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
|
|---|---|---|---|---|---|---|---|
If john is not wise then someone is not calm and vice versa. If someone is old or not brave then someone is not quiet or tall and vice versa. If fred is calm then someone is both creative and funny. Everyone who is either old or curious is both not calm and quiet and vice versa. Everyone who is either not generous or not tall is both generous and not rich. Everyone who is not calm or strong is either not happy or not creative and vice versa. Everyone who is not quiet is creative. Everyone who is curious is either not rich or tall. If susan is both not curious and patient then fred is both wise and generous and vice versa. If fred is strong or humble then susan is not calm and vice versa. Everyone who is not brave is either not tall or not old. Everyone who is either generous or not calm is both brave and curious and vice versa. If fred is generous then susan is both not old and not generous and vice versa. If john is either not rich or not creative then lucy is both funny and brave and vice versa. Everyone who is either not humble or kind is either not funny or not calm. If alice is not generous then lucy is not strong or strong. Fred is either not happy or not tall. Mary is either strong or not rich. John is not humble or not quiet. Lucy is both not happy and not wise. Paul is either old or not patient. Someone is both not strong and old. Lucy is both not calm and not wise. Susan is curious or not generous. | Lucy is not patient. | neutral | ((~wise(john))<=>(?[X]:(~calm(X))))&
((?[X]:((old(X)|~brave(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((calm(fred))=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((old(X)<~>curious(X))<=>(~calm(X)&quiet(X))))&
(![X]:((~generous(X)<~>~tall(X))=>(generous(X)&~rich(X))))&
(![X]:((~calm(X)|strong(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>creative(X)))&
(![X]:(curious(X)=>(~rich(X)<~>tall(X))))&
(((~curious(susan)&patient(susan)))<=>((wise(fred)&generous(fred))))&
(((strong(fred)|humble(fred)))<=>(~calm(susan)))&
(![X]:(~brave(X)=>(~tall(X)<~>~old(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(brave(X)&curious(X))))&
((generous(fred))<=>((~old(susan)&~generous(susan))))&
(((~rich(john)<~>~creative(john)))<=>((funny(lucy)&brave(lucy))))&
(![X]:((~humble(X)<~>kind(X))=>(~funny(X)<~>~calm(X))))&
((~generous(alice))=>((~strong(lucy)|strong(lucy))))&
((~happy(fred)<~>~tall(fred)))&
((strong(mary)<~>~rich(mary)))&
((~humble(john)|~quiet(john)))&
((~happy(lucy)&~wise(lucy)))&
((old(paul)<~>~patient(paul)))&
(?[X]:((~strong(X)&old(X))))&
((~calm(lucy)&~wise(lucy)))&
((curious(susan)|~generous(susan))) | ~patient(lucy) | [] | null | 0 |
Everyone who is wise is humble or creative and vice versa.
If lucy is brave then lucy is not tall or brave.
Everyone who is not wise or not funny is either quiet or not old.
Everyone who is strong or wise is either not happy or tall.
If john is both patient and not patient then someone is either not old or not tall and vice versa.
Everyone who is both not patient and not curious is either humble or rich and vice versa.
If someone is not strong or not calm then fred is not happy.
If john is either not strong or not tall then paul is either generous or not calm and vice versa.
Everyone who is either not humble or not funny is either not rich or not creative.
Everyone who is not creative is both not happy and patient and vice versa.
Everyone who is not creative or not strong is both not tall and not happy.
Everyone who is wise or tall is strong and vice versa.
Everyone who is creative or not wise is patient or not rich.
Everyone who is patient is either wise or rich.
If lucy is either not kind or curious then paul is both not brave and not humble.
Everyone who is not old or rich is not generous or not creative and vice versa.
Paul is either funny or not happy.
Someone is either rich or patient.
Susan is both not calm and not brave.
Fred is either not old or curious.
Someone is either not wise or old.
Someone is not creative or not quiet.
Mary is either not rich or patient. | Fred is humble. | entailment | (![X]:(wise(X)<=>(humble(X)|creative(X))))&
((brave(lucy))=>((~tall(lucy)|brave(lucy))))&
(![X]:((~wise(X)|~funny(X))=>(quiet(X)<~>~old(X))))&
(![X]:((strong(X)|wise(X))=>(~happy(X)<~>tall(X))))&
(((patient(john)&~patient(john)))<=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((~patient(X)&~curious(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~strong(X)|~calm(X))))=>(~happy(fred)))&
(((~strong(john)<~>~tall(john)))<=>((generous(paul)<~>~calm(paul))))&
(![X]:((~humble(X)<~>~funny(X))=>(~rich(X)<~>~creative(X))))&
(![X]:(~creative(X)<=>(~happy(X)&patient(X))))&
(![X]:((~creative(X)|~strong(X))=>(~tall(X)&~happy(X))))&
(![X]:((wise(X)|tall(X))<=>strong(X)))&
(![X]:((creative(X)|~wise(X))=>(patient(X)|~rich(X))))&
(![X]:(patient(X)=>(wise(X)<~>rich(X))))&
(((~kind(lucy)<~>curious(lucy)))=>((~brave(paul)&~humble(paul))))&
(![X]:((~old(X)|rich(X))<=>(~generous(X)|~creative(X))))&
((funny(paul)<~>~happy(paul)))&
(?[X]:((rich(X)<~>patient(X))))&
((~calm(susan)&~brave(susan)))&
((~old(fred)<~>curious(fred)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~creative(X)|~quiet(X))))&
((~rich(mary)<~>patient(mary))) | humble(fred) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p9",
"p12",
"p13",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4645659384768045995691449
% SZS output start Proof for 4645659384768045995691449
1. ! [X0] : (wise(X0) <=> (creative(X0) | humble(X0))) [input p0]
4. ! [X0] : ((wise(X0) | strong(X0)) => (~happy(X0) <~> tall(X0))) [input p3]
5. (~patient(john) & patient(john)) <=> ? [X0] : (~old(X0) <~> ~tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) & ~patient(X0)) <=> (humble(X0) <~> rich(X0))) [input p5]
7. ? [X0] : (~calm(X0) | ~strong(X0)) => ~happy(fred) [input p6]
10. ! [X0] : (~creative(X0) <=> (patient(X0) & ~happy(X0))) [input p9]
13. ! [X0] : ((~wise(X0) | creative(X0)) => (~rich(X0) | patient(X0))) [input p12]
14. ! [X0] : (patient(X0) => (wise(X0) <~> rich(X0))) [input p13]
19. ~brave(susan) & ~calm(susan) [input p18]
20. ~old(fred) <~> curious(fred) [input p19]
24. ~humble(fred) [input hypothesis]
28. ! [X0] : ((~happy(X0) <~> tall(X0)) | (~wise(X0) & ~strong(X0))) [ennf transformation 4]
29. ~happy(fred) | ! [X0] : (calm(X0) & strong(X0)) [ennf transformation 7]
32. ! [X0] : ((~rich(X0) | patient(X0)) | (wise(X0) & ~creative(X0))) [ennf transformation 13]
33. ! [X0] : (~rich(X0) | patient(X0) | (wise(X0) & ~creative(X0))) [flattening 32]
34. ! [X0] : ((wise(X0) <~> rich(X0)) | ~patient(X0)) [ennf transformation 14]
36. ! [X0] : ((wise(X0) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | ~wise(X0))) [nnf transformation 1]
37. ! [X0] : ((wise(X0) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | ~wise(X0))) [flattening 36]
39. ! [X0] : (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~wise(X0) & ~strong(X0))) [nnf transformation 28]
40. ((~patient(john) & patient(john)) | ! [X0] : ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (? [X0] : ((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | (patient(john) | ~patient(john))) [nnf transformation 5]
41. ((~patient(john) & patient(john)) | ! [X0] : ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (? [X0] : ((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | patient(john) | ~patient(john)) [flattening 40]
42. ((~patient(john) & patient(john)) | ! [X0] : ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (? [X1] : ((tall(X1) | old(X1)) & (~tall(X1) | ~old(X1))) | patient(john) | ~patient(john)) [rectify 41]
43. ? [X1] : ((tall(X1) | old(X1)) & (~tall(X1) | ~old(X1))) => ((tall(sK0) | old(sK0)) & (~tall(sK0) | ~old(sK0))) [choice axiom]
44. ((~patient(john) & patient(john)) | ! [X0] : ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(sK0) | old(sK0)) & (~tall(sK0) | ~old(sK0))) | patient(john) | ~patient(john)) [skolemisation 42,43]
45. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | (curious(X0) | patient(X0)))) [nnf transformation 6]
46. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | curious(X0) | patient(X0))) [flattening 45]
49. ! [X0] : ((~creative(X0) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | creative(X0))) [nnf transformation 10]
50. ! [X0] : ((~creative(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | creative(X0))) [flattening 49]
53. ! [X0] : (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ~patient(X0)) [nnf transformation 34]
61. (~curious(fred) | old(fred)) & (curious(fred) | ~old(fred)) [nnf transformation 20]
68. ~wise(X0) | humble(X0) | creative(X0) [cnf transformation 37]
69. ~humble(X0) | wise(X0) [cnf transformation 37]
70. ~creative(X0) | wise(X0) [cnf transformation 37]
79. ~tall(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
83. patient(john) | ~old(X0) | tall(X0) [cnf transformation 44]
85. ~patient(john) | ~old(X0) | tall(X0) [cnf transformation 44]
86. rich(X0) | humble(X0) | curious(X0) | patient(X0) [cnf transformation 46]
89. ~rich(X0) | humble(X0) | ~patient(X0) [cnf transformation 46]
93. ~happy(fred) | calm(X0) [cnf transformation 29]
107. patient(X0) | creative(X0) [cnf transformation 50]
108. ~patient(X0) | ~creative(X0) | happy(X0) [cnf transformation 50]
116. ~rich(X0) | patient(X0) | ~creative(X0) [cnf transformation 33]
117. ~rich(X0) | patient(X0) | wise(X0) [cnf transformation 33]
118. ~patient(X0) | wise(X0) | rich(X0) [cnf transformation 53]
119. ~rich(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 53]
132. ~calm(susan) [cnf transformation 19]
135. ~curious(fred) | old(fred) [cnf transformation 61]
141. ~humble(fred) [cnf transformation 24]
143. 1 <=> ! [X0] : (~old(X0) | tall(X0)) [avatar definition]
144. ~old(X0) | tall(X0) <- (1) [avatar component clause 143]
146. 2 <=> patient(john) [avatar definition]
149. 1 | ~2 [avatar split clause 85,146,143]
154. 1 | 2 [avatar split clause 83,146,143]
157. 4 <=> ! [X0] : calm(X0) [avatar definition]
158. calm(X0) <- (4) [avatar component clause 157]
160. 5 <=> happy(fred) [avatar definition]
162. ~happy(fred) <- (~5) [avatar component clause 160]
163. 4 | ~5 [avatar split clause 93,160,157]
192. ~rich(X0) | patient(X0) [subsumption resolution 116,107]
193. ~rich(X0) | ~wise(X0) [subsumption resolution 119,192]
227. 17 <=> old(fred) [avatar definition]
229. old(fred) <- (17) [avatar component clause 227]
231. 18 <=> curious(fred) [avatar definition]
233. ~curious(fred) <- (~18) [avatar component clause 231]
234. 17 | ~18 [avatar split clause 135,231,227]
294. wise(X0) | rich(X0) | creative(X0) [resolution 118,107]
296. rich(X0) | wise(X0) [subsumption resolution 294,70]
316. humble(X0) | curious(X0) | patient(X0) | patient(X0) | wise(X0) [resolution 86,117]
319. humble(X3) | curious(X3) | patient(X3) | ~wise(X3) [resolution 86,193]
324. humble(X0) | curious(X0) | patient(X0) | wise(X0) [duplicate literal removal 316]
325. curious(X0) | patient(X0) | wise(X0) [subsumption resolution 324,69]
326. curious(X3) | humble(X3) | patient(X3) [subsumption resolution 319,325]
351. wise(X1) | humble(X1) | ~patient(X1) [resolution 296,89]
355. wise(X5) | patient(X5) | wise(X5) [resolution 296,117]
358. wise(X5) | patient(X5) [duplicate literal removal 355]
359. ~patient(X1) | wise(X1) [subsumption resolution 351,69]
361. wise(X5) [subsumption resolution 358,359]
364. creative(X0) | humble(X0) [resolution 361,68]
553. humble(fred) | patient(fred) <- (~18) [resolution 326,233]
554. patient(fred) <- (~18) [subsumption resolution 553,141]
557. ~creative(fred) | happy(fred) <- (~18) [resolution 554,108]
559. ~creative(fred) <- (~5, ~18) [subsumption resolution 557,162]
560. humble(fred) <- (~5, ~18) [resolution 559,364]
561. $false <- (~5, ~18) [subsumption resolution 560,141]
562. 5 | 18 [avatar contradiction clause 561]
568. $false <- (4) [resolution 158,132]
571. ~4 [avatar contradiction clause 568]
576. tall(fred) <- (1, 17) [resolution 229,144]
599. happy(fred) | ~wise(fred) <- (1, 17) [resolution 576,79]
605. ~wise(fred) <- (1, ~5, 17) [subsumption resolution 599,162]
606. $false <- (1, ~5, 17) [subsumption resolution 605,361]
607. ~1 | 5 | ~17 [avatar contradiction clause 606]
609. $false [avatar sat refutation 149,154,163,234,562,571,607]
% SZS output end Proof for 4645659384768045995691449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not old is not generous.
Everyone who is either not old or curious is old or not strong and vice versa.
Everyone who is both happy and not old is not rich or not generous.
If mary is patient or humble then alice is not rich or not wise and vice versa.
If someone is both happy and not kind then fred is either happy or not kind.
If someone is not quiet then someone is either generous or tall.
If someone is either not quiet or strong then someone is not calm and vice versa.
If someone is both not rich and not patient then susan is kind and vice versa.
If someone is not calm or not old then someone is patient or not tall and vice versa.
If mary is curious or rich then someone is both calm and not humble.
Everyone who is both not calm and not brave is brave and vice versa.
Everyone who is old is rich or generous and vice versa.
If someone is funny then someone is either not tall or curious.
If lucy is not quiet then someone is either strong or tall and vice versa.
If susan is either strong or not wise then someone is calm or tall.
Everyone who is either not quiet or not generous is not funny or not quiet and vice versa.
Lucy is both humble and not patient.
Someone is not humble or not calm.
Someone is not curious.
Someone is wise or not funny. | Mary is not rich. | neutral | (![X]:((calm(X)|~old(X))=>~generous(X)))&
(![X]:((~old(X)<~>curious(X))<=>(old(X)|~strong(X))))&
(![X]:((happy(X)&~old(X))=>(~rich(X)|~generous(X))))&
(((patient(mary)|humble(mary)))<=>((~rich(alice)|~wise(alice))))&
((?[X]:((happy(X)&~kind(X))))=>((happy(fred)<~>~kind(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)<~>tall(X)))))&
((?[X]:((~quiet(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>(kind(susan)))&
((?[X]:((~calm(X)|~old(X))))<=>(?[X]:((patient(X)|~tall(X)))))&
(((curious(mary)|rich(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((~calm(X)&~brave(X))<=>brave(X)))&
(![X]:(old(X)<=>(rich(X)|generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((~quiet(lucy))<=>(?[X]:((strong(X)<~>tall(X)))))&
(((strong(susan)<~>~wise(susan)))=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~funny(X)|~quiet(X))))&
((humble(lucy)&~patient(lucy)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)|~funny(X)))) | ~rich(mary) | [] | null | 0 |
If john is wise or strong then someone is both not patient and rich and vice versa.
Everyone who is not brave or generous is either humble or happy.
Everyone who is both brave and wise is either old or not curious.
Everyone who is brave is both generous and creative and vice versa.
If mary is either not kind or not rich then john is both not funny and patient and vice versa.
Everyone who is not rich or not calm is not patient or not brave.
Everyone who is both not curious and creative is wise or kind and vice versa.
If someone is not funny or tall then someone is both not wise and not brave and vice versa.
If lucy is both brave and not brave then paul is strong or funny.
If fred is either kind or strong then susan is not wise.
If john is not generous then someone is either old or not kind and vice versa.
If fred is generous or humble then someone is either kind or not humble.
Everyone who is not quiet or not wise is both wise and not brave and vice versa.
Everyone who is not happy or rich is both happy and not strong and vice versa.
Everyone who is either brave or humble is not calm or not creative and vice versa.
Everyone who is both calm and patient is not brave and vice versa.
Fred is generous or not calm.
Someone is not tall.
Someone is either not patient or not tall.
Paul is quiet or happy. | John is not brave. | neutral | (((wise(john)|strong(john)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~brave(X)|generous(X))=>(humble(X)<~>happy(X))))&
(![X]:((brave(X)&wise(X))=>(old(X)<~>~curious(X))))&
(![X]:(brave(X)<=>(generous(X)&creative(X))))&
(((~kind(mary)<~>~rich(mary)))<=>((~funny(john)&patient(john))))&
(![X]:((~rich(X)|~calm(X))=>(~patient(X)|~brave(X))))&
(![X]:((~curious(X)&creative(X))<=>(wise(X)|kind(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(((brave(lucy)&~brave(lucy)))=>((strong(paul)|funny(paul))))&
(((kind(fred)<~>strong(fred)))=>(~wise(susan)))&
((~generous(john))<=>(?[X]:((old(X)<~>~kind(X)))))&
(((generous(fred)|humble(fred)))=>(?[X]:((kind(X)<~>~humble(X)))))&
(![X]:((~quiet(X)|~wise(X))<=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|rich(X))<=>(happy(X)&~strong(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)|~creative(X))))&
(![X]:((calm(X)&patient(X))<=>~brave(X)))&
((generous(fred)|~calm(fred)))&
(?[X]:(~tall(X)))&
(?[X]:((~patient(X)<~>~tall(X))))&
((quiet(paul)|happy(paul))) | ~brave(john) | [] | null | 0 |
Everyone who is happy is strong and vice versa. If someone is not patient then lucy is not wise and vice versa. Everyone who is either patient or wise is either not strong or not rich and vice versa. If john is happy then alice is either funny or not patient and vice versa. If someone is both creative and not generous then someone is wise or rich and vice versa. Everyone who is curious is patient. Everyone who is funny or not strong is either calm or brave and vice versa. Everyone who is quiet is both not calm and not old. Everyone who is either tall or not creative is either rich or not patient and vice versa. If fred is either not humble or tall then someone is both not tall and strong. Everyone who is either humble or not humble is kind. Everyone who is curious or old is both not quiet and humble and vice versa. Everyone who is both not quiet and not funny is strong or funny and vice versa. Everyone who is either rich or quiet is both not rich and not funny. Everyone who is not old is not old or not brave. Someone is either not tall or generous. Lucy is patient. Susan is funny or strong. Someone is patient or not tall. Someone is creative or not strong. John is curious. | Susan is not tall. | neutral | (![X]:(happy(X)<=>strong(X)))&
((?[X]:(~patient(X)))<=>(~wise(lucy)))&
(![X]:((patient(X)<~>wise(X))<=>(~strong(X)<~>~rich(X))))&
((happy(john))<=>((funny(alice)<~>~patient(alice))))&
((?[X]:((creative(X)&~generous(X))))<=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(curious(X)=>patient(X)))&
(![X]:((funny(X)|~strong(X))<=>(calm(X)<~>brave(X))))&
(![X]:(quiet(X)=>(~calm(X)&~old(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(rich(X)<~>~patient(X))))&
(((~humble(fred)<~>tall(fred)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((humble(X)<~>~humble(X))=>kind(X)))&
(![X]:((curious(X)|old(X))<=>(~quiet(X)&humble(X))))&
(![X]:((~quiet(X)&~funny(X))<=>(strong(X)|funny(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~rich(X)&~funny(X))))&
(![X]:(~old(X)=>(~old(X)|~brave(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
(patient(lucy))&
((funny(susan)|strong(susan)))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((creative(X)|~strong(X))))&
(curious(john)) | ~tall(susan) | [] | null | 0 |
Everyone who is either not rich or not brave is both kind and not strong and vice versa.
Everyone who is rich or old is both not quiet and not curious.
If someone is not calm or not tall then susan is both not kind and not funny.
If lucy is both not happy and not patient then someone is either curious or not creative and vice versa.
If someone is both not funny and rich then lucy is not strong and vice versa.
Everyone who is either humble or not creative is not curious.
If someone is either kind or tall then lucy is either humble or not quiet.
If someone is both tall and wise then alice is both not rich and quiet and vice versa.
If someone is wise then someone is rich or old and vice versa.
If john is both tall and not curious then someone is not brave and vice versa.
Everyone who is old is not happy.
Everyone who is funny is either generous or kind.
Everyone who is happy is either not quiet or patient.
If someone is both old and funny then someone is funny and vice versa.
Everyone who is both kind and not tall is both brave and creative and vice versa.
Everyone who is either generous or kind is either humble or not old and vice versa.
Fred is both brave and funny.
Paul is either not calm or curious.
Someone is rich.
Paul is old.
Someone is either not old or calm.
Fred is creative or not humble.
Susan is either generous or not brave. | John is not happy. | neutral | (![X]:((~rich(X)<~>~brave(X))<=>(kind(X)&~strong(X))))&
(![X]:((rich(X)|old(X))=>(~quiet(X)&~curious(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~kind(susan)&~funny(susan))))&
(((~happy(lucy)&~patient(lucy)))<=>(?[X]:((curious(X)<~>~creative(X)))))&
((?[X]:((~funny(X)&rich(X))))<=>(~strong(lucy)))&
(![X]:((humble(X)<~>~creative(X))=>~curious(X)))&
((?[X]:((kind(X)<~>tall(X))))=>((humble(lucy)<~>~quiet(lucy))))&
((?[X]:((tall(X)&wise(X))))<=>((~rich(alice)&quiet(alice))))&
((?[X]:(wise(X)))<=>(?[X]:((rich(X)|old(X)))))&
(((tall(john)&~curious(john)))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)=>~happy(X)))&
(![X]:(funny(X)=>(generous(X)<~>kind(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>patient(X))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((kind(X)&~tall(X))<=>(brave(X)&creative(X))))&
(![X]:((generous(X)<~>kind(X))<=>(humble(X)<~>~old(X))))&
((brave(fred)&funny(fred)))&
((~calm(paul)<~>curious(paul)))&
(?[X]:(rich(X)))&
(old(paul))&
(?[X]:((~old(X)<~>calm(X))))&
((creative(fred)|~humble(fred)))&
((generous(susan)<~>~brave(susan))) | ~happy(john) | [] | null | 0 |
Everyone who is not humble is kind or calm and vice versa.
Everyone who is kind or not calm is both wise and funny.
Everyone who is not kind is generous.
Everyone who is either brave or happy is not old or funny and vice versa.
If lucy is either not creative or calm then susan is not creative or not generous.
Everyone who is wise is not funny and vice versa.
If john is generous or not happy then fred is not quiet and vice versa.
If someone is both not kind and not tall then alice is not calm or not humble and vice versa.
Everyone who is either tall or generous is either wise or kind and vice versa.
Everyone who is not kind or creative is not patient or funny.
If someone is generous or curious then mary is wise.
If lucy is not tall then someone is either not happy or not curious.
If someone is not calm or not funny then someone is either not quiet or creative and vice versa.
Everyone who is both not calm and kind is wise.
Someone is both creative and brave.
Lucy is both not strong and not creative.
Someone is curious or funny.
Susan is either funny or not strong.
Paul is rich or tall.
Lucy is either humble or not creative. | Paul is wise. | neutral | (![X]:(~humble(X)<=>(kind(X)|calm(X))))&
(![X]:((kind(X)|~calm(X))=>(wise(X)&funny(X))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((brave(X)<~>happy(X))<=>(~old(X)|funny(X))))&
(((~creative(lucy)<~>calm(lucy)))=>((~creative(susan)|~generous(susan))))&
(![X]:(wise(X)<=>~funny(X)))&
(((generous(john)|~happy(john)))<=>(~quiet(fred)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul)))&
((humble(lucy)<~>~creative(lucy))) | wise(paul) | [] | null | 0 |
Everyone who is patient or not humble is either generous or not calm.
If someone is either not creative or quiet then alice is either quiet or not kind and vice versa.
Everyone who is kind or not kind is both calm and not patient and vice versa.
If john is both not patient and not creative then fred is wise.
Everyone who is not humble is not creative or curious.
If john is not happy then someone is either not wise or not old and vice versa.
Everyone who is either rich or happy is both happy and funny.
Everyone who is creative or happy is either not brave or not creative.
Everyone who is both curious and not wise is either not wise or not brave and vice versa.
If someone is either not curious or not rich then someone is strong or not old.
If susan is not patient or funny then fred is either wise or not happy and vice versa.
Everyone who is either humble or happy is funny or generous and vice versa.
If someone is either not brave or not creative then lucy is wise or not old.
Everyone who is rich or not patient is both not humble and not curious and vice versa.
Everyone who is both not funny and not creative is both not wise and creative and vice versa.
Everyone who is either wise or tall is both calm and quiet.
Susan is not quiet.
Someone is either not rich or not calm.
Someone is either not rich or calm.
Susan is wise.
Someone is old or not funny.
Fred is quiet or generous.
Someone is not patient or not funny.
Alice is not curious or not quiet. | Susan is tall. | entailment | (![X]:((patient(X)|~humble(X))=>(generous(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((quiet(alice)<~>~kind(alice))))&
(![X]:((kind(X)|~kind(X))<=>(calm(X)&~patient(X))))&
(((~patient(john)&~creative(john)))=>(wise(fred)))&
(![X]:(~humble(X)=>(~creative(X)|curious(X))))&
((~happy(john))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((rich(X)<~>happy(X))=>(happy(X)&funny(X))))&
(![X]:((creative(X)|happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((curious(X)&~wise(X))<=>(~wise(X)<~>~brave(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(?[X]:((strong(X)|~old(X)))))&
(((~patient(susan)|funny(susan)))<=>((wise(fred)<~>~happy(fred))))&
(![X]:((humble(X)<~>happy(X))<=>(funny(X)|generous(X))))&
((?[X]:((~brave(X)<~>~creative(X))))=>((wise(lucy)|~old(lucy))))&
(![X]:((rich(X)|~patient(X))<=>(~humble(X)&~curious(X))))&
(![X]:((~funny(X)&~creative(X))<=>(~wise(X)&creative(X))))&
(![X]:((wise(X)<~>tall(X))=>(calm(X)&quiet(X))))&
(~quiet(susan))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~rich(X)<~>calm(X))))&
(wise(susan))&
(?[X]:((old(X)|~funny(X))))&
((quiet(fred)|generous(fred)))&
(?[X]:((~patient(X)|~funny(X))))&
((~curious(alice)|~quiet(alice))) | tall(susan) | [
"p15",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3319911564440842273660056
% SZS output start Proof for 3319911564440842273660056
16. ! [X0] : ((wise(X0) <~> tall(X0)) => (quiet(X0) & calm(X0))) [input p15]
17. ~quiet(susan) [input p16]
20. wise(susan) [input p19]
25. ~tall(susan) [input hypothesis]
37. ! [X0] : ((quiet(X0) & calm(X0)) | (wise(X0) <=> tall(X0))) [ennf transformation 16]
62. ! [X0] : ((quiet(X0) & calm(X0)) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) [nnf transformation 37]
135. ~wise(X0) | tall(X0) | quiet(X0) [cnf transformation 62]
137. ~quiet(susan) [cnf transformation 17]
142. wise(susan) [cnf transformation 20]
147. ~tall(susan) [cnf transformation 25]
374. tall(susan) | quiet(susan) [resolution 135,142]
376. quiet(susan) [subsumption resolution 374,147]
377. $false [subsumption resolution 376,137]
% SZS output end Proof for 3319911564440842273660056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and brave is either not rich or not tall.
If paul is not quiet then someone is not humble.
If lucy is not humble or not funny then someone is both not quiet and creative and vice versa.
If someone is patient or wise then paul is both not happy and patient.
Everyone who is either not curious or not funny is both happy and patient and vice versa.
If alice is either strong or not patient then someone is not funny or not creative.
Everyone who is either brave or not patient is not curious or calm.
If fred is not strong then someone is brave or happy.
Everyone who is either not kind or humble is not old.
If someone is tall or not generous then alice is not curious and vice versa.
If alice is brave or rich then lucy is not humble.
If fred is both not strong and rich then john is wise or not quiet.
Everyone who is either not generous or not strong is funny and vice versa.
If lucy is either patient or humble then lucy is either not wise or not quiet.
If someone is either not old or not strong then someone is not humble or not generous.
Everyone who is not old or happy is not generous or old.
Someone is not strong.
Alice is rich.
Someone is not old.
Fred is both happy and quiet.
Alice is not generous or not happy.
Someone is not quiet.
Paul is strong.
Paul is happy. | Paul is happy. | entailment | (![X]:((tall(X)&brave(X))=>(~rich(X)<~>~tall(X))))&
((~quiet(paul))=>(?[X]:(~humble(X))))&
(((~humble(lucy)|~funny(lucy)))<=>(?[X]:((~quiet(X)&creative(X)))))&
((?[X]:((patient(X)|wise(X))))=>((~happy(paul)&patient(paul))))&
(![X]:((~curious(X)<~>~funny(X))<=>(happy(X)&patient(X))))&
(((strong(alice)<~>~patient(alice)))=>(?[X]:((~funny(X)|~creative(X)))))&
(![X]:((brave(X)<~>~patient(X))=>(~curious(X)|calm(X))))&
((~strong(fred))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~kind(X)<~>humble(X))=>~old(X)))&
((?[X]:((tall(X)|~generous(X))))<=>(~curious(alice)))&
(((brave(alice)|rich(alice)))=>(~humble(lucy)))&
(((~strong(fred)&rich(fred)))=>((wise(john)|~quiet(john))))&
(![X]:((~generous(X)<~>~strong(X))<=>funny(X)))&
(((patient(lucy)<~>humble(lucy)))=>((~wise(lucy)<~>~quiet(lucy))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~old(X)|happy(X))=>(~generous(X)|old(X))))&
(?[X]:(~strong(X)))&
(rich(alice))&
(?[X]:(~old(X)))&
((happy(fred)&quiet(fred)))&
((~generous(alice)|~happy(alice)))&
(?[X]:(~quiet(X)))&
(strong(paul))&
(happy(paul)) | happy(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7653405874570158212433367
% SZS output start Proof for 7653405874570158212433367
24. happy(paul) [input p23]
25. ~happy(paul) [input hypothesis]
123. happy(paul) [cnf transformation 24]
124. ~happy(paul) [cnf transformation 25]
173. 11 <=> happy(paul) [avatar definition]
295. 11 [avatar split clause 123,173]
296. ~11 [avatar split clause 124,173]
297. $false [avatar sat refutation 295,296]
% SZS output end Proof for 7653405874570158212433367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not quiet and rich then someone is not patient or not strong and vice versa.
If lucy is curious then susan is both humble and not calm.
Everyone who is both quiet and not rich is calm and vice versa.
If susan is either not strong or wise then someone is either not happy or old and vice versa.
Everyone who is both calm and curious is kind or curious.
If someone is old then fred is either humble or quiet and vice versa.
Everyone who is both brave and kind is not calm or strong and vice versa.
Everyone who is brave is either wise or humble.
Everyone who is not old or humble is strong or not rich.
Everyone who is humble is old or not curious.
Everyone who is either patient or not humble is not patient.
Everyone who is not patient is humble.
Everyone who is kind is either not quiet or creative and vice versa.
Everyone who is not wise or not quiet is both happy and not curious and vice versa.
If mary is calm or not patient then someone is either calm or not tall.
Everyone who is not curious or not strong is either patient or strong and vice versa.
Someone is either creative or humble.
Paul is not humble or creative.
Susan is either patient or curious.
Paul is either humble or happy.
Someone is happy. | Lucy is not happy. | neutral | (((~quiet(fred)&rich(fred)))<=>(?[X]:((~patient(X)|~strong(X)))))&
((curious(lucy))=>((humble(susan)&~calm(susan))))&
(![X]:((quiet(X)&~rich(X))<=>calm(X)))&
(((~strong(susan)<~>wise(susan)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((calm(X)&curious(X))=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>((humble(fred)<~>quiet(fred))))&
(![X]:((brave(X)&kind(X))<=>(~calm(X)|strong(X))))&
(![X]:(brave(X)=>(wise(X)<~>humble(X))))&
(![X]:((~old(X)|humble(X))=>(strong(X)|~rich(X))))&
(![X]:(humble(X)=>(old(X)|~curious(X))))&
(![X]:((patient(X)<~>~humble(X))=>~patient(X)))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(kind(X)<=>(~quiet(X)<~>creative(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(happy(X)&~curious(X))))&
(((calm(mary)|~patient(mary)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((~curious(X)|~strong(X))<=>(patient(X)<~>strong(X))))&
(?[X]:((creative(X)<~>humble(X))))&
((~humble(paul)|creative(paul)))&
((patient(susan)<~>curious(susan)))&
((humble(paul)<~>happy(paul)))&
(?[X]:(happy(X))) | ~happy(lucy) | [] | null | 0 |
If mary is either not strong or creative then susan is both not generous and not quiet and vice versa.
If fred is old or humble then someone is humble and vice versa.
If someone is either not quiet or not patient then fred is both not calm and old.
If someone is humble or not calm then fred is quiet.
Everyone who is not patient or tall is not quiet or not rich.
If fred is not creative or not old then someone is not happy.
Everyone who is not humble is not old and vice versa.
If someone is not brave then someone is funny and vice versa.
If mary is not patient or wise then someone is both calm and creative and vice versa.
Everyone who is both tall and not brave is old or not curious and vice versa.
If john is happy or not humble then john is either not kind or not creative and vice versa.
If fred is either not patient or not wise then someone is not brave or happy.
Everyone who is patient is either strong or not rich and vice versa.
Everyone who is not old is either wise or creative.
If lucy is both funny and not creative then someone is either not rich or not strong.
If someone is patient then someone is both funny and humble.
Someone is not funny or not patient.
Fred is funny or not curious.
Someone is both curious and generous.
Someone is both calm and quiet.
Someone is calm.
Alice is calm.
Someone is kind.
Someone is both not wise and not happy. | Fred is old. | entailment | (((~strong(mary)<~>creative(mary)))<=>((~generous(susan)&~quiet(susan))))&
(((old(fred)|humble(fred)))<=>(?[X]:(humble(X))))&
((?[X]:((~quiet(X)<~>~patient(X))))=>((~calm(fred)&old(fred))))&
((?[X]:((humble(X)|~calm(X))))=>(quiet(fred)))&
(![X]:((~patient(X)|tall(X))=>(~quiet(X)|~rich(X))))&
(((~creative(fred)|~old(fred)))=>(?[X]:(~happy(X))))&
(![X]:(~humble(X)<=>~old(X)))&
((?[X]:(~brave(X)))<=>(?[X]:(funny(X))))&
(((~patient(mary)|wise(mary)))<=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((tall(X)&~brave(X))<=>(old(X)|~curious(X))))&
(((happy(john)|~humble(john)))<=>((~kind(john)<~>~creative(john))))&
(((~patient(fred)<~>~wise(fred)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:(patient(X)<=>(strong(X)<~>~rich(X))))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(((funny(lucy)&~creative(lucy)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
((?[X]:(patient(X)))=>(?[X]:((funny(X)&humble(X)))))&
(?[X]:((~funny(X)|~patient(X))))&
((funny(fred)|~curious(fred)))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:(calm(X)))&
(calm(alice))&
(?[X]:(kind(X)))&
(?[X]:((~wise(X)&~happy(X)))) | old(fred) | [
"p1",
"p2",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6914656093908574612408937
% SZS output start Proof for 6914656093908574612408937
2. (humble(fred) | old(fred)) <=> ? [X0] : humble(X0) [input p1]
3. ? [X0] : (~quiet(X0) <~> ~patient(X0)) => (old(fred) & ~calm(fred)) [input p2]
7. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p6]
16. ? [X0] : patient(X0) => ? [X0] : (humble(X0) & funny(X0)) [input p15]
20. ? [X0] : (quiet(X0) & calm(X0)) [input p19]
25. ~old(fred) [input hypothesis]
27. ? [X0] : patient(X0) => ? [X1] : (humble(X1) & funny(X1)) [rectify 16]
28. (old(fred) & ~calm(fred)) | ! [X0] : (~quiet(X0) <=> ~patient(X0)) [ennf transformation 3]
37. ? [X1] : (humble(X1) & funny(X1)) | ! [X0] : ~patient(X0) [ennf transformation 27]
40. ((humble(fred) | old(fred)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~humble(fred) & ~old(fred))) [nnf transformation 2]
41. (humble(fred) | old(fred) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~humble(fred) & ~old(fred))) [flattening 40]
42. (humble(fred) | old(fred) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | (~humble(fred) & ~old(fred))) [rectify 41]
43. ? [X1] : humble(X1) => humble(sK0) [choice axiom]
44. (humble(fred) | old(fred) | ! [X0] : ~humble(X0)) & (humble(sK0) | (~humble(fred) & ~old(fred))) [skolemisation 42,43]
45. (old(fred) & ~calm(fred)) | ! [X0] : ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0))) [nnf transformation 28]
48. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 7]
71. ? [X0] : (humble(X0) & funny(X0)) | ! [X1] : ~patient(X1) [rectify 37]
72. ? [X0] : (humble(X0) & funny(X0)) => (humble(sK7) & funny(sK7)) [choice axiom]
73. (humble(sK7) & funny(sK7)) | ! [X1] : ~patient(X1) [skolemisation 71,72]
78. ? [X0] : (quiet(X0) & calm(X0)) => (quiet(sK10) & calm(sK10)) [choice axiom]
79. quiet(sK10) & calm(sK10) [skolemisation 20,78]
94. humble(fred) | old(fred) | ~humble(X0) [cnf transformation 44]
98. old(fred) | ~quiet(X0) | patient(X0) [cnf transformation 45]
106. ~humble(X0) | old(X0) [cnf transformation 48]
136. humble(sK7) | ~patient(X1) [cnf transformation 73]
142. quiet(sK10) [cnf transformation 79]
148. ~old(fred) [cnf transformation 25]
172. 5 <=> ! [X0] : ~humble(X0) [avatar definition]
173. ~humble(X0) <- (5) [avatar component clause 172]
175. 6 <=> old(fred) [avatar definition]
176. ~old(fred) <- (~6) [avatar component clause 175]
179. 7 <=> humble(fred) [avatar definition]
181. humble(fred) <- (7) [avatar component clause 179]
182. 5 | 6 | 7 [avatar split clause 94,179,175,172]
190. 9 <=> ! [X0] : (~quiet(X0) | patient(X0)) [avatar definition]
191. ~quiet(X0) | patient(X0) <- (9) [avatar component clause 190]
192. 9 | 6 [avatar split clause 98,175,190]
321. 37 <=> ! [X1] : ~patient(X1) [avatar definition]
322. ~patient(X1) <- (37) [avatar component clause 321]
324. 38 <=> humble(sK7) [avatar definition]
326. humble(sK7) <- (38) [avatar component clause 324]
327. 37 | 38 [avatar split clause 136,324,321]
351. ~6 [avatar split clause 148,175]
356. ~quiet(X0) <- (9, 37) [subsumption resolution 191,322]
361. $false <- (9, 37) [resolution 356,142]
362. ~9 | ~37 [avatar contradiction clause 361]
363. $false <- (5, 38) [subsumption resolution 326,173]
364. ~5 | ~38 [avatar contradiction clause 363]
365. old(fred) <- (7) [resolution 106,181]
368. $false <- (~6, 7) [subsumption resolution 365,176]
369. 6 | ~7 [avatar contradiction clause 368]
370. $false [avatar sat refutation 182,192,327,351,362,364,369]
% SZS output end Proof for 6914656093908574612408937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then susan is not patient. Everyone who is both humble and not creative is both humble and strong. If fred is brave then someone is either strong or not calm and vice versa. Everyone who is quiet is rich or not happy and vice versa. If lucy is not tall then someone is patient or not old and vice versa. If someone is both old and not brave then someone is tall. Everyone who is tall is patient and vice versa. If someone is either not kind or wise then someone is generous or not tall. If someone is both not quiet and quiet then someone is either not quiet or creative. Everyone who is either rich or generous is either funny or curious and vice versa. If someone is either not curious or strong then someone is rich. If someone is either not funny or old then alice is either not generous or kind. Everyone who is either not wise or humble is either not patient or not happy and vice versa. If someone is not brave or funny then fred is rich or curious. Everyone who is both not funny and not generous is either funny or happy. Everyone who is not generous or not patient is either not patient or creative and vice versa. Someone is not quiet. Someone is generous or quiet. Susan is old or not tall. Alice is funny. Mary is creative or not curious. Someone is both not calm and not old. Someone is both not calm and not humble. Someone is either not brave or not creative. | Lucy is not creative. | entailment | ((?[X]:(rich(X)))=>(~patient(susan)))&
(![X]:((humble(X)&~creative(X))=>(humble(X)&strong(X))))&
((brave(fred))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:(quiet(X)<=>(rich(X)|~happy(X))))&
((~tall(lucy))<=>(?[X]:((patient(X)|~old(X)))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:(tall(X))))&
(![X]:(tall(X)<=>patient(X)))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((generous(X)|~tall(X)))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((rich(X)<~>generous(X))<=>(funny(X)<~>curious(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:(rich(X))))&
((?[X]:((~funny(X)<~>old(X))))=>((~generous(alice)<~>kind(alice))))&
(![X]:((~wise(X)<~>humble(X))<=>(~patient(X)<~>~happy(X))))&
((?[X]:((~brave(X)|funny(X))))=>((rich(fred)|curious(fred))))&
(![X]:((~funny(X)&~generous(X))=>(funny(X)<~>happy(X))))&
(![X]:((~generous(X)|~patient(X))<=>(~patient(X)<~>creative(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((generous(X)|quiet(X))))&
((old(susan)|~tall(susan)))&
(funny(alice))&
((creative(mary)|~curious(mary)))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~creative(lucy) | [
"p4",
"p6",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2330921897490892836416281
% SZS output start Proof for 2330921897490892836416281
5. ~tall(lucy) <=> ? [X0] : (~old(X0) | patient(X0)) [input p4]
7. ! [X0] : (tall(X0) <=> patient(X0)) [input p6]
16. ! [X0] : ((~patient(X0) | ~generous(X0)) <=> (~patient(X0) <~> creative(X0))) [input p15]
22. ? [X0] : (~old(X0) & ~calm(X0)) [input p21]
25. creative(lucy) [input hypothesis]
48. (~tall(lucy) | ! [X0] : (old(X0) & ~patient(X0))) & (? [X0] : (~old(X0) | patient(X0)) | tall(lucy)) [nnf transformation 5]
49. (~tall(lucy) | ! [X0] : (old(X0) & ~patient(X0))) & (? [X1] : (~old(X1) | patient(X1)) | tall(lucy)) [rectify 48]
50. ? [X1] : (~old(X1) | patient(X1)) => (~old(sK1) | patient(sK1)) [choice axiom]
51. (~tall(lucy) | ! [X0] : (old(X0) & ~patient(X0))) & ((~old(sK1) | patient(sK1)) | tall(lucy)) [skolemisation 49,50]
55. ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))) [nnf transformation 7]
72. ! [X0] : (((~patient(X0) | ~generous(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (patient(X0) & generous(X0)))) [nnf transformation 16]
73. ! [X0] : ((~patient(X0) | ~generous(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (patient(X0) & generous(X0)))) [flattening 72]
78. ? [X0] : (~old(X0) & ~calm(X0)) => (~old(sK8) & ~calm(sK8)) [choice axiom]
79. ~old(sK8) & ~calm(sK8) [skolemisation 22,78]
97. ~tall(lucy) | old(X0) [cnf transformation 51]
100. ~patient(X0) | tall(X0) [cnf transformation 55]
134. ~creative(X0) | patient(X0) | patient(X0) [cnf transformation 73]
143. ~old(sK8) [cnf transformation 79]
148. creative(lucy) [cnf transformation 25]
149. ~creative(X0) | patient(X0) [duplicate literal removal 134]
183. 8 <=> ! [X0] : old(X0) [avatar definition]
184. old(X0) <- (8) [avatar component clause 183]
186. 9 <=> tall(lucy) [avatar definition]
189. 8 | ~9 [avatar split clause 97,186,183]
312. patient(lucy) [resolution 149,148]
313. tall(lucy) [resolution 312,100]
316. 9 [avatar split clause 313,186]
317. $false <- (8) [resolution 184,143]
320. ~8 [avatar contradiction clause 317]
321. $false [avatar sat refutation 189,316,320]
% SZS output end Proof for 2330921897490892836416281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or brave is both calm and not funny and vice versa. Everyone who is not calm is either not strong or not happy and vice versa. If alice is not quiet then susan is not wise. If john is not kind then someone is patient and vice versa. Everyone who is either brave or not rich is either quiet or not old and vice versa. Everyone who is both not quiet and strong is both funny and not patient. Everyone who is both not brave and not generous is either patient or old and vice versa. Everyone who is wise or not strong is both not brave and wise. Everyone who is humble is either not happy or not generous. If susan is not quiet or not kind then mary is not humble and vice versa. Everyone who is not kind or brave is both not quiet and creative. If lucy is tall then someone is not happy or not quiet. If someone is both rich and tall then alice is both not funny and humble. Everyone who is old is both strong and brave. Everyone who is not old is either kind or happy and vice versa. If someone is either not creative or strong then paul is rich and vice versa. Mary is rich. Someone is either not tall or not humble. Someone is generous or not rich. | Susan is not calm. | contradiction | (![X]:((~old(X)|brave(X))<=>(calm(X)&~funny(X))))&
(![X]:(~calm(X)<=>(~strong(X)<~>~happy(X))))&
((~quiet(alice))=>(~wise(susan)))&
((~kind(john))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~quiet(X)&strong(X))=>(funny(X)&~patient(X))))&
(![X]:((~brave(X)&~generous(X))<=>(patient(X)<~>old(X))))&
(![X]:((wise(X)|~strong(X))=>(~brave(X)&wise(X))))&
(![X]:(humble(X)=>(~happy(X)<~>~generous(X))))&
(((~quiet(susan)|~kind(susan)))<=>(~humble(mary)))&
(![X]:((~kind(X)|brave(X))=>(~quiet(X)&creative(X))))&
((tall(lucy))=>(?[X]:((~happy(X)|~quiet(X)))))&
((?[X]:((rich(X)&tall(X))))=>((~funny(alice)&humble(alice))))&
(![X]:(old(X)=>(strong(X)&brave(X))))&
(![X]:(~old(X)<=>(kind(X)<~>happy(X))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(rich(paul)))&
(rich(mary))&
(?[X]:((~tall(X)<~>~humble(X))))&
(?[X]:((generous(X)|~rich(X)))) | ~calm(susan) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4013307530287731158221891
% SZS output start Proof for 4013307530287731158221891
1. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~funny(X0) & calm(X0))) [input p0]
14. ! [X0] : (old(X0) => (brave(X0) & strong(X0))) [input p13]
20. ~calm(susan) [input hypothesis]
29. ! [X0] : ((brave(X0) & strong(X0)) | ~old(X0)) [ennf transformation 14]
30. ! [X0] : (((brave(X0) | ~old(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 1]
31. ! [X0] : ((brave(X0) | ~old(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [flattening 30]
55. calm(X0) | old(X0) [cnf transformation 31]
56. ~brave(X0) | calm(X0) [cnf transformation 31]
100. ~old(X0) | brave(X0) [cnf transformation 29]
113. ~calm(susan) [cnf transformation 20]
218. old(susan) [resolution 55,113]
223. brave(susan) [resolution 100,218]
226. calm(susan) [resolution 223,56]
227. $false [subsumption resolution 226,113]
% SZS output end Proof for 4013307530287731158221891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or happy is either not wise or wise.
If someone is either creative or not funny then john is kind and vice versa.
Everyone who is strong or quiet is not strong.
If someone is funny then lucy is both happy and not humble and vice versa.
If someone is either not generous or not quiet then fred is both not curious and not quiet and vice versa.
If john is either not old or not rich then someone is both quiet and not old and vice versa.
Everyone who is patient is humble or not patient and vice versa.
Everyone who is happy is either quiet or not generous.
If someone is funny then someone is both funny and rich and vice versa.
Everyone who is not rich or creative is both humble and kind and vice versa.
Everyone who is generous is not calm or curious.
If someone is both not creative and not calm then someone is not patient or wise and vice versa.
Everyone who is rich is calm or rich and vice versa.
Everyone who is rich is generous or not patient and vice versa.
Everyone who is either old or not happy is both not generous and not strong and vice versa.
Everyone who is old or not generous is humble and vice versa.
Someone is both generous and creative.
Someone is either humble or not tall.
Fred is either kind or generous.
Paul is both patient and not strong.
Susan is either curious or not strong.
Someone is not strong or not patient.
Someone is either not humble or quiet. | Fred is rich. | neutral | (![X]:((humble(X)<~>happy(X))=>(~wise(X)<~>wise(X))))&
((?[X]:((creative(X)<~>~funny(X))))<=>(kind(john)))&
(![X]:((strong(X)|quiet(X))=>~strong(X)))&
((?[X]:(funny(X)))<=>((happy(lucy)&~humble(lucy))))&
((?[X]:((~generous(X)<~>~quiet(X))))<=>((~curious(fred)&~quiet(fred))))&
(((~old(john)<~>~rich(john)))<=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:(patient(X)<=>(humble(X)|~patient(X))))&
(![X]:(happy(X)=>(quiet(X)<~>~generous(X))))&
((?[X]:(funny(X)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~rich(X)|creative(X))<=>(humble(X)&kind(X))))&
(![X]:(generous(X)=>(~calm(X)|curious(X))))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:(rich(X)<=>(calm(X)|rich(X))))&
(![X]:(rich(X)<=>(generous(X)|~patient(X))))&
(![X]:((old(X)<~>~happy(X))<=>(~generous(X)&~strong(X))))&
(![X]:((old(X)|~generous(X))<=>humble(X)))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
((kind(fred)<~>generous(fred)))&
((patient(paul)&~strong(paul)))&
((curious(susan)<~>~strong(susan)))&
(?[X]:((~strong(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X)))) | rich(fred) | [] | null | 0 |
Everyone who is either not brave or not humble is both rich and not strong and vice versa.
Everyone who is generous is both not generous and not quiet.
Everyone who is either calm or not rich is both not generous and not strong and vice versa.
Everyone who is both not kind and tall is either not creative or not funny and vice versa.
If someone is funny then lucy is patient or not creative.
Everyone who is patient is either not generous or calm and vice versa.
Everyone who is funny is kind or not patient.
Everyone who is either tall or not happy is old or happy and vice versa.
Everyone who is patient is not tall or not brave.
Everyone who is either not humble or brave is both kind and strong.
If someone is not patient or not humble then paul is either wise or funny.
If someone is both wise and tall then alice is kind or humble and vice versa.
If someone is not patient or patient then mary is either quiet or old.
If lucy is not patient or happy then lucy is either not strong or wise and vice versa.
If alice is both not brave and not wise then someone is not tall or strong and vice versa.
Everyone who is both old and brave is generous.
Fred is either strong or not calm.
Someone is rich.
Someone is either not strong or brave.
John is both not calm and quiet.
Someone is both not generous and kind.
Someone is not patient.
Paul is strong.
Someone is both old and humble. | John is rich. | entailment | (![X]:((~brave(X)<~>~humble(X))<=>(rich(X)&~strong(X))))&
(![X]:(generous(X)=>(~generous(X)&~quiet(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~kind(X)&tall(X))<=>(~creative(X)<~>~funny(X))))&
((?[X]:(funny(X)))=>((patient(lucy)|~creative(lucy))))&
(![X]:(patient(X)<=>(~generous(X)<~>calm(X))))&
(![X]:(funny(X)=>(kind(X)|~patient(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(old(X)|happy(X))))&
(![X]:(patient(X)=>(~tall(X)|~brave(X))))&
(![X]:((~humble(X)<~>brave(X))=>(kind(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>((wise(paul)<~>funny(paul))))&
((?[X]:((wise(X)&tall(X))))<=>((kind(alice)|humble(alice))))&
((?[X]:((~patient(X)|patient(X))))=>((quiet(mary)<~>old(mary))))&
(((~patient(lucy)|happy(lucy)))<=>((~strong(lucy)<~>wise(lucy))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((old(X)&brave(X))=>generous(X)))&
((strong(fred)<~>~calm(fred)))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)<~>brave(X))))&
((~calm(john)&quiet(john)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:(~patient(X)))&
(strong(paul))&
(?[X]:((old(X)&humble(X)))) | rich(john) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p8",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8508802913761332930321960
% SZS output start Proof for 8508802913761332930321960
1. ! [X0] : ((~brave(X0) <~> ~humble(X0)) <=> (~strong(X0) & rich(X0))) [input p0]
2. ! [X0] : (generous(X0) => (~quiet(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (~strong(X0) & ~generous(X0))) [input p2]
6. ! [X0] : (patient(X0) <=> (~generous(X0) <~> calm(X0))) [input p5]
8. ! [X0] : ((tall(X0) <~> ~happy(X0)) <=> (happy(X0) | old(X0))) [input p7]
9. ! [X0] : (patient(X0) => (~brave(X0) | ~tall(X0))) [input p8]
10. ! [X0] : ((~humble(X0) <~> brave(X0)) => (strong(X0) & kind(X0))) [input p9]
16. ! [X0] : ((brave(X0) & old(X0)) => generous(X0)) [input p15]
20. quiet(john) & ~calm(john) [input p19]
25. ~rich(john) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & ~generous(X0)) | ~generous(X0)) [ennf transformation 2]
31. ! [X0] : ((~brave(X0) | ~tall(X0)) | ~patient(X0)) [ennf transformation 9]
32. ! [X0] : (~brave(X0) | ~tall(X0) | ~patient(X0)) [flattening 31]
33. ! [X0] : ((strong(X0) & kind(X0)) | (~humble(X0) <=> brave(X0))) [ennf transformation 10]
36. ! [X0] : (generous(X0) | (~brave(X0) | ~old(X0))) [ennf transformation 16]
37. ! [X0] : (generous(X0) | ~brave(X0) | ~old(X0)) [flattening 36]
38. ! [X0] : ((((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))))) [nnf transformation 1]
39. ! [X0] : ((((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))))) [flattening 38]
40. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 3]
41. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [flattening 40]
44. ! [X0] : ((patient(X0) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) & (((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~patient(X0))) [nnf transformation 6]
45. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [nnf transformation 8]
46. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [flattening 45]
47. ! [X0] : ((strong(X0) & kind(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) [nnf transformation 33]
74. ~humble(X0) | rich(X0) | brave(X0) [cnf transformation 39]
75. ~brave(X0) | rich(X0) | humble(X0) [cnf transformation 39]
80. ~generous(X0) | ~generous(X0) [cnf transformation 26]
85. ~strong(X0) | calm(X0) | rich(X0) [cnf transformation 41]
97. patient(X0) | calm(X0) | generous(X0) [cnf transformation 44]
101. happy(X0) | old(X0) | tall(X0) | happy(X0) [cnf transformation 46]
103. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 46]
106. ~patient(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 32]
109. strong(X0) | brave(X0) | humble(X0) [cnf transformation 47]
135. generous(X0) | ~brave(X0) | ~old(X0) [cnf transformation 37]
141. ~calm(john) [cnf transformation 20]
149. ~rich(john) [cnf transformation 25]
150. happy(X0) | old(X0) | tall(X0) [duplicate literal removal 101]
151. ~happy(X0) | tall(X0) [duplicate literal removal 103]
152. ~generous(X0) [duplicate literal removal 80]
167. patient(X0) | calm(X0) [subsumption resolution 97,152]
169. old(X0) | tall(X0) [subsumption resolution 150,151]
272. ~old(X0) | ~brave(X0) [subsumption resolution 135,152]
306. ~brave(X0) | tall(X0) [resolution 272,169]
357. ~tall(X0) | ~brave(X0) | calm(X0) [resolution 106,167]
358. ~brave(X0) | calm(X0) [subsumption resolution 357,306]
362. brave(X0) | humble(X0) | calm(X0) | rich(X0) [resolution 109,85]
371. calm(X0) | humble(X0) | rich(X0) [subsumption resolution 362,75]
523. humble(john) | rich(john) [resolution 371,141]
528. humble(john) [subsumption resolution 523,149]
613. rich(john) | brave(john) [resolution 528,74]
615. 63 <=> brave(john) [avatar definition]
616. brave(john) <- (63) [avatar component clause 615]
628. brave(john) [subsumption resolution 613,149]
629. 63 [avatar split clause 628,615]
655. calm(john) <- (63) [resolution 616,358]
658. $false <- (63) [subsumption resolution 655,141]
659. ~63 [avatar contradiction clause 658]
660. $false [avatar sat refutation 629,659]
% SZS output end Proof for 8508802913761332930321960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not rich then susan is generous and vice versa. Everyone who is generous is funny. Everyone who is wise is both not kind and brave. If susan is either patient or not rich then mary is patient or not curious and vice versa. If someone is not funny or not strong then someone is both patient and not quiet and vice versa. Everyone who is both tall and brave is rich. Everyone who is either quiet or creative is quiet. If paul is both kind and not calm then someone is not patient or not happy and vice versa. If alice is old or brave then john is not brave or quiet. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Someone is not quiet. Mary is both generous and kind. Lucy is either not creative or humble. Alice is funny. Paul is generous. Someone is old or not tall. Someone is both not rich and brave. | John is patient. | entailment | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(((patient(susan)<~>~rich(susan)))<=>((patient(mary)|~curious(mary))))&
((?[X]:((~funny(X)|~strong(X))))<=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((tall(X)&brave(X))=>rich(X)))&
(![X]:((quiet(X)<~>creative(X))=>quiet(X)))&
(((kind(paul)&~calm(paul)))<=>(?[X]:((~patient(X)|~happy(X)))))&
(((old(alice)|brave(alice)))=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(?[X]:(~quiet(X)))&
((generous(mary)&kind(mary)))&
((~creative(lucy)<~>humble(lucy)))&
(funny(alice))&
(generous(paul))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~rich(X)&brave(X)))) | patient(john) | [
"p1",
"p7",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1616952237672328552182876
% SZS output start Proof for 1616952237672328552182876
2. ! [X0] : (generous(X0) => funny(X0)) [input p1]
8. (~calm(paul) & kind(paul)) <=> ? [X0] : (~happy(X0) | ~patient(X0)) [input p7]
13. ! [X0] : ((curious(X0) | ~calm(X0)) => ~funny(X0)) [input p12]
21. generous(paul) [input p20]
24. ~patient(john) [input hypothesis]
28. ! [X0] : (funny(X0) | ~generous(X0)) [ennf transformation 2]
33. ! [X0] : (~funny(X0) | (~curious(X0) & calm(X0))) [ennf transformation 13]
48. ((~calm(paul) & kind(paul)) | ! [X0] : (happy(X0) & patient(X0))) & (? [X0] : (~happy(X0) | ~patient(X0)) | (calm(paul) | ~kind(paul))) [nnf transformation 8]
49. ((~calm(paul) & kind(paul)) | ! [X0] : (happy(X0) & patient(X0))) & (? [X0] : (~happy(X0) | ~patient(X0)) | calm(paul) | ~kind(paul)) [flattening 48]
50. ((~calm(paul) & kind(paul)) | ! [X0] : (happy(X0) & patient(X0))) & (? [X1] : (~happy(X1) | ~patient(X1)) | calm(paul) | ~kind(paul)) [rectify 49]
51. ? [X1] : (~happy(X1) | ~patient(X1)) => (~happy(sK3) | ~patient(sK3)) [choice axiom]
52. ((~calm(paul) & kind(paul)) | ! [X0] : (happy(X0) & patient(X0))) & ((~happy(sK3) | ~patient(sK3)) | calm(paul) | ~kind(paul)) [skolemisation 50,51]
70. ~generous(X0) | funny(X0) [cnf transformation 28]
89. ~calm(paul) | patient(X0) [cnf transformation 52]
103. ~funny(X0) | calm(X0) [cnf transformation 33]
123. generous(paul) [cnf transformation 21]
126. ~patient(john) [cnf transformation 24]
207. 18 <=> calm(paul) [avatar definition]
209. ~calm(paul) <- (~18) [avatar component clause 207]
212. 19 <=> ! [X0] : patient(X0) [avatar definition]
213. patient(X0) <- (19) [avatar component clause 212]
214. 19 | ~18 [avatar split clause 89,207,212]
288. $false <- (19) [resolution 213,126]
289. ~19 [avatar contradiction clause 288]
291. funny(paul) [resolution 70,123]
311. calm(paul) [resolution 291,103]
312. $false <- (~18) [subsumption resolution 311,209]
313. 18 [avatar contradiction clause 312]
314. $false [avatar sat refutation 214,289,313]
% SZS output end Proof for 1616952237672328552182876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or tall then someone is old or calm and vice versa. Everyone who is either not tall or happy is both happy and not patient and vice versa. Everyone who is not generous is not happy. Everyone who is either creative or not calm is both not happy and happy. Everyone who is both quiet and calm is funny or not calm and vice versa. If someone is wise then someone is either creative or kind. If someone is not humble then someone is happy or funny. If mary is both kind and quiet then someone is either not patient or strong. Everyone who is both quiet and strong is either not creative or not happy. Everyone who is generous is not generous or patient and vice versa. Everyone who is strong is not generous. If someone is either humble or calm then paul is both not curious and old and vice versa. Everyone who is not strong or calm is not curious or not generous. Everyone who is not rich is both not curious and strong and vice versa. If paul is either old or not calm then someone is either not patient or strong. If lucy is both curious and not calm then fred is wise or not wise. Fred is funny or quiet. Someone is either not kind or creative. Someone is either kind or not wise. Mary is both not kind and humble. Fred is not quiet or not old. Lucy is either not wise or old. | Fred is patient. | entailment | ((?[X]:((~old(X)<~>tall(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:((creative(X)<~>~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)&calm(X))<=>(funny(X)|~calm(X))))&
((?[X]:(wise(X)))=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((happy(X)|funny(X)))))&
(((kind(mary)&quiet(mary)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((quiet(X)&strong(X))=>(~creative(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|patient(X))))&
(![X]:(strong(X)=>~generous(X)))&
((?[X]:((humble(X)<~>calm(X))))<=>((~curious(paul)&old(paul))))&
(![X]:((~strong(X)|calm(X))=>(~curious(X)|~generous(X))))&
(![X]:(~rich(X)<=>(~curious(X)&strong(X))))&
(((old(paul)<~>~calm(paul)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((curious(lucy)&~calm(lucy)))=>((wise(fred)|~wise(fred))))&
((funny(fred)|quiet(fred)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
((~kind(mary)&humble(mary)))&
((~quiet(fred)|~old(fred)))&
((~wise(lucy)<~>old(lucy))) | patient(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4261497368082945312363603
% SZS output start Proof for 4261497368082945312363603
10. ! [X0] : (generous(X0) <=> (patient(X0) | ~generous(X0))) [input p9]
23. ~patient(fred) [input hypothesis]
62. ! [X0] : ((generous(X0) | (~patient(X0) & generous(X0))) & ((patient(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 10]
63. ! [X0] : ((generous(X0) | (~patient(X0) & generous(X0))) & (patient(X0) | ~generous(X0) | ~generous(X0))) [flattening 62]
108. patient(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 63]
109. generous(X0) | generous(X0) [cnf transformation 63]
135. ~patient(fred) [cnf transformation 23]
136. patient(X0) | ~generous(X0) [duplicate literal removal 108]
137. generous(X0) [duplicate literal removal 109]
222. patient(X0) [subsumption resolution 136,137]
289. $false [subsumption resolution 135,222]
% SZS output end Proof for 4261497368082945312363603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or patient then someone is both not kind and not funny.
Everyone who is both creative and not patient is calm or happy.
If alice is both not creative and rich then lucy is both happy and humble and vice versa.
If someone is either not humble or strong then someone is humble or strong and vice versa.
If someone is not funny or old then lucy is both not strong and not creative and vice versa.
Everyone who is both not old and not patient is happy.
Everyone who is either kind or quiet is not tall.
Everyone who is not old or wise is not quiet or not curious and vice versa.
Everyone who is both not happy and not old is either kind or rich and vice versa.
If john is both not rich and funny then someone is either not wise or not quiet and vice versa.
Everyone who is curious is either not humble or not tall.
Everyone who is quiet or not funny is both not strong and curious and vice versa.
Everyone who is rich or not patient is either not wise or not kind.
Everyone who is either wise or not funny is not happy or not quiet.
If someone is wise or not humble then john is either wise or quiet and vice versa.
Everyone who is both not happy and patient is curious and vice versa.
Someone is not funny or rich.
Lucy is either not humble or creative.
Fred is either curious or wise.
Someone is either happy or calm.
Fred is not humble.
Someone is both not wise and kind.
Someone is both not humble and patient.
Someone is not curious. | Lucy is not strong. | entailment | ((?[X]:((happy(X)|patient(X))))=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((creative(X)&~patient(X))=>(calm(X)|happy(X))))&
(((~creative(alice)&rich(alice)))<=>((happy(lucy)&humble(lucy))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((humble(X)|strong(X)))))&
((?[X]:((~funny(X)|old(X))))<=>((~strong(lucy)&~creative(lucy))))&
(![X]:((~old(X)&~patient(X))=>happy(X)))&
(![X]:((kind(X)<~>quiet(X))=>~tall(X)))&
(![X]:((~old(X)|wise(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~happy(X)&~old(X))<=>(kind(X)<~>rich(X))))&
(((~rich(john)&funny(john)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:((quiet(X)|~funny(X))<=>(~strong(X)&curious(X))))&
(![X]:((rich(X)|~patient(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~funny(X))=>(~happy(X)|~quiet(X))))&
((?[X]:((wise(X)|~humble(X))))<=>((wise(john)<~>quiet(john))))&
(![X]:((~happy(X)&patient(X))<=>curious(X)))&
(?[X]:((~funny(X)|rich(X))))&
((~humble(lucy)<~>creative(lucy)))&
((curious(fred)<~>wise(fred)))&
(?[X]:((happy(X)<~>calm(X))))&
(~humble(fred))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:(~curious(X))) | ~strong(lucy) | [
"p0",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5593824703515641788662575
% SZS output start Proof for 5593824703515641788662575
1. ? [X0] : (patient(X0) | happy(X0)) => ? [X0] : (~funny(X0) & ~kind(X0)) [input p0]
5. ? [X0] : (old(X0) | ~funny(X0)) <=> (~creative(lucy) & ~strong(lucy)) [input p4]
23. ? [X0] : (patient(X0) & ~humble(X0)) [input p22]
25. strong(lucy) [input hypothesis]
26. ? [X0] : (patient(X0) | happy(X0)) => ? [X1] : (~funny(X1) & ~kind(X1)) [rectify 1]
28. ? [X1] : (~funny(X1) & ~kind(X1)) | ! [X0] : (~patient(X0) & ~happy(X0)) [ennf transformation 26]
38. ? [X0] : (~funny(X0) & ~kind(X0)) | ! [X1] : (~patient(X1) & ~happy(X1)) [rectify 28]
39. ? [X0] : (~funny(X0) & ~kind(X0)) => (~funny(sK0) & ~kind(sK0)) [choice axiom]
40. (~funny(sK0) & ~kind(sK0)) | ! [X1] : (~patient(X1) & ~happy(X1)) [skolemisation 38,39]
48. (? [X0] : (old(X0) | ~funny(X0)) | (creative(lucy) | strong(lucy))) & ((~creative(lucy) & ~strong(lucy)) | ! [X0] : (~old(X0) & funny(X0))) [nnf transformation 5]
49. (? [X0] : (old(X0) | ~funny(X0)) | creative(lucy) | strong(lucy)) & ((~creative(lucy) & ~strong(lucy)) | ! [X0] : (~old(X0) & funny(X0))) [flattening 48]
50. (? [X0] : (old(X0) | ~funny(X0)) | creative(lucy) | strong(lucy)) & ((~creative(lucy) & ~strong(lucy)) | ! [X1] : (~old(X1) & funny(X1))) [rectify 49]
51. ? [X0] : (old(X0) | ~funny(X0)) => (old(sK3) | ~funny(sK3)) [choice axiom]
52. ((old(sK3) | ~funny(sK3)) | creative(lucy) | strong(lucy)) & ((~creative(lucy) & ~strong(lucy)) | ! [X1] : (~old(X1) & funny(X1))) [skolemisation 50,51]
83. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK9) & ~humble(sK9)) [choice axiom]
84. patient(sK9) & ~humble(sK9) [skolemisation 23,83]
90. ~funny(sK0) | ~patient(X1) [cnf transformation 40]
102. ~strong(lucy) | funny(X1) [cnf transformation 52]
159. patient(sK9) [cnf transformation 84]
161. strong(lucy) [cnf transformation 25]
163. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
164. ~patient(X1) <- (1) [avatar component clause 163]
166. 2 <=> funny(sK0) [avatar definition]
168. ~funny(sK0) <- (~2) [avatar component clause 166]
169. 1 | ~2 [avatar split clause 90,166,163]
235. 17 <=> strong(lucy) [avatar definition]
256. 22 <=> ! [X1] : funny(X1) [avatar definition]
257. funny(X1) <- (22) [avatar component clause 256]
260. 22 | ~17 [avatar split clause 102,235,256]
348. 17 [avatar split clause 161,235]
349. $false <- (~2, 22) [subsumption resolution 168,257]
350. 2 | ~22 [avatar contradiction clause 349]
351. $false <- (1) [resolution 164,159]
352. ~1 [avatar contradiction clause 351]
353. $false [avatar sat refutation 169,260,348,350,352]
% SZS output end Proof for 5593824703515641788662575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or calm is both old and patient and vice versa.
If someone is not strong then someone is either not generous or quiet and vice versa.
Everyone who is not generous or patient is tall or not strong and vice versa.
Everyone who is quiet or not strong is not funny.
Everyone who is either brave or not brave is not strong or not calm.
If lucy is both quiet and generous then someone is not brave and vice versa.
Everyone who is either not patient or not generous is tall and vice versa.
If john is both generous and wise then john is wise or rich.
Everyone who is either not funny or not old is not patient or not generous and vice versa.
Everyone who is strong is not curious or not kind.
Everyone who is not calm is both rich and funny and vice versa.
If someone is either not creative or not wise then someone is not quiet.
If john is humble or creative then susan is not strong.
If someone is either not brave or not calm then someone is either not strong or not humble and vice versa.
If fred is either not creative or not kind then someone is not old and vice versa.
If someone is not rich or not humble then lucy is not brave and vice versa.
Someone is either strong or brave.
Susan is either creative or not calm.
Lucy is curious.
Someone is either not calm or not kind.
Alice is not kind.
Someone is curious or patient. | Alice is humble. | entailment | (![X]:((~humble(X)|calm(X))<=>(old(X)&patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~generous(X)<~>quiet(X)))))&
(![X]:((~generous(X)|patient(X))<=>(tall(X)|~strong(X))))&
(![X]:((quiet(X)|~strong(X))=>~funny(X)))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)|~calm(X))))&
(((quiet(lucy)&generous(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>tall(X)))&
(((generous(john)&wise(john)))=>((wise(john)|rich(john))))&
(![X]:((~funny(X)<~>~old(X))<=>(~patient(X)|~generous(X))))&
(![X]:(strong(X)=>(~curious(X)|~kind(X))))&
(![X]:(~calm(X)<=>(rich(X)&funny(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(?[X]:(~quiet(X))))&
(((humble(john)|creative(john)))=>(~strong(susan)))&
((?[X]:((~brave(X)<~>~calm(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(((~creative(fred)<~>~kind(fred)))<=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(~brave(lucy)))&
(?[X]:((strong(X)<~>brave(X))))&
((creative(susan)<~>~calm(susan)))&
(curious(lucy))&
(?[X]:((~calm(X)<~>~kind(X))))&
(~kind(alice))&
(?[X]:((curious(X)|patient(X)))) | humble(alice) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 856401692876826744988965
% SZS output start Proof for 856401692876826744988965
1. ! [X0] : ((calm(X0) | ~humble(X0)) <=> (patient(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (~strong(X0) | tall(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => ~funny(X0)) [input p3]
6. (generous(lucy) & quiet(lucy)) <=> ? [X0] : ~brave(X0) [input p5]
7. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> tall(X0)) [input p6]
9. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (~generous(X0) | ~patient(X0))) [input p8]
11. ! [X0] : (~calm(X0) <=> (funny(X0) & rich(X0))) [input p10]
16. ? [X0] : (~humble(X0) | ~rich(X0)) <=> ~brave(lucy) [input p15]
23. ~humble(alice) [input hypothesis]
27. ! [X0] : (~funny(X0) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
36. ! [X0] : (((calm(X0) | ~humble(X0)) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | ~humble(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [flattening 36]
43. ! [X0] : (((patient(X0) | ~generous(X0)) | (strong(X0) & ~tall(X0))) & ((~strong(X0) | tall(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 3]
44. ! [X0] : ((patient(X0) | ~generous(X0) | (strong(X0) & ~tall(X0))) & (~strong(X0) | tall(X0) | (~patient(X0) & generous(X0)))) [flattening 43]
46. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~generous(lucy) | ~quiet(lucy))) [nnf transformation 6]
47. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~generous(lucy) | ~quiet(lucy)) [flattening 46]
48. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~generous(lucy) | ~quiet(lucy)) [rectify 47]
49. ? [X1] : ~brave(X1) => ~brave(sK2) [choice axiom]
50. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (~brave(sK2) | ~generous(lucy) | ~quiet(lucy)) [skolemisation 48,49]
51. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ~tall(X0)) & (tall(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 7]
52. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 9]
53. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [flattening 52]
54. ! [X0] : ((~calm(X0) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | calm(X0))) [nnf transformation 11]
55. ! [X0] : ((~calm(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | calm(X0))) [flattening 54]
69. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X0] : (humble(X0) & rich(X0))) [nnf transformation 16]
70. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [rectify 69]
71. ? [X0] : (~humble(X0) | ~rich(X0)) => (~humble(sK7) | ~rich(sK7)) [choice axiom]
72. ((~humble(sK7) | ~rich(sK7)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [skolemisation 70,71]
83. ~calm(X0) | old(X0) [cnf transformation 37]
93. ~tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 44]
95. ~funny(X0) | ~quiet(X0) [cnf transformation 27]
100. quiet(lucy) | brave(X0) [cnf transformation 50]
101. generous(lucy) | brave(X0) [cnf transformation 50]
102. tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 51]
104. ~generous(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 51]
107. ~generous(X0) | ~patient(X0) | ~old(X0) | funny(X0) [cnf transformation 53]
108. ~generous(X0) | ~patient(X0) | ~funny(X0) | old(X0) [cnf transformation 53]
115. funny(X0) | calm(X0) [cnf transformation 55]
134. ~brave(lucy) | humble(X1) [cnf transformation 72]
145. ~humble(alice) [cnf transformation 23]
175. 7 <=> ! [X0] : brave(X0) [avatar definition]
176. brave(X0) <- (7) [avatar component clause 175]
178. 8 <=> generous(lucy) [avatar definition]
180. generous(lucy) <- (8) [avatar component clause 178]
181. 7 | 8 [avatar split clause 101,178,175]
183. 9 <=> quiet(lucy) [avatar definition]
185. quiet(lucy) <- (9) [avatar component clause 183]
186. 7 | 9 [avatar split clause 100,183,175]
193. ~tall(X0) | ~generous(X0) [subsumption resolution 104,93]
194. ~generous(X0) | patient(X0) [subsumption resolution 102,193]
195. ~funny(X0) | ~generous(X0) | old(X0) [subsumption resolution 108,194]
196. ~generous(X0) | ~old(X0) | funny(X0) [subsumption resolution 107,194]
279. 29 <=> brave(lucy) [avatar definition]
280. ~brave(lucy) <- (~29) [avatar component clause 279]
292. 32 <=> ! [X1] : humble(X1) [avatar definition]
293. humble(X1) <- (32) [avatar component clause 292]
294. 32 | ~29 [avatar split clause 134,279,292]
477. ~generous(X2) | old(X2) | calm(X2) [resolution 195,115]
480. ~generous(X2) | old(X2) [subsumption resolution 477,83]
481. ~old(lucy) | funny(lucy) <- (8) [resolution 196,180]
484. 54 <=> funny(lucy) [avatar definition]
486. funny(lucy) <- (54) [avatar component clause 484]
488. 55 <=> old(lucy) [avatar definition]
490. ~old(lucy) <- (~55) [avatar component clause 488]
491. 54 | ~55 | ~8 [avatar split clause 481,178,488,484]
528. old(lucy) <- (8) [resolution 480,180]
530. $false <- (8, ~55) [subsumption resolution 528,490]
531. ~8 | 55 [avatar contradiction clause 530]
532. $false <- (7, ~29) [resolution 176,280]
533. ~7 | 29 [avatar contradiction clause 532]
534. $false <- (32) [resolution 293,145]
539. ~32 [avatar contradiction clause 534]
549. ~quiet(lucy) <- (54) [resolution 486,95]
550. $false <- (9, 54) [subsumption resolution 549,185]
551. ~9 | ~54 [avatar contradiction clause 550]
552. $false [avatar sat refutation 181,186,294,491,531,533,539,551]
% SZS output end Proof for 856401692876826744988965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is creative or old then someone is not happy and vice versa.
Everyone who is curious or not happy is either not kind or quiet and vice versa.
Everyone who is curious or strong is both not rich and not happy.
If susan is not strong or not generous then someone is not generous and vice versa.
Everyone who is either generous or happy is either not kind or not curious and vice versa.
If alice is not curious then someone is rich or not brave.
Everyone who is both not funny and not rich is both not brave and calm and vice versa.
Everyone who is either rich or quiet is not wise and vice versa.
If someone is either not calm or creative then fred is either not brave or funny and vice versa.
Everyone who is either not tall or not funny is creative.
Everyone who is tall or brave is both happy and generous and vice versa.
Everyone who is not rich is not brave or rich.
If someone is both not patient and happy then someone is not humble and vice versa.
Everyone who is either wise or rich is generous or not kind and vice versa.
Everyone who is either not kind or not rich is not kind and vice versa.
If someone is both calm and creative then susan is both not happy and kind and vice versa.
Someone is wise or patient.
Fred is not tall or not wise.
Lucy is both not calm and funny.
Someone is both not generous and not patient. | Susan is not tall. | entailment | (((creative(paul)|old(paul)))<=>(?[X]:(~happy(X))))&
(![X]:((curious(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((curious(X)|strong(X))=>(~rich(X)&~happy(X))))&
(((~strong(susan)|~generous(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~kind(X)<~>~curious(X))))&
((~curious(alice))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~funny(X)&~rich(X))<=>(~brave(X)&calm(X))))&
(![X]:((rich(X)<~>quiet(X))<=>~wise(X)))&
((?[X]:((~calm(X)<~>creative(X))))<=>((~brave(fred)<~>funny(fred))))&
(![X]:((~tall(X)<~>~funny(X))=>creative(X)))&
(![X]:((tall(X)|brave(X))<=>(happy(X)&generous(X))))&
(![X]:(~rich(X)=>(~brave(X)|rich(X))))&
((?[X]:((~patient(X)&happy(X))))<=>(?[X]:(~humble(X))))&
(![X]:((wise(X)<~>rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>~rich(X))<=>~kind(X)))&
((?[X]:((calm(X)&creative(X))))<=>((~happy(susan)&kind(susan))))&
(?[X]:((wise(X)|patient(X))))&
((~tall(fred)|~wise(fred)))&
((~calm(lucy)&funny(lucy)))&
(?[X]:((~generous(X)&~patient(X)))) | ~tall(susan) | [
"p1",
"p2",
"p4",
"p7",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 441642066222800895422155
% SZS output start Proof for 441642066222800895422155
2. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p1]
3. ! [X0] : ((strong(X0) | curious(X0)) => (~happy(X0) & ~rich(X0))) [input p2]
5. ! [X0] : ((generous(X0) <~> happy(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p4]
8. ! [X0] : ((rich(X0) <~> quiet(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : ((brave(X0) | tall(X0)) <=> (generous(X0) & happy(X0))) [input p10]
14. ! [X0] : ((wise(X0) <~> rich(X0)) <=> (~kind(X0) | generous(X0))) [input p13]
15. ! [X0] : ((~kind(X0) <~> ~rich(X0)) <=> ~kind(X0)) [input p14]
21. tall(susan) [input hypothesis]
23. ! [X0] : ((~happy(X0) & ~rich(X0)) | (~strong(X0) & ~curious(X0))) [ennf transformation 3]
33. ! [X0] : (((~happy(X0) | curious(X0)) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (happy(X0) & ~curious(X0)))) [nnf transformation 2]
34. ! [X0] : ((~happy(X0) | curious(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (happy(X0) & ~curious(X0)))) [flattening 33]
40. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | wise(X0)) & (~wise(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [nnf transformation 8]
51. ! [X0] : (((brave(X0) | tall(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~brave(X0) & ~tall(X0)))) [nnf transformation 11]
52. ! [X0] : ((brave(X0) | tall(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (~brave(X0) & ~tall(X0)))) [flattening 51]
58. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [flattening 58]
60. ! [X0] : ((((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))))) [nnf transformation 15]
77. ~happy(X0) | curious(X0) | quiet(X0) | kind(X0) [cnf transformation 34]
79. ~rich(X0) | ~curious(X0) [cnf transformation 23]
81. ~curious(X0) | ~happy(X0) [cnf transformation 23]
93. ~happy(X0) | ~generous(X0) | ~kind(X0) | curious(X0) [cnf transformation 40]
102. ~rich(X0) | ~quiet(X0) | wise(X0) [cnf transformation 45]
113. ~tall(X0) | happy(X0) [cnf transformation 52]
115. ~tall(X0) | generous(X0) [cnf transformation 52]
127. ~wise(X0) | ~rich(X0) | kind(X0) [cnf transformation 59]
129. ~kind(X0) | ~kind(X0) | rich(X0) [cnf transformation 60]
131. rich(X0) | kind(X0) | kind(X0) [cnf transformation 60]
142. tall(susan) [cnf transformation 21]
143. ~kind(X0) | rich(X0) [duplicate literal removal 129]
144. rich(X0) | kind(X0) [duplicate literal removal 131]
172. 7 <=> generous(susan) [avatar definition]
173. generous(susan) <- (7) [avatar component clause 172]
182. ~generous(X0) | ~happy(X0) | ~kind(X0) [subsumption resolution 93,81]
250. rich(X0) [subsumption resolution 143,144]
252. 23 <=> happy(susan) [avatar definition]
254. happy(susan) <- (23) [avatar component clause 252]
256. 24 <=> kind(susan) [avatar definition]
258. ~kind(susan) <- (~24) [avatar component clause 256]
291. ~curious(X0) [resolution 79,250]
293. happy(susan) [resolution 113,142]
294. 23 [avatar split clause 293,252]
295. generous(susan) [resolution 115,142]
298. 7 [avatar split clause 295,172]
325. ~quiet(X1) | wise(X1) [resolution 102,250]
361. ~happy(susan) | ~kind(susan) <- (7) [resolution 182,173]
381. curious(susan) | quiet(susan) | kind(susan) <- (23) [resolution 77,254]
384. quiet(susan) | kind(susan) <- (23) [subsumption resolution 381,291]
385. quiet(susan) <- (23, ~24) [subsumption resolution 384,258]
386. wise(susan) <- (23, ~24) [resolution 385,325]
390. ~rich(susan) | kind(susan) <- (23, ~24) [resolution 386,127]
394. kind(susan) <- (23, ~24) [subsumption resolution 390,250]
395. $false <- (23, ~24) [subsumption resolution 394,258]
396. ~23 | 24 [avatar contradiction clause 395]
405. ~kind(susan) <- (7, 23) [subsumption resolution 361,254]
406. ~24 | ~7 | ~23 [avatar split clause 405,252,172,256]
407. $false [avatar sat refutation 294,298,396,406]
% SZS output end Proof for 441642066222800895422155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not funny then paul is not quiet or not generous and vice versa. Everyone who is quiet is calm or not kind and vice versa. If someone is both kind and not curious then john is wise and vice versa. Everyone who is calm is tall or not brave. If fred is both tall and not happy then john is creative and vice versa. If john is humble then alice is both not funny and not wise and vice versa. Everyone who is tall or brave is both not quiet and not kind. If susan is generous or not wise then someone is both not wise and happy and vice versa. If someone is both strong and generous then paul is not happy. Everyone who is either not wise or not generous is not funny or quiet. Everyone who is not wise is not rich or not tall. If mary is both not old and not humble then lucy is curious. Everyone who is either not old or wise is not strong or humble and vice versa. Everyone who is not patient is both strong and not curious. If someone is not creative then lucy is both strong and not rich and vice versa. Everyone who is either strong or not creative is calm. Someone is either quiet or funny. Mary is either not funny or strong. Someone is wise. Someone is generous or not funny. Mary is not quiet. Alice is either wise or not calm. Mary is not happy. | Lucy is not rich. | entailment | ((?[X]:((~happy(X)<~>~funny(X))))<=>((~quiet(paul)|~generous(paul))))&
(![X]:(quiet(X)<=>(calm(X)|~kind(X))))&
((?[X]:((kind(X)&~curious(X))))<=>(wise(john)))&
(![X]:(calm(X)=>(tall(X)|~brave(X))))&
(((tall(fred)&~happy(fred)))<=>(creative(john)))&
((humble(john))<=>((~funny(alice)&~wise(alice))))&
(![X]:((tall(X)|brave(X))=>(~quiet(X)&~kind(X))))&
(((generous(susan)|~wise(susan)))<=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((strong(X)&generous(X))))=>(~happy(paul)))&
(![X]:((~wise(X)<~>~generous(X))=>(~funny(X)|quiet(X))))&
(![X]:(~wise(X)=>(~rich(X)|~tall(X))))&
(((~old(mary)&~humble(mary)))=>(curious(lucy)))&
(![X]:((~old(X)<~>wise(X))<=>(~strong(X)|humble(X))))&
(![X]:(~patient(X)=>(strong(X)&~curious(X))))&
((?[X]:(~creative(X)))<=>((strong(lucy)&~rich(lucy))))&
(![X]:((strong(X)<~>~creative(X))=>calm(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~funny(mary)<~>strong(mary)))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)|~funny(X))))&
(~quiet(mary))&
((wise(alice)<~>~calm(alice)))&
(~happy(mary)) | ~rich(lucy) | [
"p1",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4820983977422552216241573
% SZS output start Proof for 4820983977422552216241573
2. ! [X0] : (quiet(X0) <=> (~kind(X0) | calm(X0))) [input p1]
5. (~happy(fred) & tall(fred)) <=> creative(john) [input p4]
7. ! [X0] : ((brave(X0) | tall(X0)) => (~kind(X0) & ~quiet(X0))) [input p6]
15. ? [X0] : ~creative(X0) <=> (~rich(lucy) & strong(lucy)) [input p14]
24. rich(lucy) [input hypothesis]
26. ! [X0] : (tall(X0) => (~kind(X0) & ~quiet(X0))) [pure predicate removal 7]
28. ! [X0] : ((~kind(X0) & ~quiet(X0)) | ~tall(X0)) [ennf transformation 26]
42. ! [X0] : ((quiet(X0) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | ~quiet(X0))) [nnf transformation 2]
43. ! [X0] : ((quiet(X0) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ~quiet(X0))) [flattening 42]
48. ((~happy(fred) & tall(fred)) | ~creative(john)) & (creative(john) | (happy(fred) | ~tall(fred))) [nnf transformation 5]
49. ((~happy(fred) & tall(fred)) | ~creative(john)) & (creative(john) | happy(fred) | ~tall(fred)) [flattening 48]
60. (? [X0] : ~creative(X0) | (rich(lucy) | ~strong(lucy))) & ((~rich(lucy) & strong(lucy)) | ! [X0] : creative(X0)) [nnf transformation 15]
61. (? [X0] : ~creative(X0) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X0] : creative(X0)) [flattening 60]
62. (? [X0] : ~creative(X0) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X1] : creative(X1)) [rectify 61]
63. ? [X0] : ~creative(X0) => ~creative(sK3) [choice axiom]
64. (~creative(sK3) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X1] : creative(X1)) [skolemisation 62,63]
83. kind(X0) | quiet(X0) [cnf transformation 43]
88. tall(fred) | ~creative(john) [cnf transformation 49]
93. ~tall(X0) | ~quiet(X0) [cnf transformation 28]
94. ~tall(X0) | ~kind(X0) [cnf transformation 28]
112. ~rich(lucy) | creative(X1) [cnf transformation 64]
126. rich(lucy) [cnf transformation 24]
174. 11 <=> creative(john) [avatar definition]
176. ~creative(john) <- (~11) [avatar component clause 174]
183. 13 <=> tall(fred) [avatar definition]
185. tall(fred) <- (13) [avatar component clause 183]
186. ~11 | 13 [avatar split clause 88,183,174]
253. 28 <=> rich(lucy) [avatar definition]
262. 30 <=> ! [X1] : creative(X1) [avatar definition]
263. creative(X1) <- (30) [avatar component clause 262]
264. 30 | ~28 [avatar split clause 112,253,262]
301. 28 [avatar split clause 126,253]
302. $false <- (~11, 30) [subsumption resolution 176,263]
303. 11 | ~30 [avatar contradiction clause 302]
304. ~quiet(fred) <- (13) [resolution 93,185]
305. ~kind(fred) <- (13) [resolution 94,185]
307. quiet(fred) <- (13) [resolution 305,83]
308. $false <- (13) [subsumption resolution 307,304]
309. ~13 [avatar contradiction clause 308]
310. $false [avatar sat refutation 186,264,301,303,309]
% SZS output end Proof for 4820983977422552216241573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not wise is not humble or not brave and vice versa.
If mary is both not patient and not funny then paul is old.
If someone is funny then john is not brave or not generous and vice versa.
If someone is both not curious and patient then paul is either not generous or not patient.
If someone is either not strong or humble then someone is both not creative and kind.
If someone is not happy then someone is not kind and vice versa.
Everyone who is not wise or not calm is rich or not humble and vice versa.
Everyone who is both rich and not old is either not strong or quiet.
Everyone who is both patient and not quiet is not old and vice versa.
If someone is patient or humble then lucy is either not rich or humble.
If someone is not brave or generous then mary is both not kind and happy.
Everyone who is both kind and not kind is not calm or not generous and vice versa.
If someone is brave or old then someone is calm or not humble and vice versa.
Everyone who is either not quiet or not kind is quiet and vice versa.
If mary is both not humble and curious then someone is creative or not generous and vice versa.
Everyone who is humble is brave or not humble.
Someone is not kind.
John is either not kind or brave.
Alice is creative.
Alice is either calm or not tall.
Someone is tall or calm.
Someone is creative. | John is patient. | neutral | (![X]:((~tall(X)<~>~wise(X))<=>(~humble(X)|~brave(X))))&
(((~patient(mary)&~funny(mary)))=>(old(paul)))&
((?[X]:(funny(X)))<=>((~brave(john)|~generous(john))))&
((?[X]:((~curious(X)&patient(X))))=>((~generous(paul)<~>~patient(paul))))&
((?[X]:((~strong(X)<~>humble(X))))=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(rich(X)|~humble(X))))&
(![X]:((rich(X)&~old(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((patient(X)&~quiet(X))<=>~old(X)))&
((?[X]:((patient(X)|humble(X))))=>((~rich(lucy)<~>humble(lucy))))&
((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))&
(![X]:((kind(X)&~kind(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((brave(X)|old(X))))<=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>quiet(X)))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:(humble(X)=>(brave(X)|~humble(X))))&
(?[X]:(~kind(X)))&
((~kind(john)<~>brave(john)))&
(creative(alice))&
((calm(alice)<~>~tall(alice)))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:(creative(X))) | patient(john) | [] | null | 0 |
If someone is either brave or not generous then someone is quiet.
If someone is strong or not tall then lucy is not generous or funny and vice versa.
Everyone who is rich is not tall and vice versa.
If someone is tall or wise then someone is rich.
Everyone who is either not funny or not old is either tall or not wise and vice versa.
If john is either not tall or funny then fred is not tall and vice versa.
Everyone who is not wise is either not generous or happy and vice versa.
Everyone who is not generous is funny or not calm and vice versa.
Everyone who is both not tall and happy is both not humble and not happy and vice versa.
Everyone who is either not brave or humble is either tall or not curious and vice versa.
Everyone who is either not brave or rich is not calm or humble and vice versa.
If someone is not tall then someone is both not curious and not generous.
If someone is either not quiet or not kind then alice is both tall and strong.
If susan is not brave or calm then someone is either patient or wise and vice versa.
If john is both not creative and rich then someone is either not rich or not happy and vice versa.
Lucy is not tall or not humble.
Someone is either old or not wise.
Susan is calm or creative.
Lucy is curious or patient.
Someone is either creative or not funny.
Someone is both wise and calm.
Alice is either not creative or kind. | John is humble. | entailment | ((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:(quiet(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~generous(lucy)|funny(lucy))))&
(![X]:(rich(X)<=>~tall(X)))&
((?[X]:((tall(X)|wise(X))))=>(?[X]:(rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(tall(X)<~>~wise(X))))&
(((~tall(john)<~>funny(john)))<=>(~tall(fred)))&
(![X]:(~wise(X)<=>(~generous(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(funny(X)|~calm(X))))&
(![X]:((~tall(X)&happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~calm(X)|humble(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>((tall(alice)&strong(alice))))&
(((~brave(susan)|calm(susan)))<=>(?[X]:((patient(X)<~>wise(X)))))&
(((~creative(john)&rich(john)))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
((~tall(lucy)|~humble(lucy)))&
(?[X]:((old(X)<~>~wise(X))))&
((calm(susan)|creative(susan)))&
((curious(lucy)|patient(lucy)))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((wise(X)&calm(X))))&
((~creative(alice)<~>kind(alice))) | humble(john) | [
"p2",
"p3",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2478371520456064827193207
% SZS output start Proof for 2478371520456064827193207
3. ! [X0] : (rich(X0) <=> ~tall(X0)) [input p2]
4. ? [X0] : (wise(X0) | tall(X0)) => ? [X0] : rich(X0) [input p3]
9. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (~happy(X0) & ~humble(X0))) [input p8]
15. (rich(john) & ~creative(john)) <=> ? [X0] : (~rich(X0) <~> ~happy(X0)) [input p14]
23. ~humble(john) [input hypothesis]
25. ? [X0] : (wise(X0) | tall(X0)) => ? [X1] : rich(X1) [rectify 4]
28. ? [X1] : rich(X1) | ! [X0] : (~wise(X0) & ~tall(X0)) [ennf transformation 25]
40. ! [X0] : ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))) [nnf transformation 3]
41. ? [X0] : rich(X0) | ! [X1] : (~wise(X1) & ~tall(X1)) [rectify 28]
42. ? [X0] : rich(X0) => rich(sK2) [choice axiom]
43. rich(sK2) | ! [X1] : (~wise(X1) & ~tall(X1)) [skolemisation 41,42]
49. ! [X0] : (((happy(X0) & ~tall(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 9]
50. ! [X0] : (((happy(X0) & ~tall(X0)) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ~happy(X0) | tall(X0))) [flattening 49]
63. ((rich(john) & ~creative(john)) | ! [X0] : ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (? [X0] : ((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (~rich(john) | creative(john))) [nnf transformation 15]
64. ((rich(john) & ~creative(john)) | ! [X0] : ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (? [X0] : ((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | ~rich(john) | creative(john)) [flattening 63]
65. ((rich(john) & ~creative(john)) | ! [X0] : ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (? [X1] : ((happy(X1) | rich(X1)) & (~happy(X1) | ~rich(X1))) | ~rich(john) | creative(john)) [rectify 64]
66. ? [X1] : ((happy(X1) | rich(X1)) & (~happy(X1) | ~rich(X1))) => ((happy(sK5) | rich(sK5)) & (~happy(sK5) | ~rich(sK5))) [choice axiom]
67. ((rich(john) & ~creative(john)) | ! [X0] : ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(sK5) | rich(sK5)) & (~happy(sK5) | ~rich(sK5))) | ~rich(john) | creative(john)) [skolemisation 65,66]
83. ~rich(X0) | ~tall(X0) [cnf transformation 40]
84. rich(X0) | tall(X0) [cnf transformation 40]
85. rich(sK2) | ~tall(X1) [cnf transformation 43]
107. ~happy(X0) | ~happy(X0) | tall(X0) [cnf transformation 50]
109. happy(X0) | happy(X0) | humble(X0) [cnf transformation 50]
141. rich(john) | ~rich(X0) | happy(X0) [cnf transformation 67]
153. ~humble(john) [cnf transformation 23]
154. ~happy(X0) | tall(X0) [duplicate literal removal 107]
155. humble(X0) | happy(X0) [duplicate literal removal 109]
187. 8 <=> ! [X1] : tall(X1) [avatar definition]
188. tall(X1) <- (8) [avatar component clause 187]
198. 11 <=> rich(sK2) [avatar definition]
200. rich(sK2) <- (11) [avatar component clause 198]
203. 12 <=> ! [X1] : ~tall(X1) [avatar definition]
204. ~tall(X1) <- (12) [avatar component clause 203]
205. 12 | 11 [avatar split clause 85,198,203]
211. 14 <=> tall(john) [avatar definition]
279. 28 <=> ! [X0] : (~rich(X0) | happy(X0)) [avatar definition]
280. ~rich(X0) | happy(X0) <- (28) [avatar component clause 279]
282. 29 <=> rich(john) [avatar definition]
284. rich(john) <- (29) [avatar component clause 282]
285. 28 | 29 [avatar split clause 141,282,279]
359. ~tall(sK2) <- (11) [resolution 83,200]
365. happy(john) [resolution 155,153]
368. tall(john) [resolution 365,154]
373. happy(X0) | tall(X0) <- (28) [resolution 280,84]
374. tall(X0) <- (28) [subsumption resolution 373,154]
375. 8 | ~28 [avatar split clause 374,279,187]
376. ~tall(john) <- (29) [resolution 284,83]
379. ~14 | ~29 [avatar split clause 376,282,211]
380. 14 [avatar split clause 368,211]
382. $false <- (8, 11) [resolution 188,359]
383. ~8 | ~11 [avatar contradiction clause 382]
385. $false <- (8, 12) [subsumption resolution 204,188]
386. ~8 | ~12 [avatar contradiction clause 385]
387. $false [avatar sat refutation 205,285,375,379,380,383,386]
% SZS output end Proof for 2478371520456064827193207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not humble then paul is either funny or not calm and vice versa.
Everyone who is wise is both not calm and not tall and vice versa.
Everyone who is either humble or tall is both not creative and not strong.
Everyone who is either strong or tall is either not humble or not curious.
Everyone who is not tall or funny is both humble and not tall and vice versa.
Everyone who is funny is not kind or patient and vice versa.
If someone is either brave or funny then someone is both not generous and brave.
Everyone who is not generous or wise is either not humble or not quiet.
Everyone who is both wise and not wise is both not rich and not tall and vice versa.
If someone is not creative or not brave then susan is both not calm and not creative and vice versa.
Everyone who is either generous or not humble is brave or not old and vice versa.
Everyone who is funny or not generous is both patient and old.
Everyone who is either not funny or wise is brave and vice versa.
Everyone who is creative is patient.
If someone is not generous or rich then someone is not patient or not funny.
Someone is patient or curious.
Alice is either humble or brave.
Someone is not humble or generous.
Paul is curious or happy.
Someone is either quiet or curious.
Someone is not tall. | Susan is strong. | contradiction | ((?[X]:((~kind(X)|~humble(X))))<=>((funny(paul)<~>~calm(paul))))&
(![X]:(wise(X)<=>(~calm(X)&~tall(X))))&
(![X]:((humble(X)<~>tall(X))=>(~creative(X)&~strong(X))))&
(![X]:((strong(X)<~>tall(X))=>(~humble(X)<~>~curious(X))))&
(![X]:((~tall(X)|funny(X))<=>(humble(X)&~tall(X))))&
(![X]:(funny(X)<=>(~kind(X)|patient(X))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~generous(X)|wise(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((wise(X)&~wise(X))<=>(~rich(X)&~tall(X))))&
((?[X]:((~creative(X)|~brave(X))))<=>((~calm(susan)&~creative(susan))))&
(![X]:((generous(X)<~>~humble(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(![X]:((~funny(X)<~>wise(X))<=>brave(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(?[X]:((patient(X)|curious(X))))&
((humble(alice)<~>brave(alice)))&
(?[X]:((~humble(X)|generous(X))))&
((curious(paul)|happy(paul)))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:(~tall(X))) | strong(susan) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2480140119114869225786002
% SZS output start Proof for 2480140119114869225786002
2. ! [X0] : (wise(X0) <=> (~tall(X0) & ~calm(X0))) [input p1]
3. ! [X0] : ((humble(X0) <~> tall(X0)) => (~strong(X0) & ~creative(X0))) [input p2]
5. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (~tall(X0) & humble(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> (patient(X0) | ~kind(X0))) [input p5]
7. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X0] : (brave(X0) & ~generous(X0)) [input p6]
11. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> (~old(X0) | brave(X0))) [input p10]
12. ! [X0] : ((~generous(X0) | funny(X0)) => (old(X0) & patient(X0))) [input p11]
13. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> brave(X0)) [input p12]
22. strong(susan) [input hypothesis]
23. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X1] : (brave(X1) & ~generous(X1)) [rectify 7]
26. ! [X0] : ((~strong(X0) & ~creative(X0)) | (humble(X0) <=> tall(X0))) [ennf transformation 3]
28. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : (brave(X0) <=> funny(X0)) [ennf transformation 23]
30. ! [X0] : ((old(X0) & patient(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 12]
37. ! [X0] : ((wise(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | ~wise(X0))) [nnf transformation 2]
38. ! [X0] : ((wise(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~wise(X0))) [flattening 37]
39. ! [X0] : ((~strong(X0) & ~creative(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) [nnf transformation 26]
41. ! [X0] : (((funny(X0) | ~tall(X0)) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 5]
42. ! [X0] : ((funny(X0) | ~tall(X0) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | (~funny(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ~funny(X0))) [nnf transformation 6]
44. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ~funny(X0))) [flattening 43]
45. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))) [nnf transformation 28]
46. ? [X0] : (brave(X0) & ~generous(X0)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [rectify 45]
47. ? [X0] : (brave(X0) & ~generous(X0)) => (brave(sK1) & ~generous(sK1)) [choice axiom]
48. (brave(sK1) & ~generous(sK1)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [skolemisation 46,47]
57. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 11]
58. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [flattening 57]
59. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ~brave(X0)) & (brave(X0) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 13]
80. ~tall(X0) | ~wise(X0) [cnf transformation 38]
84. ~strong(X0) | tall(X0) | ~humble(X0) [cnf transformation 39]
90. tall(X0) | humble(X0) [cnf transformation 42]
91. ~funny(X0) | humble(X0) [cnf transformation 42]
93. ~tall(X0) | ~funny(X0) [cnf transformation 42]
97. ~patient(X0) | funny(X0) [cnf transformation 44]
98. ~generous(sK1) | funny(X1) | ~brave(X1) [cnf transformation 48]
100. brave(sK1) | funny(X1) | ~brave(X1) [cnf transformation 48]
117. ~brave(X0) | generous(X0) | ~humble(X0) [cnf transformation 58]
122. generous(X0) | patient(X0) [cnf transformation 30]
125. brave(X0) | wise(X0) | funny(X0) [cnf transformation 59]
139. strong(susan) [cnf transformation 22]
174. 8 <=> brave(sK1) [avatar definition]
176. brave(sK1) <- (8) [avatar component clause 174]
179. 9 <=> ! [X1] : (funny(X1) | ~brave(X1)) [avatar definition]
180. ~brave(X1) | funny(X1) <- (9) [avatar component clause 179]
181. 9 | 8 [avatar split clause 100,174,179]
183. 10 <=> generous(sK1) [avatar definition]
185. ~generous(sK1) <- (~10) [avatar component clause 183]
187. 9 | ~10 [avatar split clause 98,183,179]
278. patient(sK1) <- (~10) [resolution 122,185]
279. funny(sK1) <- (~10) [resolution 278,97]
284. humble(sK1) <- (~10) [resolution 279,91]
302. tall(susan) | ~humble(susan) [resolution 84,139]
303. tall(susan) [subsumption resolution 302,90]
304. ~funny(susan) [resolution 303,93]
305. ~wise(susan) [resolution 303,80]
327. generous(sK1) | ~humble(sK1) <- (8) [resolution 117,176]
328. ~humble(sK1) <- (8, ~10) [subsumption resolution 327,185]
329. $false <- (8, ~10) [subsumption resolution 328,284]
330. ~8 | 10 [avatar contradiction clause 329]
359. wise(X0) | funny(X0) | funny(X0) <- (9) [resolution 125,180]
364. wise(X0) | funny(X0) <- (9) [duplicate literal removal 359]
410. funny(susan) <- (9) [resolution 364,305]
414. $false <- (9) [subsumption resolution 410,304]
415. ~9 [avatar contradiction clause 414]
416. $false [avatar sat refutation 181,187,330,415]
% SZS output end Proof for 2480140119114869225786002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then someone is not quiet or brave and vice versa.
If mary is not patient then lucy is not wise.
Everyone who is quiet is either creative or not tall and vice versa.
Everyone who is not creative or not quiet is either not tall or not patient.
If fred is both humble and not quiet then alice is either happy or not rich.
If someone is both quiet and happy then someone is brave or generous.
Everyone who is both not tall and not happy is not patient or wise and vice versa.
If someone is rich or not patient then someone is not rich or not old.
If susan is strong or not wise then someone is both not kind and brave.
Everyone who is either not happy or creative is either not creative or not funny.
Everyone who is both patient and not funny is both not tall and not funny.
Everyone who is not creative or not tall is generous or patient and vice versa.
Everyone who is both kind and generous is not tall and vice versa.
Everyone who is both tall and not generous is either generous or not generous.
Everyone who is both not strong and tall is either strong or tall and vice versa.
Someone is kind.
Mary is either calm or not curious.
Someone is not creative.
Someone is not wise.
Alice is not generous or not tall. | Fred is not brave. | entailment | ((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((~patient(mary))=>(~wise(lucy)))&
(![X]:(quiet(X)<=>(creative(X)<~>~tall(X))))&
(![X]:((~creative(X)|~quiet(X))=>(~tall(X)<~>~patient(X))))&
(((humble(fred)&~quiet(fred)))=>((happy(alice)<~>~rich(alice))))&
((?[X]:((quiet(X)&happy(X))))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(~patient(X)|wise(X))))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~rich(X)|~old(X)))))&
(((strong(susan)|~wise(susan)))=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)&~funny(X))=>(~tall(X)&~funny(X))))&
(![X]:((~creative(X)|~tall(X))<=>(generous(X)|patient(X))))&
(![X]:((kind(X)&generous(X))<=>~tall(X)))&
(![X]:((tall(X)&~generous(X))=>(generous(X)<~>~generous(X))))&
(![X]:((~strong(X)&tall(X))<=>(strong(X)<~>tall(X))))&
(?[X]:(kind(X)))&
((calm(mary)<~>~curious(mary)))&
(?[X]:(~creative(X)))&
(?[X]:(~wise(X)))&
((~generous(alice)|~tall(alice))) | ~brave(fred) | [
"p0",
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3571917517035019638945115
% SZS output start Proof for 3571917517035019638945115
1. ? [X0] : tall(X0) <=> ? [X0] : (brave(X0) | ~quiet(X0)) [input p0]
4. ! [X0] : ((~quiet(X0) | ~creative(X0)) => (~tall(X0) <~> ~patient(X0))) [input p3]
7. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> (wise(X0) | ~patient(X0))) [input p6]
12. ! [X0] : ((~tall(X0) | ~creative(X0)) <=> (patient(X0) | generous(X0))) [input p11]
21. brave(fred) [input hypothesis]
22. ? [X0] : tall(X0) <=> ? [X1] : (brave(X1) | ~quiet(X1)) [rectify 1]
28. ! [X0] : ((~tall(X0) <~> ~patient(X0)) | (quiet(X0) & creative(X0))) [ennf transformation 4]
36. (? [X0] : tall(X0) | ! [X1] : (~brave(X1) & quiet(X1))) & (? [X1] : (brave(X1) | ~quiet(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 22]
37. (? [X0] : tall(X0) | ! [X1] : (~brave(X1) & quiet(X1))) & (? [X2] : (brave(X2) | ~quiet(X2)) | ! [X3] : ~tall(X3)) [rectify 36]
38. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
39. ? [X2] : (brave(X2) | ~quiet(X2)) => (brave(sK1) | ~quiet(sK1)) [choice axiom]
40. (tall(sK0) | ! [X1] : (~brave(X1) & quiet(X1))) & ((brave(sK1) | ~quiet(sK1)) | ! [X3] : ~tall(X3)) [skolemisation 37,39,38]
42. ! [X0] : (((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | (quiet(X0) & creative(X0))) [nnf transformation 28]
46. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (happy(X0) | tall(X0)))) [nnf transformation 7]
47. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | happy(X0) | tall(X0))) [flattening 46]
51. ! [X0] : (((~tall(X0) | ~creative(X0)) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | (tall(X0) & creative(X0)))) [nnf transformation 12]
52. ! [X0] : ((~tall(X0) | ~creative(X0) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | (tall(X0) & creative(X0)))) [flattening 51]
67. tall(sK0) | ~brave(X1) [cnf transformation 40]
73. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 42]
79. ~tall(X0) | patient(X0) [cnf transformation 47]
96. ~tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 52]
114. brave(fred) [cnf transformation 21]
124. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
125. ~brave(X1) <- (1) [avatar component clause 124]
127. 2 <=> tall(sK0) [avatar definition]
129. tall(sK0) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 67,127,124]
136. 4 <=> ! [X3] : ~tall(X3) [avatar definition]
137. ~tall(X3) <- (4) [avatar component clause 136]
189. ~tall(X0) | ~patient(X0) [subsumption resolution 96,73]
190. ~tall(X0) [subsumption resolution 189,79]
191. 4 [avatar split clause 190,136]
212. $false <- (2, 4) [subsumption resolution 129,137]
213. ~2 | ~4 [avatar contradiction clause 212]
214. $false <- (1) [resolution 125,114]
215. ~1 [avatar contradiction clause 214]
216. $false [avatar sat refutation 130,191,213,215]
% SZS output end Proof for 3571917517035019638945115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then alice is brave and vice versa.
If someone is either not kind or old then someone is not patient and vice versa.
Everyone who is not strong is not happy.
Everyone who is either not creative or patient is either tall or not rich.
Everyone who is not funny is both not tall and wise and vice versa.
Everyone who is either rich or not kind is humble and vice versa.
Everyone who is both not creative and not funny is quiet and vice versa.
If mary is both not funny and not quiet then someone is not old or not creative and vice versa.
If paul is either not funny or not old then paul is not rich or not brave.
Everyone who is both not humble and strong is either not kind or not quiet and vice versa.
If susan is both not generous and not patient then john is both generous and not humble and vice versa.
If someone is not brave or tall then mary is either patient or not kind.
Everyone who is brave or patient is quiet.
If lucy is not quiet or not strong then someone is both kind and strong.
Everyone who is not tall or happy is not humble and vice versa.
If someone is both quiet and not creative then paul is both not kind and not brave.
Alice is tall or quiet.
Mary is creative or patient.
Paul is either not old or kind.
Susan is funny or not happy.
Someone is both generous and brave.
Someone is both rich and quiet.
Someone is either not quiet or not funny.
Someone is kind. | Paul is old. | contradiction | ((?[X]:(patient(X)))<=>(brave(alice)))&
((?[X]:((~kind(X)<~>old(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~strong(X)=>~happy(X)))&
(![X]:((~creative(X)<~>patient(X))=>(tall(X)<~>~rich(X))))&
(![X]:(~funny(X)<=>(~tall(X)&wise(X))))&
(![X]:((rich(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~creative(X)&~funny(X))<=>quiet(X)))&
(((~funny(mary)&~quiet(mary)))<=>(?[X]:((~old(X)|~creative(X)))))&
(((~funny(paul)<~>~old(paul)))=>((~rich(paul)|~brave(paul))))&
(![X]:((~humble(X)&strong(X))<=>(~kind(X)<~>~quiet(X))))&
(((~generous(susan)&~patient(susan)))<=>((generous(john)&~humble(john))))&
((?[X]:((~brave(X)|tall(X))))=>((patient(mary)<~>~kind(mary))))&
(![X]:((brave(X)|patient(X))=>quiet(X)))&
(((~quiet(lucy)|~strong(lucy)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~tall(X)|happy(X))<=>~humble(X)))&
((?[X]:((quiet(X)&~creative(X))))=>((~kind(paul)&~brave(paul))))&
((tall(alice)|quiet(alice)))&
((creative(mary)|patient(mary)))&
((~old(paul)<~>kind(paul)))&
((funny(susan)|~happy(susan)))&
(?[X]:((generous(X)&brave(X))))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:(kind(X))) | old(paul) | [
"p6",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6054015723602379614284456
% SZS output start Proof for 6054015723602379614284456
7. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> quiet(X0)) [input p6]
16. ? [X0] : (~creative(X0) & quiet(X0)) => (~brave(paul) & ~kind(paul)) [input p15]
19. ~old(paul) <~> kind(paul) [input p18]
22. ? [X0] : (quiet(X0) & rich(X0)) [input p21]
25. old(paul) [input hypothesis]
34. (~brave(paul) & ~kind(paul)) | ! [X0] : (creative(X0) | ~quiet(X0)) [ennf transformation 16]
48. ! [X0] : (((~funny(X0) & ~creative(X0)) | ~quiet(X0)) & (quiet(X0) | (funny(X0) | creative(X0)))) [nnf transformation 7]
49. ! [X0] : (((~funny(X0) & ~creative(X0)) | ~quiet(X0)) & (quiet(X0) | funny(X0) | creative(X0))) [flattening 48]
65. (~kind(paul) | old(paul)) & (kind(paul) | ~old(paul)) [nnf transformation 19]
68. ? [X0] : (quiet(X0) & rich(X0)) => (quiet(sK6) & rich(sK6)) [choice axiom]
69. quiet(sK6) & rich(sK6) [skolemisation 22,68]
94. ~creative(X0) | ~quiet(X0) [cnf transformation 49]
126. ~kind(paul) | creative(X0) | ~quiet(X0) [cnf transformation 34]
130. kind(paul) | ~old(paul) [cnf transformation 65]
136. quiet(sK6) [cnf transformation 69]
140. old(paul) [cnf transformation 25]
207. 16 <=> old(paul) [avatar definition]
284. 32 <=> ! [X0] : ~quiet(X0) [avatar definition]
285. ~quiet(X0) <- (32) [avatar component clause 284]
287. ~kind(paul) | ~quiet(X0) [subsumption resolution 126,94]
289. 33 <=> kind(paul) [avatar definition]
292. 32 | ~33 [avatar split clause 287,289,284]
308. ~16 | 33 [avatar split clause 130,289,207]
327. 16 [avatar split clause 140,207]
332. $false <- (32) [resolution 285,136]
333. ~32 [avatar contradiction clause 332]
334. $false [avatar sat refutation 292,308,327,333]
% SZS output end Proof for 6054015723602379614284456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not old is not generous.
If someone is both generous and not funny then lucy is both kind and old.
If fred is both curious and wise then someone is both not strong and calm.
If mary is not calm then someone is not curious or calm and vice versa.
Everyone who is old is both not strong and creative.
Everyone who is both kind and generous is kind or not happy.
If john is both rich and quiet then john is both tall and kind and vice versa.
If someone is either strong or curious then someone is not curious or not brave.
If fred is not patient then john is not old or wise.
If john is funny or brave then mary is not happy or old and vice versa.
If someone is both not wise and not calm then alice is both not humble and not old.
If someone is either kind or patient then someone is not kind or tall.
If john is brave then paul is patient or quiet and vice versa.
If paul is either humble or brave then someone is either quiet or not happy and vice versa.
If someone is both not tall and tall then lucy is happy and vice versa.
If fred is not kind or wise then someone is both quiet and not strong.
Someone is either not kind or not creative.
Someone is not wise or rich.
Someone is both kind and wise.
Paul is both creative and not tall.
John is either not quiet or rich.
Paul is humble or funny.
Someone is both not brave and creative.
Someone is both funny and rich. | Lucy is happy. | contradiction | (![X]:((~curious(X)&~old(X))=>~generous(X)))&
((?[X]:((generous(X)&~funny(X))))=>((kind(lucy)&old(lucy))))&
(((curious(fred)&wise(fred)))=>(?[X]:((~strong(X)&calm(X)))))&
((~calm(mary))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:(old(X)=>(~strong(X)&creative(X))))&
(![X]:((kind(X)&generous(X))=>(kind(X)|~happy(X))))&
(((rich(john)&quiet(john)))<=>((tall(john)&kind(john))))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~curious(X)|~brave(X)))))&
((~patient(fred))=>((~old(john)|wise(john))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&tall(X))))<=>(happy(lucy)))&
(((~kind(fred)|wise(fred)))=>(?[X]:((quiet(X)&~strong(X)))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(?[X]:((~wise(X)|rich(X))))&
(?[X]:((kind(X)&wise(X))))&
((creative(paul)&~tall(paul)))&
((~quiet(john)<~>rich(john)))&
((humble(paul)|funny(paul)))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((funny(X)&rich(X)))) | happy(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5858729084699772237184370
% SZS output start Proof for 5858729084699772237184370
15. ? [X0] : (tall(X0) & ~tall(X0)) <=> happy(lucy) [input p14]
25. happy(lucy) [input hypothesis]
64. (? [X0] : (tall(X0) & ~tall(X0)) | ~happy(lucy)) & (happy(lucy) | ! [X0] : (~tall(X0) | tall(X0))) [nnf transformation 15]
65. (? [X0] : (tall(X0) & ~tall(X0)) | ~happy(lucy)) & (happy(lucy) | ! [X1] : (~tall(X1) | tall(X1))) [rectify 64]
66. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK5) & ~tall(sK5)) [choice axiom]
67. ((tall(sK5) & ~tall(sK5)) | ~happy(lucy)) & (happy(lucy) | ! [X1] : (~tall(X1) | tall(X1))) [skolemisation 65,66]
116. ~tall(sK5) | ~happy(lucy) [cnf transformation 67]
117. tall(sK5) | ~happy(lucy) [cnf transformation 67]
136. happy(lucy) [cnf transformation 25]
316. 40 <=> happy(lucy) [avatar definition]
320. 41 <=> tall(sK5) [avatar definition]
323. ~40 | 41 [avatar split clause 117,320,316]
324. ~40 | ~41 [avatar split clause 116,320,316]
367. 40 [avatar split clause 136,316]
368. $false [avatar sat refutation 323,324,367]
% SZS output end Proof for 5858729084699772237184370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or generous then john is not creative and vice versa.
Everyone who is old or not tall is not generous.
Everyone who is kind is patient or not happy and vice versa.
Everyone who is either patient or not kind is both not creative and brave.
Everyone who is either brave or not humble is both not quiet and not brave and vice versa.
Everyone who is calm is either funny or not funny and vice versa.
If lucy is tall then susan is either humble or not funny and vice versa.
If susan is both kind and rich then john is calm or kind.
Everyone who is old or kind is both old and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
Fred is not tall or not patient.
Someone is not humble or not funny.
Lucy is not funny or not wise.
Lucy is either not brave or not humble.
Someone is calm.
Mary is not strong or not curious. | Lucy is humble. | contradiction | ((?[X]:((~humble(X)<~>generous(X))))<=>(~creative(john)))&
(![X]:((old(X)|~tall(X))=>~generous(X)))&
(![X]:(kind(X)<=>(patient(X)|~happy(X))))&
(![X]:((patient(X)<~>~kind(X))=>(~creative(X)&brave(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~funny(X))))&
((tall(lucy))<=>((humble(susan)<~>~funny(susan))))&
(((kind(susan)&rich(susan)))=>((calm(john)|kind(john))))&
(![X]:((old(X)|kind(X))<=>(old(X)&creative(X))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
((~tall(fred)|~patient(fred)))&
(?[X]:((~humble(X)|~funny(X))))&
((~funny(lucy)|~wise(lucy)))&
((~brave(lucy)<~>~humble(lucy)))&
(?[X]:(calm(X)))&
((~strong(mary)|~curious(mary))) | humble(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 181951496661598659355652
% SZS output start Proof for 181951496661598659355652
2. ! [X0] : ((~tall(X0) | old(X0)) => ~generous(X0)) [input p1]
3. ! [X0] : (kind(X0) <=> (~happy(X0) | patient(X0))) [input p2]
4. ! [X0] : ((patient(X0) <~> ~kind(X0)) => (brave(X0) & ~creative(X0))) [input p3]
5. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p4]
9. ! [X0] : ((kind(X0) | old(X0)) <=> (creative(X0) & old(X0))) [input p8]
14. ? [X0] : (creative(X0) <~> patient(X0)) => ? [X0] : creative(X0) [input p13]
16. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p15]
23. humble(lucy) [input hypothesis]
24. ? [X0] : (creative(X0) <~> patient(X0)) => ? [X1] : creative(X1) [rectify 14]
27. ! [X0] : (~generous(X0) | (tall(X0) & ~old(X0))) [ennf transformation 2]
28. ! [X0] : ((brave(X0) & ~creative(X0)) | (patient(X0) <=> ~kind(X0))) [ennf transformation 4]
33. ? [X1] : creative(X1) | ! [X0] : (creative(X0) <=> patient(X0)) [ennf transformation 24]
34. ! [X0] : ((generous(X0) & creative(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 16]
39. ! [X0] : ((kind(X0) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | ~kind(X0))) [nnf transformation 3]
40. ! [X0] : ((kind(X0) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | ~kind(X0))) [flattening 39]
41. ! [X0] : ((brave(X0) & ~creative(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [nnf transformation 28]
42. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 5]
43. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 42]
46. ! [X0] : (((kind(X0) | old(X0)) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 9]
47. ! [X0] : ((kind(X0) | old(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [flattening 46]
53. ? [X1] : creative(X1) | ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))) [nnf transformation 33]
54. ? [X0] : creative(X0) | ! [X1] : ((creative(X1) | ~patient(X1)) & (patient(X1) | ~creative(X1))) [rectify 53]
55. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
56. creative(sK1) | ! [X1] : ((creative(X1) | ~patient(X1)) & (patient(X1) | ~creative(X1))) [skolemisation 54,55]
71. ~old(X0) | ~generous(X0) [cnf transformation 27]
74. ~patient(X0) | kind(X0) [cnf transformation 40]
76. ~creative(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 41]
77. ~creative(X0) | patient(X0) | kind(X0) [cnf transformation 41]
79. brave(X0) | patient(X0) | kind(X0) [cnf transformation 41]
82. ~brave(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 43]
96. ~kind(X0) | old(X0) [cnf transformation 47]
98. ~kind(X0) | creative(X0) [cnf transformation 47]
117. creative(sK1) | patient(X1) | ~creative(X1) [cnf transformation 56]
129. ~creative(X0) | generous(X0) [cnf transformation 34]
137. humble(lucy) [cnf transformation 23]
142. ~brave(X0) | ~humble(X0) [duplicate literal removal 82]
166. brave(X0) | kind(X0) [subsumption resolution 79,74]
168. ~creative(X0) | kind(X0) [subsumption resolution 77,74]
169. ~patient(X0) | ~creative(X0) [subsumption resolution 76,74]
196. 10 <=> creative(sK1) [avatar definition]
198. creative(sK1) <- (10) [avatar component clause 196]
200. creative(sK1) | ~creative(X1) [subsumption resolution 117,169]
202. 11 <=> ! [X1] : ~creative(X1) [avatar definition]
203. ~creative(X1) <- (11) [avatar component clause 202]
204. 11 | 10 [avatar split clause 200,196,202]
273. 27 <=> humble(lucy) [avatar definition]
275. humble(lucy) <- (27) [avatar component clause 273]
277. 27 [avatar split clause 137,273]
285. generous(sK1) <- (10) [resolution 129,198]
292. ~humble(X0) | kind(X0) [resolution 166,142]
294. kind(sK1) <- (10) [resolution 168,198]
296. old(sK1) <- (10) [resolution 294,96]
298. ~generous(sK1) <- (10) [resolution 296,71]
299. $false <- (10) [subsumption resolution 298,285]
300. ~10 [avatar contradiction clause 299]
304. kind(lucy) <- (27) [resolution 292,275]
308. creative(lucy) <- (27) [resolution 304,98]
310. $false <- (11, 27) [subsumption resolution 308,203]
311. ~11 | ~27 [avatar contradiction clause 310]
312. $false [avatar sat refutation 204,277,300,311]
% SZS output end Proof for 181951496661598659355652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not generous is not funny or creative and vice versa.
If someone is not patient then lucy is tall or kind.
Everyone who is not creative or not kind is either not generous or not funny.
Everyone who is either funny or brave is both not old and not quiet and vice versa.
Everyone who is not calm is both generous and not tall.
Everyone who is either not kind or not generous is both not rich and not quiet and vice versa.
Everyone who is both calm and rich is either patient or calm.
Everyone who is not creative is curious or wise and vice versa.
Everyone who is either not creative or not old is either kind or not rich and vice versa.
Everyone who is either generous or happy is both funny and not happy.
Everyone who is humble is either not wise or not patient.
If someone is either not happy or old then someone is not tall or not wise and vice versa.
If someone is calm or not tall then mary is not calm or humble and vice versa.
Everyone who is either not strong or not quiet is both calm and not humble and vice versa.
Everyone who is creative or strong is not tall and vice versa.
Someone is old.
Fred is either not patient or happy.
Paul is either patient or not quiet.
Lucy is either kind or brave.
Someone is not old or calm. | Lucy is strong. | neutral | (![X]:((~quiet(X)&~generous(X))<=>(~funny(X)|creative(X))))&
((?[X]:(~patient(X)))=>((tall(lucy)|kind(lucy))))&
(![X]:((~creative(X)|~kind(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~old(X)&~quiet(X))))&
(![X]:(~calm(X)=>(generous(X)&~tall(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~rich(X)&~quiet(X))))&
(![X]:((calm(X)&rich(X))=>(patient(X)<~>calm(X))))&
(![X]:(~creative(X)<=>(curious(X)|wise(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((generous(X)<~>happy(X))=>(funny(X)&~happy(X))))&
(![X]:(humble(X)=>(~wise(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>((~calm(mary)|humble(mary))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(calm(X)&~humble(X))))&
(![X]:((creative(X)|strong(X))<=>~tall(X)))&
(?[X]:(old(X)))&
((~patient(fred)<~>happy(fred)))&
((patient(paul)<~>~quiet(paul)))&
((kind(lucy)<~>brave(lucy)))&
(?[X]:((~old(X)|calm(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is humble or quiet is both not wise and not quiet. If fred is both tall and strong then someone is happy or not kind and vice versa. Everyone who is both generous and not curious is curious. If someone is either not brave or not wise then alice is calm. Everyone who is tall or not strong is not calm or not brave and vice versa. Everyone who is not wise is either calm or curious and vice versa. If lucy is both wise and calm then someone is either not brave or not quiet. If paul is both quiet and not brave then lucy is either strong or not generous. Everyone who is not funny or not tall is not humble or curious and vice versa. If someone is either not generous or quiet then susan is both wise and generous and vice versa. If someone is old or not calm then john is quiet. Everyone who is rich is both funny and not wise and vice versa. If someone is either creative or generous then someone is brave or not kind and vice versa. Everyone who is both humble and kind is either old or brave and vice versa. Everyone who is both kind and generous is either quiet or funny and vice versa. Someone is strong or not rich. Someone is wise or not patient. Someone is both happy and not generous. Alice is wise. Someone is both happy and not curious. Fred is both kind and not humble. Someone is strong or old. Someone is happy or not patient. | Alice is brave. | contradiction | (![X]:((humble(X)|quiet(X))=>(~wise(X)&~quiet(X))))&
(((tall(fred)&strong(fred)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((generous(X)&~curious(X))=>curious(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>(calm(alice)))&
(![X]:((tall(X)|~strong(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>curious(X))))&
(((wise(lucy)&calm(lucy)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((quiet(paul)&~brave(paul)))=>((strong(lucy)<~>~generous(lucy))))&
(![X]:((~funny(X)|~tall(X))<=>(~humble(X)|curious(X))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((wise(susan)&generous(susan))))&
((?[X]:((old(X)|~calm(X))))=>(quiet(john)))&
(![X]:(rich(X)<=>(funny(X)&~wise(X))))&
((?[X]:((creative(X)<~>generous(X))))<=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((humble(X)&kind(X))<=>(old(X)<~>brave(X))))&
(![X]:((kind(X)&generous(X))<=>(quiet(X)<~>funny(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((happy(X)&~generous(X))))&
(wise(alice))&
(?[X]:((happy(X)&~curious(X))))&
((kind(fred)&~humble(fred)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((happy(X)|~patient(X)))) | brave(alice) | [
"p0",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6542361698150921705686279
% SZS output start Proof for 6542361698150921705686279
1. ! [X0] : ((quiet(X0) | humble(X0)) => (~quiet(X0) & ~wise(X0))) [input p0]
11. ? [X0] : (~calm(X0) | old(X0)) => quiet(john) [input p10]
14. ! [X0] : ((kind(X0) & humble(X0)) <=> (old(X0) <~> brave(X0))) [input p13]
19. wise(alice) [input p18]
24. brave(alice) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 1]
37. quiet(john) | ! [X0] : (calm(X0) & ~old(X0)) [ennf transformation 11]
65. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~kind(X0) | ~humble(X0)))) [nnf transformation 14]
66. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ~kind(X0) | ~humble(X0))) [flattening 65]
77. ~wise(X0) | ~humble(X0) [cnf transformation 29]
80. ~quiet(X0) | ~quiet(X0) [cnf transformation 29]
111. quiet(john) | ~old(X0) [cnf transformation 37]
123. humble(X0) | old(X0) | ~brave(X0) [cnf transformation 66]
135. wise(alice) [cnf transformation 19]
141. brave(alice) [cnf transformation 24]
143. ~quiet(X0) [duplicate literal removal 80]
219. ~old(X0) [subsumption resolution 111,143]
252. ~brave(X0) | humble(X0) [subsumption resolution 123,219]
269. ~humble(alice) [resolution 77,135]
273. humble(alice) [resolution 252,141]
274. $false [subsumption resolution 273,269]
% SZS output end Proof for 6542361698150921705686279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not patient is not kind and vice versa.
Everyone who is not patient is not calm and vice versa.
Everyone who is humble is both tall and humble.
Everyone who is not tall is funny or not calm and vice versa.
Everyone who is either kind or not strong is either creative or not patient and vice versa.
Everyone who is either wise or not creative is either not humble or strong and vice versa.
If someone is both tall and funny then someone is not brave or not patient and vice versa.
Everyone who is patient is both rich and not strong.
If someone is either rich or not tall then someone is generous.
Everyone who is happy or not brave is not tall.
Everyone who is both not creative and not calm is both not wise and calm and vice versa.
Everyone who is not wise is either not happy or generous and vice versa.
If susan is either not quiet or happy then mary is not brave or not tall and vice versa.
If someone is kind or old then someone is not funny or humble and vice versa.
If someone is either brave or curious then someone is happy.
Everyone who is happy is both not old and calm.
Someone is either strong or not humble.
Fred is rich.
Lucy is either rich or happy.
John is both wise and calm.
Paul is both not quiet and tall.
Someone is either patient or not creative.
Someone is not tall. | Paul is not creative. | contradiction | (![X]:((wise(X)|~patient(X))<=>~kind(X)))&
(![X]:(~patient(X)<=>~calm(X)))&
(![X]:(humble(X)=>(tall(X)&humble(X))))&
(![X]:(~tall(X)<=>(funny(X)|~calm(X))))&
(![X]:((kind(X)<~>~strong(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((wise(X)<~>~creative(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:(patient(X)=>(rich(X)&~strong(X))))&
((?[X]:((rich(X)<~>~tall(X))))=>(?[X]:(generous(X))))&
(![X]:((happy(X)|~brave(X))=>~tall(X)))&
(![X]:((~creative(X)&~calm(X))<=>(~wise(X)&calm(X))))&
(![X]:(~wise(X)<=>(~happy(X)<~>generous(X))))&
(((~quiet(susan)<~>happy(susan)))<=>((~brave(mary)|~tall(mary))))&
((?[X]:((kind(X)|old(X))))<=>(?[X]:((~funny(X)|humble(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(happy(X))))&
(![X]:(happy(X)=>(~old(X)&calm(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(rich(fred))&
((rich(lucy)<~>happy(lucy)))&
((wise(john)&calm(john)))&
((~quiet(paul)&tall(paul)))&
(?[X]:((patient(X)<~>~creative(X))))&
(?[X]:(~tall(X))) | ~creative(paul) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4846639428192546527503781
% SZS output start Proof for 4846639428192546527503781
1. ! [X0] : ((~patient(X0) | wise(X0)) <=> ~kind(X0)) [input p0]
2. ! [X0] : (~patient(X0) <=> ~calm(X0)) [input p1]
4. ! [X0] : (~tall(X0) <=> (~calm(X0) | funny(X0))) [input p3]
5. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p4]
7. ? [X0] : (funny(X0) & tall(X0)) <=> ? [X0] : (~patient(X0) | ~brave(X0)) [input p6]
8. ! [X0] : (patient(X0) => (~strong(X0) & rich(X0))) [input p7]
11. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (calm(X0) & ~wise(X0))) [input p10]
24. ~creative(paul) [input hypothesis]
25. ? [X0] : (funny(X0) & tall(X0)) <=> ? [X1] : (~patient(X1) | ~brave(X1)) [rectify 7]
30. ! [X0] : ((~strong(X0) & rich(X0)) | ~patient(X0)) [ennf transformation 8]
35. ! [X0] : (((~patient(X0) | wise(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) & ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((~patient(X0) | wise(X0) | kind(X0)) & (~kind(X0) | (patient(X0) & ~wise(X0)))) [flattening 35]
37. ! [X0] : ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))) [nnf transformation 2]
38. ! [X0] : ((~tall(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | tall(X0))) [nnf transformation 4]
39. ! [X0] : ((~tall(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | tall(X0))) [flattening 38]
40. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 5]
42. (? [X0] : (funny(X0) & tall(X0)) | ! [X1] : (patient(X1) & brave(X1))) & (? [X1] : (~patient(X1) | ~brave(X1)) | ! [X0] : (~funny(X0) | ~tall(X0))) [nnf transformation 25]
43. (? [X0] : (funny(X0) & tall(X0)) | ! [X1] : (patient(X1) & brave(X1))) & (? [X2] : (~patient(X2) | ~brave(X2)) | ! [X3] : (~funny(X3) | ~tall(X3))) [rectify 42]
44. ? [X0] : (funny(X0) & tall(X0)) => (funny(sK0) & tall(sK0)) [choice axiom]
45. ? [X2] : (~patient(X2) | ~brave(X2)) => (~patient(sK1) | ~brave(sK1)) [choice axiom]
46. ((funny(sK0) & tall(sK0)) | ! [X1] : (patient(X1) & brave(X1))) & ((~patient(sK1) | ~brave(sK1)) | ! [X3] : (~funny(X3) | ~tall(X3))) [skolemisation 43,45,44]
51. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~calm(X0) | wise(X0))) & ((calm(X0) & ~wise(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & ~creative(X0)) | ~calm(X0) | wise(X0)) & ((calm(X0) & ~wise(X0)) | calm(X0) | creative(X0))) [flattening 51]
74. ~kind(X0) | ~wise(X0) [cnf transformation 36]
78. ~patient(X0) | calm(X0) [cnf transformation 37]
82. ~funny(X0) | ~tall(X0) [cnf transformation 39]
85. ~patient(X0) | creative(X0) | kind(X0) | strong(X0) [cnf transformation 40]
102. tall(sK0) | patient(X1) [cnf transformation 46]
104. funny(sK0) | patient(X1) [cnf transformation 46]
106. ~strong(X0) | ~patient(X0) [cnf transformation 30]
114. ~calm(X0) | ~calm(X0) | wise(X0) [cnf transformation 52]
145. ~creative(paul) [cnf transformation 24]
147. ~calm(X0) | wise(X0) [duplicate literal removal 114]
153. 1 <=> ! [X1] : patient(X1) [avatar definition]
154. patient(X1) <- (1) [avatar component clause 153]
156. 2 <=> funny(sK0) [avatar definition]
158. funny(sK0) <- (2) [avatar component clause 156]
159. 1 | 2 [avatar split clause 104,156,153]
165. 4 <=> tall(sK0) [avatar definition]
167. tall(sK0) <- (4) [avatar component clause 165]
168. 1 | 4 [avatar split clause 102,165,153]
286. ~tall(sK0) <- (2) [resolution 82,158]
287. $false <- (2, 4) [subsumption resolution 286,167]
288. ~2 | ~4 [avatar contradiction clause 287]
290. calm(X0) <- (1) [resolution 154,78]
305. wise(X0) <- (1) [resolution 147,290]
367. creative(X0) | kind(X0) | strong(X0) <- (1) [resolution 85,154]
427. kind(paul) | strong(paul) <- (1) [resolution 367,145]
441. 40 <=> strong(paul) [avatar definition]
443. strong(paul) <- (40) [avatar component clause 441]
445. 41 <=> kind(paul) [avatar definition]
447. kind(paul) <- (41) [avatar component clause 445]
448. 40 | 41 | ~1 [avatar split clause 427,153,445,441]
451. ~wise(paul) <- (41) [resolution 447,74]
452. $false <- (1, 41) [subsumption resolution 451,305]
453. ~1 | ~41 [avatar contradiction clause 452]
458. ~patient(paul) <- (40) [resolution 443,106]
461. $false <- (1, 40) [subsumption resolution 458,154]
462. ~1 | ~40 [avatar contradiction clause 461]
463. $false [avatar sat refutation 159,168,288,448,453,462]
% SZS output end Proof for 4846639428192546527503781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then lucy is not calm.
Everyone who is not old or not brave is both calm and not generous and vice versa.
Everyone who is kind is generous or not kind and vice versa.
If someone is both not humble and kind then someone is not tall or not calm.
If someone is curious then someone is both patient and not curious and vice versa.
Everyone who is wise is both not generous and not old and vice versa.
If someone is either kind or not curious then someone is either quiet or not happy.
If someone is funny or not patient then john is not calm or old.
If someone is tall then paul is not happy.
Everyone who is wise or not tall is not strong and vice versa.
Everyone who is quiet or wise is either not humble or rich and vice versa.
If susan is not generous or not wise then someone is not kind or creative and vice versa.
Someone is either funny or not kind.
Paul is both not quiet and humble.
Someone is not humble.
Someone is either rich or patient.
Someone is brave or funny.
Alice is not patient or not calm. | John is brave. | entailment | ((?[X]:(calm(X)))=>(~calm(lucy)))&
(![X]:((~old(X)|~brave(X))<=>(calm(X)&~generous(X))))&
(![X]:(kind(X)<=>(generous(X)|~kind(X))))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:(wise(X)<=>(~generous(X)&~old(X))))&
((?[X]:((kind(X)<~>~curious(X))))=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((funny(X)|~patient(X))))=>((~calm(john)|old(john))))&
((?[X]:(tall(X)))=>(~happy(paul)))&
(![X]:((wise(X)|~tall(X))<=>~strong(X)))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(?[X]:((funny(X)<~>~kind(X))))&
((~quiet(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:((brave(X)|funny(X))))&
((~patient(alice)|~calm(alice))) | brave(john) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 633726561696400271199043
% SZS output start Proof for 633726561696400271199043
2. ! [X0] : ((~brave(X0) | ~old(X0)) <=> (~generous(X0) & calm(X0))) [input p1]
3. ! [X0] : (kind(X0) <=> (~kind(X0) | generous(X0))) [input p2]
19. ~brave(john) [input hypothesis]
29. ! [X0] : (((~brave(X0) | ~old(X0)) | (generous(X0) | ~calm(X0))) & ((~generous(X0) & calm(X0)) | (brave(X0) & old(X0)))) [nnf transformation 2]
30. ! [X0] : ((~brave(X0) | ~old(X0) | generous(X0) | ~calm(X0)) & ((~generous(X0) & calm(X0)) | (brave(X0) & old(X0)))) [flattening 29]
31. ! [X0] : ((kind(X0) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | ~kind(X0))) [nnf transformation 3]
32. ! [X0] : ((kind(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | ~kind(X0))) [flattening 31]
65. ~generous(X0) | brave(X0) [cnf transformation 30]
67. ~kind(X0) | generous(X0) | ~kind(X0) [cnf transformation 32]
69. kind(X0) | kind(X0) [cnf transformation 32]
101. ~brave(john) [cnf transformation 19]
102. ~kind(X0) | generous(X0) [duplicate literal removal 67]
103. kind(X0) [duplicate literal removal 69]
112. generous(X0) [subsumption resolution 102,103]
197. brave(X0) [resolution 65,112]
198. $false [resolution 197,101]
% SZS output end Proof for 633726561696400271199043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then lucy is either not rich or calm and vice versa. Everyone who is either humble or kind is not strong or kind and vice versa. If someone is not calm or not tall then mary is either not old or not rich. Everyone who is funny is both wise and not funny and vice versa. Everyone who is not kind is either not strong or rich and vice versa. If lucy is both not generous and not wise then someone is patient. Everyone who is not creative or not rich is not funny or not wise and vice versa. Everyone who is either not humble or not rich is both not happy and old and vice versa. If alice is either creative or humble then paul is both old and generous. If alice is not strong then susan is either brave or not generous. Everyone who is not creative or not patient is either not funny or generous and vice versa. Everyone who is not strong is not funny or not patient. If someone is either not kind or not happy then lucy is tall and vice versa. Everyone who is either funny or quiet is not happy or patient. Everyone who is either not brave or brave is humble and vice versa. If fred is kind then someone is not patient or funny. John is humble or not patient. Someone is curious or not curious. Someone is either not strong or tall. Someone is patient. Someone is both creative and curious. Someone is both humble and brave. Someone is either not creative or not happy. | Alice is strong. | contradiction | ((?[X]:(generous(X)))<=>((~rich(lucy)<~>calm(lucy))))&
(![X]:((humble(X)<~>kind(X))<=>(~strong(X)|kind(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~old(mary)<~>~rich(mary))))&
(![X]:(funny(X)<=>(wise(X)&~funny(X))))&
(![X]:(~kind(X)<=>(~strong(X)<~>rich(X))))&
(((~generous(lucy)&~wise(lucy)))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)|~rich(X))<=>(~funny(X)|~wise(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~happy(X)&old(X))))&
(((creative(alice)<~>humble(alice)))=>((old(paul)&generous(paul))))&
((~strong(alice))=>((brave(susan)<~>~generous(susan))))&
(![X]:((~creative(X)|~patient(X))<=>(~funny(X)<~>generous(X))))&
(![X]:(~strong(X)=>(~funny(X)|~patient(X))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(tall(lucy)))&
(![X]:((funny(X)<~>quiet(X))=>(~happy(X)|patient(X))))&
(![X]:((~brave(X)<~>brave(X))<=>humble(X)))&
((kind(fred))=>(?[X]:((~patient(X)|funny(X)))))&
((humble(john)|~patient(john)))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~strong(X)<~>tall(X))))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)&curious(X))))&
(?[X]:((humble(X)&brave(X))))&
(?[X]:((~creative(X)<~>~happy(X)))) | strong(alice) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4548905947965882116415774
% SZS output start Proof for 4548905947965882116415774
2. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (kind(X0) | ~strong(X0))) [input p1]
15. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> humble(X0)) [input p14]
24. strong(alice) [input hypothesis]
39. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~kind(X0) & strong(X0))) & ((kind(X0) | ~strong(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~kind(X0) & strong(X0))) & (kind(X0) | ~strong(X0) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [flattening 39]
60. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~humble(X0)) & (humble(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 15]
81. kind(X0) | ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 40]
86. ~kind(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 40]
128. humble(X0) | brave(X0) | brave(X0) [cnf transformation 60]
129. humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
144. strong(alice) [cnf transformation 24]
145. humble(X0) | brave(X0) [duplicate literal removal 128]
146. ~brave(X0) | humble(X0) [duplicate literal removal 129]
149. kind(X0) | ~strong(X0) | ~humble(X0) [duplicate literal removal 81]
150. ~kind(X0) | ~humble(X0) [duplicate literal removal 86]
170. ~strong(X0) | ~humble(X0) [subsumption resolution 149,150]
224. 16 <=> strong(alice) [avatar definition]
226. strong(alice) <- (16) [avatar component clause 224]
263. humble(X0) [subsumption resolution 145,146]
294. 16 [avatar split clause 144,224]
301. ~humble(alice) <- (16) [resolution 170,226]
302. $false <- (16) [subsumption resolution 301,263]
303. ~16 [avatar contradiction clause 302]
304. $false [avatar sat refutation 294,303]
% SZS output end Proof for 4548905947965882116415774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not rich is not generous or not calm. Everyone who is either not kind or not calm is either not calm or not strong. If someone is quiet then fred is either old or not brave and vice versa. If someone is either brave or kind then someone is either generous or not calm. If someone is both patient and not tall then someone is either calm or not brave. Everyone who is not old or not strong is both funny and not happy and vice versa. Everyone who is either brave or not rich is not kind and vice versa. Everyone who is calm is both not kind and generous. If susan is either not creative or not kind then someone is old and vice versa. Everyone who is either not patient or funny is both not quiet and not rich and vice versa. Everyone who is both strong and wise is either not humble or humble and vice versa. If someone is either tall or not wise then someone is both not curious and not patient. If mary is not old then someone is either not curious or wise and vice versa. Everyone who is patient or old is brave. If someone is both not wise and not generous then paul is not strong or not funny and vice versa. If someone is either not strong or curious then someone is patient. John is both not calm and not rich. John is not calm. Susan is not creative. Alice is tall or not calm. Someone is not creative. John is both funny and not humble. Someone is either not kind or quiet. Paul is not quiet or not generous. | Fred is not strong. | contradiction | (![X]:((tall(X)&~rich(X))=>(~generous(X)|~calm(X))))&
(![X]:((~kind(X)<~>~calm(X))=>(~calm(X)<~>~strong(X))))&
((?[X]:(quiet(X)))<=>((old(fred)<~>~brave(fred))))&
((?[X]:((brave(X)<~>kind(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
((?[X]:((patient(X)&~tall(X))))=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&~happy(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~kind(X)))&
(![X]:(calm(X)=>(~kind(X)&generous(X))))&
(((~creative(susan)<~>~kind(susan)))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(~quiet(X)&~rich(X))))&
(![X]:((strong(X)&wise(X))<=>(~humble(X)<~>humble(X))))&
((?[X]:((tall(X)<~>~wise(X))))=>(?[X]:((~curious(X)&~patient(X)))))&
((~old(mary))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:((patient(X)|old(X))=>brave(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~strong(paul)|~funny(paul))))&
((?[X]:((~strong(X)<~>curious(X))))=>(?[X]:(patient(X))))&
((~calm(john)&~rich(john)))&
(~calm(john))&
(~creative(susan))&
((tall(alice)|~calm(alice)))&
(?[X]:(~creative(X)))&
((funny(john)&~humble(john)))&
(?[X]:((~kind(X)<~>quiet(X))))&
((~quiet(paul)|~generous(paul))) | ~strong(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6014494603400383908552408
% SZS output start Proof for 6014494603400383908552408
11. ! [X0] : ((wise(X0) & strong(X0)) <=> (~humble(X0) <~> humble(X0))) [input p10]
25. ~strong(fred) [input hypothesis]
61. ! [X0] : (((wise(X0) & strong(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~wise(X0) | ~strong(X0)))) [nnf transformation 11]
62. ! [X0] : (((wise(X0) & strong(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~wise(X0) | ~strong(X0))) [flattening 61]
123. strong(X0) | humble(X0) | humble(X0) [cnf transformation 62]
124. strong(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 62]
155. ~strong(fred) [cnf transformation 25]
156. strong(X0) | humble(X0) [duplicate literal removal 123]
157. strong(X0) | ~humble(X0) [duplicate literal removal 124]
232. strong(X0) [subsumption resolution 156,157]
309. $false [subsumption resolution 155,232]
% SZS output end Proof for 6014494603400383908552408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is tall or not brave.
Everyone who is not funny is either patient or curious and vice versa.
Everyone who is either not calm or creative is either not patient or not quiet.
Everyone who is either not quiet or not calm is patient.
Everyone who is both tall and not brave is both happy and funny.
If someone is calm then someone is either calm or wise and vice versa.
Everyone who is either funny or not humble is not brave or humble.
Everyone who is both humble and calm is not old or not brave.
If fred is calm then john is both not creative and humble.
If someone is both not tall and not curious then mary is patient.
Everyone who is both not happy and not patient is not old and vice versa.
If lucy is either not kind or not patient then fred is not brave.
If someone is not happy or not funny then someone is not old and vice versa.
If someone is either happy or not happy then susan is calm and vice versa.
Everyone who is both not strong and curious is either old or not calm and vice versa.
Everyone who is not creative or kind is not quiet and vice versa.
John is either not old or wise.
Someone is brave.
Lucy is strong.
Someone is both humble and not curious.
Fred is patient or not wise.
Someone is not happy.
Alice is both not funny and patient.
Someone is curious or not strong. | John is creative. | neutral | ((?[X]:(strong(X)))=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:(~funny(X)<=>(patient(X)<~>curious(X))))&
(![X]:((~calm(X)<~>creative(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>patient(X)))&
(![X]:((tall(X)&~brave(X))=>(happy(X)&funny(X))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(~brave(X)|humble(X))))&
(![X]:((humble(X)&calm(X))=>(~old(X)|~brave(X))))&
((calm(fred))=>((~creative(john)&humble(john))))&
((?[X]:((~tall(X)&~curious(X))))=>(patient(mary)))&
(![X]:((~happy(X)&~patient(X))<=>~old(X)))&
(((~kind(lucy)<~>~patient(lucy)))=>(~brave(fred)))&
((?[X]:((~happy(X)|~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(calm(susan)))&
(![X]:((~strong(X)&curious(X))<=>(old(X)<~>~calm(X))))&
(![X]:((~creative(X)|kind(X))<=>~quiet(X)))&
((~old(john)<~>wise(john)))&
(?[X]:(brave(X)))&
(strong(lucy))&
(?[X]:((humble(X)&~curious(X))))&
((patient(fred)|~wise(fred)))&
(?[X]:(~happy(X)))&
((~funny(alice)&patient(alice)))&
(?[X]:((curious(X)|~strong(X)))) | creative(john) | [] | null | 0 |
Everyone who is old is not tall. Everyone who is not quiet is either curious or funny. If someone is both not rich and rich then john is either humble or not generous. If someone is either strong or not calm then someone is not tall or rich and vice versa. Everyone who is not wise or not creative is not humble or not strong. Everyone who is not generous or not humble is both old and calm. If fred is either not generous or kind then paul is calm. Everyone who is not patient or strong is brave. Everyone who is not calm is both not old and curious. Everyone who is not happy or funny is calm or old. Everyone who is not humble is old or not strong and vice versa. If john is creative then someone is both not funny and calm and vice versa. If someone is funny then someone is both creative and not quiet and vice versa. Everyone who is not rich is rich or not rich. Everyone who is not brave or not strong is either not rich or funny. Everyone who is tall or old is both humble and quiet and vice versa. Someone is both not rich and not kind. Lucy is not calm or rich. John is old or wise. Someone is brave or not funny. Susan is quiet. Someone is not tall or not rich. | Paul is not quiet. | neutral | (![X]:(old(X)=>~tall(X)))&
(![X]:(~quiet(X)=>(curious(X)<~>funny(X))))&
((?[X]:((~rich(X)&rich(X))))=>((humble(john)<~>~generous(john))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~wise(X)|~creative(X))=>(~humble(X)|~strong(X))))&
(![X]:((~generous(X)|~humble(X))=>(old(X)&calm(X))))&
(((~generous(fred)<~>kind(fred)))=>(calm(paul)))&
(![X]:((~patient(X)|strong(X))=>brave(X)))&
(![X]:(~calm(X)=>(~old(X)&curious(X))))&
(![X]:((~happy(X)|funny(X))=>(calm(X)|old(X))))&
(![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((creative(john))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~brave(X)|~strong(X))=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)|old(X))<=>(humble(X)&quiet(X))))&
(?[X]:((~rich(X)&~kind(X))))&
((~calm(lucy)|rich(lucy)))&
((old(john)|wise(john)))&
(?[X]:((brave(X)|~funny(X))))&
(quiet(susan))&
(?[X]:((~tall(X)|~rich(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is both not patient and humble is both happy and tall and vice versa.
Everyone who is calm is either not wise or happy and vice versa.
Everyone who is kind or not calm is not generous and vice versa.
If someone is not happy then paul is creative or not creative.
If someone is creative or not curious then someone is both humble and strong.
Everyone who is both kind and not generous is creative.
If someone is both calm and wise then someone is both curious and not calm and vice versa.
If mary is both creative and not creative then someone is either not strong or calm and vice versa.
Everyone who is not rich is rich.
If someone is both patient and not old then someone is both not wise and kind and vice versa.
Everyone who is wise or patient is both not wise and not generous.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Fred is quiet.
Someone is either not quiet or strong.
Mary is tall or not funny.
Paul is either curious or humble. | Paul is funny. | contradiction | (![X]:((~patient(X)&humble(X))<=>(happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~wise(X)<~>happy(X))))&
(![X]:((kind(X)|~calm(X))<=>~generous(X)))&
((?[X]:(~happy(X)))=>((creative(paul)|~creative(paul))))&
((?[X]:((creative(X)|~curious(X))))=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((kind(X)&~generous(X))=>creative(X)))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~rich(X)=>rich(X)))&
((?[X]:((patient(X)&~old(X))))<=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:((wise(X)|patient(X))=>(~wise(X)&~generous(X))))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>strong(X))))&
((tall(mary)|~funny(mary)))&
((curious(paul)<~>humble(paul))) | funny(paul) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2989099403334167476281350
% SZS output start Proof for 2989099403334167476281350
5. ? [X0] : (~curious(X0) | creative(X0)) => ? [X0] : (strong(X0) & humble(X0)) [input p4]
7. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X0] : (~calm(X0) & curious(X0)) [input p6]
9. ! [X0] : (~rich(X0) => rich(X0)) [input p8]
11. ! [X0] : ((patient(X0) | wise(X0)) => (~generous(X0) & ~wise(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> calm(X0)) => (~rich(X0) & funny(X0))) [input p11]
15. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p14]
16. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p15]
21. funny(paul) [input hypothesis]
22. ? [X0] : (~curious(X0) | creative(X0)) => ? [X1] : (strong(X1) & humble(X1)) [rectify 5]
23. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X1] : (~calm(X1) & curious(X1)) [rectify 7]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 16]
28. ? [X1] : (strong(X1) & humble(X1)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 22]
31. ! [X0] : (rich(X0) | rich(X0)) [ennf transformation 9]
32. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~patient(X0) & ~wise(X0))) [ennf transformation 11]
33. ! [X0] : ((~rich(X0) & funny(X0)) | (~funny(X0) <=> calm(X0))) [ennf transformation 12]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 15]
40. ? [X0] : (strong(X0) & humble(X0)) | ! [X1] : (curious(X1) & ~creative(X1)) [rectify 28]
41. ? [X0] : (strong(X0) & humble(X0)) => (strong(sK0) & humble(sK0)) [choice axiom]
42. (strong(sK0) & humble(sK0)) | ! [X1] : (curious(X1) & ~creative(X1)) [skolemisation 40,41]
43. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X1] : (~calm(X1) & curious(X1)) | ! [X0] : (~wise(X0) | ~calm(X0))) [nnf transformation 23]
44. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X2] : (~calm(X2) & curious(X2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [rectify 43]
45. ? [X0] : (wise(X0) & calm(X0)) => (wise(sK1) & calm(sK1)) [choice axiom]
46. ? [X2] : (~calm(X2) & curious(X2)) => (~calm(sK2) & curious(sK2)) [choice axiom]
47. ((wise(sK1) & calm(sK1)) | ! [X1] : (calm(X1) | ~curious(X1))) & ((~calm(sK2) & curious(sK2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [skolemisation 44,46,45]
58. ! [X0] : ((~rich(X0) & funny(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) [nnf transformation 33]
65. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
66. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (old(X0) | humble(X0)) => (old(sK7) | humble(sK7)) [choice axiom]
68. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK8) & happy(sK8)) [choice axiom]
69. ((old(sK7) | humble(sK7)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK8) & happy(sK8)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 66,68,67]
87. humble(sK0) | curious(X1) [cnf transformation 42]
94. wise(sK1) | calm(X1) | ~curious(X1) [cnf transformation 47]
101. rich(X0) | rich(X0) [cnf transformation 31]
106. ~wise(X0) | ~wise(X0) [cnf transformation 32]
113. ~rich(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 58]
122. ~happy(X0) | calm(X0) [cnf transformation 34]
124. happy(sK8) | ~humble(X3) [cnf transformation 69]
126. ~calm(sK8) | ~humble(X3) [cnf transformation 69]
135. funny(paul) [cnf transformation 21]
137. ~wise(X0) [duplicate literal removal 106]
138. rich(X0) [duplicate literal removal 101]
140. 1 <=> ! [X1] : curious(X1) [avatar definition]
141. curious(X1) <- (1) [avatar component clause 140]
152. 4 <=> humble(sK0) [avatar definition]
154. humble(sK0) <- (4) [avatar component clause 152]
155. 1 | 4 [avatar split clause 87,152,140]
159. 5 <=> ! [X1] : (calm(X1) | ~curious(X1)) [avatar definition]
160. ~curious(X1) | calm(X1) <- (5) [avatar component clause 159]
162. 6 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (6) [avatar component clause 162]
165. 5 | 6 [avatar split clause 94,162,159]
224. ~funny(X0) | ~calm(X0) [subsumption resolution 113,138]
253. 26 <=> calm(sK8) [avatar definition]
255. ~calm(sK8) <- (~26) [avatar component clause 253]
258. 27 <=> ! [X3] : ~humble(X3) [avatar definition]
259. ~humble(X3) <- (27) [avatar component clause 258]
260. 27 | ~26 [avatar split clause 126,253,258]
262. 28 <=> happy(sK8) [avatar definition]
264. happy(sK8) <- (28) [avatar component clause 262]
266. 27 | 28 [avatar split clause 124,262,258]
299. $false <- (4, 27) [subsumption resolution 154,259]
300. ~4 | ~27 [avatar contradiction clause 299]
301. calm(X0) <- (1, 5) [resolution 160,141]
309. ~calm(paul) [resolution 224,135]
310. $false <- (1, 5) [subsumption resolution 309,301]
311. ~1 | ~5 [avatar contradiction clause 310]
312. $false <- (6) [subsumption resolution 164,137]
313. ~6 [avatar contradiction clause 312]
317. calm(sK8) <- (28) [resolution 264,122]
318. $false <- (~26, 28) [subsumption resolution 317,255]
319. 26 | ~28 [avatar contradiction clause 318]
320. $false [avatar sat refutation 155,165,260,266,300,311,313,319]
% SZS output end Proof for 2989099403334167476281350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then lucy is not patient or strong and vice versa.
Everyone who is not wise is either not tall or tall and vice versa.
Everyone who is not funny or creative is either wise or happy.
If someone is either not brave or not funny then someone is either generous or not tall.
If someone is not calm or not tall then someone is either humble or not humble.
Everyone who is not rich or not curious is both not tall and not kind and vice versa.
Everyone who is either wise or funny is calm and vice versa.
If john is not humble or brave then someone is not quiet.
If someone is either quiet or funny then alice is not quiet.
Everyone who is not tall or not humble is not tall.
If someone is curious then john is either humble or not funny and vice versa.
Everyone who is tall or not quiet is both not strong and quiet and vice versa.
Everyone who is either not tall or not wise is both not calm and curious and vice versa.
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
John is not kind or calm.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Someone is both happy and quiet.
Fred is either not calm or funny. | John is not strong. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))<=>((~patient(lucy)|strong(lucy))))&
(![X]:(~wise(X)<=>(~tall(X)<~>tall(X))))&
(![X]:((~funny(X)|creative(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>calm(X)))&
(((~humble(john)|brave(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>funny(X))))=>(~quiet(alice)))&
(![X]:((~tall(X)|~humble(X))=>~tall(X)))&
((?[X]:(curious(X)))<=>((humble(john)<~>~funny(john))))&
(![X]:((tall(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
((~kind(john)|calm(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
(?[X]:((happy(X)&quiet(X))))&
((~calm(fred)<~>funny(fred))) | ~strong(john) | [
"p1",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7875209320392970328520021
% SZS output start Proof for 7875209320392970328520021
2. ! [X0] : (~wise(X0) <=> (~tall(X0) <~> tall(X0))) [input p1]
7. ! [X0] : ((wise(X0) <~> funny(X0)) <=> calm(X0)) [input p6]
9. ? [X0] : (quiet(X0) <~> funny(X0)) => ~quiet(alice) [input p8]
12. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (quiet(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (curious(X0) & ~calm(X0))) [input p12]
23. ~strong(john) [input hypothesis]
32. ~quiet(alice) | ! [X0] : (quiet(X0) <=> funny(X0)) [ennf transformation 9]
39. ! [X0] : ((~wise(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | wise(X0))) [nnf transformation 2]
51. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~calm(X0)) & (calm(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 7]
54. ~quiet(alice) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0))) [nnf transformation 32]
59. ! [X0] : (((~quiet(X0) | tall(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~quiet(X0) | tall(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 59]
61. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~curious(X0) | calm(X0))) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 13]
62. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ~curious(X0) | calm(X0)) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [flattening 61]
89. ~wise(X0) | tall(X0) | tall(X0) [cnf transformation 39]
90. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 39]
107. calm(X0) | wise(X0) | ~funny(X0) [cnf transformation 51]
112. ~quiet(alice) | funny(X0) | ~quiet(X0) [cnf transformation 54]
123. quiet(X0) | quiet(X0) [cnf transformation 60]
124. ~quiet(X0) | tall(X0) | ~quiet(X0) | strong(X0) [cnf transformation 60]
126. ~calm(X0) | ~tall(X0) | wise(X0) [cnf transformation 62]
150. ~strong(john) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 123]
152. ~quiet(X0) | tall(X0) | strong(X0) [duplicate literal removal 124]
153. ~wise(X0) | tall(X0) [duplicate literal removal 89]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 90]
183. ~wise(X0) [subsumption resolution 153,154]
204. ~funny(X0) | calm(X0) [subsumption resolution 107,183]
223. 15 <=> quiet(alice) [avatar definition]
225. ~quiet(alice) <- (~15) [avatar component clause 223]
228. 16 <=> ! [X0] : (funny(X0) | ~quiet(X0)) [avatar definition]
229. funny(X0) | ~quiet(X0) <- (16) [avatar component clause 228]
230. 16 | ~15 [avatar split clause 112,223,228]
247. ~calm(X0) | ~tall(X0) [subsumption resolution 126,183]
294. $false <- (~15) [subsumption resolution 225,151]
295. 15 [avatar contradiction clause 294]
298. funny(X0) <- (16) [subsumption resolution 229,151]
302. calm(X0) <- (16) [resolution 204,298]
304. ~tall(X0) <- (16) [resolution 302,247]
318. tall(X0) | strong(X0) [resolution 152,151]
319. strong(X0) <- (16) [subsumption resolution 318,304]
329. $false <- (16) [resolution 319,150]
330. ~16 [avatar contradiction clause 329]
331. $false [avatar sat refutation 230,295,330]
% SZS output end Proof for 7875209320392970328520021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not quiet is tall and vice versa.
If someone is either not calm or funny then lucy is both humble and not happy.
If someone is either rich or not happy then susan is not kind or not old.
If john is either not strong or humble then someone is not calm.
Everyone who is not rich is either not patient or not calm and vice versa.
Everyone who is either creative or not creative is strong.
Everyone who is both generous and not rich is either brave or rich.
Everyone who is either not rich or not patient is both tall and quiet.
If someone is either not generous or not curious then lucy is either not funny or rich and vice versa.
Everyone who is not creative or not happy is not brave or old.
If susan is both old and tall then alice is both not strong and happy.
Everyone who is both tall and not tall is either patient or not wise and vice versa.
If someone is quiet or old then lucy is both tall and patient.
If someone is both not funny and not calm then fred is not rich and vice versa.
Everyone who is not old is either brave or not creative and vice versa.
Everyone who is both rich and kind is both old and not curious and vice versa.
Someone is both generous and funny.
Someone is brave or not creative.
Alice is both rich and not generous.
Someone is either calm or not happy.
Someone is not funny.
Someone is either not old or not curious.
Someone is both not humble and not curious.
Susan is both funny and quiet. | Susan is strong. | entailment | (![X]:((strong(X)|~quiet(X))<=>tall(X)))&
((?[X]:((~calm(X)<~>funny(X))))=>((humble(lucy)&~happy(lucy))))&
((?[X]:((rich(X)<~>~happy(X))))=>((~kind(susan)|~old(susan))))&
(((~strong(john)<~>humble(john)))=>(?[X]:(~calm(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~creative(X))=>strong(X)))&
(![X]:((generous(X)&~rich(X))=>(brave(X)<~>rich(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(tall(X)&quiet(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>((~funny(lucy)<~>rich(lucy))))&
(![X]:((~creative(X)|~happy(X))=>(~brave(X)|old(X))))&
(((old(susan)&tall(susan)))=>((~strong(alice)&happy(alice))))&
(![X]:((tall(X)&~tall(X))<=>(patient(X)<~>~wise(X))))&
((?[X]:((quiet(X)|old(X))))=>((tall(lucy)&patient(lucy))))&
((?[X]:((~funny(X)&~calm(X))))<=>(~rich(fred)))&
(![X]:(~old(X)<=>(brave(X)<~>~creative(X))))&
(![X]:((rich(X)&kind(X))<=>(old(X)&~curious(X))))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((brave(X)|~creative(X))))&
((rich(alice)&~generous(alice)))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~old(X)<~>~curious(X))))&
(?[X]:((~humble(X)&~curious(X))))&
((funny(susan)&quiet(susan))) | strong(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 9163717513261320780306410
% SZS output start Proof for 9163717513261320780306410
6. ! [X0] : ((creative(X0) <~> ~creative(X0)) => strong(X0)) [input p5]
25. ~strong(susan) [input hypothesis]
30. ! [X0] : (strong(X0) | (creative(X0) <=> ~creative(X0))) [ennf transformation 6]
47. ! [X0] : (strong(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 30]
92. strong(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 47]
93. strong(X0) | creative(X0) | creative(X0) [cnf transformation 47]
147. ~strong(susan) [cnf transformation 25]
149. strong(X0) | ~creative(X0) [duplicate literal removal 92]
150. strong(X0) | creative(X0) [duplicate literal removal 93]
199. strong(X0) [subsumption resolution 149,150]
305. $false [subsumption resolution 147,199]
% SZS output end Proof for 9163717513261320780306410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not creative is either not tall or not wise.
If john is not curious or calm then john is not patient and vice versa.
Everyone who is not creative is either not curious or not quiet and vice versa.
Everyone who is not kind or not patient is curious or not happy and vice versa.
Everyone who is funny is both quiet and not old.
Everyone who is calm is either not calm or humble and vice versa.
If someone is not quiet then someone is either generous or not happy.
If someone is either creative or rich then someone is creative or not quiet.
Everyone who is quiet is generous or patient and vice versa.
Everyone who is both wise and not calm is not kind or not tall.
If mary is either quiet or happy then fred is not happy or not rich and vice versa.
Everyone who is brave or generous is either happy or not creative.
If someone is not tall then someone is rich.
If susan is either not happy or not kind then someone is patient or not patient and vice versa.
Everyone who is either not generous or not rich is both not happy and generous and vice versa.
Everyone who is not wise or humble is not tall or not patient and vice versa.
Someone is not tall.
Someone is either brave or not old.
Someone is humble.
Someone is not curious.
John is not generous or generous.
Mary is not calm or kind.
Lucy is both humble and not generous. | Susan is not quiet. | neutral | (![X]:((quiet(X)|~creative(X))=>(~tall(X)<~>~wise(X))))&
(((~curious(john)|calm(john)))<=>(~patient(john)))&
(![X]:(~creative(X)<=>(~curious(X)<~>~quiet(X))))&
(![X]:((~kind(X)|~patient(X))<=>(curious(X)|~happy(X))))&
(![X]:(funny(X)=>(quiet(X)&~old(X))))&
(![X]:(calm(X)<=>(~calm(X)<~>humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)<~>~happy(X)))))&
((?[X]:((creative(X)<~>rich(X))))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(quiet(X)<=>(generous(X)|patient(X))))&
(![X]:((wise(X)&~calm(X))=>(~kind(X)|~tall(X))))&
(((quiet(mary)<~>happy(mary)))<=>((~happy(fred)|~rich(fred))))&
(![X]:((brave(X)|generous(X))=>(happy(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(?[X]:(rich(X))))&
(((~happy(susan)<~>~kind(susan)))<=>(?[X]:((patient(X)|~patient(X)))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~happy(X)&generous(X))))&
(![X]:((~wise(X)|humble(X))<=>(~tall(X)|~patient(X))))&
(?[X]:(~tall(X)))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:(humble(X)))&
(?[X]:(~curious(X)))&
((~generous(john)|generous(john)))&
((~calm(mary)|kind(mary)))&
((humble(lucy)&~generous(lucy))) | ~quiet(susan) | [] | null | 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Alice is generous. | contradiction | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | generous(alice) | [
"p0",
"p4",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7355908261463095021542261
% SZS output start Proof for 7355908261463095021542261
1. ! [X0] : ((~strong(X0) | tall(X0)) => ~brave(X0)) [input p0]
5. ! [X0] : ((~brave(X0) | rich(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
12. ! [X0] : ((brave(X0) | ~happy(X0)) => ~calm(X0)) [input p11]
14. ? [X0] : (wise(X0) | ~calm(X0)) <=> (generous(alice) <~> strong(alice)) [input p13]
20. generous(paul) [input p19]
24. generous(alice) [input hypothesis]
25. ! [X0] : (~brave(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 1]
31. ! [X0] : (~calm(X0) | (~brave(X0) & happy(X0))) [ennf transformation 12]
36. ! [X0] : (((~brave(X0) | rich(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 5]
37. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [flattening 36]
52. (? [X0] : (wise(X0) | ~calm(X0)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X0] : (~wise(X0) & calm(X0))) [nnf transformation 14]
53. (? [X0] : (wise(X0) | ~calm(X0)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X1] : (~wise(X1) & calm(X1))) [rectify 52]
54. ? [X0] : (wise(X0) | ~calm(X0)) => (wise(sK2) | ~calm(sK2)) [choice axiom]
55. ((wise(sK2) | ~calm(sK2)) | ((generous(alice) | ~strong(alice)) & (strong(alice) | ~generous(alice)))) & (((~strong(alice) | ~generous(alice)) & (strong(alice) | generous(alice))) | ! [X1] : (~wise(X1) & calm(X1))) [skolemisation 53,54]
66. ~brave(X0) | strong(X0) [cnf transformation 25]
80. ~generous(X0) | brave(X0) [cnf transformation 37]
107. ~calm(X0) | ~brave(X0) [cnf transformation 31]
118. ~strong(alice) | ~generous(alice) | calm(X1) [cnf transformation 55]
138. generous(paul) [cnf transformation 20]
144. generous(alice) [cnf transformation 24]
154. 3 <=> brave(alice) [avatar definition]
155. brave(alice) <- (3) [avatar component clause 154]
193. 11 <=> strong(alice) [avatar definition]
197. 12 <=> generous(alice) [avatar definition]
199. generous(alice) <- (12) [avatar component clause 197]
215. 16 <=> ! [X1] : calm(X1) [avatar definition]
216. calm(X1) <- (16) [avatar component clause 215]
217. 16 | ~12 | ~11 [avatar split clause 118,193,197,215]
239. 12 [avatar split clause 144,197]
242. brave(paul) [resolution 80,138]
243. brave(alice) <- (12) [resolution 80,199]
246. 3 | ~12 [avatar split clause 243,197,154]
247. strong(alice) <- (3) [resolution 155,66]
251. 11 | ~3 [avatar split clause 247,154,193]
263. ~brave(X0) <- (16) [resolution 107,216]
268. $false <- (16) [resolution 263,242]
269. ~16 [avatar contradiction clause 268]
271. $false [avatar sat refutation 217,239,246,251,269]
% SZS output end Proof for 7355908261463095021542261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy and generous is either wise or calm.
Everyone who is both not generous and tall is not humble and vice versa.
Everyone who is not curious or not calm is both old and not patient and vice versa.
Everyone who is creative or not humble is creative or not funny and vice versa.
Everyone who is funny or quiet is not creative.
If susan is not old then someone is brave or not brave and vice versa.
If someone is patient or not old then lucy is not generous and vice versa.
If someone is either wise or humble then mary is both not generous and not old and vice versa.
Everyone who is both not generous and generous is both patient and not calm and vice versa.
Everyone who is creative is old.
If paul is curious then someone is generous.
Everyone who is not old is curious or not kind and vice versa.
If someone is curious or not generous then someone is both humble and rich and vice versa.
If someone is both not tall and tall then someone is strong or funny.
If someone is either wise or not quiet then susan is not old or not creative and vice versa.
Everyone who is both not happy and not curious is both funny and not calm and vice versa.
Someone is either not creative or quiet.
Someone is both not happy and not wise.
Mary is either not humble or not patient.
Lucy is not creative or not funny.
Someone is both wise and not patient.
Susan is not humble.
Someone is both generous and tall.
Alice is both kind and generous. | Paul is rich. | neutral | (![X]:((~happy(X)&generous(X))=>(wise(X)<~>calm(X))))&
(![X]:((~generous(X)&tall(X))<=>~humble(X)))&
(![X]:((~curious(X)|~calm(X))<=>(old(X)&~patient(X))))&
(![X]:((creative(X)|~humble(X))<=>(creative(X)|~funny(X))))&
(![X]:((funny(X)|quiet(X))=>~creative(X)))&
((~old(susan))<=>(?[X]:((brave(X)|~brave(X)))))&
((?[X]:((patient(X)|~old(X))))<=>(~generous(lucy)))&
((?[X]:((wise(X)<~>humble(X))))<=>((~generous(mary)&~old(mary))))&
(![X]:((~generous(X)&generous(X))<=>(patient(X)&~calm(X))))&
(![X]:(creative(X)=>old(X)))&
((curious(paul))=>(?[X]:(generous(X))))&
(![X]:(~old(X)<=>(curious(X)|~kind(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((strong(X)|funny(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~old(susan)|~creative(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(funny(X)&~calm(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(?[X]:((~happy(X)&~wise(X))))&
((~humble(mary)<~>~patient(mary)))&
((~creative(lucy)|~funny(lucy)))&
(?[X]:((wise(X)&~patient(X))))&
(~humble(susan))&
(?[X]:((generous(X)&tall(X))))&
((kind(alice)&generous(alice))) | rich(paul) | [] | null | 0 |
If john is not calm or rich then susan is not curious or not creative.
If alice is both tall and creative then someone is generous or old and vice versa.
Everyone who is wise or not wise is calm or not funny.
Everyone who is not calm or patient is tall.
Everyone who is both tall and not creative is both not patient and not old and vice versa.
If susan is not patient or not curious then someone is either not strong or not generous.
Everyone who is either not patient or brave is both patient and not calm and vice versa.
If someone is either not generous or not patient then someone is not happy or generous and vice versa.
Everyone who is both quiet and wise is both not rich and wise and vice versa.
If susan is brave or not kind then susan is either not curious or patient.
Everyone who is curious or not patient is both not brave and not calm.
If alice is not generous or brave then someone is old or happy and vice versa.
Everyone who is both rich and not quiet is not curious and vice versa.
If someone is wise or old then someone is not brave.
If mary is both happy and quiet then alice is wise and vice versa.
John is both not curious and not funny.
Someone is not kind or quiet.
Fred is not generous.
Someone is kind.
Alice is kind or not strong.
Someone is not creative or not strong.
Someone is either old or generous. | Fred is not strong. | neutral | (((~calm(john)|rich(john)))=>((~curious(susan)|~creative(susan))))&
(((tall(alice)&creative(alice)))<=>(?[X]:((generous(X)|old(X)))))&
(![X]:((wise(X)|~wise(X))=>(calm(X)|~funny(X))))&
(![X]:((~calm(X)|patient(X))=>tall(X)))&
(![X]:((tall(X)&~creative(X))<=>(~patient(X)&~old(X))))&
(((~patient(susan)|~curious(susan)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((~patient(X)<~>brave(X))<=>(patient(X)&~calm(X))))&
((?[X]:((~generous(X)<~>~patient(X))))<=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((quiet(X)&wise(X))<=>(~rich(X)&wise(X))))&
(((brave(susan)|~kind(susan)))=>((~curious(susan)<~>patient(susan))))&
(![X]:((curious(X)|~patient(X))=>(~brave(X)&~calm(X))))&
(((~generous(alice)|brave(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(![X]:((rich(X)&~quiet(X))<=>~curious(X)))&
((?[X]:((wise(X)|old(X))))=>(?[X]:(~brave(X))))&
(((happy(mary)&quiet(mary)))<=>(wise(alice)))&
((~curious(john)&~funny(john)))&
(?[X]:((~kind(X)|quiet(X))))&
(~generous(fred))&
(?[X]:(kind(X)))&
((kind(alice)|~strong(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:((old(X)<~>generous(X)))) | ~strong(fred) | [] | null | 0 |
If mary is either not curious or strong then someone is both calm and not kind and vice versa.
If someone is either tall or strong then someone is humble and vice versa.
Everyone who is not quiet or kind is happy or calm.
Everyone who is both not old and happy is both not curious and not creative and vice versa.
Everyone who is kind or tall is either wise or happy.
Everyone who is not humble or funny is either not strong or not calm.
Everyone who is wise is not humble or kind and vice versa.
If mary is both not humble and patient then alice is generous or not patient and vice versa.
Everyone who is both generous and rich is not generous.
If someone is not generous then someone is either wise or not strong and vice versa.
If fred is either not calm or wise then lucy is not strong.
Everyone who is both old and patient is either not tall or patient and vice versa.
If someone is not calm or not happy then john is both curious and not patient.
Everyone who is both not brave and not old is old.
Everyone who is old or not rich is both not tall and rich.
Everyone who is both not generous and not humble is not tall or tall and vice versa.
Someone is either happy or not happy.
Alice is both patient and not old.
John is either old or not old.
Someone is both not kind and quiet.
Mary is not humble.
Someone is not patient or tall. | Mary is patient. | contradiction | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(happy(X)|calm(X))))&
(![X]:((~old(X)&happy(X))<=>(~curious(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))=>(wise(X)<~>happy(X))))&
(![X]:((~humble(X)|funny(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~humble(X)|kind(X))))&
(((~humble(mary)&patient(mary)))<=>((generous(alice)|~patient(alice))))&
(![X]:((generous(X)&rich(X))=>~generous(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
((patient(alice)&~old(alice)))&
((old(john)<~>~old(john)))&
(?[X]:((~kind(X)&quiet(X))))&
(~humble(mary))&
(?[X]:((~patient(X)|tall(X)))) | patient(mary) | [
"p7",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4053143181394421916368437
% SZS output start Proof for 4053143181394421916368437
8. (patient(mary) & ~humble(mary)) <=> (~patient(alice) | generous(alice)) [input p7]
16. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (tall(X0) | ~tall(X0))) [input p15]
18. ~old(alice) & patient(alice) [input p17]
21. ~humble(mary) [input p20]
23. patient(mary) [input hypothesis]
54. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & ((~patient(alice) | generous(alice)) | (~patient(mary) | humble(mary))) [nnf transformation 8]
55. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & (~patient(alice) | generous(alice) | ~patient(mary) | humble(mary)) [flattening 54]
64. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 16]
65. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | humble(X0) | generous(X0))) [flattening 64]
98. ~patient(alice) | generous(alice) | ~patient(mary) | humble(mary) [cnf transformation 55]
125. ~generous(X0) | tall(X0) [cnf transformation 65]
126. ~generous(X0) | ~tall(X0) [cnf transformation 65]
131. patient(alice) [cnf transformation 18]
136. ~humble(mary) [cnf transformation 21]
138. patient(mary) [cnf transformation 23]
194. 12 <=> patient(alice) [avatar definition]
198. 13 <=> patient(mary) [avatar definition]
203. 14 <=> generous(alice) [avatar definition]
204. generous(alice) <- (14) [avatar component clause 203]
208. 15 <=> humble(mary) [avatar definition]
213. 15 | ~13 | 14 | ~12 [avatar split clause 98,194,203,198,208]
275. ~generous(X0) [subsumption resolution 125,126]
276. 12 [avatar split clause 131,194]
277. ~15 [avatar split clause 136,208]
279. 13 [avatar split clause 138,198]
280. $false <- (14) [subsumption resolution 204,275]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 213,276,277,279,281]
% SZS output end Proof for 4053143181394421916368437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not tall is happy or not happy and vice versa. Everyone who is curious is both rich and patient. Everyone who is strong or not patient is not patient. Everyone who is not quiet or not calm is either not curious or strong. Everyone who is kind or creative is generous or tall. If alice is not happy then someone is both not brave and not happy and vice versa. Everyone who is not quiet or not tall is either not patient or kind and vice versa. If someone is not kind or kind then susan is rich and vice versa. If susan is kind or generous then someone is calm or not tall. Everyone who is both strong and humble is strong or brave. If someone is both generous and strong then someone is not old or calm and vice versa. Everyone who is not brave is not happy or not funny. Everyone who is not tall or not kind is not wise or not calm. If fred is not happy or strong then fred is wise and vice versa. Someone is both not creative and not kind. Lucy is wise. Someone is either creative or not happy. Someone is wise or not tall. Alice is both not patient and not humble. Someone is not humble. | Fred is not creative. | neutral | (![X]:((~quiet(X)&~tall(X))<=>(happy(X)|~happy(X))))&
(![X]:(curious(X)=>(rich(X)&patient(X))))&
(![X]:((strong(X)|~patient(X))=>~patient(X)))&
(![X]:((~quiet(X)|~calm(X))=>(~curious(X)<~>strong(X))))&
(![X]:((kind(X)|creative(X))=>(generous(X)|tall(X))))&
((~happy(alice))<=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((~quiet(X)|~tall(X))<=>(~patient(X)<~>kind(X))))&
((?[X]:((~kind(X)|kind(X))))<=>(rich(susan)))&
(((kind(susan)|generous(susan)))=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((strong(X)&humble(X))=>(strong(X)|brave(X))))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:((~old(X)|calm(X)))))&
(![X]:(~brave(X)=>(~happy(X)|~funny(X))))&
(![X]:((~tall(X)|~kind(X))=>(~wise(X)|~calm(X))))&
(((~happy(fred)|strong(fred)))<=>(wise(fred)))&
(?[X]:((~creative(X)&~kind(X))))&
(wise(lucy))&
(?[X]:((creative(X)<~>~happy(X))))&
(?[X]:((wise(X)|~tall(X))))&
((~patient(alice)&~humble(alice)))&
(?[X]:(~humble(X))) | ~creative(fred) | [] | null | 0 |
Everyone who is both not happy and calm is not creative and vice versa.
If someone is both brave and not funny then someone is both rich and not brave.
If fred is either kind or not old then someone is not strong.
If fred is generous or humble then mary is not calm and vice versa.
Everyone who is either not generous or wise is both not rich and quiet.
Everyone who is funny is not old.
If susan is brave then john is both not calm and not generous.
Everyone who is not strong is not humble or strong and vice versa.
Everyone who is either funny or old is both not tall and funny and vice versa.
If someone is calm or humble then john is both quiet and not brave.
Everyone who is not quiet is both not funny and creative.
Everyone who is not calm is wise and vice versa.
If fred is either patient or kind then mary is both brave and happy and vice versa.
Everyone who is generous is either rich or not brave and vice versa.
If alice is humble then fred is both not brave and strong and vice versa.
Everyone who is either old or happy is either not calm or calm.
Someone is both happy and creative.
Fred is old or happy.
Paul is not happy or calm.
Someone is either patient or not kind.
Someone is quiet.
Someone is either not kind or wise.
John is either not curious or not patient. | John is not patient. | neutral | (![X]:((~happy(X)&calm(X))<=>~creative(X)))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((rich(X)&~brave(X)))))&
(((kind(fred)<~>~old(fred)))=>(?[X]:(~strong(X))))&
(((generous(fred)|humble(fred)))<=>(~calm(mary)))&
(![X]:((~generous(X)<~>wise(X))=>(~rich(X)&quiet(X))))&
(![X]:(funny(X)=>~old(X)))&
((brave(susan))=>((~calm(john)&~generous(john))))&
(![X]:(~strong(X)<=>(~humble(X)|strong(X))))&
(![X]:((funny(X)<~>old(X))<=>(~tall(X)&funny(X))))&
((?[X]:((calm(X)|humble(X))))=>((quiet(john)&~brave(john))))&
(![X]:(~quiet(X)=>(~funny(X)&creative(X))))&
(![X]:(~calm(X)<=>wise(X)))&
(((patient(fred)<~>kind(fred)))<=>((brave(mary)&happy(mary))))&
(![X]:(generous(X)<=>(rich(X)<~>~brave(X))))&
((humble(alice))<=>((~brave(fred)&strong(fred))))&
(![X]:((old(X)<~>happy(X))=>(~calm(X)<~>calm(X))))&
(?[X]:((happy(X)&creative(X))))&
((old(fred)|happy(fred)))&
((~happy(paul)|calm(paul)))&
(?[X]:((patient(X)<~>~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)<~>wise(X))))&
((~curious(john)<~>~patient(john))) | ~patient(john) | [] | null | 0 |
If someone is both strong and quiet then fred is either generous or not happy.
Everyone who is not tall is both not happy and generous and vice versa.
If someone is happy or brave then someone is both not tall and old.
If john is either not kind or creative then someone is either not old or tall and vice versa.
If mary is not funny then someone is either not brave or not creative and vice versa.
If someone is either not rich or not tall then alice is not old or not wise and vice versa.
Everyone who is not funny or old is creative or not funny and vice versa.
Everyone who is both not humble and not wise is not curious or not brave.
Everyone who is happy or calm is not quiet.
Everyone who is not kind or not quiet is quiet and vice versa.
Everyone who is both not rich and strong is either not calm or not patient and vice versa.
If mary is patient or not old then susan is not curious or rich.
Everyone who is either not calm or quiet is either old or brave.
If mary is both kind and tall then paul is both patient and not happy.
Everyone who is either not patient or rich is not kind or not generous and vice versa.
Everyone who is both funny and not patient is both not brave and old and vice versa.
Mary is not rich.
Someone is both old and not strong.
Someone is not rich.
Paul is not curious or wise.
Someone is tall or happy.
Fred is not curious. | Alice is not quiet. | contradiction | ((?[X]:((strong(X)&quiet(X))))=>((generous(fred)<~>~happy(fred))))&
(![X]:(~tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
(((~kind(john)<~>creative(john)))<=>(?[X]:((~old(X)<~>tall(X)))))&
((~funny(mary))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~old(alice)|~wise(alice))))&
(![X]:((~funny(X)|old(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)|~brave(X))))&
(![X]:((happy(X)|calm(X))=>~quiet(X)))&
(![X]:((~kind(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(mary)|~old(mary)))=>((~curious(susan)|rich(susan))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)<~>brave(X))))&
(((kind(mary)&tall(mary)))=>((patient(paul)&~happy(paul))))&
(![X]:((~patient(X)<~>rich(X))<=>(~kind(X)|~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~brave(X)&old(X))))&
(~rich(mary))&
(?[X]:((old(X)&~strong(X))))&
(?[X]:(~rich(X)))&
((~curious(paul)|wise(paul)))&
(?[X]:((tall(X)|happy(X))))&
(~curious(fred)) | ~quiet(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3627496525511488480609845
% SZS output start Proof for 3627496525511488480609845
10. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> quiet(X0)) [input p9]
23. ~quiet(alice) [input hypothesis]
56. ! [X0] : (((~quiet(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [nnf transformation 10]
57. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [flattening 56]
105. quiet(X0) | quiet(X0) [cnf transformation 57]
134. ~quiet(alice) [cnf transformation 23]
135. quiet(X0) [duplicate literal removal 105]
267. $false [subsumption resolution 134,135]
% SZS output end Proof for 3627496525511488480609845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not wise and not creative then lucy is not humble or quiet and vice versa. If someone is either strong or not tall then alice is wise or patient and vice versa. Everyone who is both old and not old is both not rich and not humble and vice versa. If someone is both not humble and not quiet then someone is generous and vice versa. Everyone who is not rich or not kind is old and vice versa. Everyone who is both not curious and creative is both not curious and rich. Everyone who is both kind and not rich is both quiet and curious and vice versa. If fred is creative or not funny then alice is not creative or strong. If someone is both brave and happy then lucy is not kind or not happy and vice versa. Everyone who is both happy and rich is either happy or generous. If alice is creative or not quiet then lucy is not quiet. If fred is both not old and not rich then someone is brave and vice versa. Everyone who is both not generous and wise is either not generous or not patient and vice versa. If someone is not strong or kind then john is not rich. Everyone who is either not wise or kind is both not funny and not wise and vice versa. Everyone who is not generous is curious or not patient. Susan is calm or funny. John is both not curious and not calm. Alice is either humble or wise. Someone is both not strong and not creative. Someone is both not creative and not kind. Alice is strong. Someone is wise or not funny. | Lucy is not funny. | contradiction | (((~wise(alice)&~creative(alice)))<=>((~humble(lucy)|quiet(lucy))))&
((?[X]:((strong(X)<~>~tall(X))))<=>((wise(alice)|patient(alice))))&
(![X]:((old(X)&~old(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:(generous(X))))&
(![X]:((~rich(X)|~kind(X))<=>old(X)))&
(![X]:((~curious(X)&creative(X))=>(~curious(X)&rich(X))))&
(![X]:((kind(X)&~rich(X))<=>(quiet(X)&curious(X))))&
(((creative(fred)|~funny(fred)))=>((~creative(alice)|strong(alice))))&
((?[X]:((brave(X)&happy(X))))<=>((~kind(lucy)|~happy(lucy))))&
(![X]:((happy(X)&rich(X))=>(happy(X)<~>generous(X))))&
(((creative(alice)|~quiet(alice)))=>(~quiet(lucy)))&
(((~old(fred)&~rich(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)|kind(X))))=>(~rich(john)))&
(![X]:((~wise(X)<~>kind(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~generous(X)=>(curious(X)|~patient(X))))&
((calm(susan)|funny(susan)))&
((~curious(john)&~calm(john)))&
((humble(alice)<~>wise(alice)))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(strong(alice))&
(?[X]:((wise(X)|~funny(X)))) | ~funny(lucy) | [
"p4",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9190570313084933795614493
% SZS output start Proof for 9190570313084933795614493
5. ! [X0] : ((~kind(X0) | ~rich(X0)) <=> old(X0)) [input p4]
9. ? [X0] : (happy(X0) & brave(X0)) <=> (~happy(lucy) | ~kind(lucy)) [input p8]
12. (~rich(fred) & ~old(fred)) <=> ? [X0] : brave(X0) [input p11]
15. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (~wise(X0) & ~funny(X0))) [input p14]
24. ~funny(lucy) [input hypothesis]
50. ! [X0] : (((~kind(X0) | ~rich(X0)) | ~old(X0)) & (old(X0) | (kind(X0) & rich(X0)))) [nnf transformation 5]
51. ! [X0] : ((~kind(X0) | ~rich(X0) | ~old(X0)) & (old(X0) | (kind(X0) & rich(X0)))) [flattening 50]
54. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & ((~happy(lucy) | ~kind(lucy)) | ! [X0] : (~happy(X0) | ~brave(X0))) [nnf transformation 9]
55. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X0] : (~happy(X0) | ~brave(X0))) [flattening 54]
56. (? [X0] : (happy(X0) & brave(X0)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : (~happy(X1) | ~brave(X1))) [rectify 55]
57. ? [X0] : (happy(X0) & brave(X0)) => (happy(sK3) & brave(sK3)) [choice axiom]
58. ((happy(sK3) & brave(sK3)) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : (~happy(X1) | ~brave(X1))) [skolemisation 56,57]
60. ((~rich(fred) & ~old(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (rich(fred) | old(fred))) [nnf transformation 12]
61. ((~rich(fred) & ~old(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | rich(fred) | old(fred)) [flattening 60]
62. ((~rich(fred) & ~old(fred)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | rich(fred) | old(fred)) [rectify 61]
63. ? [X1] : brave(X1) => brave(sK4) [choice axiom]
64. ((~rich(fred) & ~old(fred)) | ! [X0] : ~brave(X0)) & (brave(sK4) | rich(fred) | old(fred)) [skolemisation 62,63]
67. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 67]
94. rich(X0) | old(X0) [cnf transformation 51]
106. brave(sK3) | kind(lucy) [cnf transformation 58]
115. ~old(fred) | ~brave(X0) [cnf transformation 64]
116. ~rich(fred) | ~brave(X0) [cnf transformation 64]
128. ~wise(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 68]
130. ~kind(X0) | wise(X0) | wise(X0) | funny(X0) [cnf transformation 68]
143. ~funny(lucy) [cnf transformation 24]
144. ~kind(X0) | ~wise(X0) [duplicate literal removal 128]
145. ~kind(X0) | wise(X0) | funny(X0) [duplicate literal removal 130]
240. 20 <=> kind(lucy) [avatar definition]
242. kind(lucy) <- (20) [avatar component clause 240]
245. 21 <=> brave(sK3) [avatar definition]
247. brave(sK3) <- (21) [avatar component clause 245]
249. 20 | 21 [avatar split clause 106,245,240]
261. 24 <=> ! [X0] : ~brave(X0) [avatar definition]
262. ~brave(X0) <- (24) [avatar component clause 261]
264. 25 <=> rich(fred) [avatar definition]
266. ~rich(fred) <- (~25) [avatar component clause 264]
267. 24 | ~25 [avatar split clause 116,264,261]
269. 26 <=> old(fred) [avatar definition]
271. ~old(fred) <- (~26) [avatar component clause 269]
272. 24 | ~26 [avatar split clause 115,269,261]
311. old(fred) <- (~25) [resolution 94,266]
313. $false <- (~25, ~26) [subsumption resolution 311,271]
314. 25 | 26 [avatar contradiction clause 313]
315. $false <- (21, 24) [resolution 262,247]
316. ~21 | ~24 [avatar contradiction clause 315]
318. ~wise(lucy) <- (20) [resolution 144,242]
378. wise(lucy) | funny(lucy) <- (20) [resolution 145,242]
380. funny(lucy) <- (20) [subsumption resolution 378,318]
381. $false <- (20) [subsumption resolution 380,143]
382. ~20 [avatar contradiction clause 381]
384. $false [avatar sat refutation 249,267,272,314,316,382]
% SZS output end Proof for 9190570313084933795614493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or not happy is not funny. Everyone who is not quiet or not curious is not kind or not humble. Everyone who is either brave or not rich is not calm and vice versa. Everyone who is brave or not tall is brave or strong and vice versa. If someone is creative then someone is both calm and not calm and vice versa. Everyone who is quiet is funny or patient. Everyone who is not happy is either not rich or brave and vice versa. If someone is either quiet or brave then susan is not patient or not brave. If someone is both curious and not tall then paul is either not curious or not brave and vice versa. Everyone who is both not rich and kind is either not funny or creative. If paul is both not old and quiet then someone is both not quiet and patient. Everyone who is quiet is creative and vice versa. Everyone who is not quiet is both not wise and not quiet. Everyone who is not patient is not quiet. If someone is both strong and not rich then john is both not tall and not happy. Everyone who is not brave or not quiet is either strong or happy and vice versa. Someone is generous. Fred is either not old or kind. John is happy or curious. Someone is both not wise and not calm. Lucy is not generous or curious. | Susan is kind. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((~quiet(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
(?[X]:(generous(X)))&
((~old(fred)<~>kind(fred)))&
((happy(john)|curious(john)))&
(?[X]:((~wise(X)&~calm(X))))&
((~generous(lucy)|curious(lucy))) | kind(susan) | [] | null | 0 |
Everyone who is both tall and not happy is both creative and not rich.
Everyone who is humble is curious and vice versa.
Everyone who is both not tall and wise is not patient or not old.
Everyone who is quiet or not wise is both creative and patient and vice versa.
If paul is either not happy or not humble then someone is either strong or generous.
If lucy is both humble and not strong then mary is rich and vice versa.
If someone is either happy or not generous then someone is not kind or not rich.
If susan is both not generous and not humble then someone is either not calm or wise.
If someone is not humble or not curious then paul is not tall or not rich.
If someone is tall then someone is patient or not strong.
Everyone who is either not creative or not kind is both not strong and not tall.
Everyone who is either not rich or not strong is rich and vice versa.
Everyone who is not generous or patient is both not old and brave.
If someone is not tall then someone is either tall or not quiet and vice versa.
Everyone who is brave or not old is not kind or kind and vice versa.
Everyone who is both not patient and not quiet is brave or not happy.
John is kind.
Alice is humble or not quiet.
Paul is both calm and funny.
Someone is curious.
Someone is not wise or not calm. | Alice is not funny. | neutral | (![X]:((tall(X)&~happy(X))=>(creative(X)&~rich(X))))&
(![X]:(humble(X)<=>curious(X)))&
(![X]:((~tall(X)&wise(X))=>(~patient(X)|~old(X))))&
(![X]:((quiet(X)|~wise(X))<=>(creative(X)&patient(X))))&
(((~happy(paul)<~>~humble(paul)))=>(?[X]:((strong(X)<~>generous(X)))))&
(((humble(lucy)&~strong(lucy)))<=>(rich(mary)))&
((?[X]:((happy(X)<~>~generous(X))))=>(?[X]:((~kind(X)|~rich(X)))))&
(((~generous(susan)&~humble(susan)))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:((~humble(X)|~curious(X))))=>((~tall(paul)|~rich(paul))))&
((?[X]:(tall(X)))=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((~creative(X)<~>~kind(X))=>(~strong(X)&~tall(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>rich(X)))&
(![X]:((~generous(X)|patient(X))=>(~old(X)&brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((brave(X)|~old(X))<=>(~kind(X)|kind(X))))&
(![X]:((~patient(X)&~quiet(X))=>(brave(X)|~happy(X))))&
(kind(john))&
((humble(alice)|~quiet(alice)))&
((calm(paul)&funny(paul)))&
(?[X]:(curious(X)))&
(?[X]:((~wise(X)|~calm(X)))) | ~funny(alice) | [] | null | 0 |
If someone is both not curious and patient then someone is either rich or not funny.
Everyone who is not curious or not patient is both not old and not brave and vice versa.
If lucy is wise or not happy then john is happy and vice versa.
If alice is both not rich and calm then someone is either not creative or not calm.
Everyone who is not strong or not brave is not strong and vice versa.
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Everyone who is both patient and humble is not patient and vice versa.
Everyone who is not happy or humble is wise.
Everyone who is either brave or not quiet is not brave and vice versa.
Someone is either humble or wise.
Paul is both not old and not rich.
Someone is both not wise and not quiet.
Someone is either not brave or curious.
Someone is old. | Lucy is not strong. | contradiction | ((?[X]:((~curious(X)&patient(X))))=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~curious(X)|~patient(X))<=>(~old(X)&~brave(X))))&
(((wise(lucy)|~happy(lucy)))<=>(happy(john)))&
(((~rich(alice)&calm(alice)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~strong(X)))&
((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((patient(X)&humble(X))<=>~patient(X)))&
(![X]:((~happy(X)|humble(X))=>wise(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>~brave(X)))&
(?[X]:((humble(X)<~>wise(X))))&
((~old(paul)&~rich(paul)))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:(old(X))) | ~strong(lucy) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9060480355917945370536391
% SZS output start Proof for 9060480355917945370536391
13. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X0] : (~kind(X0) | ~strong(X0)) [input p12]
14. ! [X0] : ((humble(X0) & patient(X0)) <=> ~patient(X0)) [input p13]
22. ~strong(lucy) [input hypothesis]
24. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X1] : (~kind(X1) | ~strong(X1)) [rectify 13]
60. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : (kind(X1) & strong(X1))) & (? [X1] : (~kind(X1) | ~strong(X1)) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 24]
61. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : (kind(X1) & strong(X1))) & (? [X2] : (~kind(X2) | ~strong(X2)) | ! [X3] : (~humble(X3) | strong(X3))) [rectify 60]
62. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK4) & ~strong(sK4)) [choice axiom]
63. ? [X2] : (~kind(X2) | ~strong(X2)) => (~kind(sK5) | ~strong(sK5)) [choice axiom]
64. ((humble(sK4) & ~strong(sK4)) | ! [X1] : (kind(X1) & strong(X1))) & ((~kind(sK5) | ~strong(sK5)) | ! [X3] : (~humble(X3) | strong(X3))) [skolemisation 61,63,62]
65. ! [X0] : (((humble(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) | ~patient(X0)))) [nnf transformation 14]
66. ! [X0] : (((humble(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | ~humble(X0) | ~patient(X0))) [flattening 65]
115. humble(sK4) | strong(X1) [cnf transformation 64]
117. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 66]
118. patient(X0) | patient(X0) [cnf transformation 66]
135. ~strong(lucy) [cnf transformation 22]
138. ~patient(X0) | ~humble(X0) [duplicate literal removal 117]
139. patient(X0) [duplicate literal removal 118]
271. 29 <=> humble(sK4) [avatar definition]
273. humble(sK4) <- (29) [avatar component clause 271]
276. 30 <=> ! [X1] : strong(X1) [avatar definition]
277. strong(X1) <- (30) [avatar component clause 276]
278. 30 | 29 [avatar split clause 115,271,276]
297. ~humble(X0) [subsumption resolution 138,139]
309. $false <- (29) [subsumption resolution 273,297]
310. ~29 [avatar contradiction clause 309]
313. $false <- (30) [resolution 277,135]
316. ~30 [avatar contradiction clause 313]
317. $false [avatar sat refutation 278,310,316]
% SZS output end Proof for 9060480355917945370536391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is both not humble and quiet and vice versa. If fred is both rich and not curious then someone is old. Everyone who is either generous or happy is either happy or quiet and vice versa. Everyone who is wise is not wise or kind. Everyone who is not patient or not happy is happy. Everyone who is creative or not tall is rich or not brave and vice versa. If someone is both brave and creative then lucy is either not generous or not humble and vice versa. If susan is not quiet then someone is not tall. If someone is not tall then someone is either strong or happy and vice versa. Everyone who is humble is both tall and brave. If someone is not patient or quiet then someone is not humble or not generous and vice versa. If someone is both not calm and not humble then susan is not tall or happy. If someone is either not calm or not humble then mary is both brave and not happy and vice versa. If someone is not generous or old then fred is either not patient or calm. If fred is not patient then paul is either not rich or happy. If someone is not old or not creative then someone is old or rich. Someone is calm. Someone is either not brave or kind. Someone is wise or creative. Susan is both generous and not tall. Paul is humble or patient. Lucy is not creative. Fred is either tall or calm. | Paul is not happy. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((rich(fred)&~curious(fred)))=>(?[X]:(old(X))))&
(![X]:((generous(X)<~>happy(X))<=>(happy(X)<~>quiet(X))))&
(![X]:(wise(X)=>(~wise(X)|kind(X))))&
(![X]:((~patient(X)|~happy(X))=>happy(X)))&
(![X]:((creative(X)|~tall(X))<=>(rich(X)|~brave(X))))&
((?[X]:((brave(X)&creative(X))))<=>((~generous(lucy)<~>~humble(lucy))))&
((~quiet(susan))=>(?[X]:(~tall(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(humble(X)=>(tall(X)&brave(X))))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
((?[X]:((~calm(X)&~humble(X))))=>((~tall(susan)|happy(susan))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>((brave(mary)&~happy(mary))))&
((?[X]:((~generous(X)|old(X))))=>((~patient(fred)<~>calm(fred))))&
((~patient(fred))=>((~rich(paul)<~>happy(paul))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((old(X)|rich(X)))))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
(?[X]:((wise(X)|creative(X))))&
((generous(susan)&~tall(susan)))&
((humble(paul)|patient(paul)))&
(~creative(lucy))&
((tall(fred)<~>calm(fred))) | ~happy(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 517692392935224606590329
% SZS output start Proof for 517692392935224606590329
5. ! [X0] : ((~happy(X0) | ~patient(X0)) => happy(X0)) [input p4]
24. ~happy(paul) [input hypothesis]
32. ! [X0] : (happy(X0) | (happy(X0) & patient(X0))) [ennf transformation 5]
95. happy(X0) | happy(X0) [cnf transformation 32]
142. ~happy(paul) [cnf transformation 24]
143. happy(X0) [duplicate literal removal 95]
326. $false [subsumption resolution 142,143]
% SZS output end Proof for 517692392935224606590329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and brave then someone is wise or not old and vice versa.
Everyone who is either not curious or curious is not strong and vice versa.
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. | Paul is curious. | entailment | (![X]:((~rich(X)|~creative(X))<=>(quiet(X)<~>rich(X))))&
(((~old(alice)&brave(alice)))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~curious(X)<~>curious(X))<=>~strong(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)))) | curious(paul) | [
"p4",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1063260067192317582413866
% SZS output start Proof for 1063260067192317582413866
5. ! [X0] : ((curious(X0) <~> humble(X0)) => (~rich(X0) & rich(X0))) [input p4]
11. ! [X0] : (~humble(X0) => (~quiet(X0) & happy(X0))) [input p10]
20. quiet(paul) | ~happy(paul) [input p19]
25. ~curious(paul) [input hypothesis]
27. ! [X0] : ((~rich(X0) & rich(X0)) | (curious(X0) <=> humble(X0))) [ennf transformation 5]
30. ! [X0] : ((~quiet(X0) & happy(X0)) | humble(X0)) [ennf transformation 11]
43. ! [X0] : ((~rich(X0) & rich(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 27]
88. rich(X0) | curious(X0) | ~humble(X0) [cnf transformation 43]
90. ~rich(X0) | curious(X0) | ~humble(X0) [cnf transformation 43]
109. happy(X0) | humble(X0) [cnf transformation 30]
110. ~quiet(X0) | humble(X0) [cnf transformation 30]
139. quiet(paul) | ~happy(paul) [cnf transformation 20]
147. ~curious(paul) [cnf transformation 25]
202. ~humble(X0) | curious(X0) [subsumption resolution 88,90]
262. 22 <=> happy(paul) [avatar definition]
264. ~happy(paul) <- (~22) [avatar component clause 262]
266. 23 <=> quiet(paul) [avatar definition]
268. quiet(paul) <- (23) [avatar component clause 266]
269. ~22 | 23 [avatar split clause 139,266,262]
296. humble(paul) <- (~22) [resolution 109,264]
311. curious(paul) <- (~22) [resolution 202,296]
312. $false <- (~22) [subsumption resolution 311,147]
313. 22 [avatar contradiction clause 312]
314. humble(paul) <- (23) [resolution 268,110]
315. curious(paul) <- (23) [resolution 314,202]
316. $false <- (23) [subsumption resolution 315,147]
317. ~23 [avatar contradiction clause 316]
318. $false [avatar sat refutation 269,313,317]
% SZS output end Proof for 1063260067192317582413866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both happy and not creative is both patient and funny and vice versa.
If someone is either strong or not patient then someone is not old or patient and vice versa.
If john is not happy then paul is not humble or not generous.
If someone is humble or funny then paul is not strong.
If someone is brave or strong then paul is creative or not brave and vice versa.
If someone is kind or generous then someone is both patient and not calm.
If alice is not old then fred is wise or not patient and vice versa.
Everyone who is creative is both not strong and not calm.
If someone is not rich or strong then lucy is happy and vice versa.
Everyone who is not tall or not generous is both not rich and patient.
If alice is not rich then alice is both not quiet and not rich.
If someone is not happy then fred is not strong and vice versa.
If someone is both wise and not humble then someone is calm.
Everyone who is not kind is not humble or funny.
Everyone who is rich or not old is both not wise and calm and vice versa.
Everyone who is both not quiet and strong is both not rich and not tall.
Someone is either not patient or creative.
Fred is either humble or not quiet.
Someone is kind or not wise.
Someone is both calm and not generous.
John is both not quiet and strong.
Fred is either not generous or humble.
Fred is either happy or creative.
Paul is happy or strong. | Paul is happy. | neutral | (![X]:((happy(X)&~creative(X))<=>(patient(X)&funny(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>(?[X]:((~old(X)|patient(X)))))&
((~happy(john))=>((~humble(paul)|~generous(paul))))&
((?[X]:((humble(X)|funny(X))))=>(~strong(paul)))&
((?[X]:((brave(X)|strong(X))))<=>((creative(paul)|~brave(paul))))&
((?[X]:((kind(X)|generous(X))))=>(?[X]:((patient(X)&~calm(X)))))&
((~old(alice))<=>((wise(fred)|~patient(fred))))&
(![X]:(creative(X)=>(~strong(X)&~calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(happy(lucy)))&
(![X]:((~tall(X)|~generous(X))=>(~rich(X)&patient(X))))&
((~rich(alice))=>((~quiet(alice)&~rich(alice))))&
((?[X]:(~happy(X)))<=>(~strong(fred)))&
((?[X]:((wise(X)&~humble(X))))=>(?[X]:(calm(X))))&
(![X]:(~kind(X)=>(~humble(X)|funny(X))))&
(![X]:((rich(X)|~old(X))<=>(~wise(X)&calm(X))))&
(![X]:((~quiet(X)&strong(X))=>(~rich(X)&~tall(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
((humble(fred)<~>~quiet(fred)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((calm(X)&~generous(X))))&
((~quiet(john)&strong(john)))&
((~generous(fred)<~>humble(fred)))&
((happy(fred)<~>creative(fred)))&
((happy(paul)|strong(paul))) | happy(paul) | [] | null | 0 |
If someone is both rich and brave then someone is either not generous or brave.
Everyone who is old is either not quiet or tall.
Everyone who is funny is both generous and not brave.
If someone is both not strong and strong then someone is creative.
Everyone who is either humble or not humble is not funny and vice versa.
If susan is not humble or funny then john is either patient or brave.
Everyone who is brave or not kind is happy.
Everyone who is not strong or not funny is both old and patient.
Everyone who is happy is both generous and not creative.
Everyone who is not patient or funny is both not funny and wise.
Everyone who is not patient or quiet is curious or tall and vice versa.
If susan is both rich and not happy then alice is either not rich or not calm.
If someone is both brave and not calm then someone is both creative and not strong and vice versa.
Everyone who is humble or not strong is either not brave or humble.
If someone is either rich or old then susan is patient.
If someone is old or brave then john is not kind or old.
Fred is curious.
Mary is not funny.
Susan is both wise and tall.
Someone is both not humble and curious.
Someone is either kind or not tall.
Someone is either not old or not brave.
Susan is not rich. | Fred is not tall. | contradiction | ((?[X]:((rich(X)&brave(X))))=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:(old(X)=>(~quiet(X)<~>tall(X))))&
(![X]:(funny(X)=>(generous(X)&~brave(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:(creative(X))))&
(![X]:((humble(X)<~>~humble(X))<=>~funny(X)))&
(((~humble(susan)|funny(susan)))=>((patient(john)<~>brave(john))))&
(![X]:((brave(X)|~kind(X))=>happy(X)))&
(![X]:((~strong(X)|~funny(X))=>(old(X)&patient(X))))&
(![X]:(happy(X)=>(generous(X)&~creative(X))))&
(![X]:((~patient(X)|funny(X))=>(~funny(X)&wise(X))))&
(![X]:((~patient(X)|quiet(X))<=>(curious(X)|tall(X))))&
(((rich(susan)&~happy(susan)))=>((~rich(alice)<~>~calm(alice))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((humble(X)|~strong(X))=>(~brave(X)<~>humble(X))))&
((?[X]:((rich(X)<~>old(X))))=>(patient(susan)))&
((?[X]:((old(X)|brave(X))))=>((~kind(john)|old(john))))&
(curious(fred))&
(~funny(mary))&
((wise(susan)&tall(susan)))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
(~rich(susan)) | ~tall(fred) | [
"p1",
"p4",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5105612172739893110867380
% SZS output start Proof for 5105612172739893110867380
2. ! [X0] : (old(X0) => (~quiet(X0) <~> tall(X0))) [input p1]
5. ! [X0] : ((humble(X0) <~> ~humble(X0)) <=> ~funny(X0)) [input p4]
8. ! [X0] : ((~funny(X0) | ~strong(X0)) => (patient(X0) & old(X0))) [input p7]
11. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> (tall(X0) | curious(X0))) [input p10]
17. curious(fred) [input p16]
24. ~tall(fred) [input hypothesis]
31. ! [X0] : ((~quiet(X0) <~> tall(X0)) | ~old(X0)) [ennf transformation 2]
36. ! [X0] : ((patient(X0) & old(X0)) | (funny(X0) & strong(X0))) [ennf transformation 8]
49. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ~old(X0)) [nnf transformation 31]
53. ! [X0] : ((((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | funny(X0)) & (~funny(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0))))) [nnf transformation 5]
55. ! [X0] : (((quiet(X0) | ~patient(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (~quiet(X0) & patient(X0)))) [nnf transformation 11]
56. ! [X0] : ((quiet(X0) | ~patient(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | (~quiet(X0) & patient(X0)))) [flattening 55]
75. ~quiet(X0) | tall(X0) | ~old(X0) [cnf transformation 49]
80. ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 53]
81. ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 53]
91. old(X0) | funny(X0) [cnf transformation 36]
93. patient(X0) | funny(X0) [cnf transformation 36]
100. quiet(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 56]
116. curious(fred) [cnf transformation 17]
126. ~tall(fred) [cnf transformation 24]
129. ~funny(X0) | ~humble(X0) [duplicate literal removal 80]
130. ~funny(X0) | humble(X0) [duplicate literal removal 81]
144. ~funny(X0) [subsumption resolution 129,130]
159. patient(X0) [subsumption resolution 93,144]
160. old(X0) [subsumption resolution 91,144]
162. ~curious(X0) | quiet(X0) [subsumption resolution 100,159]
225. quiet(fred) [resolution 162,116]
228. tall(fred) | ~old(fred) [resolution 75,225]
230. ~old(fred) [subsumption resolution 228,126]
231. $false [subsumption resolution 230,160]
% SZS output end Proof for 5105612172739893110867380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious or not funny then mary is funny and vice versa.
Everyone who is either curious or generous is calm.
Everyone who is not wise is both not happy and not patient and vice versa.
If fred is not old or creative then someone is both not patient and not funny and vice versa.
Everyone who is both tall and kind is not patient.
If someone is either not brave or humble then someone is either not brave or kind.
Everyone who is quiet is both not patient and not wise and vice versa.
If paul is both not happy and not rich then someone is strong or not patient and vice versa.
If someone is not creative or old then someone is either old or not strong and vice versa.
If mary is humble then someone is either strong or creative and vice versa.
If alice is both creative and not patient then alice is not humble or not strong.
If someone is creative or not funny then paul is not funny or not creative and vice versa.
Everyone who is either funny or not brave is not rich and vice versa.
Everyone who is not creative or tall is not quiet and vice versa.
Everyone who is not funny or curious is not generous or not patient and vice versa.
Everyone who is both not calm and not tall is both kind and not quiet.
Alice is not happy.
Mary is both not wise and not funny.
Someone is tall or not old.
Fred is not kind or not humble.
Alice is not funny or wise.
Someone is brave or not generous.
Someone is happy or not calm. | Alice is not calm. | neutral | (((~curious(paul)|~funny(paul)))<=>(funny(mary)))&
(![X]:((curious(X)<~>generous(X))=>calm(X)))&
(![X]:(~wise(X)<=>(~happy(X)&~patient(X))))&
(((~old(fred)|creative(fred)))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:((tall(X)&kind(X))=>~patient(X)))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:(quiet(X)<=>(~patient(X)&~wise(X))))&
(((~happy(paul)&~rich(paul)))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((~creative(X)|old(X))))<=>(?[X]:((old(X)<~>~strong(X)))))&
((humble(mary))<=>(?[X]:((strong(X)<~>creative(X)))))&
(((creative(alice)&~patient(alice)))=>((~humble(alice)|~strong(alice))))&
((?[X]:((creative(X)|~funny(X))))<=>((~funny(paul)|~creative(paul))))&
(![X]:((funny(X)<~>~brave(X))<=>~rich(X)))&
(![X]:((~creative(X)|tall(X))<=>~quiet(X)))&
(![X]:((~funny(X)|curious(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(~happy(alice))&
((~wise(mary)&~funny(mary)))&
(?[X]:((tall(X)|~old(X))))&
((~kind(fred)|~humble(fred)))&
((~funny(alice)|wise(alice)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((happy(X)|~calm(X)))) | ~calm(alice) | [] | null | 0 |
If someone is both not rich and creative then alice is brave or kind and vice versa.
If someone is old or generous then fred is either not rich or not happy and vice versa.
Everyone who is either not generous or old is both not brave and not strong.
If susan is not old or not happy then someone is either old or not old.
Everyone who is both not old and not generous is not curious and vice versa.
If someone is both strong and not calm then someone is not quiet or not humble and vice versa.
Everyone who is either not quiet or not curious is either not funny or old and vice versa.
Everyone who is not curious or funny is either curious or strong.
If alice is wise or strong then someone is not creative or curious and vice versa.
If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa.
Everyone who is either strong or rich is either not strong or tall.
If someone is calm then lucy is curious and vice versa.
If mary is either old or not generous then someone is either not kind or generous and vice versa.
Everyone who is not strong or tall is tall and vice versa.
If paul is either patient or rich then someone is either not funny or not happy and vice versa.
If fred is either not wise or humble then someone is not generous or quiet.
Someone is either not wise or not funny.
Alice is both generous and wise.
Someone is both humble and happy.
Paul is both not old and not quiet.
Someone is old or generous.
Alice is not quiet or wise.
Someone is either not tall or old.
Alice is not creative. | Paul is curious. | entailment | ((?[X]:((~rich(X)&creative(X))))<=>((brave(alice)|kind(alice))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(((~old(susan)|~happy(susan)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:((~old(X)&~generous(X))<=>~curious(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~curious(X)|funny(X))=>(curious(X)<~>strong(X))))&
(((wise(alice)|strong(alice)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
(?[X]:((~wise(X)<~>~funny(X))))&
((generous(alice)&wise(alice)))&
(?[X]:((humble(X)&happy(X))))&
((~old(paul)&~quiet(paul)))&
(?[X]:((old(X)|generous(X))))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~tall(X)<~>old(X))))&
(~creative(alice)) | curious(paul) | [
"p2",
"p4",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3730899105925202600133631
% SZS output start Proof for 3730899105925202600133631
3. ! [X0] : ((~generous(X0) <~> old(X0)) => (~strong(X0) & ~brave(X0))) [input p2]
5. ! [X0] : ((~generous(X0) & ~old(X0)) <=> ~curious(X0)) [input p4]
8. ! [X0] : ((funny(X0) | ~curious(X0)) => (curious(X0) <~> strong(X0))) [input p7]
20. ~quiet(paul) & ~old(paul) [input p19]
25. ~curious(paul) [input hypothesis]
27. ! [X0] : ((~strong(X0) & ~brave(X0)) | (~generous(X0) <=> old(X0))) [ennf transformation 3]
29. ! [X0] : ((curious(X0) <~> strong(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 8]
41. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 27]
45. ! [X0] : (((~generous(X0) & ~old(X0)) | curious(X0)) & (~curious(X0) | (generous(X0) | old(X0)))) [nnf transformation 5]
46. ! [X0] : (((~generous(X0) & ~old(X0)) | curious(X0)) & (~curious(X0) | generous(X0) | old(X0))) [flattening 45]
53. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (~funny(X0) & curious(X0))) [nnf transformation 29]
105. ~strong(X0) | old(X0) | generous(X0) [cnf transformation 41]
113. ~generous(X0) | curious(X0) [cnf transformation 46]
127. strong(X0) | curious(X0) | curious(X0) [cnf transformation 53]
172. ~old(paul) [cnf transformation 20]
179. ~curious(paul) [cnf transformation 25]
182. curious(X0) | strong(X0) [duplicate literal removal 127]
450. strong(paul) [resolution 182,179]
463. old(paul) | generous(paul) [resolution 105,450]
467. generous(paul) [subsumption resolution 463,172]
589. curious(paul) [resolution 467,113]
590. $false [subsumption resolution 589,179]
% SZS output end Proof for 3730899105925202600133631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | John is not happy. | contradiction | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | ~happy(john) | [
"p0",
"p1",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8512465371928027031844812
% SZS output start Proof for 8512465371928027031844812
1. ! [X0] : ((generous(X0) | quiet(X0)) => (creative(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~old(X0)) => ~quiet(X0)) [input p1]
4. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (kind(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~curious(X0) & calm(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (rich(X0) | ~generous(X0))) [input p15]
24. ~happy(john) [input hypothesis]
27. ! [X0] : ((creative(X0) & tall(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (curious(X0) & old(X0))) [ennf transformation 2]
33. ! [X0] : ((~curious(X0) & calm(X0)) | (strong(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 41]
64. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & ((rich(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & (rich(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 64]
74. ~generous(X0) | tall(X0) [cnf transformation 27]
78. ~quiet(X0) | curious(X0) [cnf transformation 28]
83. quiet(X0) | ~tall(X0) | kind(X0) [cnf transformation 42]
84. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
101. calm(X0) | happy(X0) [cnf transformation 33]
103. ~curious(X0) | happy(X0) [cnf transformation 33]
123. ~calm(X0) | generous(X0) [cnf transformation 65]
136. ~happy(john) [cnf transformation 24]
150. ~tall(X0) | quiet(X0) [subsumption resolution 83,84]
311. happy(X2) | generous(X2) [resolution 123,101]
391. generous(john) [resolution 311,136]
400. tall(john) [resolution 391,74]
412. quiet(john) [resolution 400,150]
427. curious(john) [resolution 412,78]
441. happy(john) [resolution 427,103]
442. $false [subsumption resolution 441,136]
% SZS output end Proof for 8512465371928027031844812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not funny is not creative and vice versa. Everyone who is both not patient and humble is not patient or wise and vice versa. Everyone who is both not brave and tall is patient. If someone is generous then fred is either not quiet or generous. If lucy is wise or tall then someone is not creative or not brave. If mary is quiet or not old then someone is curious. Everyone who is not wise or not rich is both not quiet and not old and vice versa. Everyone who is not quiet or not patient is both wise and not tall and vice versa. Everyone who is either not funny or not kind is kind or not calm. Everyone who is tall or funny is both not funny and not quiet. If john is generous or not curious then fred is either wise or creative. If paul is curious then someone is either curious or quiet. If someone is both not patient and old then paul is not strong. Everyone who is both wise and not kind is either patient or strong and vice versa. If lucy is not humble then someone is either generous or wise and vice versa. Mary is not old or funny. John is either old or generous. Paul is either humble or curious. Paul is not kind or old. Mary is both not calm and strong. Paul is either rich or not happy. Someone is curious. | Fred is rich. | entailment | (![X]:((~happy(X)&~funny(X))<=>~creative(X)))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)|wise(X))))&
(![X]:((~brave(X)&tall(X))=>patient(X)))&
((?[X]:(generous(X)))=>((~quiet(fred)<~>generous(fred))))&
(((wise(lucy)|tall(lucy)))=>(?[X]:((~creative(X)|~brave(X)))))&
(((quiet(mary)|~old(mary)))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&~old(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(wise(X)&~tall(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(kind(X)|~calm(X))))&
(![X]:((tall(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((generous(john)|~curious(john)))=>((wise(fred)<~>creative(fred))))&
((curious(paul))=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:((~patient(X)&old(X))))=>(~strong(paul)))&
(![X]:((wise(X)&~kind(X))<=>(patient(X)<~>strong(X))))&
((~humble(lucy))<=>(?[X]:((generous(X)<~>wise(X)))))&
((~old(mary)|funny(mary)))&
((old(john)<~>generous(john)))&
((humble(paul)<~>curious(paul)))&
((~kind(paul)|old(paul)))&
((~calm(mary)&strong(mary)))&
((rich(paul)<~>~happy(paul)))&
(?[X]:(curious(X))) | rich(fred) | [
"p1",
"p3",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6735870940346321085416198
% SZS output start Proof for 6735870940346321085416198
2. ! [X0] : ((humble(X0) & ~patient(X0)) <=> (wise(X0) | ~patient(X0))) [input p1]
4. ? [X0] : generous(X0) => (~quiet(fred) <~> generous(fred)) [input p3]
7. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (~old(X0) & ~quiet(X0))) [input p6]
8. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~tall(X0) & wise(X0))) [input p7]
15. ~humble(lucy) <=> ? [X0] : (generous(X0) <~> wise(X0)) [input p14]
23. ~rich(fred) [input hypothesis]
28. (~quiet(fred) <~> generous(fred)) | ! [X0] : ~generous(X0) [ennf transformation 4]
37. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (~humble(X0) | patient(X0)))) [nnf transformation 2]
38. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | ~humble(X0) | patient(X0))) [flattening 37]
39. ((~generous(fred) | quiet(fred)) & (generous(fred) | ~quiet(fred))) | ! [X0] : ~generous(X0) [nnf transformation 28]
44. ! [X0] : (((~rich(X0) | ~wise(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 7]
45. ! [X0] : ((~rich(X0) | ~wise(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [flattening 44]
46. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 8]
47. ! [X0] : ((~patient(X0) | ~quiet(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [flattening 46]
54. (~humble(lucy) | ! [X0] : ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) & (? [X0] : ((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | humble(lucy)) [nnf transformation 15]
55. (~humble(lucy) | ! [X0] : ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) & (? [X1] : ((~wise(X1) | ~generous(X1)) & (wise(X1) | generous(X1))) | humble(lucy)) [rectify 54]
56. ? [X1] : ((~wise(X1) | ~generous(X1)) & (wise(X1) | generous(X1))) => ((~wise(sK3) | ~generous(sK3)) & (wise(sK3) | generous(sK3))) [choice axiom]
57. (~humble(lucy) | ! [X0] : ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) & (((~wise(sK3) | ~generous(sK3)) & (wise(sK3) | generous(sK3))) | humble(lucy)) [skolemisation 55,56]
68. ~wise(X0) | ~patient(X0) [cnf transformation 38]
69. humble(X0) | patient(X0) [cnf transformation 38]
73. ~generous(fred) | quiet(fred) | ~generous(X0) [cnf transformation 39]
78. ~quiet(X0) | wise(X0) [cnf transformation 45]
79. ~quiet(X0) | rich(X0) [cnf transformation 45]
83. wise(X0) | quiet(X0) [cnf transformation 47]
108. ~humble(lucy) | generous(X0) | ~wise(X0) [cnf transformation 57]
119. ~rich(fred) [cnf transformation 23]
122. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
123. ~generous(X0) <- (1) [avatar component clause 122]
125. 2 <=> quiet(fred) [avatar definition]
127. quiet(fred) <- (2) [avatar component clause 125]
129. 3 <=> generous(fred) [avatar definition]
131. ~generous(fred) <- (~3) [avatar component clause 129]
132. 1 | 2 | ~3 [avatar split clause 73,129,125,122]
166. wise(X0) [subsumption resolution 83,78]
207. ~humble(lucy) | generous(X0) [subsumption resolution 108,166]
209. 19 <=> ! [X0] : generous(X0) [avatar definition]
210. generous(X0) <- (19) [avatar component clause 209]
212. 20 <=> humble(lucy) [avatar definition]
214. ~humble(lucy) <- (~20) [avatar component clause 212]
215. 19 | ~20 [avatar split clause 207,212,209]
255. ~patient(X0) [resolution 68,166]
256. patient(lucy) <- (~20) [resolution 69,214]
258. $false <- (~20) [subsumption resolution 256,255]
259. 20 [avatar contradiction clause 258]
262. $false <- (~3, 19) [resolution 210,131]
265. 3 | ~19 [avatar contradiction clause 262]
268. rich(fred) <- (2) [resolution 79,127]
269. $false <- (2) [subsumption resolution 268,119]
270. ~2 [avatar contradiction clause 269]
271. $false <- (1, 19) [subsumption resolution 123,210]
272. ~1 | ~19 [avatar contradiction clause 271]
273. $false [avatar sat refutation 132,215,259,265,270,272]
% SZS output end Proof for 6735870940346321085416198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or rich then someone is either old or not kind. Everyone who is both kind and brave is not humble and vice versa. If someone is not patient or not rich then someone is either curious or not generous and vice versa. If someone is both rich and patient then someone is either not creative or old and vice versa. If fred is both kind and curious then someone is happy or not generous. If lucy is both not patient and happy then someone is both not brave and not generous. Everyone who is not generous or old is not curious and vice versa. Everyone who is tall or not happy is both quiet and brave and vice versa. If john is not rich or not kind then fred is either tall or old. Everyone who is not strong or calm is both tall and not creative. Everyone who is kind or not generous is generous or curious and vice versa. If john is either calm or not happy then susan is not tall. Everyone who is not rich or not curious is not calm and vice versa. Everyone who is both rich and humble is both not kind and patient. Everyone who is either not old or not humble is either humble or tall and vice versa. If someone is both not quiet and tall then lucy is not funny and vice versa. Paul is not creative or funny. Alice is not creative. Susan is either not patient or not strong. John is either not happy or old. Someone is happy. | John is not old. | contradiction | ((?[X]:((~kind(X)|rich(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((kind(X)&brave(X))<=>~humble(X)))&
((?[X]:((~patient(X)|~rich(X))))<=>(?[X]:((curious(X)<~>~generous(X)))))&
((?[X]:((rich(X)&patient(X))))<=>(?[X]:((~creative(X)<~>old(X)))))&
(((kind(fred)&curious(fred)))=>(?[X]:((happy(X)|~generous(X)))))&
(((~patient(lucy)&happy(lucy)))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~generous(X)|old(X))<=>~curious(X)))&
(![X]:((tall(X)|~happy(X))<=>(quiet(X)&brave(X))))&
(((~rich(john)|~kind(john)))=>((tall(fred)<~>old(fred))))&
(![X]:((~strong(X)|calm(X))=>(tall(X)&~creative(X))))&
(![X]:((kind(X)|~generous(X))<=>(generous(X)|curious(X))))&
(((calm(john)<~>~happy(john)))=>(~tall(susan)))&
(![X]:((~rich(X)|~curious(X))<=>~calm(X)))&
(![X]:((rich(X)&humble(X))=>(~kind(X)&patient(X))))&
(![X]:((~old(X)<~>~humble(X))<=>(humble(X)<~>tall(X))))&
((?[X]:((~quiet(X)&tall(X))))<=>(~funny(lucy)))&
((~creative(paul)|funny(paul)))&
(~creative(alice))&
((~patient(susan)<~>~strong(susan)))&
((~happy(john)<~>old(john)))&
(?[X]:(happy(X))) | ~old(john) | [
"p6",
"p8",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2104793264363515318817122
% SZS output start Proof for 2104793264363515318817122
7. ! [X0] : ((old(X0) | ~generous(X0)) <=> ~curious(X0)) [input p6]
9. (~kind(john) | ~rich(john)) => (tall(fred) <~> old(fred)) [input p8]
10. ! [X0] : ((calm(X0) | ~strong(X0)) => (~creative(X0) & tall(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | kind(X0)) <=> (curious(X0) | generous(X0))) [input p10]
13. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> (humble(X0) <~> tall(X0))) [input p14]
22. ~old(john) [input hypothesis]
31. (tall(fred) <~> old(fred)) | (kind(john) & rich(john)) [ennf transformation 9]
32. ! [X0] : ((~creative(X0) & tall(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 10]
56. ! [X0] : (((old(X0) | ~generous(X0)) | curious(X0)) & (~curious(X0) | (~old(X0) & generous(X0)))) [nnf transformation 7]
57. ! [X0] : ((old(X0) | ~generous(X0) | curious(X0)) & (~curious(X0) | (~old(X0) & generous(X0)))) [flattening 56]
60. ((~old(fred) | ~tall(fred)) & (old(fred) | tall(fred))) | (kind(john) & rich(john)) [nnf transformation 31]
61. ! [X0] : (((~generous(X0) | kind(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 11]
62. ! [X0] : ((~generous(X0) | kind(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | (generous(X0) & ~kind(X0)))) [flattening 61]
64. ! [X0] : (((~curious(X0) | ~rich(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((~curious(X0) | ~rich(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & rich(X0)))) [flattening 64]
66. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 15]
97. ~curious(X0) | generous(X0) [cnf transformation 57]
99. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 57]
105. old(fred) | tall(fred) | rich(john) [cnf transformation 60]
107. ~old(fred) | ~tall(fred) | rich(john) [cnf transformation 60]
110. ~calm(X0) | tall(X0) [cnf transformation 32]
114. curious(X0) | generous(X0) | generous(X0) [cnf transformation 62]
121. ~curious(X0) | ~rich(X0) | calm(X0) [cnf transformation 65]
125. tall(X0) | humble(X0) | ~old(X0) | humble(X0) [cnf transformation 66]
126. ~tall(X0) | ~humble(X0) | ~humble(X0) | old(X0) [cnf transformation 66]
128. ~humble(X0) | ~old(X0) | tall(X0) | ~humble(X0) [cnf transformation 66]
131. humble(X0) | old(X0) | humble(X0) | ~tall(X0) [cnf transformation 66]
142. ~old(john) [cnf transformation 22]
143. tall(X0) | humble(X0) | ~old(X0) [duplicate literal removal 125]
144. ~tall(X0) | ~humble(X0) | old(X0) [duplicate literal removal 126]
145. ~humble(X0) | ~old(X0) | tall(X0) [duplicate literal removal 128]
146. ~tall(X0) | old(X0) | humble(X0) [duplicate literal removal 131]
147. curious(X0) | generous(X0) [duplicate literal removal 114]
272. 29 <=> tall(fred) [avatar definition]
273. tall(fred) <- (29) [avatar component clause 272]
274. ~tall(fred) <- (~29) [avatar component clause 272]
276. 30 <=> old(fred) [avatar definition]
277. old(fred) <- (30) [avatar component clause 276]
278. ~old(fred) <- (~30) [avatar component clause 276]
281. 31 <=> rich(john) [avatar definition]
283. rich(john) <- (31) [avatar component clause 281]
284. 31 | ~29 | ~30 [avatar split clause 107,276,272,281]
286. 31 | 29 | 30 [avatar split clause 105,276,272,281]
288. generous(X0) [subsumption resolution 147,97]
294. 33 <=> calm(john) [avatar definition]
296. calm(john) <- (33) [avatar component clause 294]
303. ~tall(X0) | old(X0) [subsumption resolution 144,146]
304. ~old(X0) | tall(X0) [subsumption resolution 143,145]
339. 42 <=> old(john) [avatar definition]
341. ~old(john) <- (~42) [avatar component clause 339]
344. ~42 [avatar split clause 142,339]
392. old(fred) <- (29) [resolution 303,273]
393. $false <- (29, ~30) [subsumption resolution 392,278]
394. ~29 | 30 [avatar contradiction clause 393]
396. tall(fred) <- (30) [resolution 304,277]
398. $false <- (~29, 30) [subsumption resolution 396,274]
399. 29 | ~30 [avatar contradiction clause 398]
413. curious(X0) | old(X0) [resolution 99,288]
438. ~rich(X0) | old(X0) | calm(X0) [resolution 413,121]
459. old(john) | calm(john) <- (31) [resolution 438,283]
460. calm(john) <- (31, ~42) [subsumption resolution 459,341]
463. 33 | ~31 | 42 [avatar split clause 460,339,281,294]
467. tall(john) <- (33) [resolution 296,110]
488. old(john) <- (33) [resolution 467,303]
492. $false <- (33, ~42) [subsumption resolution 488,341]
493. ~33 | 42 [avatar contradiction clause 492]
494. $false [avatar sat refutation 284,286,344,394,399,463,493]
% SZS output end Proof for 2104793264363515318817122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not humble is not happy or wise.
Everyone who is either funny or wise is kind or not calm.
Everyone who is not creative or not calm is both not kind and tall and vice versa.
If mary is both wise and not kind then someone is both humble and not happy.
Everyone who is not patient is brave.
Everyone who is either not creative or not tall is rich.
If someone is not strong or not patient then susan is old.
If someone is both not tall and not creative then someone is either not happy or calm and vice versa.
If someone is both not humble and calm then someone is both not quiet and rich.
Everyone who is both not generous and not patient is not old or creative.
If susan is either not calm or curious then someone is old.
If mary is both rich and not creative then fred is not old.
Everyone who is either kind or humble is kind.
If someone is both brave and quiet then someone is generous or not brave and vice versa.
Everyone who is both generous and creative is either creative or not kind and vice versa.
Everyone who is both not humble and not old is tall and vice versa.
Someone is both curious and brave.
John is not brave or humble.
John is either not tall or not quiet.
Paul is either not strong or wise.
Someone is not quiet or rich.
Paul is kind or not tall.
Someone is kind.
Someone is not curious or not tall. | Mary is wise. | neutral | (![X]:((generous(X)&~humble(X))=>(~happy(X)|wise(X))))&
(![X]:((funny(X)<~>wise(X))=>(kind(X)|~calm(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&tall(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((~creative(X)<~>~tall(X))=>rich(X)))&
((?[X]:((~strong(X)|~patient(X))))=>(old(susan)))&
((?[X]:((~tall(X)&~creative(X))))<=>(?[X]:((~happy(X)<~>calm(X)))))&
((?[X]:((~humble(X)&calm(X))))=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((~generous(X)&~patient(X))=>(~old(X)|creative(X))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:(old(X))))&
(((rich(mary)&~creative(mary)))=>(~old(fred)))&
(![X]:((kind(X)<~>humble(X))=>kind(X)))&
((?[X]:((brave(X)&quiet(X))))<=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:((generous(X)&creative(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((~humble(X)&~old(X))<=>tall(X)))&
(?[X]:((curious(X)&brave(X))))&
((~brave(john)|humble(john)))&
((~tall(john)<~>~quiet(john)))&
((~strong(paul)<~>wise(paul)))&
(?[X]:((~quiet(X)|rich(X))))&
((kind(paul)|~tall(paul)))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)|~tall(X)))) | wise(mary) | [] | null | 0 |
If john is not quiet then alice is not patient and vice versa.
If someone is patient then fred is both not kind and not generous and vice versa.
If someone is both kind and patient then someone is not funny or wise and vice versa.
Everyone who is not strong is both not old and patient and vice versa.
Everyone who is not strong is calm and vice versa.
If alice is both not brave and not tall then someone is creative or brave.
Everyone who is either humble or generous is old.
If john is both old and not calm then mary is both not funny and not old and vice versa.
If alice is rich or not rich then alice is both humble and not quiet.
Everyone who is either brave or not strong is both calm and brave and vice versa.
Everyone who is either patient or quiet is not humble or not tall and vice versa.
Everyone who is either not creative or not happy is either quiet or not creative.
Everyone who is humble or patient is either rich or not brave.
If alice is not old then fred is not kind or tall.
If john is not patient or brave then mary is not funny and vice versa.
Everyone who is not funny is creative or not kind and vice versa.
Lucy is either quiet or curious.
Someone is not kind.
Someone is both strong and old.
Someone is not curious or not brave.
Someone is not funny.
Someone is curious or not generous. | Alice is calm. | contradiction | ((~quiet(john))<=>(~patient(alice)))&
((?[X]:(patient(X)))<=>((~kind(fred)&~generous(fred))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((quiet(lucy)<~>curious(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((strong(X)&old(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)|~generous(X)))) | calm(alice) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4628632138235911458827894
% SZS output start Proof for 4628632138235911458827894
5. ! [X0] : (~strong(X0) <=> calm(X0)) [input p4]
10. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) & calm(X0))) [input p9]
23. calm(alice) [input hypothesis]
46. ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))) [nnf transformation 5]
52. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 10]
53. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 52]
86. calm(X0) | strong(X0) [cnf transformation 46]
87. ~calm(X0) | ~strong(X0) [cnf transformation 46]
99. calm(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 53]
102. brave(X0) | brave(X0) | strong(X0) [cnf transformation 53]
104. strong(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 53]
134. calm(alice) [cnf transformation 23]
137. brave(X0) | strong(X0) [duplicate literal removal 102]
138. strong(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 104]
250. ~brave(X0) | ~calm(X0) [subsumption resolution 138,87]
251. calm(X0) | ~brave(X0) [subsumption resolution 99,86]
252. ~brave(X0) [subsumption resolution 251,250]
298. ~strong(alice) [resolution 87,134]
304. strong(X0) [resolution 137,252]
306. $false [resolution 304,298]
% SZS output end Proof for 4628632138235911458827894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not humble is strong or not funny and vice versa.
Everyone who is both not patient and wise is both patient and funny and vice versa.
Everyone who is generous is either not rich or generous and vice versa.
If fred is both not strong and old then alice is both funny and not happy and vice versa.
Everyone who is either not curious or not quiet is either wise or not strong.
Everyone who is either kind or not wise is both not funny and rich and vice versa.
If someone is not quiet then lucy is both tall and not wise.
If someone is not kind then someone is quiet.
Everyone who is both happy and not patient is either calm or not kind.
Everyone who is not rich is both not kind and patient and vice versa.
Everyone who is either not humble or not old is curious or brave.
If lucy is not quiet or generous then alice is generous or quiet.
If someone is both happy and generous then someone is calm and vice versa.
If alice is both tall and humble then someone is either creative or rich.
If someone is either not happy or not creative then susan is not tall or not rich and vice versa.
Someone is not patient.
Alice is either not calm or strong.
Someone is not kind or humble.
Someone is not calm or not brave.
Someone is not wise or creative.
Fred is quiet or not creative.
Fred is not funny. | Susan is not tall. | neutral | (![X]:((~generous(X)|~humble(X))<=>(strong(X)|~funny(X))))&
(![X]:((~patient(X)&wise(X))<=>(patient(X)&funny(X))))&
(![X]:(generous(X)<=>(~rich(X)<~>generous(X))))&
(((~strong(fred)&old(fred)))<=>((funny(alice)&~happy(alice))))&
(![X]:((~curious(X)<~>~quiet(X))=>(wise(X)<~>~strong(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~funny(X)&rich(X))))&
((?[X]:(~quiet(X)))=>((tall(lucy)&~wise(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:(quiet(X))))&
(![X]:((happy(X)&~patient(X))=>(calm(X)<~>~kind(X))))&
(![X]:(~rich(X)<=>(~kind(X)&patient(X))))&
(![X]:((~humble(X)<~>~old(X))=>(curious(X)|brave(X))))&
(((~quiet(lucy)|generous(lucy)))=>((generous(alice)|quiet(alice))))&
((?[X]:((happy(X)&generous(X))))<=>(?[X]:(calm(X))))&
(((tall(alice)&humble(alice)))=>(?[X]:((creative(X)<~>rich(X)))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>((~tall(susan)|~rich(susan))))&
(?[X]:(~patient(X)))&
((~calm(alice)<~>strong(alice)))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((~calm(X)|~brave(X))))&
(?[X]:((~wise(X)|creative(X))))&
((quiet(fred)|~creative(fred)))&
(~funny(fred)) | ~tall(susan) | [] | null | 0 |
Everyone who is strong is not curious or not tall. Everyone who is not happy is both quiet and calm. If alice is both not creative and not curious then someone is not calm and vice versa. If someone is either funny or not humble then someone is wise or not humble and vice versa. If alice is both not strong and tall then alice is not calm and vice versa. If someone is not strong then someone is either not kind or not quiet and vice versa. Everyone who is both quiet and not tall is both calm and not strong and vice versa. Everyone who is strong or not patient is happy. Everyone who is both old and generous is strong or curious. If susan is both curious and patient then john is both wise and not generous and vice versa. If someone is both not patient and not tall then someone is patient and vice versa. If susan is not brave or not strong then someone is both not patient and kind and vice versa. Everyone who is either happy or not tall is not curious. Everyone who is both patient and not tall is not kind or not rich. Everyone who is not strong or rich is both not kind and generous. Everyone who is rich or not wise is either not calm or kind and vice versa. Someone is either creative or happy. Mary is either happy or brave. Lucy is either not calm or not happy. Someone is either not rich or not calm. Lucy is both not quiet and not calm. Someone is not tall or brave. Someone is both funny and generous. Someone is funny. | Alice is not generous. | neutral | (![X]:(strong(X)=>(~curious(X)|~tall(X))))&
(![X]:(~happy(X)=>(quiet(X)&calm(X))))&
(((~creative(alice)&~curious(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((wise(X)|~humble(X)))))&
(((~strong(alice)&tall(alice)))<=>(~calm(alice)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~tall(X))<=>(calm(X)&~strong(X))))&
(![X]:((strong(X)|~patient(X))=>happy(X)))&
(![X]:((old(X)&generous(X))=>(strong(X)|curious(X))))&
(((curious(susan)&patient(susan)))<=>((wise(john)&~generous(john))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:(patient(X))))&
(((~brave(susan)|~strong(susan)))<=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:((happy(X)<~>~tall(X))=>~curious(X)))&
(![X]:((patient(X)&~tall(X))=>(~kind(X)|~rich(X))))&
(![X]:((~strong(X)|rich(X))=>(~kind(X)&generous(X))))&
(![X]:((rich(X)|~wise(X))<=>(~calm(X)<~>kind(X))))&
(?[X]:((creative(X)<~>happy(X))))&
((happy(mary)<~>brave(mary)))&
((~calm(lucy)<~>~happy(lucy)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~quiet(lucy)&~calm(lucy)))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:((funny(X)&generous(X))))&
(?[X]:(funny(X))) | ~generous(alice) | [] | null | 0 |
If someone is both not brave and humble then john is either not creative or not happy.
Everyone who is either happy or not happy is curious.
Everyone who is either not creative or not quiet is not quiet or happy.
If john is brave or not kind then paul is strong or not old and vice versa.
Everyone who is either not creative or generous is either not rich or not old and vice versa.
If alice is humble then someone is either not rich or humble and vice versa.
Everyone who is both not quiet and rich is both patient and not patient.
If someone is not funny or calm then someone is not funny or not calm and vice versa.
If someone is both not humble and not happy then susan is kind or wise.
If someone is both not old and wise then someone is both strong and happy and vice versa.
Everyone who is rich or tall is tall or not generous and vice versa.
If mary is either creative or not brave then someone is old.
Everyone who is not quiet or old is both funny and patient.
If someone is not humble or wise then someone is both kind and humble and vice versa.
If paul is humble then susan is quiet.
Someone is either strong or not quiet.
Someone is both not patient and strong.
Fred is both strong and creative.
Lucy is not patient.
Alice is either not funny or not kind.
Susan is both kind and strong.
Someone is either not quiet or not strong.
John is not humble. | John is not curious. | contradiction | ((?[X]:((~brave(X)&humble(X))))=>((~creative(john)<~>~happy(john))))&
(![X]:((happy(X)<~>~happy(X))=>curious(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~quiet(X)|happy(X))))&
(((brave(john)|~kind(john)))<=>((strong(paul)|~old(paul))))&
(![X]:((~creative(X)<~>generous(X))<=>(~rich(X)<~>~old(X))))&
((humble(alice))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~quiet(X)&rich(X))=>(patient(X)&~patient(X))))&
((?[X]:((~funny(X)|calm(X))))<=>(?[X]:((~funny(X)|~calm(X)))))&
((?[X]:((~humble(X)&~happy(X))))=>((kind(susan)|wise(susan))))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((rich(X)|tall(X))<=>(tall(X)|~generous(X))))&
(((creative(mary)<~>~brave(mary)))=>(?[X]:(old(X))))&
(![X]:((~quiet(X)|old(X))=>(funny(X)&patient(X))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((kind(X)&humble(X)))))&
((humble(paul))=>(quiet(susan)))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&strong(X))))&
((strong(fred)&creative(fred)))&
(~patient(lucy))&
((~funny(alice)<~>~kind(alice)))&
((kind(susan)&strong(susan)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(~humble(john)) | ~curious(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4121983695428310538954976
% SZS output start Proof for 4121983695428310538954976
2. ! [X0] : ((happy(X0) <~> ~happy(X0)) => curious(X0)) [input p1]
24. ~curious(john) [input hypothesis]
29. ! [X0] : (curious(X0) | (happy(X0) <=> ~happy(X0))) [ennf transformation 2]
40. ! [X0] : (curious(X0) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 29]
80. curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 40]
81. curious(X0) | happy(X0) | happy(X0) [cnf transformation 40]
141. ~curious(john) [cnf transformation 24]
143. curious(X0) | ~happy(X0) [duplicate literal removal 80]
144. curious(X0) | happy(X0) [duplicate literal removal 81]
158. curious(X0) [subsumption resolution 143,144]
353. $false [subsumption resolution 141,158]
% SZS output end Proof for 4121983695428310538954976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative then someone is either not rich or not humble. Everyone who is wise or humble is calm. Everyone who is not kind or not rich is either calm or not old. Everyone who is rich or happy is either not brave or not rich and vice versa. Everyone who is wise or not rich is both not old and not rich and vice versa. If someone is not old then paul is calm or tall. Everyone who is patient or funny is not strong. Everyone who is either old or patient is both not rich and not happy. If lucy is not old then mary is patient and vice versa. If lucy is funny then alice is either not generous or calm. If john is wise or not old then someone is both not humble and not generous. Everyone who is calm or generous is old and vice versa. Everyone who is patient or not rich is not humble and vice versa. If someone is happy or not patient then someone is kind or not kind and vice versa. Everyone who is calm or funny is not curious or funny and vice versa. If mary is strong or not curious then someone is not generous and vice versa. Fred is both not quiet and not patient. Someone is either not creative or wise. Lucy is old. Alice is old. Lucy is either kind or not humble. Someone is both not funny and old. Fred is either not rich or wise. Alice is calm. | John is wise. | contradiction | ((?[X]:((~old(X)|creative(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((wise(X)|humble(X))=>calm(X)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>~old(X))))&
(![X]:((rich(X)|happy(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((wise(X)|~rich(X))<=>(~old(X)&~rich(X))))&
((?[X]:(~old(X)))=>((calm(paul)|tall(paul))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
((~old(lucy))<=>(patient(mary)))&
((funny(lucy))=>((~generous(alice)<~>calm(alice))))&
(((wise(john)|~old(john)))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((calm(X)|generous(X))<=>old(X)))&
(![X]:((patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
((~quiet(fred)&~patient(fred)))&
(?[X]:((~creative(X)<~>wise(X))))&
(old(lucy))&
(old(alice))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~funny(X)&old(X))))&
((~rich(fred)<~>wise(fred)))&
(calm(alice)) | wise(john) | [
"p1",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4733949496250488901184650
% SZS output start Proof for 4733949496250488901184650
2. ! [X0] : ((humble(X0) | wise(X0)) => calm(X0)) [input p1]
5. ! [X0] : ((~rich(X0) | wise(X0)) <=> (~rich(X0) & ~old(X0))) [input p4]
12. ! [X0] : ((generous(X0) | calm(X0)) <=> old(X0)) [input p11]
25. wise(john) [input hypothesis]
31. ! [X0] : (calm(X0) | (~humble(X0) & ~wise(X0))) [ennf transformation 2]
44. ! [X0] : (((~rich(X0) | wise(X0)) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | (rich(X0) & ~wise(X0)))) [nnf transformation 5]
45. ! [X0] : ((~rich(X0) | wise(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | (rich(X0) & ~wise(X0)))) [flattening 44]
51. ! [X0] : (((generous(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (~generous(X0) & ~calm(X0)))) [nnf transformation 12]
52. ! [X0] : ((generous(X0) | calm(X0) | ~old(X0)) & (old(X0) | (~generous(X0) & ~calm(X0)))) [flattening 51]
78. ~wise(X0) | calm(X0) [cnf transformation 31]
90. ~wise(X0) | ~old(X0) [cnf transformation 45]
109. ~calm(X0) | old(X0) [cnf transformation 52]
138. wise(john) [cnf transformation 25]
185. 10 <=> old(john) [avatar definition]
186. ~old(john) <- (~10) [avatar component clause 185]
194. 12 <=> wise(john) [avatar definition]
195. wise(john) <- (12) [avatar component clause 194]
262. 12 [avatar split clause 138,194]
263. calm(john) <- (12) [resolution 78,195]
264. ~old(john) <- (12) [resolution 90,195]
265. ~10 | ~12 [avatar split clause 264,194,185]
271. old(john) <- (12) [resolution 109,263]
272. $false <- (~10, 12) [subsumption resolution 271,186]
273. 10 | ~12 [avatar contradiction clause 272]
274. $false [avatar sat refutation 262,265,273]
% SZS output end Proof for 4733949496250488901184650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then lucy is either not rich or calm.
If someone is not creative then someone is calm or tall and vice versa.
Everyone who is both not quiet and not creative is not generous or not wise and vice versa.
Everyone who is both rich and curious is either not patient or wise and vice versa.
Everyone who is either not kind or calm is not creative or not kind.
If someone is either not quiet or not brave then john is not humble or calm and vice versa.
Everyone who is calm is either not brave or not tall.
Everyone who is not wise or not creative is both curious and funny and vice versa.
Everyone who is either not funny or creative is not quiet and vice versa.
If paul is both happy and not wise then someone is rich or creative and vice versa.
Everyone who is not patient is either curious or not tall and vice versa.
If someone is either not quiet or old then fred is either not quiet or happy.
Everyone who is either not brave or not generous is not wise.
If someone is not brave then susan is kind or not wise and vice versa.
If someone is either not funny or creative then susan is both funny and not kind.
Everyone who is not quiet or kind is both creative and quiet.
Someone is both not creative and wise.
Someone is brave.
Someone is rich or generous. | Lucy is not funny. | contradiction | ((?[X]:(brave(X)))=>((~rich(lucy)<~>calm(lucy))))&
((?[X]:(~creative(X)))<=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>(~generous(X)|~wise(X))))&
(![X]:((rich(X)&curious(X))<=>(~patient(X)<~>wise(X))))&
(![X]:((~kind(X)<~>calm(X))=>(~creative(X)|~kind(X))))&
((?[X]:((~quiet(X)<~>~brave(X))))<=>((~humble(john)|calm(john))))&
(![X]:(calm(X)=>(~brave(X)<~>~tall(X))))&
(![X]:((~wise(X)|~creative(X))<=>(curious(X)&funny(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~quiet(X)))&
(((happy(paul)&~wise(paul)))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:(~patient(X)<=>(curious(X)<~>~tall(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~quiet(fred)<~>happy(fred))))&
(![X]:((~brave(X)<~>~generous(X))=>~wise(X)))&
((?[X]:(~brave(X)))<=>((kind(susan)|~wise(susan))))&
((?[X]:((~funny(X)<~>creative(X))))=>((funny(susan)&~kind(susan))))&
(![X]:((~quiet(X)|kind(X))=>(creative(X)&quiet(X))))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:(brave(X)))&
(?[X]:((rich(X)|generous(X)))) | ~funny(lucy) | [
"p2",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6879748439530044544927323
% SZS output start Proof for 6879748439530044544927323
3. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~wise(X0) | ~generous(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (funny(X0) & curious(X0))) [input p7]
10. (~wise(paul) & happy(paul)) <=> ? [X0] : (creative(X0) | rich(X0)) [input p9]
16. ! [X0] : ((kind(X0) | ~quiet(X0)) => (quiet(X0) & creative(X0))) [input p15]
20. ~funny(lucy) [input hypothesis]
29. ! [X0] : ((quiet(X0) & creative(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 16]
36. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & ((~wise(X0) | ~generous(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 3]
37. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & (~wise(X0) | ~generous(X0) | creative(X0) | quiet(X0))) [flattening 36]
47. ! [X0] : (((~creative(X0) | ~wise(X0)) | (~funny(X0) | ~curious(X0))) & ((funny(X0) & curious(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 8]
48. ! [X0] : ((~creative(X0) | ~wise(X0) | ~funny(X0) | ~curious(X0)) & ((funny(X0) & curious(X0)) | (creative(X0) & wise(X0)))) [flattening 47]
50. ((~wise(paul) & happy(paul)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | (wise(paul) | ~happy(paul))) [nnf transformation 10]
51. ((~wise(paul) & happy(paul)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | wise(paul) | ~happy(paul)) [flattening 50]
52. ((~wise(paul) & happy(paul)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X1] : (creative(X1) | rich(X1)) | wise(paul) | ~happy(paul)) [rectify 51]
53. ? [X1] : (creative(X1) | rich(X1)) => (creative(sK3) | rich(sK3)) [choice axiom]
54. ((~wise(paul) & happy(paul)) | ! [X0] : (~creative(X0) & ~rich(X0))) & ((creative(sK3) | rich(sK3)) | wise(paul) | ~happy(paul)) [skolemisation 52,53]
77. ~quiet(X0) | wise(X0) [cnf transformation 37]
99. funny(X0) | creative(X0) [cnf transformation 48]
109. ~wise(paul) | ~creative(X0) [cnf transformation 54]
129. quiet(X0) | quiet(X0) [cnf transformation 29]
135. ~funny(lucy) [cnf transformation 20]
136. quiet(X0) [duplicate literal removal 129]
207. 16 <=> ! [X0] : ~creative(X0) [avatar definition]
208. ~creative(X0) <- (16) [avatar component clause 207]
210. 17 <=> wise(paul) [avatar definition]
212. ~wise(paul) <- (~17) [avatar component clause 210]
213. 16 | ~17 [avatar split clause 109,210,207]
294. wise(X0) [resolution 77,136]
296. $false <- (~17) [resolution 294,212]
297. 17 [avatar contradiction clause 296]
302. creative(lucy) [resolution 99,135]
303. $false <- (16) [subsumption resolution 302,208]
304. ~16 [avatar contradiction clause 303]
305. $false [avatar sat refutation 213,297,304]
% SZS output end Proof for 6879748439530044544927323
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | Paul is strong. | entailment | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | strong(paul) | [
"p0",
"p1",
"p10",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4348041320909620726203170
% SZS output start Proof for 4348041320909620726203170
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. ~strong(paul) [input hypothesis]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
80. ~brave(X0) | strong(X0) [cnf transformation 39]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. ~strong(paul) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
179. 8 <=> old(lucy) [avatar definition]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
271. strong(X1) <- (11) [resolution 194,80]
286. $false <- (11) [resolution 271,143]
289. ~11 [avatar contradiction clause 286]
290. $false [avatar sat refutation 196,250,251,265,289]
% SZS output end Proof for 4348041320909620726203170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then paul is both not tall and not strong and vice versa. Everyone who is rich or not generous is both curious and kind. Everyone who is not creative is kind or not wise. Everyone who is not brave is both generous and not kind. If john is either not patient or curious then someone is patient or tall and vice versa. Everyone who is both not funny and humble is either patient or funny. If paul is not funny then someone is not quiet. Everyone who is not tall or quiet is not curious. Everyone who is both not kind and not calm is funny or not happy and vice versa. If someone is both not quiet and brave then paul is either not patient or curious and vice versa. If lucy is either generous or rich then mary is calm or not patient and vice versa. If mary is either creative or not quiet then lucy is both brave and funny and vice versa. Everyone who is brave is not happy and vice versa. Everyone who is quiet is not patient and vice versa. Everyone who is both not humble and happy is both kind and not rich and vice versa. Someone is either quiet or strong. Someone is either not happy or strong. Someone is creative or not rich. Fred is patient. Someone is kind or not quiet. Alice is not rich. Someone is old. Lucy is both not tall and not creative. | Paul is curious. | contradiction | ((?[X]:(patient(X)))<=>((~tall(paul)&~strong(paul))))&
(![X]:((rich(X)|~generous(X))=>(curious(X)&kind(X))))&
(![X]:(~creative(X)=>(kind(X)|~wise(X))))&
(![X]:(~brave(X)=>(generous(X)&~kind(X))))&
(((~patient(john)<~>curious(john)))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((~funny(X)&humble(X))=>(patient(X)<~>funny(X))))&
((~funny(paul))=>(?[X]:(~quiet(X))))&
(![X]:((~tall(X)|quiet(X))=>~curious(X)))&
(![X]:((~kind(X)&~calm(X))<=>(funny(X)|~happy(X))))&
((?[X]:((~quiet(X)&brave(X))))<=>((~patient(paul)<~>curious(paul))))&
(((generous(lucy)<~>rich(lucy)))<=>((calm(mary)|~patient(mary))))&
(((creative(mary)<~>~quiet(mary)))<=>((brave(lucy)&funny(lucy))))&
(![X]:(brave(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>~patient(X)))&
(![X]:((~humble(X)&happy(X))<=>(kind(X)&~rich(X))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((creative(X)|~rich(X))))&
(patient(fred))&
(?[X]:((kind(X)|~quiet(X))))&
(~rich(alice))&
(?[X]:(old(X)))&
((~tall(lucy)&~creative(lucy))) | curious(paul) | [
"p0",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8876926019387406678844327
% SZS output start Proof for 8876926019387406678844327
1. ? [X0] : patient(X0) <=> (~strong(paul) & ~tall(paul)) [input p0]
8. ! [X0] : ((quiet(X0) | ~tall(X0)) => ~curious(X0)) [input p7]
19. patient(fred) [input p18]
24. curious(paul) [input hypothesis]
32. ! [X0] : (~curious(X0) | (~quiet(X0) & tall(X0))) [ennf transformation 8]
33. (? [X0] : patient(X0) | (strong(paul) | tall(paul))) & ((~strong(paul) & ~tall(paul)) | ! [X0] : ~patient(X0)) [nnf transformation 1]
34. (? [X0] : patient(X0) | strong(paul) | tall(paul)) & ((~strong(paul) & ~tall(paul)) | ! [X0] : ~patient(X0)) [flattening 33]
35. (? [X0] : patient(X0) | strong(paul) | tall(paul)) & ((~strong(paul) & ~tall(paul)) | ! [X1] : ~patient(X1)) [rectify 34]
36. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
37. (patient(sK0) | strong(paul) | tall(paul)) & ((~strong(paul) & ~tall(paul)) | ! [X1] : ~patient(X1)) [skolemisation 35,36]
69. ~tall(paul) | ~patient(X1) [cnf transformation 37]
87. ~curious(X0) | tall(X0) [cnf transformation 32]
125. patient(fred) [cnf transformation 19]
130. curious(paul) [cnf transformation 24]
133. 1 <=> tall(paul) [avatar definition]
146. 4 <=> ! [X1] : ~patient(X1) [avatar definition]
147. ~patient(X1) <- (4) [avatar component clause 146]
149. 4 | ~1 [avatar split clause 69,133,146]
185. 12 <=> curious(paul) [avatar definition]
186. curious(paul) <- (12) [avatar component clause 185]
291. 12 [avatar split clause 130,185]
292. $false <- (4) [resolution 147,125]
293. ~4 [avatar contradiction clause 292]
296. tall(paul) <- (12) [resolution 87,186]
301. 1 | ~12 [avatar split clause 296,185,133]
302. $false [avatar sat refutation 149,291,293,301]
% SZS output end Proof for 8876926019387406678844327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is either not kind or brave and vice versa.
Everyone who is not rich or brave is both funny and old.
If paul is both quiet and not humble then paul is both not quiet and not humble and vice versa.
If someone is not generous or not creative then alice is both strong and old.
Everyone who is strong is not curious or not calm.
Everyone who is not humble is wise.
Everyone who is not creative is not humble or not kind and vice versa.
Everyone who is not brave is calm or not happy.
Everyone who is not funny or patient is both not strong and not generous and vice versa.
If someone is either generous or curious then fred is funny or creative.
If lucy is not tall then alice is either not kind or not patient and vice versa.
Everyone who is not creative is not curious or not wise and vice versa.
If someone is creative or calm then fred is not strong or not brave and vice versa.
Everyone who is humble or calm is not rich and vice versa.
Everyone who is either not funny or not old is both not funny and old.
Everyone who is quiet is humble or curious and vice versa.
Someone is happy or not patient.
Susan is patient.
Someone is not creative.
Someone is either rich or not calm.
Someone is not humble or funny.
Mary is not strong.
Mary is both funny and not quiet.
Someone is both not curious and kind. | Paul is not humble. | contradiction | ((?[X]:(kind(X)))<=>(?[X]:((~kind(X)<~>brave(X)))))&
(![X]:((~rich(X)|brave(X))=>(funny(X)&old(X))))&
(((quiet(paul)&~humble(paul)))<=>((~quiet(paul)&~humble(paul))))&
((?[X]:((~generous(X)|~creative(X))))=>((strong(alice)&old(alice))))&
(![X]:(strong(X)=>(~curious(X)|~calm(X))))&
(![X]:(~humble(X)=>wise(X)))&
(![X]:(~creative(X)<=>(~humble(X)|~kind(X))))&
(![X]:(~brave(X)=>(calm(X)|~happy(X))))&
(![X]:((~funny(X)|patient(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((generous(X)<~>curious(X))))=>((funny(fred)|creative(fred))))&
((~tall(lucy))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:(~creative(X)<=>(~curious(X)|~wise(X))))&
((?[X]:((creative(X)|calm(X))))<=>((~strong(fred)|~brave(fred))))&
(![X]:((humble(X)|calm(X))<=>~rich(X)))&
(![X]:((~funny(X)<~>~old(X))=>(~funny(X)&old(X))))&
(![X]:(quiet(X)<=>(humble(X)|curious(X))))&
(?[X]:((happy(X)|~patient(X))))&
(patient(susan))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)<~>~calm(X))))&
(?[X]:((~humble(X)|funny(X))))&
(~strong(mary))&
((funny(mary)&~quiet(mary)))&
(?[X]:((~curious(X)&kind(X)))) | ~humble(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6339420172002621530236181
% SZS output start Proof for 6339420172002621530236181
3. (~humble(paul) & quiet(paul)) <=> (~humble(paul) & ~quiet(paul)) [input p2]
25. ~humble(paul) [input hypothesis]
42. ((~humble(paul) & quiet(paul)) | (humble(paul) | quiet(paul))) & ((~humble(paul) & ~quiet(paul)) | (humble(paul) | ~quiet(paul))) [nnf transformation 3]
43. ((~humble(paul) & quiet(paul)) | humble(paul) | quiet(paul)) & ((~humble(paul) & ~quiet(paul)) | humble(paul) | ~quiet(paul)) [flattening 42]
81. ~quiet(paul) | humble(paul) | ~quiet(paul) [cnf transformation 43]
83. quiet(paul) | humble(paul) | quiet(paul) [cnf transformation 43]
134. ~humble(paul) [cnf transformation 25]
137. ~quiet(paul) | humble(paul) [duplicate literal removal 81]
138. quiet(paul) | humble(paul) [duplicate literal removal 83]
165. 7 <=> humble(paul) [avatar definition]
169. 8 <=> quiet(paul) [avatar definition]
172. 7 | 8 [avatar split clause 138,169,165]
173. 7 | ~8 [avatar split clause 137,169,165]
270. ~7 [avatar split clause 134,165]
271. $false [avatar sat refutation 172,173,270]
% SZS output end Proof for 6339420172002621530236181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not quiet or creative then fred is both not quiet and old. If lucy is funny then someone is rich and vice versa. Everyone who is either happy or not generous is not generous or not brave and vice versa. If someone is calm or quiet then someone is either creative or not kind and vice versa. Everyone who is not generous or not patient is either not calm or curious and vice versa. If someone is both kind and calm then someone is not humble or not funny. Everyone who is not patient is not brave or not calm. If mary is wise then someone is both not rich and not happy. Everyone who is calm or not kind is not curious or creative and vice versa. If someone is both not rich and funny then lucy is both happy and not curious. If someone is both not funny and not wise then someone is both tall and humble. If fred is brave then susan is either creative or calm. If lucy is humble then susan is not kind or humble and vice versa. Everyone who is either curious or not brave is brave or not happy and vice versa. Everyone who is rich or curious is both generous and not creative and vice versa. Everyone who is either not wise or not humble is either curious or not funny and vice versa. Mary is tall. Lucy is not tall or kind. Paul is strong or tall. Someone is both patient and kind. Lucy is not wise or not patient. Mary is either quiet or funny. Alice is humble or not kind. Susan is either wise or not strong. | Fred is not calm. | entailment | (((~quiet(fred)|creative(fred)))=>((~quiet(fred)&old(fred))))&
((funny(lucy))<=>(?[X]:(rich(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~generous(X)|~brave(X))))&
((?[X]:((calm(X)|quiet(X))))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~generous(X)|~patient(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((kind(X)&calm(X))))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:(~patient(X)=>(~brave(X)|~calm(X))))&
((wise(mary))=>(?[X]:((~rich(X)&~happy(X)))))&
(![X]:((calm(X)|~kind(X))<=>(~curious(X)|creative(X))))&
((?[X]:((~rich(X)&funny(X))))=>((happy(lucy)&~curious(lucy))))&
((?[X]:((~funny(X)&~wise(X))))=>(?[X]:((tall(X)&humble(X)))))&
((brave(fred))=>((creative(susan)<~>calm(susan))))&
((humble(lucy))<=>((~kind(susan)|humble(susan))))&
(![X]:((curious(X)<~>~brave(X))<=>(brave(X)|~happy(X))))&
(![X]:((rich(X)|curious(X))<=>(generous(X)&~creative(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(curious(X)<~>~funny(X))))&
(tall(mary))&
((~tall(lucy)|kind(lucy)))&
((strong(paul)|tall(paul)))&
(?[X]:((patient(X)&kind(X))))&
((~wise(lucy)|~patient(lucy)))&
((quiet(mary)<~>funny(mary)))&
((humble(alice)|~kind(alice)))&
((wise(susan)<~>~strong(susan))) | ~calm(fred) | [
"p2",
"p4",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5672843810781219950558379
% SZS output start Proof for 5672843810781219950558379
3. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (~brave(X0) | ~generous(X0))) [input p2]
5. ! [X0] : ((~patient(X0) | ~generous(X0)) <=> (~calm(X0) <~> curious(X0))) [input p4]
9. ! [X0] : ((~kind(X0) | calm(X0)) <=> (creative(X0) | ~curious(X0))) [input p8]
14. ! [X0] : ((curious(X0) <~> ~brave(X0)) <=> (~happy(X0) | brave(X0))) [input p13]
15. ! [X0] : ((curious(X0) | rich(X0)) <=> (~creative(X0) & generous(X0))) [input p14]
25. calm(fred) [input hypothesis]
42. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 3]
43. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [flattening 42]
49. ! [X0] : (((~patient(X0) | ~generous(X0)) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (patient(X0) & generous(X0)))) [nnf transformation 5]
50. ! [X0] : ((~patient(X0) | ~generous(X0) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (patient(X0) & generous(X0)))) [flattening 49]
56. ! [X0] : (((~kind(X0) | calm(X0)) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | (kind(X0) & ~calm(X0)))) [nnf transformation 9]
57. ! [X0] : ((~kind(X0) | calm(X0) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | (kind(X0) & ~calm(X0)))) [flattening 56]
64. ! [X0] : ((((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0))))) [nnf transformation 14]
65. ! [X0] : ((((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0))))) [flattening 64]
66. ! [X0] : (((curious(X0) | rich(X0)) | (creative(X0) | ~generous(X0))) & ((~creative(X0) & generous(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 15]
67. ! [X0] : ((curious(X0) | rich(X0) | creative(X0) | ~generous(X0)) & ((~creative(X0) & generous(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 66]
77. ~brave(X0) | ~generous(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 43]
80. ~generous(X0) | happy(X0) | brave(X0) [cnf transformation 43]
81. generous(X0) | ~happy(X0) | generous(X0) [cnf transformation 43]
89. ~calm(X0) | curious(X0) | generous(X0) [cnf transformation 50]
99. ~curious(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
113. ~happy(X0) | brave(X0) | curious(X0) | brave(X0) [cnf transformation 65]
115. ~brave(X0) | curious(X0) | happy(X0) [cnf transformation 65]
119. ~curious(X0) | generous(X0) [cnf transformation 67]
121. ~curious(X0) | ~creative(X0) [cnf transformation 67]
142. calm(fred) [cnf transformation 25]
143. ~happy(X0) | brave(X0) | curious(X0) [duplicate literal removal 113]
145. ~brave(X0) | ~generous(X0) | ~happy(X0) [duplicate literal removal 77]
146. ~happy(X0) | generous(X0) [duplicate literal removal 81]
148. 1 <=> creative(fred) [avatar definition]
169. ~brave(X0) | ~happy(X0) [subsumption resolution 145,146]
257. 26 <=> brave(fred) [avatar definition]
258. brave(fred) <- (26) [avatar component clause 257]
259. ~brave(fred) <- (~26) [avatar component clause 257]
285. ~brave(X0) | curious(X0) [subsumption resolution 115,169]
286. ~happy(X0) | curious(X0) [subsumption resolution 143,285]
353. curious(fred) | generous(fred) [resolution 89,142]
355. generous(fred) [subsumption resolution 353,119]
364. 45 <=> curious(fred) [avatar definition]
366. curious(fred) <- (45) [avatar component clause 364]
377. happy(fred) | brave(fred) [resolution 355,80]
378. happy(fred) <- (~26) [subsumption resolution 377,259]
380. curious(fred) <- (~26) [resolution 378,286]
382. 45 | 26 [avatar split clause 380,257,364]
388. curious(fred) <- (26) [resolution 258,285]
390. 45 | ~26 [avatar split clause 388,257,364]
394. ~creative(fred) <- (45) [resolution 366,121]
397. creative(fred) | ~calm(fred) <- (45) [resolution 99,366]
401. creative(fred) <- (45) [subsumption resolution 397,142]
402. 1 | ~45 [avatar split clause 401,364,148]
403. ~1 | ~45 [avatar split clause 394,364,148]
404. $false [avatar sat refutation 382,390,402,403]
% SZS output end Proof for 5672843810781219950558379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or patient is not creative and vice versa. If someone is both not generous and not curious then someone is not tall or not kind. Everyone who is both calm and happy is not curious and vice versa. Everyone who is either quiet or happy is either not patient or not quiet and vice versa. Everyone who is not happy is not tall. If lucy is not quiet or not tall then fred is both not tall and not strong and vice versa. Everyone who is not calm is brave or happy. If someone is either not generous or generous then susan is not creative and vice versa. If susan is either creative or happy then mary is either generous or curious and vice versa. If someone is either old or not calm then alice is both wise and not happy and vice versa. Everyone who is patient or not kind is not humble. If susan is not rich then alice is both not generous and humble and vice versa. Everyone who is not creative or not funny is not rich or not patient and vice versa. Everyone who is brave is both curious and rich and vice versa. If alice is strong then someone is either tall or funny. Everyone who is not funny or brave is either not happy or not strong and vice versa. Fred is patient or creative. Someone is either not generous or strong. Mary is both wise and happy. Someone is either quiet or generous. Someone is either not curious or old. Fred is both not humble and brave. Someone is both not generous and not happy. Paul is either rich or quiet. | Lucy is not patient. | contradiction | (![X]:((~brave(X)<~>patient(X))<=>~creative(X)))&
((?[X]:((~generous(X)&~curious(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:((calm(X)&happy(X))<=>~curious(X)))&
(![X]:((quiet(X)<~>happy(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(~happy(X)=>~tall(X)))&
(((~quiet(lucy)|~tall(lucy)))<=>((~tall(fred)&~strong(fred))))&
(![X]:(~calm(X)=>(brave(X)|happy(X))))&
((?[X]:((~generous(X)<~>generous(X))))<=>(~creative(susan)))&
(((creative(susan)<~>happy(susan)))<=>((generous(mary)<~>curious(mary))))&
((?[X]:((old(X)<~>~calm(X))))<=>((wise(alice)&~happy(alice))))&
(![X]:((patient(X)|~kind(X))=>~humble(X)))&
((~rich(susan))<=>((~generous(alice)&humble(alice))))&
(![X]:((~creative(X)|~funny(X))<=>(~rich(X)|~patient(X))))&
(![X]:(brave(X)<=>(curious(X)&rich(X))))&
((strong(alice))=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:((~funny(X)|brave(X))<=>(~happy(X)<~>~strong(X))))&
((patient(fred)|creative(fred)))&
(?[X]:((~generous(X)<~>strong(X))))&
((wise(mary)&happy(mary)))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:((~curious(X)<~>old(X))))&
((~humble(fred)&brave(fred)))&
(?[X]:((~generous(X)&~happy(X))))&
((rich(paul)<~>quiet(paul))) | ~patient(lucy) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1105321698055654888353223
% SZS output start Proof for 1105321698055654888353223
1. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> ~creative(X0)) [input p0]
4. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> (~patient(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : (~happy(X0) => ~tall(X0)) [input p4]
6. (~tall(lucy) | ~quiet(lucy)) <=> (~strong(fred) & ~tall(fred)) [input p5]
13. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> (~patient(X0) | ~rich(X0))) [input p12]
14. ! [X0] : (brave(X0) <=> (rich(X0) & curious(X0))) [input p13]
16. ! [X0] : ((brave(X0) | ~funny(X0)) <=> (~happy(X0) <~> ~strong(X0))) [input p15]
22. brave(fred) & ~humble(fred) [input p21]
25. ~patient(lucy) [input hypothesis]
28. ! [X0] : (~tall(X0) | happy(X0)) [ennf transformation 5]
33. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | creative(X0)) & (~creative(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 1]
39. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 4]
40. ((~tall(lucy) | ~quiet(lucy)) | (strong(fred) | tall(fred))) & ((~strong(fred) & ~tall(fred)) | (tall(lucy) & quiet(lucy))) [nnf transformation 6]
41. (~tall(lucy) | ~quiet(lucy) | strong(fred) | tall(fred)) & ((~strong(fred) & ~tall(fred)) | (tall(lucy) & quiet(lucy))) [flattening 40]
54. ! [X0] : (((~funny(X0) | ~creative(X0)) | (patient(X0) & rich(X0))) & ((~patient(X0) | ~rich(X0)) | (funny(X0) & creative(X0)))) [nnf transformation 13]
55. ! [X0] : ((~funny(X0) | ~creative(X0) | (patient(X0) & rich(X0))) & (~patient(X0) | ~rich(X0) | (funny(X0) & creative(X0)))) [flattening 54]
56. ! [X0] : ((brave(X0) | (~rich(X0) | ~curious(X0))) & ((rich(X0) & curious(X0)) | ~brave(X0))) [nnf transformation 14]
57. ! [X0] : ((brave(X0) | ~rich(X0) | ~curious(X0)) & ((rich(X0) & curious(X0)) | ~brave(X0))) [flattening 56]
61. ! [X0] : (((brave(X0) | ~funny(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~brave(X0) & funny(X0)))) [nnf transformation 16]
62. ! [X0] : ((brave(X0) | ~funny(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~brave(X0) & funny(X0)))) [flattening 61]
76. ~creative(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 33]
86. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 39]
89. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 39]
91. ~tall(X0) | happy(X0) [cnf transformation 28]
95. ~strong(fred) | tall(lucy) [cnf transformation 41]
121. ~rich(X0) | ~patient(X0) | creative(X0) [cnf transformation 55]
126. ~brave(X0) | rich(X0) [cnf transformation 57]
133. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 62]
146. brave(fred) [cnf transformation 22]
151. ~patient(lucy) [cnf transformation 25]
155. quiet(X0) | patient(X0) | ~happy(X0) [duplicate literal removal 86]
157. ~quiet(X0) | ~happy(X0) | patient(X0) [duplicate literal removal 89]
170. ~happy(X0) | patient(X0) [subsumption resolution 155,157]
177. 5 <=> strong(fred) [avatar definition]
178. ~strong(fred) <- (~5) [avatar component clause 177]
185. 7 <=> tall(lucy) [avatar definition]
186. tall(lucy) <- (7) [avatar component clause 185]
189. 7 | ~5 [avatar split clause 95,177,185]
283. 26 <=> patient(fred) [avatar definition]
284. ~patient(fred) <- (~26) [avatar component clause 283]
285. patient(fred) <- (26) [avatar component clause 283]
287. 27 <=> creative(fred) [avatar definition]
289. creative(fred) <- (27) [avatar component clause 287]
338. rich(fred) [resolution 126,146]
451. ~patient(fred) | creative(fred) [resolution 121,338]
462. creative(fred) <- (26) [subsumption resolution 451,285]
463. 27 | ~26 [avatar split clause 462,283,287]
487. ~brave(fred) | ~patient(fred) <- (27) [resolution 289,76]
489. ~patient(fred) <- (27) [subsumption resolution 487,146]
492. ~26 | ~27 [avatar split clause 489,287,283]
525. happy(fred) | strong(fred) [resolution 133,146]
526. happy(fred) <- (~5) [subsumption resolution 525,178]
554. patient(fred) <- (~5) [resolution 526,170]
556. $false <- (~5, ~26) [subsumption resolution 554,284]
557. 5 | 26 [avatar contradiction clause 556]
573. happy(lucy) <- (7) [resolution 186,91]
577. patient(lucy) <- (7) [resolution 573,170]
587. $false <- (7) [subsumption resolution 577,151]
588. ~7 [avatar contradiction clause 587]
589. $false [avatar sat refutation 189,463,492,557,588]
% SZS output end Proof for 1105321698055654888353223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not calm then paul is either not kind or funny. If fred is not brave then paul is not generous or tall. Everyone who is kind is both rich and not creative. Everyone who is generous or not rich is either patient or not happy and vice versa. If someone is both not brave and humble then someone is either not kind or not strong and vice versa. Everyone who is not calm or not kind is both strong and not curious and vice versa. If someone is either calm or not old then someone is either not happy or creative. Everyone who is not calm or wise is not wise and vice versa. If someone is either funny or not old then someone is not rich or not curious. If someone is both not kind and not creative then lucy is not brave and vice versa. Everyone who is not curious is both not rich and happy. If lucy is either brave or not humble then someone is kind or calm and vice versa. Everyone who is both not brave and not rich is not kind or not curious. If paul is curious or not creative then paul is both not kind and not brave and vice versa. If someone is both curious and tall then paul is both wise and not calm and vice versa. Everyone who is kind is either strong or not kind. Susan is not funny or quiet. Susan is brave or wise. Lucy is tall or not happy. Someone is both not creative and old. Someone is both not tall and strong. Mary is both not wise and humble. Someone is not happy or not creative. Fred is brave or rich. | Fred is rich. | contradiction | ((?[X]:((~funny(X)|~calm(X))))=>((~kind(paul)<~>funny(paul))))&
((~brave(fred))=>((~generous(paul)|tall(paul))))&
(![X]:(kind(X)=>(rich(X)&~creative(X))))&
(![X]:((generous(X)|~rich(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))<=>~wise(X)))&
((?[X]:((funny(X)<~>~old(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~kind(X)&~creative(X))))<=>(~brave(lucy)))&
(![X]:(~curious(X)=>(~rich(X)&happy(X))))&
(((brave(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~brave(X)&~rich(X))=>(~kind(X)|~curious(X))))&
(((curious(paul)|~creative(paul)))<=>((~kind(paul)&~brave(paul))))&
((?[X]:((curious(X)&tall(X))))<=>((wise(paul)&~calm(paul))))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
((~funny(susan)|quiet(susan)))&
((brave(susan)|wise(susan)))&
((tall(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((~tall(X)&strong(X))))&
((~wise(mary)&humble(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((brave(fred)|rich(fred))) | rich(fred) | [
"p2",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7104377160033519441348717
% SZS output start Proof for 7104377160033519441348717
3. ! [X0] : (kind(X0) => (~creative(X0) & rich(X0))) [input p2]
6. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (~curious(X0) & strong(X0))) [input p5]
8. ! [X0] : ((wise(X0) | ~calm(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : (~curious(X0) => (happy(X0) & ~rich(X0))) [input p10]
12. (brave(lucy) <~> ~humble(lucy)) <=> ? [X0] : (calm(X0) | kind(X0)) [input p11]
25. rich(fred) [input hypothesis]
33. ! [X0] : ((~creative(X0) & rich(X0)) | ~kind(X0)) [ennf transformation 3]
36. ! [X0] : ((happy(X0) & ~rich(X0)) | curious(X0)) [ennf transformation 11]
48. ! [X0] : (((~kind(X0) | ~calm(X0)) | (curious(X0) | ~strong(X0))) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | ~calm(X0) | curious(X0) | ~strong(X0)) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [flattening 48]
54. ! [X0] : (((wise(X0) | ~calm(X0)) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [flattening 54]
64. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X0] : (calm(X0) | kind(X0)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [nnf transformation 12]
65. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X1] : (calm(X1) | kind(X1)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [rectify 64]
66. ? [X1] : (calm(X1) | kind(X1)) => (calm(sK5) | kind(sK5)) [choice axiom]
67. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & ((calm(sK5) | kind(sK5)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [skolemisation 65,66]
87. ~kind(X0) | rich(X0) [cnf transformation 33]
103. ~curious(X0) | calm(X0) [cnf transformation 49]
111. ~wise(X0) | ~wise(X0) [cnf transformation 55]
112. wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 55]
118. ~rich(X0) | curious(X0) [cnf transformation 36]
120. calm(sK5) | kind(sK5) | ~humble(lucy) | ~brave(lucy) [cnf transformation 67]
121. calm(sK5) | kind(sK5) | brave(lucy) | humble(lucy) [cnf transformation 67]
123. ~humble(lucy) | brave(lucy) | ~calm(X0) [cnf transformation 67]
125. humble(lucy) | ~brave(lucy) | ~calm(X0) [cnf transformation 67]
148. rich(fred) [cnf transformation 25]
150. ~wise(X0) [duplicate literal removal 111]
151. ~calm(X0) | wise(X0) [duplicate literal removal 112]
249. 23 <=> brave(lucy) [avatar definition]
267. 27 <=> ! [X0] : ~calm(X0) [avatar definition]
268. ~calm(X0) <- (27) [avatar component clause 267]
270. 28 <=> humble(lucy) [avatar definition]
273. 27 | ~23 | 28 [avatar split clause 125,270,249,267]
278. 27 | 23 | ~28 [avatar split clause 123,270,249,267]
281. 30 <=> kind(sK5) [avatar definition]
283. kind(sK5) <- (30) [avatar component clause 281]
285. 31 <=> calm(sK5) [avatar definition]
287. calm(sK5) <- (31) [avatar component clause 285]
288. 28 | 23 | 30 | 31 [avatar split clause 121,285,281,249,270]
289. ~23 | ~28 | 30 | 31 [avatar split clause 120,285,281,270,249]
342. 41 <=> rich(fred) [avatar definition]
344. rich(fred) <- (41) [avatar component clause 342]
346. 41 [avatar split clause 148,342]
358. rich(sK5) <- (30) [resolution 87,283]
360. curious(fred) <- (41) [resolution 118,344]
361. curious(sK5) <- (30) [resolution 118,358]
363. calm(fred) <- (41) [resolution 360,103]
364. $false <- (27, 41) [subsumption resolution 363,268]
365. ~27 | ~41 [avatar contradiction clause 364]
370. calm(sK5) <- (30) [resolution 361,103]
371. 31 | ~30 [avatar split clause 370,281,285]
372. wise(sK5) <- (31) [resolution 287,151]
373. $false <- (31) [subsumption resolution 372,150]
374. ~31 [avatar contradiction clause 373]
375. $false [avatar sat refutation 273,278,288,289,346,365,371,374]
% SZS output end Proof for 7104377160033519441348717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both wise and patient then someone is either old or strong.
Everyone who is either not wise or quiet is both not old and patient and vice versa.
If someone is happy then paul is not wise or strong.
If susan is brave or humble then someone is humble or rich and vice versa.
If someone is old then lucy is both patient and wise and vice versa.
Everyone who is curious is either rich or not generous.
Everyone who is either not happy or not humble is both quiet and happy.
Everyone who is both creative and tall is patient or not calm.
Everyone who is both kind and funny is humble and vice versa.
If fred is both not curious and not brave then someone is creative or not rich and vice versa.
If someone is old or strong then someone is not rich.
If mary is either brave or not strong then mary is either not happy or curious and vice versa.
If fred is both not generous and not curious then susan is not brave or creative.
Everyone who is both not curious and not tall is happy or patient and vice versa.
If someone is brave or creative then paul is both not quiet and creative.
Everyone who is both not happy and creative is not tall or calm and vice versa.
Someone is either not calm or not tall.
Someone is either not old or calm.
Fred is curious or not creative.
Someone is not funny or old. | Fred is brave. | contradiction | (((wise(lucy)&patient(lucy)))=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>(~old(X)&patient(X))))&
((?[X]:(happy(X)))=>((~wise(paul)|strong(paul))))&
(((brave(susan)|humble(susan)))<=>(?[X]:((humble(X)|rich(X)))))&
((?[X]:(old(X)))<=>((patient(lucy)&wise(lucy))))&
(![X]:(curious(X)=>(rich(X)<~>~generous(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)&tall(X))=>(patient(X)|~calm(X))))&
(![X]:((kind(X)&funny(X))<=>humble(X)))&
(((~curious(fred)&~brave(fred)))<=>(?[X]:((creative(X)|~rich(X)))))&
((?[X]:((old(X)|strong(X))))=>(?[X]:(~rich(X))))&
(((brave(mary)<~>~strong(mary)))<=>((~happy(mary)<~>curious(mary))))&
(((~generous(fred)&~curious(fred)))=>((~brave(susan)|creative(susan))))&
(![X]:((~curious(X)&~tall(X))<=>(happy(X)|patient(X))))&
((?[X]:((brave(X)|creative(X))))=>((~quiet(paul)&creative(paul))))&
(![X]:((~happy(X)&creative(X))<=>(~tall(X)|calm(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|old(X)))) | brave(fred) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1861776683100149408279253
% SZS output start Proof for 1861776683100149408279253
10. (~brave(fred) & ~curious(fred)) <=> ? [X0] : (~rich(X0) | creative(X0)) [input p9]
15. ? [X0] : (creative(X0) | brave(X0)) => (creative(paul) & ~quiet(paul)) [input p14]
21. brave(fred) [input hypothesis]
34. (creative(paul) & ~quiet(paul)) | ! [X0] : (~creative(X0) & ~brave(X0)) [ennf transformation 15]
54. ((~brave(fred) & ~curious(fred)) | ! [X0] : (rich(X0) & ~creative(X0))) & (? [X0] : (~rich(X0) | creative(X0)) | (brave(fred) | curious(fred))) [nnf transformation 10]
55. ((~brave(fred) & ~curious(fred)) | ! [X0] : (rich(X0) & ~creative(X0))) & (? [X0] : (~rich(X0) | creative(X0)) | brave(fred) | curious(fred)) [flattening 54]
56. ((~brave(fred) & ~curious(fred)) | ! [X0] : (rich(X0) & ~creative(X0))) & (? [X1] : (~rich(X1) | creative(X1)) | brave(fred) | curious(fred)) [rectify 55]
57. ? [X1] : (~rich(X1) | creative(X1)) => (~rich(sK3) | creative(sK3)) [choice axiom]
58. ((~brave(fred) & ~curious(fred)) | ! [X0] : (rich(X0) & ~creative(X0))) & ((~rich(sK3) | creative(sK3)) | brave(fred) | curious(fred)) [skolemisation 56,57]
104. ~brave(fred) | ~creative(X0) [cnf transformation 58]
124. creative(paul) | ~brave(X0) [cnf transformation 34]
137. brave(fred) [cnf transformation 21]
209. 17 <=> brave(fred) [avatar definition]
210. brave(fred) <- (17) [avatar component clause 209]
214. 18 <=> ! [X0] : ~creative(X0) [avatar definition]
215. ~creative(X0) <- (18) [avatar component clause 214]
216. 18 | ~17 [avatar split clause 104,209,214]
275. 30 <=> creative(paul) [avatar definition]
277. creative(paul) <- (30) [avatar component clause 275]
280. 31 <=> ! [X0] : ~brave(X0) [avatar definition]
281. ~brave(X0) <- (31) [avatar component clause 280]
282. 31 | 30 [avatar split clause 124,275,280]
326. 17 [avatar split clause 137,209]
335. $false <- (18, 30) [resolution 277,215]
336. ~18 | ~30 [avatar contradiction clause 335]
337. $false <- (17, 31) [resolution 281,210]
338. ~17 | ~31 [avatar contradiction clause 337]
339. $false [avatar sat refutation 216,282,326,336,338]
% SZS output end Proof for 1861776683100149408279253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or brave.
Alice is either tall or kind.
Mary is brave or not quiet.
Someone is tall. | Alice is calm. | neutral | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
((tall(alice)<~>kind(alice)))&
((brave(mary)|~quiet(mary)))&
(?[X]:(tall(X))) | calm(alice) | [] | null | 0 |
If someone is not calm or not generous then fred is both not creative and quiet and vice versa.
If lucy is both old and humble then lucy is quiet or not kind.
Everyone who is both not kind and calm is not old or rich and vice versa.
If someone is both generous and not humble then fred is brave or old.
Everyone who is rich is both happy and not rich and vice versa.
If john is both not humble and tall then mary is humble.
Everyone who is both not quiet and wise is both generous and tall.
Everyone who is curious is both not kind and not calm and vice versa.
Everyone who is either strong or old is not funny.
Everyone who is either not wise or brave is both not brave and funny.
If someone is not wise or not quiet then someone is either not wise or strong.
Everyone who is either not calm or not funny is strong.
If lucy is brave or humble then someone is not generous or humble and vice versa.
Everyone who is patient or not old is both not quiet and tall.
Everyone who is rich is strong or not strong.
If mary is both calm and not creative then susan is both old and not generous.
Someone is not rich or old.
Lucy is either humble or curious.
John is not brave or not rich.
Someone is both humble and not creative.
Alice is not old or not quiet.
Someone is either not curious or not strong.
Someone is not curious or not strong.
Fred is either old or not happy. | Lucy is rich. | contradiction | ((?[X]:((~calm(X)|~generous(X))))<=>((~creative(fred)&quiet(fred))))&
(((old(lucy)&humble(lucy)))=>((quiet(lucy)|~kind(lucy))))&
(![X]:((~kind(X)&calm(X))<=>(~old(X)|rich(X))))&
((?[X]:((generous(X)&~humble(X))))=>((brave(fred)|old(fred))))&
(![X]:(rich(X)<=>(happy(X)&~rich(X))))&
(((~humble(john)&tall(john)))=>(humble(mary)))&
(![X]:((~quiet(X)&wise(X))=>(generous(X)&tall(X))))&
(![X]:(curious(X)<=>(~kind(X)&~calm(X))))&
(![X]:((strong(X)<~>old(X))=>~funny(X)))&
(![X]:((~wise(X)<~>brave(X))=>(~brave(X)&funny(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((~calm(X)<~>~funny(X))=>strong(X)))&
(((brave(lucy)|humble(lucy)))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((patient(X)|~old(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>(strong(X)|~strong(X))))&
(((calm(mary)&~creative(mary)))=>((old(susan)&~generous(susan))))&
(?[X]:((~rich(X)|old(X))))&
((humble(lucy)<~>curious(lucy)))&
((~brave(john)|~rich(john)))&
(?[X]:((humble(X)&~creative(X))))&
((~old(alice)|~quiet(alice)))&
(?[X]:((~curious(X)<~>~strong(X))))&
(?[X]:((~curious(X)|~strong(X))))&
((old(fred)<~>~happy(fred))) | rich(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3992576934071355785790814
% SZS output start Proof for 3992576934071355785790814
5. ! [X0] : (rich(X0) <=> (~rich(X0) & happy(X0))) [input p4]
25. rich(lucy) [input hypothesis]
52. ! [X0] : ((rich(X0) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | ~rich(X0))) [nnf transformation 5]
53. ! [X0] : ((rich(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | ~rich(X0))) [flattening 52]
92. ~rich(X0) | ~rich(X0) [cnf transformation 53]
133. rich(lucy) [cnf transformation 25]
135. ~rich(X0) [duplicate literal removal 92]
293. $false [subsumption resolution 133,135]
% SZS output end Proof for 3992576934071355785790814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or not creative then someone is both generous and not strong and vice versa. If mary is not curious then someone is not wise. Everyone who is both curious and not old is both not happy and not strong. If someone is both not funny and not humble then lucy is both patient and strong and vice versa. If paul is patient or tall then someone is both rich and funny. Everyone who is both rich and not strong is both not strong and funny. Everyone who is either not old or not kind is both not old and brave. Everyone who is not humble or not wise is tall or not old. Everyone who is wise is either not creative or not tall. Everyone who is not old or brave is both not funny and not old. Everyone who is both not curious and not generous is not curious and vice versa. Everyone who is not brave is not curious or not old and vice versa. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. Someone is either not humble or creative. Someone is both patient and not old. Alice is either rich or not happy. Paul is wise. Someone is either quiet or brave. Alice is not patient. Someone is either funny or not kind. Someone is both old and wise. | Alice is not happy. | contradiction | ((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((~curious(mary))=>(?[X]:(~wise(X))))&
(![X]:((curious(X)&~old(X))=>(~happy(X)&~strong(X))))&
((?[X]:((~funny(X)&~humble(X))))<=>((patient(lucy)&strong(lucy))))&
(((patient(paul)|tall(paul)))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((rich(X)&~strong(X))=>(~strong(X)&funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~old(X)&brave(X))))&
(![X]:((~humble(X)|~wise(X))=>(tall(X)|~old(X))))&
(![X]:(wise(X)=>(~creative(X)<~>~tall(X))))&
(![X]:((~old(X)|brave(X))=>(~funny(X)&~old(X))))&
(![X]:((~curious(X)&~generous(X))<=>~curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(![X]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:((patient(X)&~old(X))))&
((rich(alice)<~>~happy(alice)))&
(wise(paul))&
(?[X]:((quiet(X)<~>brave(X))))&
(~patient(alice))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((old(X)&wise(X)))) | ~happy(alice) | [
"p6",
"p9",
"p11",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2285984181810895778868726
% SZS output start Proof for 2285984181810895778868726
7. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (brave(X0) & ~old(X0))) [input p6]
10. ! [X0] : ((brave(X0) | ~old(X0)) => (~old(X0) & ~funny(X0))) [input p9]
12. ! [X0] : (~brave(X0) <=> (~old(X0) | ~curious(X0))) [input p11]
15. ! [X0] : ((patient(X0) <~> ~creative(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((creative(X0) <~> happy(X0)) <=> (brave(X0) <~> ~kind(X0))) [input p15]
22. ~patient(alice) [input p21]
25. ~happy(alice) [input hypothesis]
34. ! [X0] : ((brave(X0) & ~old(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 7]
38. ! [X0] : ((~old(X0) & ~funny(X0)) | (~brave(X0) & old(X0))) [ennf transformation 10]
54. ! [X0] : ((brave(X0) & ~old(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 34]
58. ! [X0] : ((~brave(X0) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 12]
59. ! [X0] : ((~brave(X0) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | brave(X0))) [flattening 58]
66. ! [X0] : ((((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | old(X0)) & (~old(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0))))) [nnf transformation 15]
67. ! [X0] : ((((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))))) [nnf transformation 16]
102. ~old(X0) | ~old(X0) | kind(X0) [cnf transformation 54]
103. ~kind(X0) | brave(X0) | old(X0) [cnf transformation 54]
112. ~brave(X0) | ~old(X0) [cnf transformation 38]
118. ~brave(X0) | old(X0) [cnf transformation 59]
126. ~old(X0) | patient(X0) | creative(X0) [cnf transformation 66]
127. ~creative(X0) | patient(X0) | old(X0) [cnf transformation 66]
129. ~kind(X0) | brave(X0) | happy(X0) | ~creative(X0) [cnf transformation 67]
134. happy(X0) | creative(X0) | brave(X0) | kind(X0) [cnf transformation 67]
146. ~patient(alice) [cnf transformation 22]
151. ~happy(alice) [cnf transformation 25]
152. ~old(X0) | kind(X0) [duplicate literal removal 102]
236. ~brave(X0) [subsumption resolution 118,112]
252. kind(X0) | creative(X0) | happy(X0) [subsumption resolution 134,236]
254. ~kind(X0) | happy(X0) | ~creative(X0) [subsumption resolution 129,236]
270. 25 <=> happy(alice) [avatar definition]
271. ~happy(alice) <- (~25) [avatar component clause 270]
286. ~25 [avatar split clause 151,270]
365. creative(X1) | happy(X1) | brave(X1) | old(X1) [resolution 252,103]
376. happy(X1) | creative(X1) | old(X1) [subsumption resolution 365,236]
478. 48 <=> creative(alice) [avatar definition]
480. creative(alice) <- (48) [avatar component clause 478]
484. creative(alice) | old(alice) <- (~25) [resolution 376,271]
491. 49 <=> old(alice) [avatar definition]
493. old(alice) <- (49) [avatar component clause 491]
494. 49 | 48 | 25 [avatar split clause 484,270,478,491]
551. patient(alice) | old(alice) <- (48) [resolution 480,127]
553. old(alice) <- (48) [subsumption resolution 551,146]
554. 49 | ~48 [avatar split clause 553,478,491]
556. patient(alice) | creative(alice) <- (49) [resolution 493,126]
560. kind(alice) <- (49) [resolution 493,152]
681. happy(alice) | ~creative(alice) <- (49) [resolution 560,254]
685. ~creative(alice) <- (~25, 49) [subsumption resolution 681,271]
688. ~48 | 25 | ~49 [avatar split clause 685,491,270,478]
689. creative(alice) <- (49) [subsumption resolution 556,146]
690. 48 | ~49 [avatar split clause 689,491,478]
692. $false [avatar sat refutation 286,494,554,688,690]
% SZS output end Proof for 2285984181810895778868726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or strong is either not generous or generous and vice versa. If susan is creative or generous then someone is not kind and vice versa. Everyone who is not quiet is either not kind or not happy and vice versa. Everyone who is not tall is either not funny or not rich. If alice is tall or happy then someone is either not patient or creative. Everyone who is rich or patient is both humble and creative and vice versa. If someone is either not funny or generous then john is both not rich and not generous. If someone is rich then mary is either generous or calm. Everyone who is both not brave and tall is quiet or not quiet and vice versa. Everyone who is quiet is not strong and vice versa. Everyone who is not curious or not brave is both not rich and not curious and vice versa. Everyone who is both calm and patient is not wise and vice versa. Everyone who is either not calm or generous is rich. Everyone who is both calm and old is either not generous or not old. If someone is humble or brave then someone is calm. Someone is not wise or curious. Someone is patient or not generous. Mary is either not patient or quiet. Someone is either not humble or not curious. Someone is both wise and not patient. | Susan is not patient. | neutral | (![X]:((rich(X)<~>strong(X))<=>(~generous(X)<~>generous(X))))&
(((creative(susan)|generous(susan)))<=>(?[X]:(~kind(X))))&
(![X]:(~quiet(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:(~tall(X)=>(~funny(X)<~>~rich(X))))&
(((tall(alice)|happy(alice)))=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:((rich(X)|patient(X))<=>(humble(X)&creative(X))))&
((?[X]:((~funny(X)<~>generous(X))))=>((~rich(john)&~generous(john))))&
((?[X]:(rich(X)))=>((generous(mary)<~>calm(mary))))&
(![X]:((~brave(X)&tall(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(quiet(X)<=>~strong(X)))&
(![X]:((~curious(X)|~brave(X))<=>(~rich(X)&~curious(X))))&
(![X]:((calm(X)&patient(X))<=>~wise(X)))&
(![X]:((~calm(X)<~>generous(X))=>rich(X)))&
(![X]:((calm(X)&old(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(calm(X))))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((patient(X)|~generous(X))))&
((~patient(mary)<~>quiet(mary)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((wise(X)&~patient(X)))) | ~patient(susan) | [] | null | 0 |
If john is both not generous and not rich then fred is not calm or kind and vice versa. Everyone who is either not creative or creative is both brave and funny and vice versa. Everyone who is not brave or not strong is wise or not creative. Everyone who is either not quiet or not brave is wise and vice versa. Everyone who is not kind is either calm or not calm and vice versa. Everyone who is curious or strong is not funny or not kind and vice versa. Everyone who is both not generous and strong is both curious and wise and vice versa. If someone is both not creative and strong then fred is both old and not happy and vice versa. Everyone who is both not tall and happy is not kind and vice versa. Everyone who is not funny or strong is either not tall or brave. Everyone who is not quiet or not tall is not happy or rich and vice versa. If mary is not brave then paul is not humble. If mary is kind or not humble then someone is not rich. Everyone who is not kind is not generous or not strong. If someone is both patient and generous then susan is either not funny or kind and vice versa. Everyone who is not strong is funny or not humble. Someone is happy. Someone is not kind. Someone is rich or not kind. Someone is rich. Susan is not patient or not old. | Paul is not strong. | entailment | (((~generous(john)&~rich(john)))<=>((~calm(fred)|kind(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(![X]:((~funny(X)|strong(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(~happy(X)|rich(X))))&
((~brave(mary))=>(~humble(paul)))&
(((kind(mary)|~humble(mary)))=>(?[X]:(~rich(X))))&
(![X]:(~kind(X)=>(~generous(X)|~strong(X))))&
((?[X]:((patient(X)&generous(X))))<=>((~funny(susan)<~>kind(susan))))&
(![X]:(~strong(X)=>(funny(X)|~humble(X))))&
(?[X]:(happy(X)))&
(?[X]:(~kind(X)))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:(rich(X)))&
((~patient(susan)|~old(susan))) | ~strong(paul) | [
"p1",
"p4",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3797167441814289614331758
% SZS output start Proof for 3797167441814289614331758
2. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p1]
5. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p4]
9. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p8]
10. ! [X0] : ((strong(X0) | ~funny(X0)) => (~tall(X0) <~> brave(X0))) [input p9]
22. strong(paul) [input hypothesis]
25. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 10]
34. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 2]
35. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 34]
37. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 5]
47. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 9]
48. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 47]
49. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~strong(X0) & funny(X0))) [nnf transformation 25]
71. brave(X0) | creative(X0) | creative(X0) [cnf transformation 35]
72. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 35]
85. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
86. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 37]
100. ~tall(X0) | kind(X0) [cnf transformation 48]
105. ~brave(X0) | tall(X0) | ~strong(X0) [cnf transformation 49]
126. strong(paul) [cnf transformation 22]
127. ~kind(X0) | ~calm(X0) [duplicate literal removal 85]
128. ~kind(X0) | calm(X0) [duplicate literal removal 86]
129. brave(X0) | creative(X0) [duplicate literal removal 71]
130. brave(X0) | ~creative(X0) [duplicate literal removal 72]
155. brave(X0) [subsumption resolution 129,130]
158. ~kind(X0) [subsumption resolution 127,128]
186. ~tall(X0) [subsumption resolution 100,158]
187. tall(X0) | ~strong(X0) [subsumption resolution 105,155]
188. ~strong(X0) [subsumption resolution 187,186]
203. $false [subsumption resolution 126,188]
% SZS output end Proof for 3797167441814289614331758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not calm is not humble. Everyone who is not generous is not patient. Everyone who is both rich and kind is not curious and vice versa. Everyone who is calm is funny. If someone is not generous or patient then someone is curious and vice versa. If someone is either tall or not tall then susan is not wise or strong. Everyone who is either brave or curious is either not creative or not kind. If fred is either not brave or not curious then someone is both strong and tall and vice versa. If paul is not humble or not tall then someone is both generous and funny and vice versa. Everyone who is not tall or patient is either not funny or not humble and vice versa. Everyone who is not curious is either not generous or not patient. Everyone who is patient is either not brave or not old. If someone is not funny then alice is both funny and not kind and vice versa. If mary is both not wise and kind then john is both calm and not funny. If someone is either creative or not strong then someone is not funny or creative and vice versa. Everyone who is both tall and patient is curious and vice versa. Susan is not kind or humble. Someone is both curious and wise. Paul is happy or not quiet. Mary is either not generous or not old. Mary is either humble or not funny. Alice is not happy or old. Someone is calm. John is not brave. | Mary is not rich. | contradiction | (![X]:((rich(X)&~calm(X))=>~humble(X)))&
(![X]:(~generous(X)=>~patient(X)))&
(![X]:((rich(X)&kind(X))<=>~curious(X)))&
(![X]:(calm(X)=>funny(X)))&
((?[X]:((~generous(X)|patient(X))))<=>(?[X]:(curious(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>((~wise(susan)|strong(susan))))&
(![X]:((brave(X)<~>curious(X))=>(~creative(X)<~>~kind(X))))&
(((~brave(fred)<~>~curious(fred)))<=>(?[X]:((strong(X)&tall(X)))))&
(((~humble(paul)|~tall(paul)))<=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((~tall(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~patient(X))))&
(![X]:(patient(X)=>(~brave(X)<~>~old(X))))&
((?[X]:(~funny(X)))<=>((funny(alice)&~kind(alice))))&
(((~wise(mary)&kind(mary)))=>((calm(john)&~funny(john))))&
((?[X]:((creative(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|creative(X)))))&
(![X]:((tall(X)&patient(X))<=>curious(X)))&
((~kind(susan)|humble(susan)))&
(?[X]:((curious(X)&wise(X))))&
((happy(paul)|~quiet(paul)))&
((~generous(mary)<~>~old(mary)))&
((humble(mary)<~>~funny(mary)))&
((~happy(alice)|old(alice)))&
(?[X]:(calm(X)))&
(~brave(john)) | ~rich(mary) | [
"p2",
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5246255592126780296411104
% SZS output start Proof for 5246255592126780296411104
3. ! [X0] : ((kind(X0) & rich(X0)) <=> ~curious(X0)) [input p2]
10. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (~funny(X0) <~> ~humble(X0))) [input p9]
16. ! [X0] : ((patient(X0) & tall(X0)) <=> curious(X0)) [input p15]
21. humble(mary) <~> ~funny(mary) [input p20]
25. ~rich(mary) [input hypothesis]
41. ! [X0] : (((kind(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) | ~rich(X0)))) [nnf transformation 3]
42. ! [X0] : (((kind(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | ~kind(X0) | ~rich(X0))) [flattening 41]
59. ! [X0] : (((patient(X0) | ~tall(X0)) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) & (((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | (~patient(X0) & tall(X0)))) [nnf transformation 10]
60. ! [X0] : ((patient(X0) | ~tall(X0) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) & (((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | (~patient(X0) & tall(X0)))) [flattening 59]
73. ! [X0] : (((patient(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | (~patient(X0) | ~tall(X0)))) [nnf transformation 16]
74. ! [X0] : (((patient(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | ~patient(X0) | ~tall(X0))) [flattening 73]
78. (funny(mary) | ~humble(mary)) & (~funny(mary) | humble(mary)) [nnf transformation 21]
84. curious(X0) | rich(X0) [cnf transformation 42]
108. ~funny(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 60]
110. ~patient(X0) | funny(X0) | humble(X0) [cnf transformation 60]
130. ~curious(X0) | patient(X0) [cnf transformation 74]
136. ~funny(mary) | humble(mary) [cnf transformation 78]
137. funny(mary) | ~humble(mary) [cnf transformation 78]
140. ~rich(mary) [cnf transformation 25]
323. 40 <=> humble(mary) [avatar definition]
324. humble(mary) <- (40) [avatar component clause 323]
325. ~humble(mary) <- (~40) [avatar component clause 323]
327. 41 <=> funny(mary) [avatar definition]
328. ~funny(mary) <- (~41) [avatar component clause 327]
329. funny(mary) <- (41) [avatar component clause 327]
330. ~40 | 41 [avatar split clause 137,327,323]
331. 40 | ~41 [avatar split clause 136,327,323]
342. patient(X1) | rich(X1) [resolution 130,84]
552. funny(X1) | rich(X1) | humble(X1) [resolution 342,110]
740. rich(mary) | humble(mary) <- (~41) [resolution 552,328]
745. humble(mary) <- (~41) [subsumption resolution 740,140]
746. $false <- (~40, ~41) [subsumption resolution 745,325]
747. 40 | 41 [avatar contradiction clause 746]
758. ~humble(mary) | ~patient(mary) <- (41) [resolution 329,108]
760. ~patient(mary) <- (40, 41) [subsumption resolution 758,324]
768. rich(mary) <- (40, 41) [resolution 760,342]
769. $false <- (40, 41) [subsumption resolution 768,140]
770. ~40 | ~41 [avatar contradiction clause 769]
771. $false [avatar sat refutation 330,331,747,770]
% SZS output end Proof for 5246255592126780296411104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and creative then someone is old or kind and vice versa.
If someone is either not patient or strong then someone is not humble.
Everyone who is not funny or happy is either not kind or strong.
Everyone who is both happy and tall is either not kind or old and vice versa.
Everyone who is not brave is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is happy. | contradiction | ((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((old(X)|kind(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)|happy(X))=>(~kind(X)<~>strong(X))))&
(![X]:((happy(X)&tall(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>~calm(X)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | happy(paul) | [
"p0",
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6592926457631955726614650
% SZS output start Proof for 6592926457631955726614650
1. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (kind(X0) | old(X0)) [input p0]
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
15. ? [X0] : creative(X0) <=> (rich(paul) & brave(paul)) [input p14]
20. ? [X0] : old(X0) [input p19]
24. happy(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (kind(X1) | old(X1)) [rectify 1]
40. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X1] : (kind(X1) | old(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X2] : (kind(X2) | old(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 40]
42. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
43. ? [X2] : (kind(X2) | old(X2)) => (kind(sK1) | old(sK1)) [choice axiom]
44. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~kind(X1) & ~old(X1))) & ((kind(sK1) | old(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 41,43,42]
54. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
55. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 54]
67. (? [X0] : creative(X0) | (~rich(paul) | ~brave(paul))) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [nnf transformation 15]
68. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [flattening 67]
69. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [rectify 68]
70. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
71. (creative(sK6) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [skolemisation 69,70]
78. ? [X0] : old(X0) => old(sK10) [choice axiom]
79. old(sK10) [skolemisation 20,78]
88. creative(sK0) | ~old(X1) [cnf transformation 44]
111. ~brave(X0) | ~happy(X0) [cnf transformation 55]
129. brave(paul) | ~creative(X1) [cnf transformation 71]
137. old(sK10) [cnf transformation 79]
142. happy(paul) [cnf transformation 24]
147. 2 <=> creative(sK0) [avatar definition]
149. creative(sK0) <- (2) [avatar component clause 147]
152. 3 <=> ! [X1] : ~old(X1) [avatar definition]
153. ~old(X1) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 88,147,152]
286. 33 <=> brave(paul) [avatar definition]
287. brave(paul) <- (33) [avatar component clause 286]
299. 36 <=> ! [X1] : ~creative(X1) [avatar definition]
300. ~creative(X1) <- (36) [avatar component clause 299]
302. 36 | 33 [avatar split clause 129,286,299]
369. ~happy(paul) <- (33) [resolution 111,287]
370. $false <- (33) [subsumption resolution 369,142]
371. ~33 [avatar contradiction clause 370]
373. $false <- (2, 36) [resolution 300,149]
378. ~2 | ~36 [avatar contradiction clause 373]
379. $false <- (3) [resolution 153,137]
382. ~3 [avatar contradiction clause 379]
383. $false [avatar sat refutation 154,302,371,378,382]
% SZS output end Proof for 6592926457631955726614650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not humble is curious or not wise and vice versa.
Everyone who is curious or wise is both not patient and patient and vice versa.
Everyone who is both rich and patient is strong or old and vice versa.
Everyone who is old is both not curious and generous and vice versa.
If lucy is both patient and generous then paul is either not humble or creative.
If someone is either not old or not strong then someone is not brave and vice versa.
If someone is not rich then susan is generous and vice versa.
Everyone who is generous is funny.
Everyone who is wise is both not kind and brave.
If susan is either patient or not rich then mary is patient or not curious and vice versa.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is kind is either rich or quiet and vice versa.
Someone is strong.
Someone is either rich or not strong.
John is either not happy or funny.
Fred is not tall.
John is not quiet or not brave.
Someone is not wise or curious.
Someone is both humble and not wise.
Someone is both not wise and humble. | Alice is not generous. | contradiction | (![X]:((funny(X)<~>~humble(X))<=>(curious(X)|~wise(X))))&
(![X]:((curious(X)|wise(X))<=>(~patient(X)&patient(X))))&
(![X]:((rich(X)&patient(X))<=>(strong(X)|old(X))))&
(![X]:(old(X)<=>(~curious(X)&generous(X))))&
(((patient(lucy)&generous(lucy)))=>((~humble(paul)<~>creative(paul))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~rich(X)))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(((patient(susan)<~>~rich(susan)))<=>((patient(mary)|~curious(mary))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(kind(X)<=>(rich(X)<~>quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)<~>~strong(X))))&
((~happy(john)<~>funny(john)))&
(~tall(fred))&
((~quiet(john)|~brave(john)))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((humble(X)&~wise(X))))&
(?[X]:((~wise(X)&humble(X)))) | ~generous(alice) | [
"p2",
"p3",
"p10",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6761635064423936120274571
% SZS output start Proof for 6761635064423936120274571
3. ! [X0] : ((patient(X0) & rich(X0)) <=> (old(X0) | strong(X0))) [input p2]
4. ! [X0] : (old(X0) <=> (generous(X0) & ~curious(X0))) [input p3]
11. ? [X0] : (happy(X0) | ~strong(X0)) <=> (~creative(alice) & old(alice)) [input p10]
14. ! [X0] : ((funny(X0) | ~rich(X0)) <=> (~quiet(X0) | ~kind(X0))) [input p13]
15. ! [X0] : (kind(X0) <=> (rich(X0) <~> quiet(X0))) [input p14]
18. ~happy(john) <~> funny(john) [input p17]
24. ~generous(alice) [input hypothesis]
37. ! [X0] : (((patient(X0) & rich(X0)) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | (~patient(X0) | ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : (((patient(X0) & rich(X0)) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | ~patient(X0) | ~rich(X0))) [flattening 37]
39. ! [X0] : ((old(X0) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | ~old(X0))) [nnf transformation 4]
40. ! [X0] : ((old(X0) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | ~old(X0))) [flattening 39]
53. (? [X0] : (happy(X0) | ~strong(X0)) | (creative(alice) | ~old(alice))) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [nnf transformation 11]
54. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [flattening 53]
55. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [rectify 54]
56. ? [X0] : (happy(X0) | ~strong(X0)) => (happy(sK3) | ~strong(sK3)) [choice axiom]
57. ((happy(sK3) | ~strong(sK3)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [skolemisation 55,56]
63. ! [X0] : (((funny(X0) | ~rich(X0)) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | (~funny(X0) & rich(X0)))) [nnf transformation 14]
64. ! [X0] : ((funny(X0) | ~rich(X0) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | (~funny(X0) & rich(X0)))) [flattening 63]
65. ! [X0] : ((kind(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~kind(X0))) [nnf transformation 15]
71. (~funny(john) | happy(john)) & (funny(john) | ~happy(john)) [nnf transformation 18]
90. ~strong(X0) | rich(X0) [cnf transformation 38]
95. ~old(X0) | generous(X0) [cnf transformation 40]
114. old(alice) | strong(X1) [cnf transformation 57]
115. old(alice) | ~happy(X1) [cnf transformation 57]
127. ~quiet(X0) | ~kind(X0) | rich(X0) [cnf transformation 64]
129. ~rich(X0) | funny(X0) | kind(X0) [cnf transformation 64]
130. ~rich(X0) | funny(X0) | quiet(X0) [cnf transformation 64]
132. ~quiet(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 65]
139. ~funny(john) | happy(john) [cnf transformation 71]
146. ~generous(alice) [cnf transformation 24]
203. 13 <=> ! [X1] : rich(X1) [avatar definition]
204. rich(X1) <- (13) [avatar component clause 203]
225. 17 <=> old(alice) [avatar definition]
226. old(alice) <- (17) [avatar component clause 225]
242. 21 <=> ! [X1] : ~happy(X1) [avatar definition]
243. ~happy(X1) <- (21) [avatar component clause 242]
246. 22 <=> ! [X1] : strong(X1) [avatar definition]
247. strong(X1) <- (22) [avatar component clause 246]
249. 21 | 17 [avatar split clause 115,225,242]
250. 22 | 17 [avatar split clause 114,225,246]
261. ~quiet(X0) | ~kind(X0) [subsumption resolution 132,127]
273. 27 <=> happy(john) [avatar definition]
275. happy(john) <- (27) [avatar component clause 273]
277. 28 <=> funny(john) [avatar definition]
279. ~funny(john) <- (~28) [avatar component clause 277]
280. 27 | ~28 [avatar split clause 139,277,273]
300. generous(alice) <- (17) [resolution 95,226]
301. $false <- (17) [subsumption resolution 300,146]
302. ~17 [avatar contradiction clause 301]
306. rich(X1) <- (22) [resolution 247,90]
309. 13 | ~22 [avatar split clause 306,246,203]
329. kind(X0) | funny(X0) <- (13) [resolution 129,204]
341. quiet(X0) | funny(X0) <- (13) [resolution 130,204]
355. funny(X2) | ~kind(X2) <- (13) [resolution 341,261]
357. funny(X2) <- (13) [subsumption resolution 355,329]
360. $false <- (13, ~28) [resolution 357,279]
362. ~13 | 28 [avatar contradiction clause 360]
364. $false <- (21, 27) [subsumption resolution 275,243]
365. ~21 | ~27 [avatar contradiction clause 364]
366. $false [avatar sat refutation 249,250,280,302,309,362,365]
% SZS output end Proof for 6761635064423936120274571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or calm is either not wise or brave.
Everyone who is both not quiet and funny is curious.
Everyone who is strong is humble and vice versa.
If alice is quiet or generous then lucy is both rich and wise.
Everyone who is both not kind and happy is both not old and not brave and vice versa.
If paul is not tall then fred is either kind or not calm.
Everyone who is either not humble or not happy is rich or not rich.
Everyone who is strong is both not old and not funny and vice versa.
If someone is creative or quiet then someone is old or funny.
Everyone who is either not patient or not tall is not brave and vice versa.
Everyone who is quiet is either humble or calm.
Everyone who is not strong or generous is not tall.
If someone is either not humble or not kind then someone is not brave.
Everyone who is brave or not humble is both quiet and strong and vice versa.
Everyone who is both tall and calm is kind or tall.
Everyone who is patient or creative is not strong.
Someone is not rich.
Someone is either not calm or funny.
Fred is both not kind and not curious.
Susan is not calm or not curious. | Susan is calm. | neutral | (![X]:((~happy(X)|calm(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~quiet(X)&funny(X))=>curious(X)))&
(![X]:(strong(X)<=>humble(X)))&
(((quiet(alice)|generous(alice)))=>((rich(lucy)&wise(lucy))))&
(![X]:((~kind(X)&happy(X))<=>(~old(X)&~brave(X))))&
((~tall(paul))=>((kind(fred)<~>~calm(fred))))&
(![X]:((~humble(X)<~>~happy(X))=>(rich(X)|~rich(X))))&
(![X]:(strong(X)<=>(~old(X)&~funny(X))))&
((?[X]:((creative(X)|quiet(X))))=>(?[X]:((old(X)|funny(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>~brave(X)))&
(![X]:(quiet(X)=>(humble(X)<~>calm(X))))&
(![X]:((~strong(X)|generous(X))=>~tall(X)))&
((?[X]:((~humble(X)<~>~kind(X))))=>(?[X]:(~brave(X))))&
(![X]:((brave(X)|~humble(X))<=>(quiet(X)&strong(X))))&
(![X]:((tall(X)&calm(X))=>(kind(X)|tall(X))))&
(![X]:((patient(X)|creative(X))=>~strong(X)))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)<~>funny(X))))&
((~kind(fred)&~curious(fred)))&
((~calm(susan)|~curious(susan))) | calm(susan) | [] | null | 0 |
If someone is curious then paul is both strong and wise and vice versa. Everyone who is both not calm and not funny is not kind or calm. If someone is creative or not wise then john is patient. If fred is kind or not happy then someone is not strong. If someone is not curious then someone is funny or not patient. If someone is not generous or strong then someone is creative. Everyone who is not generous is not calm or not strong and vice versa. If someone is generous then someone is not funny or not happy and vice versa. If paul is old or not brave then susan is calm and vice versa. If lucy is quiet or not humble then paul is either not wise or not quiet. If mary is funny or tall then someone is not funny and vice versa. Everyone who is either not wise or wise is not calm or rich and vice versa. Everyone who is both patient and generous is generous or humble. Everyone who is either not calm or wise is wise and vice versa. If fred is both not patient and patient then alice is either creative or not wise and vice versa. Everyone who is not happy is either brave or not brave. Fred is not creative or generous. Someone is not curious. Someone is either not strong or kind. Someone is either not kind or creative. Alice is both creative and brave. | Alice is not rich. | contradiction | ((?[X]:(curious(X)))<=>((strong(paul)&wise(paul))))&
(![X]:((~calm(X)&~funny(X))=>(~kind(X)|calm(X))))&
((?[X]:((creative(X)|~wise(X))))=>(patient(john)))&
(((kind(fred)|~happy(fred)))=>(?[X]:(~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)|~patient(X)))))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(creative(X))))&
(![X]:(~generous(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(((old(paul)|~brave(paul)))<=>(calm(susan)))&
(((quiet(lucy)|~humble(lucy)))=>((~wise(paul)<~>~quiet(paul))))&
(((funny(mary)|tall(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~calm(X)|rich(X))))&
(![X]:((patient(X)&generous(X))=>(generous(X)|humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>wise(X)))&
(((~patient(fred)&patient(fred)))<=>((creative(alice)<~>~wise(alice))))&
(![X]:(~happy(X)=>(brave(X)<~>~brave(X))))&
((~creative(fred)|generous(fred)))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((~kind(X)<~>creative(X))))&
((creative(alice)&brave(alice))) | ~rich(alice) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9120095521909737591349048
% SZS output start Proof for 9120095521909737591349048
12. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) | ~calm(X0))) [input p11]
14. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> wise(X0)) [input p13]
22. ~rich(alice) [input hypothesis]
64. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 12]
65. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 64]
66. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~wise(X0)) & (wise(X0) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 14]
103. rich(X0) | ~calm(X0) | wise(X0) | wise(X0) [cnf transformation 65]
104. rich(X0) | ~calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 65]
109. wise(X0) | wise(X0) | calm(X0) [cnf transformation 66]
112. ~wise(X0) | calm(X0) | ~wise(X0) [cnf transformation 66]
129. ~rich(alice) [cnf transformation 22]
130. wise(X0) | calm(X0) [duplicate literal removal 109]
131. ~wise(X0) | calm(X0) [duplicate literal removal 112]
132. rich(X0) | ~calm(X0) | wise(X0) [duplicate literal removal 103]
133. rich(X0) | ~calm(X0) | ~wise(X0) [duplicate literal removal 104]
267. ~calm(X0) | rich(X0) [subsumption resolution 132,133]
268. calm(X0) [subsumption resolution 130,131]
323. rich(X0) [resolution 267,268]
324. $false [resolution 323,129]
% SZS output end Proof for 9120095521909737591349048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not tall or curious then fred is both wise and patient and vice versa.
If alice is not funny then someone is both not happy and funny.
Everyone who is not funny is not tall.
If susan is not funny or tall then paul is not humble or strong and vice versa.
Everyone who is either not humble or not funny is not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
If john is both curious and not creative then someone is either creative or not kind.
Someone is either wise or not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is not creative or curious.
Someone is not tall or patient.
Mary is either not strong or generous. | Mary is not funny. | contradiction | (((~tall(lucy)|curious(lucy)))<=>((wise(fred)&patient(fred))))&
((~funny(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~funny(X)=>~tall(X)))&
(((~funny(susan)|tall(susan)))<=>((~humble(paul)|strong(paul))))&
(![X]:((~humble(X)<~>~funny(X))<=>~tall(X)))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:((~tall(X)|patient(X))))&
((~strong(mary)<~>generous(mary))) | ~funny(mary) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4328592379239027074823560
% SZS output start Proof for 4328592379239027074823560
3. ! [X0] : (~funny(X0) => ~tall(X0)) [input p2]
13. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & ~calm(X0))) [input p12]
23. ~funny(mary) [input hypothesis]
27. ! [X0] : (~tall(X0) | funny(X0)) [ennf transformation 3]
33. ! [X0] : ((tall(X0) & ~calm(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 13]
57. ! [X0] : ((tall(X0) & ~calm(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 33]
82. ~tall(X0) | funny(X0) [cnf transformation 27]
111. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
112. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
131. ~funny(mary) [cnf transformation 23]
134. tall(X0) | quiet(X0) [duplicate literal removal 111]
135. tall(X0) | ~quiet(X0) [duplicate literal removal 112]
267. tall(X0) [subsumption resolution 134,135]
311. funny(X0) [resolution 82,267]
312. $false [resolution 311,131]
% SZS output end Proof for 4328592379239027074823560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or funny then someone is happy or not quiet and vice versa. Everyone who is old is both brave and not patient and vice versa. Everyone who is strong or happy is both wise and not kind. If john is brave then someone is both not curious and tall. Everyone who is rich is either strong or brave. If someone is either not old or quiet then someone is either not kind or not patient and vice versa. Everyone who is generous or rich is not humble or generous. Everyone who is either not funny or not brave is either happy or quiet and vice versa. Everyone who is both curious and not wise is quiet or not funny. If someone is both not calm and calm then someone is either not funny or brave. Everyone who is curious is calm or not strong. If mary is either calm or tall then someone is either not patient or calm and vice versa. Everyone who is strong is both generous and tall and vice versa. Everyone who is either old or not tall is either not rich or funny and vice versa. If someone is quiet or brave then mary is not quiet. Everyone who is either tall or curious is not curious or creative. Alice is brave. Paul is not rich. Susan is both not patient and not funny. Someone is either curious or quiet. Someone is both curious and not creative. Someone is either old or not quiet. Susan is wise or not tall. | Mary is quiet. | contradiction | ((?[X]:((brave(X)<~>funny(X))))<=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:(old(X)<=>(brave(X)&~patient(X))))&
(![X]:((strong(X)|happy(X))=>(wise(X)&~kind(X))))&
((brave(john))=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:(rich(X)=>(strong(X)<~>brave(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((generous(X)|rich(X))=>(~humble(X)|generous(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(happy(X)<~>quiet(X))))&
(![X]:((curious(X)&~wise(X))=>(quiet(X)|~funny(X))))&
((?[X]:((~calm(X)&calm(X))))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:(curious(X)=>(calm(X)|~strong(X))))&
(((calm(mary)<~>tall(mary)))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(strong(X)<=>(generous(X)&tall(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((quiet(X)|brave(X))))=>(~quiet(mary)))&
(![X]:((tall(X)<~>curious(X))=>(~curious(X)|creative(X))))&
(brave(alice))&
(~rich(paul))&
((~patient(susan)&~funny(susan)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
((wise(susan)|~tall(susan))) | quiet(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5511155771891447516774124
% SZS output start Proof for 5511155771891447516774124
15. ? [X0] : (brave(X0) | quiet(X0)) => ~quiet(mary) [input p14]
24. quiet(mary) [input hypothesis]
38. ~quiet(mary) | ! [X0] : (~brave(X0) & ~quiet(X0)) [ennf transformation 15]
130. ~quiet(mary) | ~quiet(X0) [cnf transformation 38]
144. quiet(mary) [cnf transformation 24]
264. 27 <=> quiet(mary) [avatar definition]
265. quiet(mary) <- (27) [avatar component clause 264]
269. 28 <=> ! [X0] : ~quiet(X0) [avatar definition]
270. ~quiet(X0) <- (28) [avatar component clause 269]
271. 28 | ~27 [avatar split clause 130,264,269]
292. 27 [avatar split clause 144,264]
293. $false <- (27, 28) [subsumption resolution 265,270]
294. ~27 | ~28 [avatar contradiction clause 293]
297. $false [avatar sat refutation 271,292,294]
% SZS output end Proof for 5511155771891447516774124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not funny is happy or not patient and vice versa.
Everyone who is both wise and not kind is strong or not humble and vice versa.
Everyone who is either not generous or funny is either quiet or not rich.
If fred is both not calm and not kind then lucy is not happy or funny and vice versa.
If mary is both generous and not creative then paul is not tall or not funny.
If paul is either curious or quiet then someone is both not brave and creative.
Everyone who is both rich and not generous is both funny and not kind and vice versa.
If susan is not old then someone is both not tall and not wise and vice versa.
If someone is both not quiet and not happy then someone is either old or not wise and vice versa.
Everyone who is either not calm or strong is either not creative or not old.
If mary is not funny then susan is either not rich or patient.
If susan is curious then fred is either tall or rich and vice versa.
If someone is not curious or strong then someone is strong or not quiet.
If john is patient then someone is rich.
If someone is either not calm or not kind then fred is kind and vice versa.
Everyone who is both not humble and not tall is not old or strong.
Someone is wise.
Lucy is both not rich and creative.
Someone is humble.
Lucy is not calm.
Someone is strong.
Lucy is both quiet and curious.
Someone is calm.
Someone is either not kind or strong. | Lucy is not generous. | contradiction | (![X]:((~tall(X)|~funny(X))<=>(happy(X)|~patient(X))))&
(![X]:((wise(X)&~kind(X))<=>(strong(X)|~humble(X))))&
(![X]:((~generous(X)<~>funny(X))=>(quiet(X)<~>~rich(X))))&
(((~calm(fred)&~kind(fred)))<=>((~happy(lucy)|funny(lucy))))&
(((generous(mary)&~creative(mary)))=>((~tall(paul)|~funny(paul))))&
(((curious(paul)<~>quiet(paul)))=>(?[X]:((~brave(X)&creative(X)))))&
(![X]:((rich(X)&~generous(X))<=>(funny(X)&~kind(X))))&
((~old(susan))<=>(?[X]:((~tall(X)&~wise(X)))))&
((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:((old(X)<~>~wise(X)))))&
(![X]:((~calm(X)<~>strong(X))=>(~creative(X)<~>~old(X))))&
((~funny(mary))=>((~rich(susan)<~>patient(susan))))&
((curious(susan))<=>((tall(fred)<~>rich(fred))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:((strong(X)|~quiet(X)))))&
((patient(john))=>(?[X]:(rich(X))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(kind(fred)))&
(![X]:((~humble(X)&~tall(X))=>(~old(X)|strong(X))))&
(?[X]:(wise(X)))&
((~rich(lucy)&creative(lucy)))&
(?[X]:(humble(X)))&
(~calm(lucy))&
(?[X]:(strong(X)))&
((quiet(lucy)&curious(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~kind(X)<~>strong(X)))) | ~generous(lucy) | [
"p2",
"p3",
"p6",
"p14",
"p17",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6248688173407860463250110
% SZS output start Proof for 6248688173407860463250110
3. ! [X0] : ((~generous(X0) <~> funny(X0)) => (quiet(X0) <~> ~rich(X0))) [input p2]
4. (~kind(fred) & ~calm(fred)) <=> (funny(lucy) | ~happy(lucy)) [input p3]
7. ! [X0] : ((~generous(X0) & rich(X0)) <=> (~kind(X0) & funny(X0))) [input p6]
15. ? [X0] : (~calm(X0) <~> ~kind(X0)) <=> kind(fred) [input p14]
18. creative(lucy) & ~rich(lucy) [input p17]
20. ~calm(lucy) [input p19]
22. curious(lucy) & quiet(lucy) [input p21]
25. ~generous(lucy) [input hypothesis]
29. ! [X0] : ((quiet(X0) <~> ~rich(X0)) | (~generous(X0) <=> funny(X0))) [ennf transformation 3]
43. ! [X0] : (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ((~generous(X0) | ~funny(X0)) & (funny(X0) | generous(X0)))) [nnf transformation 29]
44. ((~kind(fred) & ~calm(fred)) | (~funny(lucy) & happy(lucy))) & ((funny(lucy) | ~happy(lucy)) | (kind(fred) | calm(fred))) [nnf transformation 4]
45. ((~kind(fred) & ~calm(fred)) | (~funny(lucy) & happy(lucy))) & (funny(lucy) | ~happy(lucy) | kind(fred) | calm(fred)) [flattening 44]
49. ! [X0] : (((~generous(X0) & rich(X0)) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | (generous(X0) | ~rich(X0)))) [nnf transformation 7]
50. ! [X0] : (((~generous(X0) & rich(X0)) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | generous(X0) | ~rich(X0))) [flattening 49]
68. (? [X0] : ((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~kind(fred)) & (kind(fred) | ! [X0] : ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) [nnf transformation 15]
69. (? [X0] : ((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~kind(fred)) & (kind(fred) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) [rectify 68]
70. ? [X0] : ((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) => ((kind(sK6) | calm(sK6)) & (~kind(sK6) | ~calm(sK6))) [choice axiom]
71. (((kind(sK6) | calm(sK6)) & (~kind(sK6) | ~calm(sK6))) | ~kind(fred)) & (kind(fred) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) [skolemisation 69,70]
94. ~quiet(X0) | rich(X0) | funny(X0) | generous(X0) [cnf transformation 43]
100. ~kind(fred) | ~funny(lucy) [cnf transformation 45]
106. ~funny(X0) | kind(X0) | rich(X0) [cnf transformation 50]
130. kind(fred) | ~kind(X1) | calm(X1) [cnf transformation 71]
136. ~rich(lucy) [cnf transformation 18]
139. ~calm(lucy) [cnf transformation 20]
141. quiet(lucy) [cnf transformation 22]
146. ~generous(lucy) [cnf transformation 25]
148. 1 <=> funny(lucy) [avatar definition]
149. funny(lucy) <- (1) [avatar component clause 148]
152. 2 <=> kind(fred) [avatar definition]
155. ~1 | ~2 [avatar split clause 100,152,148]
318. 38 <=> ! [X1] : (~kind(X1) | calm(X1)) [avatar definition]
319. ~kind(X1) | calm(X1) <- (38) [avatar component clause 318]
320. 38 | 2 [avatar split clause 130,152,318]
343. rich(lucy) | funny(lucy) | generous(lucy) [resolution 94,141]
344. funny(lucy) | generous(lucy) [subsumption resolution 343,136]
348. funny(lucy) [subsumption resolution 344,146]
349. 1 [avatar split clause 348,148]
355. kind(lucy) | rich(lucy) <- (1) [resolution 149,106]
357. kind(lucy) <- (1) [subsumption resolution 355,136]
363. calm(lucy) <- (1, 38) [resolution 357,319]
365. $false <- (1, 38) [subsumption resolution 363,139]
366. ~1 | ~38 [avatar contradiction clause 365]
367. $false [avatar sat refutation 155,320,349,366]
% SZS output end Proof for 6248688173407860463250110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and not generous is funny and vice versa.
If mary is curious or calm then alice is either not humble or not creative and vice versa.
If someone is not rich then fred is both not humble and old.
If someone is either not tall or quiet then fred is either not tall or tall and vice versa.
If susan is not strong then fred is curious and vice versa.
If mary is curious then alice is both patient and not kind.
If someone is not old then paul is creative or not quiet.
Everyone who is either strong or not humble is either not wise or not quiet.
Everyone who is not generous or curious is both not quiet and strong.
Everyone who is either creative or not strong is not kind or humble.
If alice is curious then someone is not wise or curious.
If someone is both kind and happy then someone is calm or wise.
Everyone who is rich is not humble or quiet and vice versa.
If someone is not tall or creative then fred is not calm and vice versa.
If lucy is not curious then someone is funny or not rich.
If someone is both not funny and wise then lucy is both not rich and rich and vice versa.
Lucy is either rich or creative.
Someone is either not humble or not wise.
Susan is both calm and not humble.
Lucy is brave.
Someone is either kind or humble.
Someone is both not curious and not humble.
Susan is quiet.
Alice is both not curious and strong. | Alice is not curious. | entailment | (![X]:((~creative(X)&~generous(X))<=>funny(X)))&
(((curious(mary)|calm(mary)))<=>((~humble(alice)<~>~creative(alice))))&
((?[X]:(~rich(X)))=>((~humble(fred)&old(fred))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>((~tall(fred)<~>tall(fred))))&
((~strong(susan))<=>(curious(fred)))&
((curious(mary))=>((patient(alice)&~kind(alice))))&
((?[X]:(~old(X)))=>((creative(paul)|~quiet(paul))))&
(![X]:((strong(X)<~>~humble(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~generous(X)|curious(X))=>(~quiet(X)&strong(X))))&
(![X]:((creative(X)<~>~strong(X))=>(~kind(X)|humble(X))))&
((curious(alice))=>(?[X]:((~wise(X)|curious(X)))))&
((?[X]:((kind(X)&happy(X))))=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(rich(X)<=>(~humble(X)|quiet(X))))&
((?[X]:((~tall(X)|creative(X))))<=>(~calm(fred)))&
((~curious(lucy))=>(?[X]:((funny(X)|~rich(X)))))&
((?[X]:((~funny(X)&wise(X))))<=>((~rich(lucy)&rich(lucy))))&
((rich(lucy)<~>creative(lucy)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((calm(susan)&~humble(susan)))&
(brave(lucy))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:((~curious(X)&~humble(X))))&
(quiet(susan))&
((~curious(alice)&strong(alice))) | ~curious(alice) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7885830755029288368857835
% SZS output start Proof for 7885830755029288368857835
24. strong(alice) & ~curious(alice) [input p23]
25. curious(alice) [input hypothesis]
129. ~curious(alice) [cnf transformation 24]
131. curious(alice) [cnf transformation 25]
198. 13 <=> curious(alice) [avatar definition]
279. ~13 [avatar split clause 129,198]
280. 13 [avatar split clause 131,198]
281. $false [avatar sat refutation 279,280]
% SZS output end Proof for 7885830755029288368857835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both tall and not funny and vice versa. Everyone who is either not funny or happy is creative or rich and vice versa. Everyone who is both kind and strong is either curious or not patient. Everyone who is not creative or not funny is either calm or wise and vice versa. If someone is both not kind and not humble then fred is both brave and not rich. If fred is both kind and creative then fred is not brave and vice versa. If lucy is not humble then someone is not rich or quiet. Everyone who is not brave is not curious and vice versa. Everyone who is not creative or not calm is not humble or quiet. If susan is either not calm or creative then someone is not humble or quiet and vice versa. Everyone who is both not quiet and not strong is not funny and vice versa. Everyone who is both not generous and not curious is brave and vice versa. Everyone who is both not tall and not quiet is both not quiet and not calm. If alice is not rich or creative then someone is not humble or not funny and vice versa. If paul is both not creative and wise then fred is not calm. If someone is creative then fred is either generous or not creative and vice versa. Fred is either not wise or not generous. Someone is either not wise or not humble. Someone is happy or wise. Someone is either humble or not quiet. Someone is not rich. Someone is either not brave or not creative. | Fred is not curious. | entailment | (![X]:(patient(X)<=>(tall(X)&~funny(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(creative(X)|rich(X))))&
(![X]:((kind(X)&strong(X))=>(curious(X)<~>~patient(X))))&
(![X]:((~creative(X)|~funny(X))<=>(calm(X)<~>wise(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((brave(fred)&~rich(fred))))&
(((kind(fred)&creative(fred)))<=>(~brave(fred)))&
((~humble(lucy))=>(?[X]:((~rich(X)|quiet(X)))))&
(![X]:(~brave(X)<=>~curious(X)))&
(![X]:((~creative(X)|~calm(X))=>(~humble(X)|quiet(X))))&
(((~calm(susan)<~>creative(susan)))<=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((~quiet(X)&~strong(X))<=>~funny(X)))&
(![X]:((~generous(X)&~curious(X))<=>brave(X)))&
(![X]:((~tall(X)&~quiet(X))=>(~quiet(X)&~calm(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((~humble(X)|~funny(X)))))&
(((~creative(paul)&wise(paul)))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>((generous(fred)<~>~creative(fred))))&
((~wise(fred)<~>~generous(fred)))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~curious(fred) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4397939938900084014209794
% SZS output start Proof for 4397939938900084014209794
8. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p7]
12. ! [X0] : ((~curious(X0) & ~generous(X0)) <=> brave(X0)) [input p11]
23. curious(fred) [input hypothesis]
45. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 8]
52. ! [X0] : (((~curious(X0) & ~generous(X0)) | ~brave(X0)) & (brave(X0) | (curious(X0) | generous(X0)))) [nnf transformation 12]
53. ! [X0] : (((~curious(X0) & ~generous(X0)) | ~brave(X0)) & (brave(X0) | curious(X0) | generous(X0))) [flattening 52]
100. ~curious(X0) | brave(X0) [cnf transformation 45]
101. ~brave(X0) | curious(X0) [cnf transformation 45]
115. ~curious(X0) | ~brave(X0) [cnf transformation 53]
137. curious(fred) [cnf transformation 23]
203. ~brave(X0) [subsumption resolution 115,101]
294. brave(fred) [resolution 100,137]
295. $false [subsumption resolution 294,203]
% SZS output end Proof for 4397939938900084014209794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
If someone is both not curious and old then mary is tall.
Everyone who is not happy is not patient and vice versa.
Everyone who is calm or curious is both calm and kind.
Everyone who is both not creative and not humble is old or tall.
Everyone who is both not kind and brave is creative or tall.
Alice is either funny or not humble.
Someone is not curious or strong.
Mary is not humble or kind.
Someone is generous.
Someone is both not wise and not generous.
John is old or quiet. | Alice is not creative. | entailment | (![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
((?[X]:((~curious(X)&old(X))))=>(tall(mary)))&
(![X]:(~happy(X)<=>~patient(X)))&
(![X]:((calm(X)|curious(X))=>(calm(X)&kind(X))))&
(![X]:((~creative(X)&~humble(X))=>(old(X)|tall(X))))&
(![X]:((~kind(X)&brave(X))=>(creative(X)|tall(X))))&
((funny(alice)<~>~humble(alice)))&
(?[X]:((~curious(X)|strong(X))))&
((~humble(mary)|kind(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&~generous(X))))&
((old(john)|quiet(john))) | ~creative(alice) | [
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7440123128291059635299815
% SZS output start Proof for 7440123128291059635299815
7. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p6]
9. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p8]
10. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X0] : (patient(X0) & ~kind(X0)) [input p9]
14. ! [X0] : ((curious(X0) | calm(X0)) => (kind(X0) & calm(X0))) [input p13]
23. creative(alice) [input hypothesis]
24. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X1] : (patient(X1) & ~kind(X1)) [rectify 10]
29. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 7]
35. ! [X0] : ((kind(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 14]
52. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 9]
53. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 52]
54. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X1] : (patient(X1) & ~kind(X1)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) [nnf transformation 24]
55. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X2] : (patient(X2) & ~kind(X2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [rectify 54]
56. ? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) => ((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) [choice axiom]
57. ? [X2] : (patient(X2) & ~kind(X2)) => (patient(sK2) & ~kind(sK2)) [choice axiom]
58. (((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) | ! [X1] : (~patient(X1) | kind(X1))) & ((patient(sK2) & ~kind(sK2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [skolemisation 55,57,56]
93. creative(X0) | calm(X0) [cnf transformation 29]
99. ~creative(X0) | kind(X0) [cnf transformation 53]
100. ~creative(X0) | ~funny(X0) [cnf transformation 53]
102. ~kind(sK2) | funny(X3) | ~creative(X3) [cnf transformation 58]
113. kind(X0) | ~calm(X0) [cnf transformation 35]
124. creative(alice) [cnf transformation 23]
152. 6 <=> ! [X1] : kind(X1) [avatar definition]
153. kind(X1) <- (6) [avatar component clause 152]
171. 10 <=> ! [X3] : ~creative(X3) [avatar definition]
172. ~creative(X3) <- (10) [avatar component clause 171]
183. ~kind(sK2) | ~creative(X3) [subsumption resolution 102,100]
185. 13 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~13) [avatar component clause 185]
188. 10 | ~13 [avatar split clause 183,185,171]
229. kind(X0) | calm(X0) [resolution 99,93]
230. kind(X0) [subsumption resolution 229,113]
231. 6 [avatar split clause 230,152]
233. $false <- (6, ~13) [resolution 153,187]
234. ~6 | 13 [avatar contradiction clause 233]
236. $false <- (10) [resolution 172,124]
238. ~10 [avatar contradiction clause 236]
239. $false [avatar sat refutation 188,231,234,238]
% SZS output end Proof for 7440123128291059635299815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not old is either not tall or not calm and vice versa.
Everyone who is both patient and kind is not humble or brave and vice versa.
Everyone who is both tall and strong is both generous and not tall and vice versa.
If someone is not patient or creative then mary is wise or tall.
If susan is not curious or curious then fred is both not humble and not tall and vice versa.
Everyone who is both not wise and creative is calm or happy and vice versa.
Everyone who is not wise is not curious and vice versa.
Everyone who is either happy or brave is both not curious and funny.
Everyone who is both not creative and generous is not calm.
Everyone who is not wise is not humble and vice versa.
If someone is wise then someone is curious or not quiet and vice versa.
If someone is either not brave or not creative then paul is wise and vice versa.
If lucy is both calm and rich then mary is either not curious or not happy and vice versa.
If mary is both generous and not funny then susan is both tall and rich.
Everyone who is either curious or quiet is not rich.
Lucy is kind.
Alice is either curious or brave.
Susan is funny or creative.
John is not wise.
Alice is not strong.
Fred is either not humble or not calm.
Someone is both humble and not strong.
Someone is both happy and tall. | Fred is not calm. | contradiction | (![X]:((~kind(X)<~>~old(X))<=>(~tall(X)<~>~calm(X))))&
(![X]:((patient(X)&kind(X))<=>(~humble(X)|brave(X))))&
(![X]:((tall(X)&strong(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~patient(X)|creative(X))))=>((wise(mary)|tall(mary))))&
(((~curious(susan)|curious(susan)))<=>((~humble(fred)&~tall(fred))))&
(![X]:((~wise(X)&creative(X))<=>(calm(X)|happy(X))))&
(![X]:(~wise(X)<=>~curious(X)))&
(![X]:((happy(X)<~>brave(X))=>(~curious(X)&funny(X))))&
(![X]:((~creative(X)&generous(X))=>~calm(X)))&
(![X]:(~wise(X)<=>~humble(X)))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>(wise(paul)))&
(((calm(lucy)&rich(lucy)))<=>((~curious(mary)<~>~happy(mary))))&
(((generous(mary)&~funny(mary)))=>((tall(susan)&rich(susan))))&
(![X]:((curious(X)<~>quiet(X))=>~rich(X)))&
(kind(lucy))&
((curious(alice)<~>brave(alice)))&
((funny(susan)|creative(susan)))&
(~wise(john))&
(~strong(alice))&
((~humble(fred)<~>~calm(fred)))&
(?[X]:((humble(X)&~strong(X))))&
(?[X]:((happy(X)&tall(X)))) | ~calm(fred) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8143712175120792066651563
% SZS output start Proof for 8143712175120792066651563
5. (curious(susan) | ~curious(susan)) <=> (~tall(fred) & ~humble(fred)) [input p4]
21. ~humble(fred) <~> ~calm(fred) [input p20]
24. ~calm(fred) [input hypothesis]
40. ((curious(susan) | ~curious(susan)) | (tall(fred) | humble(fred))) & ((~tall(fred) & ~humble(fred)) | (~curious(susan) & curious(susan))) [nnf transformation 5]
41. (curious(susan) | ~curious(susan) | tall(fred) | humble(fred)) & ((~tall(fred) & ~humble(fred)) | (~curious(susan) & curious(susan))) [flattening 40]
60. (calm(fred) | humble(fred)) & (~calm(fred) | ~humble(fred)) [nnf transformation 21]
84. ~humble(fred) | curious(susan) [cnf transformation 41]
85. ~humble(fred) | ~curious(susan) [cnf transformation 41]
122. calm(fred) | humble(fred) [cnf transformation 60]
127. ~calm(fred) [cnf transformation 24]
147. 5 <=> curious(susan) [avatar definition]
157. 7 <=> humble(fred) [avatar definition]
160. ~5 | ~7 [avatar split clause 85,157,147]
161. 5 | ~7 [avatar split clause 84,157,147]
241. 25 <=> calm(fred) [avatar definition]
244. 7 | 25 [avatar split clause 122,241,157]
246. ~25 [avatar split clause 127,241]
247. $false [avatar sat refutation 160,161,244,246]
% SZS output end Proof for 8143712175120792066651563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is not patient and vice versa. Everyone who is either not generous or not brave is both not happy and not funny and vice versa. Everyone who is curious is either not kind or kind and vice versa. Everyone who is kind or not rich is not wise or not strong. Everyone who is not old is kind or not funny and vice versa. If someone is either brave or patient then lucy is either not strong or generous and vice versa. Everyone who is brave or calm is kind or not humble and vice versa. If mary is not kind then someone is not patient or strong and vice versa. If someone is both humble and curious then alice is happy or not creative. Everyone who is strong or old is not rich or calm and vice versa. Everyone who is either old or not tall is either quiet or rich and vice versa. If mary is both old and not curious then lucy is not curious or wise. If someone is not old then someone is either patient or not calm. Everyone who is funny is either not curious or humble and vice versa. Everyone who is not old is rich. Everyone who is either not tall or tall is not strong. John is both humble and happy. Someone is either not funny or happy. Someone is either not rich or not strong. Someone is both not kind and not humble. Fred is generous. Fred is not quiet. Someone is not wise. | Fred is not rich. | contradiction | (![X]:((~calm(X)<~>~brave(X))<=>~patient(X)))&
(![X]:((~generous(X)<~>~brave(X))<=>(~happy(X)&~funny(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>kind(X))))&
(![X]:((kind(X)|~rich(X))=>(~wise(X)|~strong(X))))&
(![X]:(~old(X)<=>(kind(X)|~funny(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>((~strong(lucy)<~>generous(lucy))))&
(![X]:((brave(X)|calm(X))<=>(kind(X)|~humble(X))))&
((~kind(mary))<=>(?[X]:((~patient(X)|strong(X)))))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)|~creative(alice))))&
(![X]:((strong(X)|old(X))<=>(~rich(X)|calm(X))))&
(![X]:((old(X)<~>~tall(X))<=>(quiet(X)<~>rich(X))))&
(((old(mary)&~curious(mary)))=>((~curious(lucy)|wise(lucy))))&
((?[X]:(~old(X)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>humble(X))))&
(![X]:(~old(X)=>rich(X)))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
((humble(john)&happy(john)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
(?[X]:((~kind(X)&~humble(X))))&
(generous(fred))&
(~quiet(fred))&
(?[X]:(~wise(X))) | ~rich(fred) | [
"p1",
"p2",
"p4",
"p6",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3485951223153087584948968
% SZS output start Proof for 3485951223153087584948968
2. ! [X0] : ((~generous(X0) <~> ~brave(X0)) <=> (~funny(X0) & ~happy(X0))) [input p1]
3. ! [X0] : (curious(X0) <=> (~kind(X0) <~> kind(X0))) [input p2]
5. ! [X0] : (~old(X0) <=> (~funny(X0) | kind(X0))) [input p4]
7. ! [X0] : ((calm(X0) | brave(X0)) <=> (~humble(X0) | kind(X0))) [input p6]
14. ! [X0] : (funny(X0) <=> (~curious(X0) <~> humble(X0))) [input p13]
15. ! [X0] : (~old(X0) => rich(X0)) [input p14]
21. generous(fred) [input p20]
24. ~rich(fred) [input hypothesis]
32. ! [X0] : (rich(X0) | old(X0)) [ennf transformation 15]
35. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [nnf transformation 2]
36. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [flattening 35]
37. ! [X0] : ((curious(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~curious(X0))) [nnf transformation 3]
38. ! [X0] : ((~old(X0) | (funny(X0) & ~kind(X0))) & ((~funny(X0) | kind(X0)) | old(X0))) [nnf transformation 5]
39. ! [X0] : ((~old(X0) | (funny(X0) & ~kind(X0))) & (~funny(X0) | kind(X0) | old(X0))) [flattening 38]
44. ! [X0] : (((calm(X0) | brave(X0)) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | (~calm(X0) & ~brave(X0)))) [nnf transformation 7]
45. ! [X0] : ((calm(X0) | brave(X0) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | (~calm(X0) & ~brave(X0)))) [flattening 44]
57. ! [X0] : ((funny(X0) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | ~funny(X0))) [nnf transformation 14]
76. ~funny(X0) | ~generous(X0) | brave(X0) [cnf transformation 36]
81. curious(X0) | kind(X0) | kind(X0) [cnf transformation 37]
82. curious(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 37]
86. ~old(X0) | ~kind(X0) [cnf transformation 39]
87. ~old(X0) | funny(X0) [cnf transformation 39]
96. ~humble(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
118. humble(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 57]
122. old(X0) | rich(X0) [cnf transformation 32]
133. generous(fred) [cnf transformation 21]
136. ~rich(fred) [cnf transformation 24]
139. curious(X0) | kind(X0) [duplicate literal removal 81]
140. ~kind(X0) | curious(X0) [duplicate literal removal 82]
141. curious(X0) [subsumption resolution 139,140]
207. ~funny(X0) | humble(X0) [subsumption resolution 118,141]
230. rich(X0) | funny(X0) [resolution 122,87]
234. funny(fred) [resolution 230,136]
235. humble(fred) [resolution 234,207]
294. ~generous(fred) | brave(fred) [resolution 76,234]
295. brave(fred) [subsumption resolution 294,133]
310. 25 <=> old(fred) [avatar definition]
311. ~old(fred) <- (~25) [avatar component clause 310]
312. old(fred) <- (25) [avatar component clause 310]
314. 26 <=> kind(fred) [avatar definition]
316. kind(fred) <- (26) [avatar component clause 314]
320. kind(fred) | ~brave(fred) [resolution 96,235]
321. kind(fred) [subsumption resolution 320,295]
322. 26 [avatar split clause 321,314]
542. ~kind(fred) <- (25) [resolution 312,86]
543. $false <- (25, 26) [subsumption resolution 542,316]
544. ~25 | ~26 [avatar contradiction clause 543]
549. rich(fred) <- (~25) [resolution 311,122]
553. $false <- (~25) [subsumption resolution 549,136]
554. 25 [avatar contradiction clause 553]
555. $false [avatar sat refutation 322,544,554]
% SZS output end Proof for 3485951223153087584948968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or not humble then lucy is not strong and vice versa.
If someone is both not kind and not creative then fred is either not humble or not patient.
If fred is either humble or not curious then mary is old or calm.
If someone is not brave then lucy is either not rich or brave.
Everyone who is both kind and humble is quiet or humble and vice versa.
Everyone who is either funny or humble is either not funny or patient and vice versa.
Everyone who is both curious and patient is not patient or not quiet and vice versa.
Everyone who is either strong or not creative is tall or not tall.
If someone is not brave then someone is not curious or strong.
Everyone who is either not humble or quiet is old.
If mary is both not happy and curious then someone is either not tall or patient.
If paul is both calm and not humble then someone is both quiet and wise and vice versa.
If lucy is strong then alice is not brave and vice versa.
Everyone who is not humble is either wise or not creative.
If lucy is either not generous or not quiet then someone is not quiet or wise and vice versa.
If susan is either not quiet or wise then lucy is either generous or not rich and vice versa.
Someone is old.
Alice is not wise.
Fred is either patient or not wise.
Someone is either not kind or not quiet.
Paul is not wise.
Paul is not humble or not quiet.
Someone is patient.
Someone is both not humble and not tall. | Alice is quiet. | contradiction | ((?[X]:((~strong(X)<~>~humble(X))))<=>(~strong(lucy)))&
((?[X]:((~kind(X)&~creative(X))))=>((~humble(fred)<~>~patient(fred))))&
(((humble(fred)<~>~curious(fred)))=>((old(mary)|calm(mary))))&
((?[X]:(~brave(X)))=>((~rich(lucy)<~>brave(lucy))))&
(![X]:((kind(X)&humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((curious(X)&patient(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((strong(X)<~>~creative(X))=>(tall(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~humble(X)<~>quiet(X))=>old(X)))&
(((~happy(mary)&curious(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((calm(paul)&~humble(paul)))<=>(?[X]:((quiet(X)&wise(X)))))&
((strong(lucy))<=>(~brave(alice)))&
(![X]:(~humble(X)=>(wise(X)<~>~creative(X))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(((~quiet(susan)<~>wise(susan)))<=>((generous(lucy)<~>~rich(lucy))))&
(?[X]:(old(X)))&
(~wise(alice))&
((patient(fred)<~>~wise(fred)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(~wise(paul))&
((~humble(paul)|~quiet(paul)))&
(?[X]:(patient(X)))&
(?[X]:((~humble(X)&~tall(X)))) | quiet(alice) | [
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8593767214921409426348103
% SZS output start Proof for 8593767214921409426348103
5. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) | quiet(X0))) [input p4]
6. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (~funny(X0) <~> patient(X0))) [input p5]
7. ! [X0] : ((patient(X0) & curious(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p6]
25. quiet(alice) [input hypothesis]
43. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | ~humble(X0) | ~kind(X0))) [flattening 43]
45. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 6]
46. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 7]
47. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | ~patient(X0) | ~curious(X0))) [flattening 46]
83. ~quiet(X0) | humble(X0) [cnf transformation 44]
88. ~patient(X0) | funny(X0) | funny(X0) | ~humble(X0) [cnf transformation 45]
92. ~humble(X0) | ~funny(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 45]
96. patient(X0) | patient(X0) [cnf transformation 47]
133. quiet(alice) [cnf transformation 25]
135. patient(X0) [duplicate literal removal 96]
137. ~patient(X0) | funny(X0) | ~humble(X0) [duplicate literal removal 88]
139. ~humble(X0) | ~funny(X0) | ~patient(X0) [duplicate literal removal 92]
188. ~patient(X0) | ~humble(X0) [subsumption resolution 137,139]
278. humble(alice) [resolution 83,133]
294. ~humble(X0) [resolution 188,135]
299. $false [resolution 294,278]
% SZS output end Proof for 8593767214921409426348103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not old is strong and vice versa. Everyone who is either not rich or not generous is not old and vice versa. If fred is both not humble and quiet then fred is not funny or generous and vice versa. Everyone who is strong or wise is not tall or humble. If someone is either quiet or kind then someone is either curious or not curious and vice versa. Everyone who is not brave is quiet. Everyone who is happy is tall. If someone is calm then someone is creative. If someone is not rich or not calm then someone is not tall. Everyone who is both not tall and rich is humble or patient and vice versa. Everyone who is both not curious and not wise is old or not calm and vice versa. Everyone who is both not kind and not calm is old and vice versa. Everyone who is either not strong or rich is both rich and not patient. Everyone who is either curious or not generous is wise or not funny and vice versa. Everyone who is both not rich and not creative is either not humble or not kind and vice versa. Everyone who is either rich or humble is both kind and strong and vice versa. Mary is brave or rich. Someone is not wise or not kind. Lucy is quiet. Someone is not tall or funny. Susan is quiet. Someone is not happy or not wise. Alice is either not calm or quiet. | Lucy is not happy. | entailment | (![X]:((~funny(X)&~old(X))<=>strong(X)))&
(![X]:((~rich(X)<~>~generous(X))<=>~old(X)))&
(((~humble(fred)&quiet(fred)))<=>((~funny(fred)|generous(fred))))&
(![X]:((strong(X)|wise(X))=>(~tall(X)|humble(X))))&
((?[X]:((quiet(X)<~>kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
(![X]:(~brave(X)=>quiet(X)))&
(![X]:(happy(X)=>tall(X)))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
((?[X]:((~rich(X)|~calm(X))))=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)&rich(X))<=>(humble(X)|patient(X))))&
(![X]:((~curious(X)&~wise(X))<=>(old(X)|~calm(X))))&
(![X]:((~kind(X)&~calm(X))<=>old(X)))&
(![X]:((~strong(X)<~>rich(X))=>(rich(X)&~patient(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(wise(X)|~funny(X))))&
(![X]:((~rich(X)&~creative(X))<=>(~humble(X)<~>~kind(X))))&
(![X]:((rich(X)<~>humble(X))<=>(kind(X)&strong(X))))&
((brave(mary)|rich(mary)))&
(?[X]:((~wise(X)|~kind(X))))&
(quiet(lucy))&
(?[X]:((~tall(X)|funny(X))))&
(quiet(susan))&
(?[X]:((~happy(X)|~wise(X))))&
((~calm(alice)<~>quiet(alice))) | ~happy(lucy) | [
"p3",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9094277834352091985645620
% SZS output start Proof for 9094277834352091985645620
4. ! [X0] : ((wise(X0) | strong(X0)) => (humble(X0) | ~tall(X0))) [input p3]
7. ! [X0] : (happy(X0) => tall(X0)) [input p6]
10. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (patient(X0) | humble(X0))) [input p9]
13. ! [X0] : ((~strong(X0) <~> rich(X0)) => (~patient(X0) & rich(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> humble(X0)) <=> (strong(X0) & kind(X0))) [input p15]
24. happy(lucy) [input hypothesis]
30. ! [X0] : ((humble(X0) | ~tall(X0)) | (~wise(X0) & ~strong(X0))) [ennf transformation 4]
31. ! [X0] : (humble(X0) | ~tall(X0) | (~wise(X0) & ~strong(X0))) [flattening 30]
32. ! [X0] : (tall(X0) | ~happy(X0)) [ennf transformation 7]
35. ! [X0] : ((~patient(X0) & rich(X0)) | (~strong(X0) <=> rich(X0))) [ennf transformation 13]
52. ! [X0] : (((rich(X0) & ~tall(X0)) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 10]
53. ! [X0] : (((rich(X0) & ~tall(X0)) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | ~rich(X0) | tall(X0))) [flattening 52]
58. ! [X0] : ((~patient(X0) & rich(X0)) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) [nnf transformation 35]
63. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [nnf transformation 16]
64. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [flattening 63]
84. ~tall(X0) | humble(X0) | ~strong(X0) [cnf transformation 31]
94. ~happy(X0) | tall(X0) [cnf transformation 32]
99. ~tall(X0) | ~humble(X0) [cnf transformation 53]
111. rich(X0) | rich(X0) | strong(X0) [cnf transformation 58]
129. strong(X0) | humble(X0) | ~rich(X0) [cnf transformation 64]
140. happy(lucy) [cnf transformation 24]
141. rich(X0) | strong(X0) [duplicate literal removal 111]
210. humble(X0) | strong(X0) [subsumption resolution 129,141]
249. tall(lucy) [resolution 94,140]
250. ~humble(lucy) [resolution 249,99]
252. strong(lucy) [resolution 210,250]
288. humble(lucy) | ~strong(lucy) [resolution 84,249]
289. ~strong(lucy) [subsumption resolution 288,250]
290. $false [subsumption resolution 289,252]
% SZS output end Proof for 9094277834352091985645620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet then someone is funny.
Everyone who is patient is not generous.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is humble is either not funny or not strong and vice versa.
Everyone who is not brave is both generous and wise and vice versa.
If susan is not old or not calm then fred is both brave and strong and vice versa.
If alice is patient then someone is not creative or kind and vice versa.
If mary is not strong then alice is both brave and wise.
Everyone who is both not wise and not kind is not creative or not brave.
If someone is not strong or not old then paul is not quiet.
If someone is not quiet or humble then mary is humble or not wise.
If mary is brave or not strong then paul is both happy and curious.
Everyone who is either not quiet or old is either not happy or not calm and vice versa.
If susan is either calm or not tall then alice is not wise or not rich and vice versa.
If fred is humble then alice is either generous or not wise and vice versa.
If someone is not kind or curious then someone is happy or old.
Paul is humble.
Alice is either not quiet or not tall.
Someone is both not old and tall.
Mary is not humble.
Lucy is both not brave and not strong.
Someone is either not humble or not kind.
Lucy is not curious.
Someone is not tall or quiet. | Lucy is wise. | entailment | ((~quiet(paul))=>(?[X]:(funny(X))))&
(![X]:(patient(X)=>~generous(X)))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(humble(X)<=>(~funny(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>(generous(X)&wise(X))))&
(((~old(susan)|~calm(susan)))<=>((brave(fred)&strong(fred))))&
((patient(alice))<=>(?[X]:((~creative(X)|kind(X)))))&
((~strong(mary))=>((brave(alice)&wise(alice))))&
(![X]:((~wise(X)&~kind(X))=>(~creative(X)|~brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(~quiet(paul)))&
((?[X]:((~quiet(X)|humble(X))))=>((humble(mary)|~wise(mary))))&
(((brave(mary)|~strong(mary)))=>((happy(paul)&curious(paul))))&
(![X]:((~quiet(X)<~>old(X))<=>(~happy(X)<~>~calm(X))))&
(((calm(susan)<~>~tall(susan)))<=>((~wise(alice)|~rich(alice))))&
((humble(fred))<=>((generous(alice)<~>~wise(alice))))&
((?[X]:((~kind(X)|curious(X))))=>(?[X]:((happy(X)|old(X)))))&
(humble(paul))&
((~quiet(alice)<~>~tall(alice)))&
(?[X]:((~old(X)&tall(X))))&
(~humble(mary))&
((~brave(lucy)&~strong(lucy)))&
(?[X]:((~humble(X)<~>~kind(X))))&
(~curious(lucy))&
(?[X]:((~tall(X)|quiet(X)))) | wise(lucy) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6164639131407102861332719
% SZS output start Proof for 6164639131407102861332719
5. ! [X0] : (~brave(X0) <=> (wise(X0) & generous(X0))) [input p4]
21. ~strong(lucy) & ~brave(lucy) [input p20]
25. ~wise(lucy) [input hypothesis]
41. ! [X0] : ((~brave(X0) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | brave(X0))) [nnf transformation 5]
42. ! [X0] : ((~brave(X0) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | brave(X0))) [flattening 41]
75. wise(X0) | brave(X0) [cnf transformation 42]
122. ~brave(lucy) [cnf transformation 21]
128. ~wise(lucy) [cnf transformation 25]
309. brave(lucy) [resolution 75,128]
311. $false [subsumption resolution 309,122]
% SZS output end Proof for 6164639131407102861332719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is not generous or old.
Everyone who is either funny or strong is happy.
Everyone who is strong is either quiet or wise.
Everyone who is either not wise or calm is both kind and brave and vice versa.
Everyone who is kind or not creative is both kind and not wise.
Everyone who is creative or not happy is both patient and curious and vice versa.
Everyone who is either not tall or funny is both generous and not old.
If someone is not quiet then someone is either not brave or quiet and vice versa.
If mary is both not patient and brave then someone is both not strong and not creative and vice versa.
Everyone who is both not strong and quiet is not calm or quiet.
If someone is either not curious or not creative then john is calm and vice versa.
Everyone who is both not tall and not curious is not brave and vice versa.
If susan is both calm and not calm then paul is both not creative and not brave.
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
Paul is either calm or not generous.
Susan is either calm or not generous.
Susan is strong or humble.
Someone is both kind and generous.
Someone is wise or not generous.
Paul is both not quiet and not tall. | Paul is not strong. | neutral | (![X]:((~old(X)|happy(X))=>(~generous(X)|old(X))))&
(![X]:((funny(X)<~>strong(X))=>happy(X)))&
(![X]:(strong(X)=>(quiet(X)<~>wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(kind(X)&brave(X))))&
(![X]:((kind(X)|~creative(X))=>(kind(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~tall(X)<~>funny(X))=>(generous(X)&~old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((~patient(mary)&brave(mary)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((~strong(X)&quiet(X))=>(~calm(X)|quiet(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(calm(john)))&
(![X]:((~tall(X)&~curious(X))<=>~brave(X)))&
(((calm(susan)&~calm(susan)))=>((~creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
((calm(paul)<~>~generous(paul)))&
((calm(susan)<~>~generous(susan)))&
((strong(susan)|humble(susan)))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~quiet(paul)&~tall(paul))) | ~strong(paul) | [] | null | 0 |
If someone is both not funny and rich then someone is patient and vice versa. Everyone who is not rich is either creative or not happy. If someone is either not calm or not brave then someone is both quiet and generous and vice versa. Everyone who is not strong is not calm or curious and vice versa. Everyone who is curious or not wise is either tall or quiet. Everyone who is either strong or not generous is kind. If someone is either not calm or funny then john is not curious and vice versa. Everyone who is not wise or not strong is not rich and vice versa. Everyone who is both brave and not strong is either happy or calm. If someone is generous then someone is both creative and not curious. Everyone who is both funny and curious is either kind or patient. If someone is not tall or not happy then someone is both not calm and not strong. If john is either curious or quiet then lucy is either strong or calm and vice versa. Everyone who is either not quiet or old is both quiet and generous and vice versa. Everyone who is both generous and old is generous or humble. Everyone who is not funny is creative or not brave and vice versa. Lucy is either brave or not old. John is not old. Someone is tall or calm. Someone is both not wise and kind. Susan is both not rich and not old. Someone is wise or humble. Someone is not strong or not creative. Someone is both not curious and wise. | Lucy is curious. | entailment | ((?[X]:((~funny(X)&rich(X))))<=>(?[X]:(patient(X))))&
(![X]:(~rich(X)=>(creative(X)<~>~happy(X))))&
((?[X]:((~calm(X)<~>~brave(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:(~strong(X)<=>(~calm(X)|curious(X))))&
(![X]:((curious(X)|~wise(X))=>(tall(X)<~>quiet(X))))&
(![X]:((strong(X)<~>~generous(X))=>kind(X)))&
((?[X]:((~calm(X)<~>funny(X))))<=>(~curious(john)))&
(![X]:((~wise(X)|~strong(X))<=>~rich(X)))&
(![X]:((brave(X)&~strong(X))=>(happy(X)<~>calm(X))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:((funny(X)&curious(X))=>(kind(X)<~>patient(X))))&
((?[X]:((~tall(X)|~happy(X))))=>(?[X]:((~calm(X)&~strong(X)))))&
(((curious(john)<~>quiet(john)))<=>((strong(lucy)<~>calm(lucy))))&
(![X]:((~quiet(X)<~>old(X))<=>(quiet(X)&generous(X))))&
(![X]:((generous(X)&old(X))=>(generous(X)|humble(X))))&
(![X]:(~funny(X)<=>(creative(X)|~brave(X))))&
((brave(lucy)<~>~old(lucy)))&
(~old(john))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((~wise(X)&kind(X))))&
((~rich(susan)&~old(susan)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~curious(X)&wise(X)))) | curious(lucy) | [
"p1",
"p3",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9026681904456325576501277
% SZS output start Proof for 9026681904456325576501277
2. ! [X0] : (~rich(X0) => (creative(X0) <~> ~happy(X0))) [input p1]
4. ! [X0] : (~strong(X0) <=> (curious(X0) | ~calm(X0))) [input p3]
5. ! [X0] : ((~wise(X0) | curious(X0)) => (tall(X0) <~> quiet(X0))) [input p4]
7. ? [X0] : (~calm(X0) <~> funny(X0)) <=> ~curious(john) [input p6]
8. ! [X0] : ((~strong(X0) | ~wise(X0)) <=> ~rich(X0)) [input p7]
9. ! [X0] : ((~strong(X0) & brave(X0)) => (happy(X0) <~> calm(X0))) [input p8]
12. ? [X0] : (~happy(X0) | ~tall(X0)) => ? [X0] : (~strong(X0) & ~calm(X0)) [input p11]
13. (curious(john) <~> quiet(john)) <=> (strong(lucy) <~> calm(lucy)) [input p12]
14. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (generous(X0) & quiet(X0))) [input p13]
16. ! [X0] : (~funny(X0) <=> (~brave(X0) | creative(X0))) [input p15]
18. ~old(john) [input p17]
25. ~curious(lucy) [input hypothesis]
29. ? [X0] : (~happy(X0) | ~tall(X0)) => ? [X1] : (~strong(X1) & ~calm(X1)) [rectify 12]
32. ! [X0] : ((creative(X0) <~> ~happy(X0)) | rich(X0)) [ennf transformation 2]
33. ! [X0] : ((tall(X0) <~> quiet(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 5]
35. ! [X0] : ((happy(X0) <~> calm(X0)) | (strong(X0) | ~brave(X0))) [ennf transformation 9]
36. ! [X0] : ((happy(X0) <~> calm(X0)) | strong(X0) | ~brave(X0)) [flattening 35]
40. ? [X1] : (~strong(X1) & ~calm(X1)) | ! [X0] : (happy(X0) & tall(X0)) [ennf transformation 29]
46. ! [X0] : (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | rich(X0)) [nnf transformation 32]
52. ! [X0] : ((~strong(X0) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | strong(X0))) [nnf transformation 4]
53. ! [X0] : ((~strong(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | strong(X0))) [flattening 52]
54. ! [X0] : (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (wise(X0) & ~curious(X0))) [nnf transformation 33]
56. (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | curious(john)) & (~curious(john) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [nnf transformation 7]
57. (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | curious(john)) & (~curious(john) | ! [X1] : ((~calm(X1) | ~funny(X1)) & (funny(X1) | calm(X1)))) [rectify 56]
58. ? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) => ((~funny(sK4) | calm(sK4)) & (funny(sK4) | ~calm(sK4))) [choice axiom]
59. (((~funny(sK4) | calm(sK4)) & (funny(sK4) | ~calm(sK4))) | curious(john)) & (~curious(john) | ! [X1] : ((~calm(X1) | ~funny(X1)) & (funny(X1) | calm(X1)))) [skolemisation 57,58]
60. ! [X0] : (((~strong(X0) | ~wise(X0)) | rich(X0)) & (~rich(X0) | (strong(X0) & wise(X0)))) [nnf transformation 8]
61. ! [X0] : ((~strong(X0) | ~wise(X0) | rich(X0)) & (~rich(X0) | (strong(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | strong(X0) | ~brave(X0)) [nnf transformation 36]
67. ? [X0] : (~strong(X0) & ~calm(X0)) | ! [X1] : (happy(X1) & tall(X1)) [rectify 40]
68. ? [X0] : (~strong(X0) & ~calm(X0)) => (~strong(sK6) & ~calm(sK6)) [choice axiom]
69. (~strong(sK6) & ~calm(sK6)) | ! [X1] : (happy(X1) & tall(X1)) [skolemisation 67,68]
70. (((~quiet(john) | ~curious(john)) & (quiet(john) | curious(john))) | ((strong(lucy) | ~calm(lucy)) & (calm(lucy) | ~strong(lucy)))) & (((~calm(lucy) | ~strong(lucy)) & (calm(lucy) | strong(lucy))) | ((curious(john) | ~quiet(john)) & (quiet(john) | ~curious(john)))) [nnf transformation 13]
71. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 14]
72. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 71]
73. ! [X0] : ((~funny(X0) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | funny(X0))) [nnf transformation 16]
74. ! [X0] : ((~funny(X0) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | funny(X0))) [flattening 73]
87. ~happy(X0) | creative(X0) | rich(X0) [cnf transformation 46]
95. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 53]
96. ~strong(X0) | calm(X0) [cnf transformation 53]
100. ~tall(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 54]
104. ~curious(john) | funny(X1) | calm(X1) [cnf transformation 59]
109. ~rich(X0) | strong(X0) [cnf transformation 61]
111. calm(X0) | happy(X0) | strong(X0) | ~brave(X0) [cnf transformation 62]
117. ~calm(sK6) | tall(X1) [cnf transformation 69]
119. ~strong(sK6) | tall(X1) [cnf transformation 69]
122. calm(lucy) | strong(lucy) | curious(john) | ~quiet(john) [cnf transformation 70]
124. ~calm(lucy) | ~strong(lucy) | curious(john) | ~quiet(john) [cnf transformation 70]
129. quiet(X0) | old(X0) | quiet(X0) [cnf transformation 72]
136. ~creative(X0) | ~funny(X0) [cnf transformation 74]
137. ~funny(X0) | brave(X0) [cnf transformation 74]
140. ~old(john) [cnf transformation 18]
149. ~curious(lucy) [cnf transformation 25]
150. old(X0) | quiet(X0) [duplicate literal removal 129]
205. 13 <=> curious(john) [avatar definition]
207. curious(john) <- (13) [avatar component clause 205]
223. 17 <=> ! [X1] : (funny(X1) | calm(X1)) [avatar definition]
224. calm(X1) | funny(X1) <- (17) [avatar component clause 223]
225. 17 | ~13 [avatar split clause 104,205,223]
226. ~brave(X0) | happy(X0) | calm(X0) [subsumption resolution 111,96]
244. 22 <=> strong(sK6) [avatar definition]
246. ~strong(sK6) <- (~22) [avatar component clause 244]
249. 23 <=> ! [X1] : tall(X1) [avatar definition]
250. tall(X1) <- (23) [avatar component clause 249]
251. 23 | ~22 [avatar split clause 119,244,249]
253. 24 <=> calm(sK6) [avatar definition]
255. ~calm(sK6) <- (~24) [avatar component clause 253]
257. 23 | ~24 [avatar split clause 117,253,249]
259. 25 <=> calm(lucy) [avatar definition]
260. calm(lucy) <- (25) [avatar component clause 259]
263. 26 <=> strong(lucy) [avatar definition]
267. 27 <=> quiet(john) [avatar definition]
268. quiet(john) <- (27) [avatar component clause 267]
272. ~strong(lucy) | curious(john) | ~quiet(john) [subsumption resolution 124,96]
273. ~27 | 13 | ~26 [avatar split clause 272,263,205,267]
276. calm(lucy) | curious(john) | ~quiet(john) [subsumption resolution 122,96]
277. ~27 | 13 | 25 [avatar split clause 276,259,205,267]
311. quiet(john) [resolution 150,140]
316. 27 [avatar split clause 311,267]
368. curious(lucy) | strong(lucy) <- (25) [resolution 260,95]
370. strong(lucy) <- (25) [subsumption resolution 368,149]
373. 26 | ~25 [avatar split clause 370,259,263]
394. funny(sK6) <- (17, ~24) [resolution 224,255]
451. brave(sK6) <- (17, ~24) [resolution 394,137]
538. happy(sK6) | calm(sK6) <- (17, ~24) [resolution 451,226]
540. happy(sK6) <- (17, ~24) [subsumption resolution 538,255]
571. creative(sK6) | rich(sK6) <- (17, ~24) [resolution 540,87]
573. 65 <=> rich(sK6) [avatar definition]
575. rich(sK6) <- (65) [avatar component clause 573]
577. 66 <=> creative(sK6) [avatar definition]
579. creative(sK6) <- (66) [avatar component clause 577]
580. 65 | 66 | ~17 | 24 [avatar split clause 571,253,223,577,573]
648. strong(sK6) <- (65) [resolution 575,109]
650. $false <- (~22, 65) [subsumption resolution 648,246]
651. 22 | ~65 [avatar contradiction clause 650]
656. ~curious(X1) | ~quiet(X1) <- (23) [resolution 250,100]
670. funny(sK6) <- (17, ~24) [resolution 255,224]
681. ~quiet(john) <- (13, 23) [resolution 656,207]
683. $false <- (13, 23, 27) [subsumption resolution 681,268]
684. ~13 | ~23 | ~27 [avatar contradiction clause 683]
691. ~funny(sK6) <- (66) [resolution 579,136]
692. $false <- (17, ~24, 66) [subsumption resolution 691,670]
693. ~17 | 24 | ~66 [avatar contradiction clause 692]
694. $false [avatar sat refutation 225,251,257,273,277,316,373,580,651,684,693]
% SZS output end Proof for 9026681904456325576501277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not curious is either funny or not patient and vice versa.
Everyone who is rich is both curious and not wise.
Everyone who is both old and not brave is both happy and not humble.
Everyone who is both not creative and not generous is either patient or not humble and vice versa.
Everyone who is generous or curious is not curious and vice versa.
If lucy is not curious or old then someone is either not brave or not wise and vice versa.
If someone is kind or creative then someone is either creative or tall and vice versa.
If someone is both not brave and kind then someone is either brave or not rich.
If someone is either not humble or not quiet then fred is both not brave and brave.
Everyone who is tall or not strong is both funny and not patient and vice versa.
Everyone who is both creative and not brave is not strong.
If john is either tall or not quiet then someone is tall.
If someone is not old then paul is not generous or not rich.
Someone is not kind.
Susan is both not curious and old.
Someone is both not curious and not patient.
Fred is not wise.
Paul is kind or not calm. | John is curious. | contradiction | (![X]:((humble(X)<~>~curious(X))<=>(funny(X)<~>~patient(X))))&
(![X]:(rich(X)=>(curious(X)&~wise(X))))&
(![X]:((old(X)&~brave(X))=>(happy(X)&~humble(X))))&
(![X]:((~creative(X)&~generous(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((generous(X)|curious(X))<=>~curious(X)))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~humble(X)<~>~quiet(X))))=>((~brave(fred)&brave(fred))))&
(![X]:((tall(X)|~strong(X))<=>(funny(X)&~patient(X))))&
(![X]:((creative(X)&~brave(X))=>~strong(X)))&
(((tall(john)<~>~quiet(john)))=>(?[X]:(tall(X))))&
((?[X]:(~old(X)))=>((~generous(paul)|~rich(paul))))&
(?[X]:(~kind(X)))&
((~curious(susan)&old(susan)))&
(?[X]:((~curious(X)&~patient(X))))&
(~wise(fred))&
((kind(paul)|~calm(paul))) | curious(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5694634916966261413767492
% SZS output start Proof for 5694634916966261413767492
5. ! [X0] : ((curious(X0) | generous(X0)) <=> ~curious(X0)) [input p4]
19. curious(john) [input hypothesis]
37. ! [X0] : (((curious(X0) | generous(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & ~generous(X0)))) [nnf transformation 5]
38. ! [X0] : ((curious(X0) | generous(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & ~generous(X0)))) [flattening 37]
81. ~curious(X0) | ~curious(X0) [cnf transformation 38]
116. curious(john) [cnf transformation 19]
117. ~curious(X0) [duplicate literal removal 81]
224. $false [subsumption resolution 116,117]
% SZS output end Proof for 5694634916966261413767492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not creative or humble then someone is not humble and vice versa. If alice is not calm or strong then someone is either not creative or not quiet and vice versa. Everyone who is both not patient and not creative is either not brave or quiet. Everyone who is either curious or not brave is either happy or brave. Everyone who is either not old or not happy is both brave and not generous. Everyone who is not old or not quiet is happy. If john is either generous or rich then someone is calm or not quiet. Everyone who is not generous or not creative is creative and vice versa. If someone is both not wise and not humble then susan is either not happy or not calm and vice versa. Everyone who is either funny or generous is either quiet or kind and vice versa. If mary is not brave then susan is wise or not rich and vice versa. If someone is not funny or calm then susan is brave or happy and vice versa. Everyone who is creative is either kind or quiet. If john is either brave or not old then someone is either patient or not tall and vice versa. If mary is either not humble or not kind then susan is both not tall and funny and vice versa. Everyone who is both not patient and not quiet is generous and vice versa. Susan is not brave or generous. Someone is either curious or not humble. Someone is generous or not generous. Someone is not quiet or not kind. Lucy is either not generous or quiet. Someone is not brave or funny. | Mary is funny. | entailment | (((~creative(mary)|humble(mary)))<=>(?[X]:(~humble(X))))&
(((~calm(alice)|strong(alice)))<=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((~patient(X)&~creative(X))=>(~brave(X)<~>quiet(X))))&
(![X]:((curious(X)<~>~brave(X))=>(happy(X)<~>brave(X))))&
(![X]:((~old(X)<~>~happy(X))=>(brave(X)&~generous(X))))&
(![X]:((~old(X)|~quiet(X))=>happy(X)))&
(((generous(john)<~>rich(john)))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:((~generous(X)|~creative(X))<=>creative(X)))&
((?[X]:((~wise(X)&~humble(X))))<=>((~happy(susan)<~>~calm(susan))))&
(![X]:((funny(X)<~>generous(X))<=>(quiet(X)<~>kind(X))))&
((~brave(mary))<=>((wise(susan)|~rich(susan))))&
((?[X]:((~funny(X)|calm(X))))<=>((brave(susan)|happy(susan))))&
(![X]:(creative(X)=>(kind(X)<~>quiet(X))))&
(((brave(john)<~>~old(john)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(((~humble(mary)<~>~kind(mary)))<=>((~tall(susan)&funny(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>generous(X)))&
((~brave(susan)|generous(susan)))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~quiet(X)|~kind(X))))&
((~generous(lucy)<~>quiet(lucy)))&
(?[X]:((~brave(X)|funny(X)))) | funny(mary) | [
"p7",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6677007795302921635134728
% SZS output start Proof for 6677007795302921635134728
8. ! [X0] : ((~creative(X0) | ~generous(X0)) <=> creative(X0)) [input p7]
10. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (quiet(X0) <~> kind(X0))) [input p9]
13. ! [X0] : (creative(X0) => (kind(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> generous(X0)) [input p15]
23. ~funny(mary) [input hypothesis]
30. ! [X0] : ((kind(X0) <~> quiet(X0)) | ~creative(X0)) [ennf transformation 13]
47. ! [X0] : (((~creative(X0) | ~generous(X0)) | ~creative(X0)) & (creative(X0) | (creative(X0) & generous(X0)))) [nnf transformation 8]
48. ! [X0] : ((~creative(X0) | ~generous(X0) | ~creative(X0)) & (creative(X0) | (creative(X0) & generous(X0)))) [flattening 47]
53. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 10]
61. ! [X0] : (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~creative(X0)) [nnf transformation 30]
68. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) | patient(X0)))) [nnf transformation 16]
69. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ~generous(X0)) & (generous(X0) | quiet(X0) | patient(X0))) [flattening 68]
104. creative(X0) | creative(X0) [cnf transformation 48]
105. ~creative(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 48]
116. ~quiet(X0) | funny(X0) | kind(X0) | generous(X0) [cnf transformation 53]
117. ~kind(X0) | funny(X0) | quiet(X0) | generous(X0) [cnf transformation 53]
127. quiet(X0) | kind(X0) | ~creative(X0) [cnf transformation 61]
128. ~quiet(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 61]
145. ~generous(X0) | ~quiet(X0) [cnf transformation 69]
154. ~funny(mary) [cnf transformation 23]
155. creative(X0) [duplicate literal removal 104]
156. ~generous(X0) | ~creative(X0) [duplicate literal removal 105]
285. ~kind(X0) | ~quiet(X0) [subsumption resolution 128,155]
286. kind(X0) | quiet(X0) [subsumption resolution 127,155]
326. 36 <=> kind(mary) [avatar definition]
327. ~kind(mary) <- (~36) [avatar component clause 326]
328. kind(mary) <- (36) [avatar component clause 326]
371. quiet(mary) <- (~36) [resolution 286,327]
415. funny(mary) | kind(mary) | generous(mary) <- (~36) [resolution 116,371]
417. kind(mary) | generous(mary) <- (~36) [subsumption resolution 415,154]
418. generous(mary) <- (~36) [subsumption resolution 417,327]
436. ~quiet(mary) <- (~36) [resolution 418,145]
442. $false <- (~36) [subsumption resolution 436,371]
443. 36 [avatar contradiction clause 442]
452. ~quiet(mary) <- (36) [resolution 328,285]
453. funny(X0) | quiet(X0) | generous(X0) | quiet(X0) [resolution 117,286]
455. funny(X0) | quiet(X0) | generous(X0) [duplicate literal removal 453]
473. quiet(mary) | generous(mary) [resolution 455,154]
479. generous(mary) <- (36) [subsumption resolution 473,452]
492. ~creative(mary) <- (36) [resolution 479,156]
497. $false <- (36) [subsumption resolution 492,155]
498. ~36 [avatar contradiction clause 497]
499. $false [avatar sat refutation 443,498]
% SZS output end Proof for 6677007795302921635134728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not quiet then mary is not patient and vice versa.
Everyone who is not strong is either not rich or wise.
Everyone who is creative is tall or funny and vice versa.
Everyone who is both not kind and not happy is not wise or calm.
Everyone who is either not funny or not patient is both not funny and not quiet and vice versa.
If mary is either wise or not tall then john is not humble.
Everyone who is either curious or calm is either creative or funny.
Everyone who is both rich and quiet is either calm or not quiet.
If someone is not funny then alice is both creative and curious and vice versa.
If fred is not quiet or not creative then mary is both happy and humble.
Everyone who is tall is both not calm and not tall and vice versa.
If someone is both not happy and strong then someone is not happy or not calm and vice versa.
If fred is not curious or patient then john is either not kind or not happy and vice versa.
If someone is not rich or not tall then someone is calm or patient and vice versa.
If alice is not brave then mary is not generous and vice versa.
Someone is not tall.
Fred is either funny or not calm.
Mary is both happy and rich.
John is not generous.
Someone is curious or calm.
Someone is quiet.
Someone is either not kind or generous.
Susan is either not creative or calm. | Susan is tall. | contradiction | ((?[X]:((calm(X)&~quiet(X))))<=>(~patient(mary)))&
(![X]:(~strong(X)=>(~rich(X)<~>wise(X))))&
(![X]:(creative(X)<=>(tall(X)|funny(X))))&
(![X]:((~kind(X)&~happy(X))=>(~wise(X)|calm(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~funny(X)&~quiet(X))))&
(((wise(mary)<~>~tall(mary)))=>(~humble(john)))&
(![X]:((curious(X)<~>calm(X))=>(creative(X)<~>funny(X))))&
(![X]:((rich(X)&quiet(X))=>(calm(X)<~>~quiet(X))))&
((?[X]:(~funny(X)))<=>((creative(alice)&curious(alice))))&
(((~quiet(fred)|~creative(fred)))=>((happy(mary)&humble(mary))))&
(![X]:(tall(X)<=>(~calm(X)&~tall(X))))&
((?[X]:((~happy(X)&strong(X))))<=>(?[X]:((~happy(X)|~calm(X)))))&
(((~curious(fred)|patient(fred)))<=>((~kind(john)<~>~happy(john))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((~brave(alice))<=>(~generous(mary)))&
(?[X]:(~tall(X)))&
((funny(fred)<~>~calm(fred)))&
((happy(mary)&rich(mary)))&
(~generous(john))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)<~>generous(X))))&
((~creative(susan)<~>calm(susan))) | tall(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8474715481262355715700813
% SZS output start Proof for 8474715481262355715700813
11. ! [X0] : (tall(X0) <=> (~tall(X0) & ~calm(X0))) [input p10]
24. tall(susan) [input hypothesis]
52. ! [X0] : ((tall(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [nnf transformation 11]
53. ! [X0] : ((tall(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [flattening 52]
109. ~tall(X0) | ~tall(X0) [cnf transformation 53]
140. tall(susan) [cnf transformation 24]
141. ~tall(X0) [duplicate literal removal 109]
336. $false [subsumption resolution 140,141]
% SZS output end Proof for 8474715481262355715700813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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