong(paul) <- (31) [resolution 84,278]
300. strong(paul) <- (31) [subsumption resolution 299,118]
301. 32 | ~31 [avatar split clause 300,276,280]
305. quiet(paul) <- (32) [resolution 282,100]
309. $false <- (32) [subsumption resolution 305,117]
310. ~32 [avatar contradiction clause 309]
311. $false [avatar sat refutation 283,301,310]
% SZS output end Proof for 2758343934705065736969125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
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