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 mary is funny then fred is not creative or humble and vice versa. If someone is tall then john is both rich and patient. If someone is both rich and tall then susan is happy. Everyone who is either generous or happy is either not humble or generous and vice versa. If lucy is not funny or happy then someone is both not old and not quiet. Everyone who is creative or wise is both generous and wise and vice versa. Everyone who is both not wise and rich is both not generous and brave and vice versa. Everyone who is both not rich and not patient is generous and vice versa. If fred is either not tall or not wise then someone is calm. If someone is either not tall or funny then someone is both wise and not calm and vice versa. If someone is either curious or old then john is both tall and not humble and vice versa. Everyone who is not old or old is both not curious and strong and vice versa. If someone is brave then mary is funny and vice versa. If mary is patient or not strong then someone is either brave or quiet. Everyone who is either not rich or not kind is both quiet and not humble. Everyone who is either not funny or old is both creative and not wise. Someone is funny or patient. Someone is not calm or generous. Susan is not kind or not rich. Someone is both brave and strong. Alice is both happy and not kind. Someone is both strong and not calm. Someone is creative. | Fred is not tall. | neutral | ((funny(mary))<=>((~creative(fred)|humble(fred))))&
((?[X]:(tall(X)))=>((rich(john)&patient(john))))&
((?[X]:((rich(X)&tall(X))))=>(happy(susan)))&
(![X]:((generous(X)<~>happy(X))<=>(~humble(X)<~>generous(X))))&
(((~funny(lucy)|happy(lucy)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((creative(X)|wise(X))<=>(generous(X)&wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(~generous(X)&brave(X))))&
(![X]:((~rich(X)&~patient(X))<=>generous(X)))&
(((~tall(fred)<~>~wise(fred)))=>(?[X]:(calm(X))))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
((?[X]:((curious(X)<~>old(X))))<=>((tall(john)&~humble(john))))&
(![X]:((~old(X)|old(X))<=>(~curious(X)&strong(X))))&
((?[X]:(brave(X)))<=>(funny(mary)))&
(((patient(mary)|~strong(mary)))=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~rich(X)<~>~kind(X))=>(quiet(X)&~humble(X))))&
(![X]:((~funny(X)<~>old(X))=>(creative(X)&~wise(X))))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~calm(X)|generous(X))))&
((~kind(susan)|~rich(susan)))&
(?[X]:((brave(X)&strong(X))))&
((happy(alice)&~kind(alice)))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:(creative(X))) | ~tall(fred) | [] | null | 0 |
If someone is both calm and not rich then someone is old and vice versa.
If alice is both not funny and strong then susan is patient or not calm.
If someone is either not wise or not brave then someone is strong or curious.
If someone is creative or patient then alice is generous and vice versa.
Everyone who is strong is patient or brave and vice versa.
Everyone who is not funny is not patient or not brave.
If paul is either humble or not happy then someone is both happy and kind.
Everyone who is curious or not kind is not kind and vice versa.
If someone is both old and humble then paul is either generous or not kind and vice versa.
If susan is not generous or old then someone is not brave or not curious.
Everyone who is calm is both not creative and funny and vice versa.
Everyone who is kind is not humble and vice versa.
If someone is wise or not wise then someone is rich.
Everyone who is rich or old is both patient and not old.
Everyone who is not quiet is curious and vice versa.
If someone is both funny and not calm then someone is both not rich and not creative and vice versa.
Someone is either patient or not kind.
John is quiet.
Someone is both brave and humble.
Susan is both not humble and not happy.
Someone is both not quiet and generous.
Someone is both not funny and not patient. | John is curious. | contradiction | ((?[X]:((calm(X)&~rich(X))))<=>(?[X]:(old(X))))&
(((~funny(alice)&strong(alice)))=>((patient(susan)|~calm(susan))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((creative(X)|patient(X))))<=>(generous(alice)))&
(![X]:(strong(X)<=>(patient(X)|brave(X))))&
(![X]:(~funny(X)=>(~patient(X)|~brave(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((curious(X)|~kind(X))<=>~kind(X)))&
((?[X]:((old(X)&humble(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~generous(susan)|old(susan)))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(calm(X)<=>(~creative(X)&funny(X))))&
(![X]:(kind(X)<=>~humble(X)))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|old(X))=>(patient(X)&~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(?[X]:((patient(X)<~>~kind(X))))&
(quiet(john))&
(?[X]:((brave(X)&humble(X))))&
((~humble(susan)&~happy(susan)))&
(?[X]:((~quiet(X)&generous(X))))&
(?[X]:((~funny(X)&~patient(X)))) | curious(john) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8736773829801344985178850
% SZS output start Proof for 8736773829801344985178850
15. ! [X0] : (~quiet(X0) <=> curious(X0)) [input p14]
18. quiet(john) [input p17]
23. curious(john) [input hypothesis]
69. ! [X0] : ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))) [nnf transformation 15]
124. ~quiet(X0) | ~curious(X0) [cnf transformation 69]
131. quiet(john) [cnf transformation 18]
140. curious(john) [cnf transformation 23]
341. ~curious(john) [resolution 124,131]
343. $false [subsumption resolution 341,140]
% SZS output end Proof for 8736773829801344985178850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not wise is either curious or happy. Everyone who is strong or humble is either brave or not happy. Everyone who is either patient or curious is either creative or not curious. Everyone who is both patient and happy is not funny or not wise and vice versa. If lucy is kind then someone is either not wise or not calm. If someone is not generous or brave then someone is not tall or not calm. Everyone who is quiet or not generous is both calm and not old and vice versa. Everyone who is not brave is kind or not wise. Everyone who is happy or not rich is both not kind and not calm. Everyone who is brave or tall is both quiet and tall and vice versa. Everyone who is calm is both not humble and not wise. Everyone who is either happy or brave is curious and vice versa. If mary is rich then alice is either calm or curious. Everyone who is both not patient and strong is not strong. Everyone who is both not strong and funny is both not rich and old. Everyone who is either not quiet or old is both strong and not tall and vice versa. John is either humble or not curious. Someone is either not generous or rich. Someone is rich. Someone is both patient and rich. Someone is either funny or not wise. Someone is both happy and not humble. John is strong or not quiet. | John is wise. | entailment | (![X]:((~rich(X)&~wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((strong(X)|humble(X))=>(brave(X)<~>~happy(X))))&
(![X]:((patient(X)<~>curious(X))=>(creative(X)<~>~curious(X))))&
(![X]:((patient(X)&happy(X))<=>(~funny(X)|~wise(X))))&
((kind(lucy))=>(?[X]:((~wise(X)<~>~calm(X)))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(~brave(X)=>(kind(X)|~wise(X))))&
(![X]:((happy(X)|~rich(X))=>(~kind(X)&~calm(X))))&
(![X]:((brave(X)|tall(X))<=>(quiet(X)&tall(X))))&
(![X]:(calm(X)=>(~humble(X)&~wise(X))))&
(![X]:((happy(X)<~>brave(X))<=>curious(X)))&
((rich(mary))=>((calm(alice)<~>curious(alice))))&
(![X]:((~patient(X)&strong(X))=>~strong(X)))&
(![X]:((~strong(X)&funny(X))=>(~rich(X)&old(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(strong(X)&~tall(X))))&
((humble(john)<~>~curious(john)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((happy(X)&~humble(X))))&
((strong(john)|~quiet(john))) | wise(john) | [
"p1",
"p3",
"p6",
"p8",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 424782204287787815109439
% SZS output start Proof for 424782204287787815109439
2. ! [X0] : ((humble(X0) | strong(X0)) => (brave(X0) <~> ~happy(X0))) [input p1]
4. ! [X0] : ((happy(X0) & patient(X0)) <=> (~wise(X0) | ~funny(X0))) [input p3]
7. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (~old(X0) & calm(X0))) [input p6]
9. ! [X0] : ((~rich(X0) | happy(X0)) => (~calm(X0) & ~kind(X0))) [input p8]
10. ! [X0] : ((tall(X0) | brave(X0)) <=> (tall(X0) & quiet(X0))) [input p9]
12. ! [X0] : ((happy(X0) <~> brave(X0)) <=> curious(X0)) [input p11]
17. humble(john) <~> ~curious(john) [input p16]
24. ~wise(john) [input hypothesis]
28. ! [X0] : ((brave(X0) <~> ~happy(X0)) | (~humble(X0) & ~strong(X0))) [ennf transformation 2]
34. ! [X0] : ((~calm(X0) & ~kind(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 9]
42. ! [X0] : (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~humble(X0) & ~strong(X0))) [nnf transformation 28]
44. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~happy(X0) | ~patient(X0))) [flattening 44]
52. ! [X0] : (((~generous(X0) | quiet(X0)) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 7]
53. ! [X0] : ((~generous(X0) | quiet(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [flattening 52]
54. ! [X0] : (((tall(X0) | brave(X0)) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 10]
55. ! [X0] : ((tall(X0) | brave(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 54]
56. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~curious(X0)) & (curious(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 12]
60. (curious(john) | ~humble(john)) & (~curious(john) | humble(john)) [nnf transformation 17]
76. ~humble(X0) | brave(X0) | ~happy(X0) [cnf transformation 42]
87. happy(X0) | wise(X0) [cnf transformation 45]
92. ~quiet(X0) | calm(X0) [cnf transformation 53]
100. ~calm(X0) | ~happy(X0) [cnf transformation 34]
102. ~brave(X0) | quiet(X0) [cnf transformation 55]
109. ~happy(X0) | brave(X0) | curious(X0) [cnf transformation 56]
124. ~curious(john) | humble(john) [cnf transformation 60]
136. ~wise(john) [cnf transformation 24]
188. 11 <=> humble(john) [avatar definition]
189. humble(john) <- (11) [avatar component clause 188]
192. 12 <=> curious(john) [avatar definition]
196. 11 | ~12 [avatar split clause 124,192,188]
222. 18 <=> quiet(john) [avatar definition]
223. quiet(john) <- (18) [avatar component clause 222]
400. 38 <=> happy(john) [avatar definition]
401. happy(john) <- (38) [avatar component clause 400]
402. ~happy(john) <- (~38) [avatar component clause 400]
404. 39 <=> brave(john) [avatar definition]
406. brave(john) <- (39) [avatar component clause 404]
409. wise(john) <- (~38) [resolution 402,87]
412. $false <- (~38) [subsumption resolution 409,136]
413. 38 [avatar contradiction clause 412]
415. brave(john) | curious(john) <- (38) [resolution 401,109]
418. 12 | 39 | ~38 [avatar split clause 415,400,404,192]
419. brave(john) | ~happy(john) <- (11) [resolution 189,76]
420. brave(john) <- (11, 38) [subsumption resolution 419,401]
421. 39 | ~11 | ~38 [avatar split clause 420,400,188,404]
427. quiet(john) <- (39) [resolution 406,102]
430. 18 | ~39 [avatar split clause 427,404,222]
434. calm(john) <- (18) [resolution 223,92]
438. ~happy(john) <- (18) [resolution 434,100]
439. $false <- (18, 38) [subsumption resolution 438,401]
440. ~18 | ~38 [avatar contradiction clause 439]
441. $false [avatar sat refutation 196,413,418,421,430,440]
% SZS output end Proof for 424782204287787815109439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not kind is wise. If alice is either calm or humble then susan is both not wise and not quiet and vice versa. Everyone who is both not brave and not curious is both not patient and not tall and vice versa. If susan is either quiet or curious then someone is either not wise or not old and vice versa. Everyone who is both not rich and not calm is either tall or not wise and vice versa. Everyone who is wise is both not wise and not tall. Everyone who is not humble or generous is both not curious and quiet. Everyone who is either not brave or happy is creative or patient and vice versa. Everyone who is both not brave and generous is funny or wise. Everyone who is both not kind and humble is both not creative and patient and vice versa. Everyone who is not funny or not curious is both not curious and not brave. If someone is not humble then alice is both generous and kind and vice versa. If john is both quiet and not humble then paul is tall or not rich. If fred is not brave then john is either not humble or not tall and vice versa. Everyone who is not humble is strong or not creative. If john is either not creative or strong then susan is both not strong and not kind and vice versa. Someone is not humble or not creative. Someone is either not calm or strong. Someone is either strong or not strong. Someone is humble or strong. Fred is both not calm and kind. Someone is both not quiet and calm. Susan is not wise or happy. | Alice is not quiet. | neutral | (![X]:((~generous(X)<~>~kind(X))=>wise(X)))&
(((calm(alice)<~>humble(alice)))<=>((~wise(susan)&~quiet(susan))))&
(![X]:((~brave(X)&~curious(X))<=>(~patient(X)&~tall(X))))&
(((quiet(susan)<~>curious(susan)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~rich(X)&~calm(X))<=>(tall(X)<~>~wise(X))))&
(![X]:(wise(X)=>(~wise(X)&~tall(X))))&
(![X]:((~humble(X)|generous(X))=>(~curious(X)&quiet(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(creative(X)|patient(X))))&
(![X]:((~brave(X)&generous(X))=>(funny(X)|wise(X))))&
(![X]:((~kind(X)&humble(X))<=>(~creative(X)&patient(X))))&
(![X]:((~funny(X)|~curious(X))=>(~curious(X)&~brave(X))))&
((?[X]:(~humble(X)))<=>((generous(alice)&kind(alice))))&
(((quiet(john)&~humble(john)))=>((tall(paul)|~rich(paul))))&
((~brave(fred))<=>((~humble(john)<~>~tall(john))))&
(![X]:(~humble(X)=>(strong(X)|~creative(X))))&
(((~creative(john)<~>strong(john)))<=>((~strong(susan)&~kind(susan))))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((humble(X)|strong(X))))&
((~calm(fred)&kind(fred)))&
(?[X]:((~quiet(X)&calm(X))))&
((~wise(susan)|happy(susan))) | ~quiet(alice) | [] | null | 0 |
Everyone who is both not tall and not brave is either curious or not old and vice versa.
Everyone who is creative is humble.
If fred is kind or rich then someone is not generous.
If mary is either patient or brave then mary is both not creative and strong.
Everyone who is either rich or not quiet is either strong or not creative and vice versa.
Everyone who is not tall is both not brave and rich.
Everyone who is either tall or curious is not happy.
Everyone who is quiet or brave is either not rich or not strong and vice versa.
Everyone who is not wise is both not strong and not old and vice versa.
Everyone who is happy or quiet is not creative or tall and vice versa.
If someone is either generous or brave then john is both quiet and old.
Everyone who is tall is both generous and not generous and vice versa.
If john is either not generous or old then paul is happy and vice versa.
If someone is both creative and not humble then someone is both tall and creative and vice versa.
Everyone who is not creative or kind is funny or not generous and vice versa.
Everyone who is either not humble or not calm is either not happy or not old and vice versa.
Someone is not tall.
Fred is quiet or rich.
Someone is both not patient and not generous.
Someone is either old or not funny.
Someone is both rich and not happy. | John is not calm. | neutral | (![X]:((~tall(X)&~brave(X))<=>(curious(X)<~>~old(X))))&
(![X]:(creative(X)=>humble(X)))&
(((kind(fred)|rich(fred)))=>(?[X]:(~generous(X))))&
(((patient(mary)<~>brave(mary)))=>((~creative(mary)&strong(mary))))&
(![X]:((rich(X)<~>~quiet(X))<=>(strong(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(~brave(X)&rich(X))))&
(![X]:((tall(X)<~>curious(X))=>~happy(X)))&
(![X]:((quiet(X)|brave(X))<=>(~rich(X)<~>~strong(X))))&
(![X]:(~wise(X)<=>(~strong(X)&~old(X))))&
(![X]:((happy(X)|quiet(X))<=>(~creative(X)|tall(X))))&
((?[X]:((generous(X)<~>brave(X))))=>((quiet(john)&old(john))))&
(![X]:(tall(X)<=>(generous(X)&~generous(X))))&
(((~generous(john)<~>old(john)))<=>(happy(paul)))&
((?[X]:((creative(X)&~humble(X))))<=>(?[X]:((tall(X)&creative(X)))))&
(![X]:((~creative(X)|kind(X))<=>(funny(X)|~generous(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(~happy(X)<~>~old(X))))&
(?[X]:(~tall(X)))&
((quiet(fred)|rich(fred)))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:((rich(X)&~happy(X)))) | ~calm(john) | [] | null | 0 |
Everyone who is not patient or not humble is both generous and humble. If alice is not old or tall then someone is happy or not wise. If mary is either tall or strong then lucy is either not quiet or not tall and vice versa. Everyone who is either not generous or rich is not creative and vice versa. If mary is either not creative or not kind then susan is either not curious or happy. Everyone who is not tall or kind is either strong or not patient and vice versa. Everyone who is either not happy or brave is brave or patient. Everyone who is either not funny or not kind is patient and vice versa. Everyone who is tall is both not calm and calm. If mary is not quiet then someone is strong or not humble. Everyone who is not wise or not funny is old or not rich and vice versa. If mary is creative then someone is both curious and not wise and vice versa. Everyone who is not humble or not calm is both quiet and not tall. If paul is both not strong and humble then alice is both not curious and curious and vice versa. Everyone who is not patient or rich is both not brave and not quiet. Everyone who is strong is not patient or old and vice versa. Mary is either kind or creative. Someone is either quiet or not kind. Someone is kind. Someone is brave. Lucy is old. Alice is calm or rich. Someone is not old or not creative. Someone is either not calm or happy. | Mary is strong. | entailment | (![X]:((~patient(X)|~humble(X))=>(generous(X)&humble(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((happy(X)|~wise(X)))))&
(((tall(mary)<~>strong(mary)))<=>((~quiet(lucy)<~>~tall(lucy))))&
(![X]:((~generous(X)<~>rich(X))<=>~creative(X)))&
(((~creative(mary)<~>~kind(mary)))=>((~curious(susan)<~>happy(susan))))&
(![X]:((~tall(X)|kind(X))<=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))=>(brave(X)|patient(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>patient(X)))&
(![X]:(tall(X)=>(~calm(X)&calm(X))))&
((~quiet(mary))=>(?[X]:((strong(X)|~humble(X)))))&
(![X]:((~wise(X)|~funny(X))<=>(old(X)|~rich(X))))&
((creative(mary))<=>(?[X]:((curious(X)&~wise(X)))))&
(![X]:((~humble(X)|~calm(X))=>(quiet(X)&~tall(X))))&
(((~strong(paul)&humble(paul)))<=>((~curious(alice)&curious(alice))))&
(![X]:((~patient(X)|rich(X))=>(~brave(X)&~quiet(X))))&
(![X]:(strong(X)<=>(~patient(X)|old(X))))&
((kind(mary)<~>creative(mary)))&
(?[X]:((quiet(X)<~>~kind(X))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
(old(lucy))&
((calm(alice)|rich(alice)))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:((~calm(X)<~>happy(X)))) | strong(mary) | [
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6990777678624325996731148
% SZS output start Proof for 6990777678624325996731148
6. ! [X0] : ((kind(X0) | ~tall(X0)) <=> (strong(X0) <~> ~patient(X0))) [input p5]
9. ! [X0] : (tall(X0) => (calm(X0) & ~calm(X0))) [input p8]
16. ! [X0] : (strong(X0) <=> (old(X0) | ~patient(X0))) [input p15]
25. ~strong(mary) [input hypothesis]
31. ! [X0] : ((calm(X0) & ~calm(X0)) | ~tall(X0)) [ennf transformation 9]
40. ! [X0] : (((kind(X0) | ~tall(X0)) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) & (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | (~kind(X0) & tall(X0)))) [nnf transformation 6]
41. ! [X0] : ((kind(X0) | ~tall(X0) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) & (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | (~kind(X0) & tall(X0)))) [flattening 40]
54. ! [X0] : ((strong(X0) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ~strong(X0))) [nnf transformation 16]
55. ! [X0] : ((strong(X0) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~strong(X0))) [flattening 54]
91. ~patient(X0) | strong(X0) | tall(X0) [cnf transformation 41]
103. ~calm(X0) | ~tall(X0) [cnf transformation 31]
104. ~tall(X0) | calm(X0) [cnf transformation 31]
126. strong(X0) | patient(X0) [cnf transformation 55]
139. ~strong(mary) [cnf transformation 25]
173. 8 <=> strong(mary) [avatar definition]
175. ~strong(mary) <- (~8) [avatar component clause 173]
204. ~tall(X0) [subsumption resolution 103,104]
281. ~8 [avatar split clause 139,173]
287. patient(mary) <- (~8) [resolution 126,175]
319. strong(mary) | tall(mary) <- (~8) [resolution 287,91]
320. tall(mary) <- (~8) [subsumption resolution 319,175]
321. $false <- (~8) [subsumption resolution 320,204]
322. 8 [avatar contradiction clause 321]
323. $false [avatar sat refutation 281,322]
% SZS output end Proof for 6990777678624325996731148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both tall and not calm then someone is both happy and not tall. If paul is both tall and not happy then someone is both calm and happy. Everyone who is creative is both not funny and rich. If lucy is either generous or not rich then someone is happy or not funny and vice versa. Everyone who is either humble or not calm is not happy. Everyone who is happy is humble and vice versa. Everyone who is either not curious or not funny is strong and vice versa. Everyone who is either not kind or not rich is either not happy or brave and vice versa. Everyone who is both not calm and not humble is not rich or wise and vice versa. If alice is not calm then someone is not strong or not brave and vice versa. Everyone who is happy is not curious or not happy and vice versa. If lucy is not tall then mary is not kind or not funny and vice versa. Everyone who is either creative or not old is kind and vice versa. If someone is either generous or not calm then paul is either tall or not kind and vice versa. Everyone who is either not happy or not strong is both not creative and strong. If mary is not kind then fred is not old and vice versa. Fred is both not calm and not brave. Fred is either not tall or not quiet. Alice is not wise or quiet. Susan is not generous. Someone is strong or not humble. Mary is quiet or not happy. Someone is creative or not curious. | Paul is kind. | neutral | (((tall(fred)&~calm(fred)))=>(?[X]:((happy(X)&~tall(X)))))&
(((tall(paul)&~happy(paul)))=>(?[X]:((calm(X)&happy(X)))))&
(![X]:(creative(X)=>(~funny(X)&rich(X))))&
(((generous(lucy)<~>~rich(lucy)))<=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~happy(X)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~curious(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~rich(X)|wise(X))))&
((~calm(alice))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(happy(X)<=>(~curious(X)|~happy(X))))&
((~tall(lucy))<=>((~kind(mary)|~funny(mary))))&
(![X]:((creative(X)<~>~old(X))<=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((tall(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~strong(X))=>(~creative(X)&strong(X))))&
((~kind(mary))<=>(~old(fred)))&
((~calm(fred)&~brave(fred)))&
((~tall(fred)<~>~quiet(fred)))&
((~wise(alice)|quiet(alice)))&
(~generous(susan))&
(?[X]:((strong(X)|~humble(X))))&
((quiet(mary)|~happy(mary)))&
(?[X]:((creative(X)|~curious(X)))) | kind(paul) | [] | null | 0 |
If someone is both not humble and not generous then paul is both not funny and old and vice versa.
Everyone who is wise or strong is rich or not patient and vice versa.
Everyone who is kind is either curious or not generous and vice versa.
If paul is either not quiet or generous then john is either strong or calm.
Everyone who is not rich is either patient or happy and vice versa.
If paul is wise then lucy is rich.
Everyone who is kind is both not strong and patient.
Everyone who is old is not creative and vice versa.
If mary is both curious and humble then someone is not wise or patient and vice versa.
If mary is old then alice is either not rich or not tall and vice versa.
Everyone who is not creative or humble is both happy and not quiet and vice versa.
Everyone who is humble or calm is not quiet and vice versa.
If susan is not generous or not brave then someone is both not calm and funny and vice versa.
Everyone who is calm or curious is not brave or not humble.
Everyone who is both creative and calm is creative or calm.
Everyone who is either not kind or not curious is both not old and calm and vice versa.
Someone is both not tall and quiet.
Mary is both not curious and happy.
Someone is both curious and not generous.
Alice is both not quiet and not rich.
Mary is both not creative and brave.
Someone is either not patient or not happy.
Mary is quiet or not curious. | Paul is not old. | neutral | ((?[X]:((~humble(X)&~generous(X))))<=>((~funny(paul)&old(paul))))&
(![X]:((wise(X)|strong(X))<=>(rich(X)|~patient(X))))&
(![X]:(kind(X)<=>(curious(X)<~>~generous(X))))&
(((~quiet(paul)<~>generous(paul)))=>((strong(john)<~>calm(john))))&
(![X]:(~rich(X)<=>(patient(X)<~>happy(X))))&
((wise(paul))=>(rich(lucy)))&
(![X]:(kind(X)=>(~strong(X)&patient(X))))&
(![X]:(old(X)<=>~creative(X)))&
(((curious(mary)&humble(mary)))<=>(?[X]:((~wise(X)|patient(X)))))&
((old(mary))<=>((~rich(alice)<~>~tall(alice))))&
(![X]:((~creative(X)|humble(X))<=>(happy(X)&~quiet(X))))&
(![X]:((humble(X)|calm(X))<=>~quiet(X)))&
(((~generous(susan)|~brave(susan)))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:((calm(X)|curious(X))=>(~brave(X)|~humble(X))))&
(![X]:((creative(X)&calm(X))=>(creative(X)|calm(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>(~old(X)&calm(X))))&
(?[X]:((~tall(X)&quiet(X))))&
((~curious(mary)&happy(mary)))&
(?[X]:((curious(X)&~generous(X))))&
((~quiet(alice)&~rich(alice)))&
((~creative(mary)&brave(mary)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((quiet(mary)|~curious(mary))) | ~old(paul) | [] | null | 0 |
Everyone who is either not funny or quiet is not curious. Everyone who is both old and not rich is creative and vice versa. Everyone who is not rich is not patient and vice versa. Everyone who is not creative is both quiet and generous and vice versa. If someone is not brave or not generous then someone is either rich or not rich. If john is either not happy or tall then mary is both funny and tall. Everyone who is either patient or not creative is happy or not strong. Everyone who is generous is both kind and curious and vice versa. Everyone who is either strong or generous is not funny or rich and vice versa. Everyone who is not creative is both not brave and strong. If someone is funny then someone is not curious or not brave. Everyone who is not patient or not old is not strong or not curious and vice versa. If someone is happy or rich then john is either not rich or not humble. Everyone who is both calm and not tall is humble or tall. Everyone who is either not old or curious is not rich or humble and vice versa. If someone is not brave or generous then mary is both not kind and happy. Fred is humble or not curious. Alice is not generous. Someone is quiet or tall. Mary is not strong. Paul is both not rich and humble. Someone is happy or funny. Fred is either not calm or calm. | Paul is curious. | entailment | (![X]:((~funny(X)<~>quiet(X))=>~curious(X)))&
(![X]:((old(X)&~rich(X))<=>creative(X)))&
(![X]:(~rich(X)<=>~patient(X)))&
(![X]:(~creative(X)<=>(quiet(X)&generous(X))))&
((?[X]:((~brave(X)|~generous(X))))=>(?[X]:((rich(X)<~>~rich(X)))))&
(((~happy(john)<~>tall(john)))=>((funny(mary)&tall(mary))))&
(![X]:((patient(X)<~>~creative(X))=>(happy(X)|~strong(X))))&
(![X]:(generous(X)<=>(kind(X)&curious(X))))&
(![X]:((strong(X)<~>generous(X))<=>(~funny(X)|rich(X))))&
(![X]:(~creative(X)=>(~brave(X)&strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~curious(X)|~brave(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~strong(X)|~curious(X))))&
((?[X]:((happy(X)|rich(X))))=>((~rich(john)<~>~humble(john))))&
(![X]:((calm(X)&~tall(X))=>(humble(X)|tall(X))))&
(![X]:((~old(X)<~>curious(X))<=>(~rich(X)|humble(X))))&
((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))&
((humble(fred)|~curious(fred)))&
(~generous(alice))&
(?[X]:((quiet(X)|tall(X))))&
(~strong(mary))&
((~rich(paul)&humble(paul)))&
(?[X]:((happy(X)|funny(X))))&
((~calm(fred)<~>calm(fred))) | curious(paul) | [
"p1",
"p3",
"p7",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3197880967789249167715813
% SZS output start Proof for 3197880967789249167715813
2. ! [X0] : ((~rich(X0) & old(X0)) <=> creative(X0)) [input p1]
4. ! [X0] : (~creative(X0) <=> (generous(X0) & quiet(X0))) [input p3]
8. ! [X0] : (generous(X0) <=> (curious(X0) & kind(X0))) [input p7]
9. ! [X0] : ((strong(X0) <~> generous(X0)) <=> (rich(X0) | ~funny(X0))) [input p8]
10. ! [X0] : (~creative(X0) => (strong(X0) & ~brave(X0))) [input p9]
12. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (~curious(X0) | ~strong(X0))) [input p11]
15. ! [X0] : ((~old(X0) <~> curious(X0)) <=> (humble(X0) | ~rich(X0))) [input p14]
24. ~curious(paul) [input hypothesis]
32. ! [X0] : ((strong(X0) & ~brave(X0)) | creative(X0)) [ennf transformation 10]
39. ! [X0] : (((~rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) | ~old(X0)))) [nnf transformation 2]
40. ! [X0] : (((~rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | rich(X0) | ~old(X0))) [flattening 39]
42. ! [X0] : ((~creative(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | creative(X0))) [nnf transformation 4]
43. ! [X0] : ((~creative(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | creative(X0))) [flattening 42]
50. ! [X0] : ((generous(X0) | (~curious(X0) | ~kind(X0))) & ((curious(X0) & kind(X0)) | ~generous(X0))) [nnf transformation 8]
51. ! [X0] : ((generous(X0) | ~curious(X0) | ~kind(X0)) & ((curious(X0) & kind(X0)) | ~generous(X0))) [flattening 50]
52. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [flattening 52]
57. ! [X0] : (((~old(X0) | ~patient(X0)) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | (old(X0) & patient(X0)))) [nnf transformation 12]
58. ! [X0] : ((~old(X0) | ~patient(X0) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | (old(X0) & patient(X0)))) [flattening 57]
60. ! [X0] : ((((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (~humble(X0) & rich(X0))) & ((humble(X0) | ~rich(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (~humble(X0) & rich(X0))) & (humble(X0) | ~rich(X0) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0))))) [flattening 60]
70. ~creative(X0) | old(X0) [cnf transformation 40]
71. ~creative(X0) | ~rich(X0) [cnf transformation 40]
75. generous(X0) | creative(X0) [cnf transformation 43]
88. ~generous(X0) | curious(X0) [cnf transformation 51]
95. ~strong(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 53]
97. strong(X0) | creative(X0) [cnf transformation 32]
100. ~strong(X0) | ~curious(X0) | old(X0) [cnf transformation 58]
110. ~old(X0) | curious(X0) | rich(X0) [cnf transformation 61]
127. ~curious(paul) [cnf transformation 24]
162. 8 <=> ! [X0] : ~rich(X0) [avatar definition]
163. ~rich(X0) <- (8) [avatar component clause 162]
232. creative(X0) | curious(X0) [resolution 88,75]
264. ~generous(X1) | ~rich(X1) | creative(X1) [resolution 95,97]
265. ~rich(X1) | creative(X1) [subsumption resolution 264,75]
266. ~rich(X1) [subsumption resolution 265,71]
267. 8 [avatar split clause 266,162]
274. ~curious(X1) | old(X1) | creative(X1) [resolution 100,97]
276. old(X1) | creative(X1) [subsumption resolution 274,232]
277. old(X1) [subsumption resolution 276,70]
286. curious(X0) | rich(X0) [resolution 110,277]
290. curious(X0) <- (8) [subsumption resolution 286,163]
294. $false <- (8) [resolution 290,127]
297. ~8 [avatar contradiction clause 294]
299. $false [avatar sat refutation 267,297]
% SZS output end Proof for 3197880967789249167715813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either not quiet or patient. Everyone who is not quiet or not old is quiet and vice versa. Everyone who is both not humble and not quiet is not generous and vice versa. Everyone who is either curious or not tall is both funny and tall. If someone is both tall and strong then susan is either generous or not curious and vice versa. Everyone who is both rich and happy is either curious or strong. If susan is both not calm and funny then alice is not tall or not funny and vice versa. Everyone who is both old and kind is both not patient and not rich. Everyone who is not happy is not old. If john is both not generous and rich then someone is not strong and vice versa. Everyone who is both not curious and not humble is not wise. If someone is not strong or not humble then paul is either funny or quiet. If someone is both not happy and calm then john is either not calm or happy and vice versa. Everyone who is happy or humble is either kind or curious. Everyone who is not generous is not creative or old. Everyone who is funny or not generous is either happy or old. Susan is happy or quiet. Someone is both patient and not wise. Susan is either not kind or curious. Someone is calm or patient. Someone is not creative or not strong. Someone is not funny or not humble. Lucy is either rich or tall. Someone is kind or humble. | John is quiet. | entailment | (![X]:(~humble(X)=>(~quiet(X)<~>patient(X))))&
(![X]:((~quiet(X)|~old(X))<=>quiet(X)))&
(![X]:((~humble(X)&~quiet(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~tall(X))=>(funny(X)&tall(X))))&
((?[X]:((tall(X)&strong(X))))<=>((generous(susan)<~>~curious(susan))))&
(![X]:((rich(X)&happy(X))=>(curious(X)<~>strong(X))))&
(((~calm(susan)&funny(susan)))<=>((~tall(alice)|~funny(alice))))&
(![X]:((old(X)&kind(X))=>(~patient(X)&~rich(X))))&
(![X]:(~happy(X)=>~old(X)))&
(((~generous(john)&rich(john)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&~humble(X))=>~wise(X)))&
((?[X]:((~strong(X)|~humble(X))))=>((funny(paul)<~>quiet(paul))))&
((?[X]:((~happy(X)&calm(X))))<=>((~calm(john)<~>happy(john))))&
(![X]:((happy(X)|humble(X))=>(kind(X)<~>curious(X))))&
(![X]:(~generous(X)=>(~creative(X)|old(X))))&
(![X]:((funny(X)|~generous(X))=>(happy(X)<~>old(X))))&
((happy(susan)|quiet(susan)))&
(?[X]:((patient(X)&~wise(X))))&
((~kind(susan)<~>curious(susan)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:((~funny(X)|~humble(X))))&
((rich(lucy)<~>tall(lucy)))&
(?[X]:((kind(X)|humble(X)))) | quiet(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7139459661250033768696030
% SZS output start Proof for 7139459661250033768696030
2. ! [X0] : ((~old(X0) | ~quiet(X0)) <=> quiet(X0)) [input p1]
25. ~quiet(john) [input hypothesis]
41. ! [X0] : (((~old(X0) | ~quiet(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) & quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((~old(X0) | ~quiet(X0) | ~quiet(X0)) & (quiet(X0) | (old(X0) & quiet(X0)))) [flattening 41]
77. quiet(X0) | quiet(X0) [cnf transformation 42]
133. ~quiet(john) [cnf transformation 25]
135. quiet(X0) [duplicate literal removal 77]
271. $false [subsumption resolution 133,135]
% SZS output end Proof for 7139459661250033768696030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not funny is kind and vice versa.
If someone is either not kind or strong then someone is not curious or not creative and vice versa.
Everyone who is not happy or not old is happy or not curious and vice versa.
If mary is either not rich or generous then someone is both not creative and not quiet and vice versa.
Everyone who is happy is not wise.
Everyone who is both generous and not rich is not calm or calm and vice versa.
Everyone who is patient or creative is both not tall and tall.
If lucy is happy then fred is humble and vice versa.
Everyone who is both old and not wise is not calm or rich.
If someone is both not wise and happy then someone is either not happy or not generous.
If someone is either not patient or old then someone is patient and vice versa.
If alice is either not strong or patient then alice is not generous or not tall and vice versa.
Everyone who is generous is not rich or not generous and vice versa.
Everyone who is brave is not humble.
If someone is both brave and humble then someone is creative or not kind.
If susan is creative or tall then fred is quiet or not calm.
Someone is not creative or wise.
Someone is either happy or wise.
Someone is both humble and not patient.
John is wise.
Someone is not funny or tall.
Susan is both strong and kind.
Paul is not strong. | Susan is tall. | neutral | (![X]:((calm(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((~curious(X)|~creative(X)))))&
(![X]:((~happy(X)|~old(X))<=>(happy(X)|~curious(X))))&
(((~rich(mary)<~>generous(mary)))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:(happy(X)=>~wise(X)))&
(![X]:((generous(X)&~rich(X))<=>(~calm(X)|calm(X))))&
(![X]:((patient(X)|creative(X))=>(~tall(X)&tall(X))))&
((happy(lucy))<=>(humble(fred)))&
(![X]:((old(X)&~wise(X))=>(~calm(X)|rich(X))))&
((?[X]:((~wise(X)&happy(X))))=>(?[X]:((~happy(X)<~>~generous(X)))))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(patient(X))))&
(((~strong(alice)<~>patient(alice)))<=>((~generous(alice)|~tall(alice))))&
(![X]:(generous(X)<=>(~rich(X)|~generous(X))))&
(![X]:(brave(X)=>~humble(X)))&
((?[X]:((brave(X)&humble(X))))=>(?[X]:((creative(X)|~kind(X)))))&
(((creative(susan)|tall(susan)))=>((quiet(fred)|~calm(fred))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:((humble(X)&~patient(X))))&
(wise(john))&
(?[X]:((~funny(X)|tall(X))))&
((strong(susan)&kind(susan)))&
(~strong(paul)) | tall(susan) | [] | null | 0 |
Everyone who is not patient or not quiet is either kind or not curious.
Everyone who is both not quiet and happy is quiet or rich and vice versa.
Everyone who is both calm and not rich is either wise or generous.
Everyone who is humble or not old is both happy and not curious.
If mary is both not kind and not quiet then paul is not humble or brave.
Everyone who is not creative is not calm.
If someone is both old and not curious then paul is either quiet or curious and vice versa.
If someone is both patient and wise then mary is either not brave or not generous.
If susan is rich then paul is either not strong or not kind.
Everyone who is not tall is both not humble and calm.
Everyone who is either not funny or curious is both not rich and curious and vice versa.
Everyone who is both calm and patient is not old or not creative.
Everyone who is either quiet or not rich is happy.
Everyone who is either not wise or rich is either calm or not humble.
Everyone who is not happy or creative is not tall.
If paul is not funny or not tall then someone is either generous or not brave.
Someone is not creative or calm.
Someone is both not old and not patient.
Susan is kind.
Someone is not humble.
Someone is not quiet.
Lucy is both not humble and not brave.
Fred is either strong or humble. | Susan is happy. | entailment | (![X]:((~patient(X)|~quiet(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~quiet(X)&happy(X))<=>(quiet(X)|rich(X))))&
(![X]:((calm(X)&~rich(X))=>(wise(X)<~>generous(X))))&
(![X]:((humble(X)|~old(X))=>(happy(X)&~curious(X))))&
(((~kind(mary)&~quiet(mary)))=>((~humble(paul)|brave(paul))))&
(![X]:(~creative(X)=>~calm(X)))&
((?[X]:((old(X)&~curious(X))))<=>((quiet(paul)<~>curious(paul))))&
((?[X]:((patient(X)&wise(X))))=>((~brave(mary)<~>~generous(mary))))&
((rich(susan))=>((~strong(paul)<~>~kind(paul))))&
(![X]:(~tall(X)=>(~humble(X)&calm(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~rich(X)&curious(X))))&
(![X]:((calm(X)&patient(X))=>(~old(X)|~creative(X))))&
(![X]:((quiet(X)<~>~rich(X))=>happy(X)))&
(![X]:((~wise(X)<~>rich(X))=>(calm(X)<~>~humble(X))))&
(![X]:((~happy(X)|creative(X))=>~tall(X)))&
(((~funny(paul)|~tall(paul)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:((~old(X)&~patient(X))))&
(kind(susan))&
(?[X]:(~humble(X)))&
(?[X]:(~quiet(X)))&
((~humble(lucy)&~brave(lucy)))&
((strong(fred)<~>humble(fred))) | happy(susan) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 852111399517046149926862
% SZS output start Proof for 852111399517046149926862
2. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (rich(X0) | quiet(X0))) [input p1]
13. ! [X0] : ((quiet(X0) <~> ~rich(X0)) => happy(X0)) [input p12]
24. ~happy(susan) [input hypothesis]
37. ! [X0] : (happy(X0) | (quiet(X0) <=> ~rich(X0))) [ennf transformation 13]
42. ! [X0] : (((happy(X0) & ~quiet(X0)) | (~rich(X0) & ~quiet(X0))) & ((rich(X0) | quiet(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((happy(X0) & ~quiet(X0)) | (~rich(X0) & ~quiet(X0))) & (rich(X0) | quiet(X0) | ~happy(X0) | quiet(X0))) [flattening 42]
53. ! [X0] : (happy(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) [nnf transformation 37]
71. rich(X0) | quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 43]
72. ~quiet(X0) | ~quiet(X0) [cnf transformation 43]
75. ~rich(X0) | happy(X0) [cnf transformation 43]
104. happy(X0) | quiet(X0) | rich(X0) [cnf transformation 53]
125. ~happy(susan) [cnf transformation 24]
128. rich(X0) | quiet(X0) | ~happy(X0) [duplicate literal removal 71]
129. ~quiet(X0) [duplicate literal removal 72]
130. rich(X0) | ~happy(X0) [subsumption resolution 128,129]
194. happy(X0) | rich(X0) [subsumption resolution 104,129]
195. rich(X0) [subsumption resolution 194,130]
240. happy(X0) [resolution 75,195]
241. $false [resolution 240,125]
% SZS output end Proof for 852111399517046149926862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and tall is strong and vice versa.
Everyone who is both tall and not strong is not calm and vice versa.
Everyone who is curious is either not humble or not tall.
Everyone who is not tall is either not kind or not curious.
Everyone who is either not wise or funny is both strong and curious and vice versa.
Everyone who is either humble or not happy is funny.
If someone is wise or not humble then john is both old and strong.
Everyone who is both creative and rich is not funny or kind.
If someone is not funny or kind then someone is brave or kind.
Everyone who is tall or not kind is either old or strong.
Everyone who is both not humble and curious is both quiet and not happy and vice versa.
If alice is both creative and not creative then alice is both not brave and brave.
Everyone who is not quiet or not happy is patient and vice versa.
If someone is strong or not generous then someone is either not patient or humble and vice versa.
If john is both funny and not brave then paul is rich and vice versa.
Everyone who is either happy or not happy is both old and not calm.
Fred is either not old or quiet.
Someone is quiet.
Someone is kind.
Alice is patient.
Someone is not generous.
Someone is either not curious or not tall.
Susan is quiet. | Alice is old. | entailment | (![X]:((strong(X)&tall(X))<=>strong(X)))&
(![X]:((tall(X)&~strong(X))<=>~calm(X)))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>~curious(X))))&
(![X]:((~wise(X)<~>funny(X))<=>(strong(X)&curious(X))))&
(![X]:((humble(X)<~>~happy(X))=>funny(X)))&
((?[X]:((wise(X)|~humble(X))))=>((old(john)&strong(john))))&
(![X]:((creative(X)&rich(X))=>(~funny(X)|kind(X))))&
((?[X]:((~funny(X)|kind(X))))=>(?[X]:((brave(X)|kind(X)))))&
(![X]:((tall(X)|~kind(X))=>(old(X)<~>strong(X))))&
(![X]:((~humble(X)&curious(X))<=>(quiet(X)&~happy(X))))&
(((creative(alice)&~creative(alice)))=>((~brave(alice)&brave(alice))))&
(![X]:((~quiet(X)|~happy(X))<=>patient(X)))&
((?[X]:((strong(X)|~generous(X))))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(((funny(john)&~brave(john)))<=>(rich(paul)))&
(![X]:((happy(X)<~>~happy(X))=>(old(X)&~calm(X))))&
((~old(fred)<~>quiet(fred)))&
(?[X]:(quiet(X)))&
(?[X]:(kind(X)))&
(patient(alice))&
(?[X]:(~generous(X)))&
(?[X]:((~curious(X)<~>~tall(X))))&
(quiet(susan)) | old(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8092227544100791560640938
% SZS output start Proof for 8092227544100791560640938
16. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (~calm(X0) & old(X0))) [input p15]
24. ~old(alice) [input hypothesis]
39. ! [X0] : ((~calm(X0) & old(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 16]
62. ! [X0] : ((~calm(X0) & old(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 39]
119. old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 62]
120. old(X0) | happy(X0) | happy(X0) [cnf transformation 62]
132. ~old(alice) [cnf transformation 24]
133. old(X0) | ~happy(X0) [duplicate literal removal 119]
134. old(X0) | happy(X0) [duplicate literal removal 120]
222. old(X0) [subsumption resolution 133,134]
234. $false [subsumption resolution 132,222]
% SZS output end Proof for 8092227544100791560640938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not calm is generous and vice versa. If susan is both not tall and not quiet then susan is both not generous and not curious and vice versa. Everyone who is both not calm and kind is not creative or not funny and vice versa. If mary is funny or old then someone is not calm and vice versa. Everyone who is both not humble and not wise is both calm and not wise and vice versa. If john is both not brave and quiet then mary is either not funny or calm and vice versa. Everyone who is either old or calm is both not tall and humble and vice versa. If someone is either old or wise then someone is curious or not tall and vice versa. If someone is generous then lucy is either strong or not curious and vice versa. Everyone who is rich or not strong is both quiet and patient. If lucy is curious or humble then someone is quiet and vice versa. Everyone who is both brave and not happy is rich or not brave. If paul is old or not rich then mary is not creative or not calm and vice versa. Everyone who is wise or not kind is both not tall and not generous and vice versa. Everyone who is either generous or not happy is not happy and vice versa. Everyone who is either tall or humble is either kind or not funny. Susan is funny. Paul is calm. Someone is rich. Someone is both wise and not brave. John is both kind and not generous. Someone is brave or quiet. Lucy is both rich and strong. Someone is either not patient or not calm. | Mary is calm. | neutral | (![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(((~tall(susan)&~quiet(susan)))<=>((~generous(susan)&~curious(susan))))&
(![X]:((~calm(X)&kind(X))<=>(~creative(X)|~funny(X))))&
(((funny(mary)|old(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((~humble(X)&~wise(X))<=>(calm(X)&~wise(X))))&
(((~brave(john)&quiet(john)))<=>((~funny(mary)<~>calm(mary))))&
(![X]:((old(X)<~>calm(X))<=>(~tall(X)&humble(X))))&
((?[X]:((old(X)<~>wise(X))))<=>(?[X]:((curious(X)|~tall(X)))))&
((?[X]:(generous(X)))<=>((strong(lucy)<~>~curious(lucy))))&
(![X]:((rich(X)|~strong(X))=>(quiet(X)&patient(X))))&
(((curious(lucy)|humble(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:((brave(X)&~happy(X))=>(rich(X)|~brave(X))))&
(((old(paul)|~rich(paul)))<=>((~creative(mary)|~calm(mary))))&
(![X]:((wise(X)|~kind(X))<=>(~tall(X)&~generous(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~happy(X)))&
(![X]:((tall(X)<~>humble(X))=>(kind(X)<~>~funny(X))))&
(funny(susan))&
(calm(paul))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)&~brave(X))))&
((kind(john)&~generous(john)))&
(?[X]:((brave(X)|quiet(X))))&
((rich(lucy)&strong(lucy)))&
(?[X]:((~patient(X)<~>~calm(X)))) | calm(mary) | [] | null | 0 |
Everyone who is not wise is both wise and quiet.
Everyone who is not strong or not quiet is not quiet.
Everyone who is both brave and not patient is either tall or not happy and vice versa.
Everyone who is both not tall and not rich is brave or not brave and vice versa.
Everyone who is either not kind or quiet is not calm.
If john is both quiet and old then someone is either not happy or patient and vice versa.
Everyone who is either not wise or old is both kind and happy.
If lucy is not funny or not rich then someone is not generous and vice versa.
Everyone who is patient or not rich is either tall or calm.
Everyone who is not funny or kind is both not old and creative and vice versa.
If paul is patient or creative then alice is not quiet.
If susan is either creative or not creative then someone is either not brave or not humble and vice versa.
If alice is either strong or calm then someone is not quiet.
If someone is both not funny and not rich then alice is strong and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
Everyone who is not humble is strong or generous.
Someone is either not humble or creative.
Paul is either patient or quiet.
Someone is either not strong or not brave.
Someone is humble or not generous.
Someone is either not strong or quiet.
Alice is not curious or kind.
Paul is not generous. | Paul is happy. | entailment | (![X]:(~wise(X)=>(wise(X)&quiet(X))))&
(![X]:((~strong(X)|~quiet(X))=>~quiet(X)))&
(![X]:((brave(X)&~patient(X))<=>(tall(X)<~>~happy(X))))&
(![X]:((~tall(X)&~rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~kind(X)<~>quiet(X))=>~calm(X)))&
(((quiet(john)&old(john)))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>old(X))=>(kind(X)&happy(X))))&
(((~funny(lucy)|~rich(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:((patient(X)|~rich(X))=>(tall(X)<~>calm(X))))&
(![X]:((~funny(X)|kind(X))<=>(~old(X)&creative(X))))&
(((patient(paul)|creative(paul)))=>(~quiet(alice)))&
(((creative(susan)<~>~creative(susan)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((strong(alice)<~>calm(alice)))=>(?[X]:(~quiet(X))))&
((?[X]:((~funny(X)&~rich(X))))<=>(strong(alice)))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(![X]:(~humble(X)=>(strong(X)|generous(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
((patient(paul)<~>quiet(paul)))&
(?[X]:((~strong(X)<~>~brave(X))))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~curious(alice)|kind(alice)))&
(~generous(paul)) | happy(paul) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7629039884614241917663948
% SZS output start Proof for 7629039884614241917663948
1. ! [X0] : (~wise(X0) => (quiet(X0) & wise(X0))) [input p0]
3. ! [X0] : ((~patient(X0) & brave(X0)) <=> (tall(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (~brave(X0) | brave(X0))) [input p3]
6. (old(john) & quiet(john)) <=> ? [X0] : (~happy(X0) <~> patient(X0)) [input p5]
7. ! [X0] : ((~wise(X0) <~> old(X0)) => (happy(X0) & kind(X0))) [input p6]
10. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (creative(X0) & ~old(X0))) [input p9]
24. ~happy(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) & wise(X0)) | wise(X0)) [ennf transformation 1]
29. ! [X0] : ((happy(X0) & kind(X0)) | (~wise(X0) <=> old(X0))) [ennf transformation 7]
35. ! [X0] : (((~patient(X0) & brave(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (patient(X0) | ~brave(X0)))) [nnf transformation 3]
36. ! [X0] : (((~patient(X0) & brave(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | patient(X0) | ~brave(X0))) [flattening 35]
37. ! [X0] : (((~rich(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (rich(X0) | tall(X0)))) [nnf transformation 4]
38. ! [X0] : (((~rich(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | rich(X0) | tall(X0))) [flattening 37]
40. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (~old(john) | ~quiet(john))) [nnf transformation 6]
41. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~old(john) | ~quiet(john)) [flattening 40]
42. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X1] : ((~patient(X1) | happy(X1)) & (patient(X1) | ~happy(X1))) | ~old(john) | ~quiet(john)) [rectify 41]
43. ? [X1] : ((~patient(X1) | happy(X1)) & (patient(X1) | ~happy(X1))) => ((~patient(sK0) | happy(sK0)) & (patient(sK0) | ~happy(sK0))) [choice axiom]
44. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (((~patient(sK0) | happy(sK0)) & (patient(sK0) | ~happy(sK0))) | ~old(john) | ~quiet(john)) [skolemisation 42,43]
45. ! [X0] : ((happy(X0) & kind(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) [nnf transformation 29]
52. ! [X0] : (((kind(X0) | ~funny(X0)) | (~creative(X0) | old(X0))) & ((creative(X0) & ~old(X0)) | (~kind(X0) & funny(X0)))) [nnf transformation 10]
53. ! [X0] : ((kind(X0) | ~funny(X0) | ~creative(X0) | old(X0)) & ((creative(X0) & ~old(X0)) | (~kind(X0) & funny(X0)))) [flattening 52]
78. wise(X0) | wise(X0) [cnf transformation 26]
87. ~patient(X0) | tall(X0) | happy(X0) [cnf transformation 36]
89. ~tall(X0) | ~brave(X0) [cnf transformation 38]
90. ~tall(X0) | brave(X0) [cnf transformation 38]
99. old(john) | patient(X0) | happy(X0) [cnf transformation 44]
102. kind(X0) | ~wise(X0) | ~old(X0) [cnf transformation 45]
113. ~old(X0) | ~kind(X0) [cnf transformation 53]
147. ~happy(paul) [cnf transformation 24]
152. wise(X0) [duplicate literal removal 78]
154. ~tall(X0) [subsumption resolution 89,90]
159. 2 <=> old(john) [avatar definition]
161. old(john) <- (2) [avatar component clause 159]
164. 3 <=> ! [X0] : (patient(X0) | happy(X0)) [avatar definition]
165. happy(X0) | patient(X0) <- (3) [avatar component clause 164]
166. 3 | 2 [avatar split clause 99,159,164]
184. ~old(X0) | kind(X0) [subsumption resolution 102,152]
189. ~old(X0) [subsumption resolution 113,184]
200. 9 <=> patient(paul) [avatar definition]
201. patient(paul) <- (9) [avatar component clause 200]
286. $false <- (2) [subsumption resolution 161,189]
287. ~2 [avatar contradiction clause 286]
293. patient(paul) <- (3) [resolution 165,147]
310. tall(paul) | happy(paul) <- (9) [resolution 87,201]
312. happy(paul) <- (9) [subsumption resolution 310,154]
313. $false <- (9) [subsumption resolution 312,147]
314. ~9 [avatar contradiction clause 313]
319. 9 | ~3 [avatar split clause 293,164,200]
320. $false [avatar sat refutation 166,287,314,319]
% SZS output end Proof for 7629039884614241917663948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not calm is either not humble or not rich and vice versa. If someone is either not curious or not old then someone is not funny. If someone is humble then someone is not calm and vice versa. If someone is not quiet then someone is either not generous or rich and vice versa. If john is both brave and kind then paul is patient or not curious. If someone is not tall or not strong then john is humble and vice versa. Everyone who is either patient or creative is not calm or not generous and vice versa. If someone is either not calm or not creative then someone is either not quiet or brave and vice versa. If someone is quiet or not old then john is both not creative and not humble. If alice is not patient then alice is tall or not wise and vice versa. If someone is humble then john is not humble. Everyone who is strong is both calm and not funny and vice versa. Everyone who is old is tall or curious. If someone is wise then mary is not rich or not humble. Everyone who is either curious or not generous is humble and vice versa. Susan is tall. Someone is either curious or rich. Someone is not quiet or brave. John is either not strong or not generous. Fred is curious or not strong. Someone is both not creative and not rich. | Susan is not kind. | neutral | (![X]:((~quiet(X)<~>~calm(X))<=>(~humble(X)<~>~rich(X))))&
((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:(~funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(![X]:(old(X)=>(tall(X)|curious(X))))&
((?[X]:(wise(X)))=>((~rich(mary)|~humble(mary))))&
(![X]:((curious(X)<~>~generous(X))<=>humble(X)))&
(tall(susan))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~quiet(X)|brave(X))))&
((~strong(john)<~>~generous(john)))&
((curious(fred)|~strong(fred)))&
(?[X]:((~creative(X)&~rich(X)))) | ~kind(susan) | [] | null | 0 |
If paul is both not patient and happy then john is either brave or humble and vice versa. If someone is either not tall or not strong then someone is either happy or patient. Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. Someone is either humble or funny. Susan is both happy and not funny. Paul is not funny. Someone is both humble and happy. Alice is generous or not curious. Someone is not rich or wise. Someone is tall or not wise. Mary is either strong or not curious. | Alice is quiet. | contradiction | (((~patient(paul)&happy(paul)))<=>((brave(john)<~>humble(john))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
(?[X]:((humble(X)<~>funny(X))))&
((happy(susan)&~funny(susan)))&
(~funny(paul))&
(?[X]:((humble(X)&happy(X))))&
((generous(alice)|~curious(alice)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(mary)<~>~curious(mary))) | quiet(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2504414896570039502459547
% SZS output start Proof for 2504414896570039502459547
8. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p7]
24. quiet(alice) [input hypothesis]
53. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 8]
54. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 53]
91. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
120. quiet(alice) [cnf transformation 24]
121. ~quiet(X0) [duplicate literal removal 91]
269. $false [subsumption resolution 120,121]
% SZS output end Proof for 2504414896570039502459547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not calm is either happy or not funny and vice versa.
Everyone who is both not strong and not brave is either creative or not curious.
Everyone who is both not humble and patient is both creative and funny and vice versa.
Everyone who is rich or happy is not wise and vice versa.
Everyone who is not funny or old is both not wise and strong and vice versa.
Everyone who is humble or not humble is creative and vice versa.
If someone is either wise or not quiet then someone is patient or kind and vice versa.
If someone is not strong then mary is both not creative and funny.
Everyone who is not happy is not kind.
If someone is funny or calm then lucy is either not wise or old and vice versa.
Everyone who is patient is either generous or not generous and vice versa.
If someone is quiet then someone is either funny or brave.
If someone is not patient or curious then mary is both not tall and creative.
Everyone who is both not funny and not kind is either rich or not humble.
If fred is either patient or old then mary is both tall and happy and vice versa.
Someone is either rich or generous.
Alice is calm or not brave.
Someone is either not curious or not wise.
Fred is not calm or not generous.
Someone is both curious and not humble.
Mary is not calm.
Mary is generous. | Fred is not brave. | neutral | (![X]:((~curious(X)<~>~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~strong(X)&~brave(X))=>(creative(X)<~>~curious(X))))&
(![X]:((~humble(X)&patient(X))<=>(creative(X)&funny(X))))&
(![X]:((rich(X)|happy(X))<=>~wise(X)))&
(![X]:((~funny(X)|old(X))<=>(~wise(X)&strong(X))))&
(![X]:((humble(X)|~humble(X))<=>creative(X)))&
((?[X]:((wise(X)<~>~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:(~strong(X)))=>((~creative(mary)&funny(mary))))&
(![X]:(~happy(X)=>~kind(X)))&
((?[X]:((funny(X)|calm(X))))<=>((~wise(lucy)<~>old(lucy))))&
(![X]:(patient(X)<=>(generous(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((~patient(X)|curious(X))))=>((~tall(mary)&creative(mary))))&
(![X]:((~funny(X)&~kind(X))=>(rich(X)<~>~humble(X))))&
(((patient(fred)<~>old(fred)))<=>((tall(mary)&happy(mary))))&
(?[X]:((rich(X)<~>generous(X))))&
((calm(alice)|~brave(alice)))&
(?[X]:((~curious(X)<~>~wise(X))))&
((~calm(fred)|~generous(fred)))&
(?[X]:((curious(X)&~humble(X))))&
(~calm(mary))&
(generous(mary)) | ~brave(fred) | [] | null | 0 |
Everyone who is both quiet and not calm is creative and vice versa.
Everyone who is not old or humble is quiet.
Everyone who is not wise is creative or brave and vice versa.
If someone is either rich or not quiet then someone is either not happy or old.
If someone is both generous and kind then someone is both wise and calm and vice versa.
Everyone who is either calm or generous is both not generous and wise.
If someone is either not curious or not patient then fred is not quiet or not strong.
If someone is either not rich or kind then someone is not quiet and vice versa.
Everyone who is generous or not curious is either not tall or tall and vice versa.
Everyone who is both not generous and not old is both funny and not calm.
If someone is not creative or not funny then alice is curious or tall and vice versa.
Everyone who is either generous or not humble is both funny and brave and vice versa.
If alice is not strong or not humble then someone is both kind and curious and vice versa.
If alice is both not happy and rich then someone is brave.
Everyone who is not creative or not brave is humble.
Everyone who is either quiet or tall is either not happy or generous and vice versa.
Lucy is not strong.
Alice is rich.
Someone is either rich or not generous.
Lucy is strong or not kind.
Someone is curious.
Someone is both humble and old.
Someone is both not strong and funny.
Someone is rich. | Fred is not wise. | neutral | (![X]:((quiet(X)&~calm(X))<=>creative(X)))&
(![X]:((~old(X)|humble(X))=>quiet(X)))&
(![X]:(~wise(X)<=>(creative(X)|brave(X))))&
((?[X]:((rich(X)<~>~quiet(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
((?[X]:((generous(X)&kind(X))))<=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((calm(X)<~>generous(X))=>(~generous(X)&wise(X))))&
((?[X]:((~curious(X)<~>~patient(X))))=>((~quiet(fred)|~strong(fred))))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|~curious(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((~generous(X)&~old(X))=>(funny(X)&~calm(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>((curious(alice)|tall(alice))))&
(![X]:((generous(X)<~>~humble(X))<=>(funny(X)&brave(X))))&
(((~strong(alice)|~humble(alice)))<=>(?[X]:((kind(X)&curious(X)))))&
(((~happy(alice)&rich(alice)))=>(?[X]:(brave(X))))&
(![X]:((~creative(X)|~brave(X))=>humble(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)<~>generous(X))))&
(~strong(lucy))&
(rich(alice))&
(?[X]:((rich(X)<~>~generous(X))))&
((strong(lucy)|~kind(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)&old(X))))&
(?[X]:((~strong(X)&funny(X))))&
(?[X]:(rich(X))) | ~wise(fred) | [] | null | 0 |
If john is either not curious or not humble then someone is either happy or not creative and vice versa.
If someone is not kind or not funny then someone is calm or not funny and vice versa.
Everyone who is not happy is not wise.
If mary is happy or not calm then someone is either not calm or humble and vice versa.
Everyone who is both not rich and not brave is both calm and brave and vice versa.
Everyone who is brave or creative is not patient and vice versa.
Everyone who is funny is both old and wise.
Everyone who is either not calm or not old is both old and patient and vice versa.
If susan is either not humble or not rich then susan is not patient.
If susan is both not calm and not creative then someone is not creative or not generous and vice versa.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is not quiet or rich is not creative or not calm and vice versa.
Everyone who is both not wise and humble is not wise or creative and vice versa.
If fred is quiet or not tall then paul is brave or not wise and vice versa.
If john is both kind and quiet then susan is not humble or not quiet.
If susan is curious then someone is both not brave and not generous and vice versa.
Someone is not strong.
Someone is kind.
Lucy is not patient.
Someone is either calm or wise.
Someone is not tall.
Someone is both not wise and curious.
Someone is either not tall or wise.
Someone is either strong or generous. | Susan is creative. | contradiction | (((~curious(john)<~>~humble(john)))<=>(?[X]:((happy(X)<~>~creative(X)))))&
((?[X]:((~kind(X)|~funny(X))))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(~happy(X)=>~wise(X)))&
(((happy(mary)|~calm(mary)))<=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:((~rich(X)&~brave(X))<=>(calm(X)&brave(X))))&
(![X]:((brave(X)|creative(X))<=>~patient(X)))&
(![X]:(funny(X)=>(old(X)&wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(old(X)&patient(X))))&
(((~humble(susan)<~>~rich(susan)))=>(~patient(susan)))&
(((~calm(susan)&~creative(susan)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~wise(X)&humble(X))<=>(~wise(X)|creative(X))))&
(((quiet(fred)|~tall(fred)))<=>((brave(paul)|~wise(paul))))&
(((kind(john)&quiet(john)))=>((~humble(susan)|~quiet(susan))))&
((curious(susan))<=>(?[X]:((~brave(X)&~generous(X)))))&
(?[X]:(~strong(X)))&
(?[X]:(kind(X)))&
(~patient(lucy))&
(?[X]:((calm(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:((~tall(X)<~>wise(X))))&
(?[X]:((strong(X)<~>generous(X)))) | creative(susan) | [
"p9",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6240000878648153017415972
% SZS output start Proof for 6240000878648153017415972
10. (~creative(susan) & ~calm(susan)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p9]
11. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p10]
13. ! [X0] : ((humble(X0) & ~wise(X0)) <=> (creative(X0) | ~wise(X0))) [input p12]
20. ? [X0] : (calm(X0) <~> wise(X0)) [input p19]
25. creative(susan) [input hypothesis]
53. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | (creative(susan) | calm(susan))) [nnf transformation 10]
54. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | creative(susan) | calm(susan)) [flattening 53]
55. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | creative(susan) | calm(susan)) [rectify 54]
56. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK4) | ~creative(sK4)) [choice axiom]
57. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK4) | ~creative(sK4)) | creative(susan) | calm(susan)) [skolemisation 55,56]
58. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 11]
59. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 58]
62. ! [X0] : (((humble(X0) & ~wise(X0)) | (~creative(X0) & wise(X0))) & ((creative(X0) | ~wise(X0)) | (~humble(X0) | wise(X0)))) [nnf transformation 13]
63. ! [X0] : (((humble(X0) & ~wise(X0)) | (~creative(X0) & wise(X0))) & (creative(X0) | ~wise(X0) | ~humble(X0) | wise(X0))) [flattening 62]
74. ? [X0] : ((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) [nnf transformation 20]
75. ? [X0] : ((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) => ((~wise(sK8) | ~calm(sK8)) & (wise(sK8) | calm(sK8))) [choice axiom]
76. (~wise(sK8) | ~calm(sK8)) & (wise(sK8) | calm(sK8)) [skolemisation 74,75]
126. ~creative(susan) | creative(X0) [cnf transformation 57]
128. ~calm(X0) | ~humble(X0) [cnf transformation 59]
129. ~calm(X0) | humble(X0) [cnf transformation 59]
137. ~wise(X0) | ~creative(X0) [cnf transformation 63]
151. wise(sK8) | calm(sK8) [cnf transformation 76]
160. creative(susan) [cnf transformation 25]
208. 10 <=> ! [X1] : ~calm(X1) [avatar definition]
209. ~calm(X1) <- (10) [avatar component clause 208]
270. 24 <=> creative(susan) [avatar definition]
275. 25 <=> ! [X0] : creative(X0) [avatar definition]
276. creative(X0) <- (25) [avatar component clause 275]
277. 25 | ~24 [avatar split clause 126,270,275]
293. ~calm(X0) [subsumption resolution 128,129]
294. 10 [avatar split clause 293,208]
347. 40 <=> calm(sK8) [avatar definition]
348. calm(sK8) <- (40) [avatar component clause 347]
351. 41 <=> wise(sK8) [avatar definition]
352. wise(sK8) <- (41) [avatar component clause 351]
355. 40 | 41 [avatar split clause 151,351,347]
376. 24 [avatar split clause 160,270]
379. $false <- (10, 40) [resolution 348,209]
380. ~10 | ~40 [avatar contradiction clause 379]
384. ~creative(sK8) <- (41) [resolution 137,352]
385. $false <- (25, 41) [subsumption resolution 384,276]
386. ~25 | ~41 [avatar contradiction clause 385]
387. $false [avatar sat refutation 277,294,355,376,380,386]
% SZS output end Proof for 6240000878648153017415972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not creative or calm then alice is wise.
Everyone who is brave or not generous is either not curious or funny.
Everyone who is both not patient and not kind is both quiet and not funny and vice versa.
If john is funny then someone is not old and vice versa.
Everyone who is either quiet or not funny is either not tall or generous and vice versa.
Everyone who is not brave is either not humble or tall.
Everyone who is not humble is either strong or quiet.
Everyone who is both not funny and not curious is not humble.
If alice is strong or not tall then someone is generous and vice versa.
If someone is either quiet or not patient then someone is either quiet or not calm and vice versa.
If someone is both not brave and not patient then someone is both funny and generous and vice versa.
If someone is not rich then someone is humble or not generous and vice versa.
If someone is both happy and wise then someone is both brave and not strong and vice versa.
Everyone who is strong is strong or not quiet and vice versa.
If paul is either not humble or not generous then someone is either not tall or old.
Everyone who is happy is both not humble and not kind and vice versa.
Someone is patient.
Someone is both tall and old.
Someone is rich.
Alice is either not calm or tall.
Someone is brave.
Mary is not brave or generous.
Someone is either not patient or strong. | Alice is wise. | neutral | (((~creative(john)<~>calm(john)))=>(wise(alice)))&
(![X]:((brave(X)|~generous(X))=>(~curious(X)<~>funny(X))))&
(![X]:((~patient(X)&~kind(X))<=>(quiet(X)&~funny(X))))&
((funny(john))<=>(?[X]:(~old(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~tall(X)<~>generous(X))))&
(![X]:(~brave(X)=>(~humble(X)<~>tall(X))))&
(![X]:(~humble(X)=>(strong(X)<~>quiet(X))))&
(![X]:((~funny(X)&~curious(X))=>~humble(X)))&
(((strong(alice)|~tall(alice)))<=>(?[X]:(generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))<=>(?[X]:((funny(X)&generous(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((humble(X)|~generous(X)))))&
((?[X]:((happy(X)&wise(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(![X]:(strong(X)<=>(strong(X)|~quiet(X))))&
(((~humble(paul)<~>~generous(paul)))=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:(happy(X)<=>(~humble(X)&~kind(X))))&
(?[X]:(patient(X)))&
(?[X]:((tall(X)&old(X))))&
(?[X]:(rich(X)))&
((~calm(alice)<~>tall(alice)))&
(?[X]:(brave(X)))&
((~brave(mary)|generous(mary)))&
(?[X]:((~patient(X)<~>strong(X)))) | wise(alice) | [] | null | 0 |
If someone is humble or kind then someone is both quiet and not old and vice versa. If someone is either not brave or not quiet then someone is not generous. Everyone who is both not funny and not brave is calm and vice versa. Everyone who is brave or old is both not rich and curious and vice versa. If mary is wise or not happy then someone is curious or kind. If someone is either not patient or quiet then someone is not calm or creative and vice versa. Everyone who is not wise or patient is either not patient or rich. Everyone who is either not kind or not old is either not rich or quiet. Everyone who is both old and not tall is not humble or not quiet and vice versa. Everyone who is both not rich and calm is both not wise and not creative and vice versa. If susan is both not rich and wise then someone is both tall and quiet and vice versa. Everyone who is both happy and not strong is either creative or not generous and vice versa. If someone is both curious and funny then alice is rich. If someone is both funny and wise then someone is not kind. Everyone who is not brave or strong is either not creative or happy and vice versa. Everyone who is kind or calm is either tall or not calm. Someone is humble. Someone is calm. Someone is not brave or tall. Someone is both not patient and not quiet. Alice is either not kind or creative. Someone is generous or calm. Someone is quiet. | Susan is not happy. | neutral | ((?[X]:((humble(X)|kind(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>calm(X)))&
(![X]:((brave(X)|old(X))<=>(~rich(X)&curious(X))))&
(((wise(mary)|~happy(mary)))=>(?[X]:((curious(X)|kind(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((~wise(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&~creative(X))))&
(((~rich(susan)&wise(susan)))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:((curious(X)&funny(X))))=>(rich(alice)))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)<~>happy(X))))&
(![X]:((kind(X)|calm(X))=>(tall(X)<~>~calm(X))))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
((~kind(alice)<~>creative(alice)))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:(quiet(X))) | ~happy(susan) | [] | null | 0 |
If someone is both not wise and not funny then paul is not creative or generous. If someone is quiet or not quiet then someone is not patient or strong and vice versa. Everyone who is creative or not generous is either not quiet or old and vice versa. If someone is both not strong and funny then someone is not strong or happy. Everyone who is both generous and happy is both not kind and old. If john is not funny or not tall then someone is not rich and vice versa. If someone is quiet or not rich then someone is calm or not calm. Everyone who is either wise or calm is not strong or rich and vice versa. If mary is not generous or creative then someone is not funny or humble and vice versa. Everyone who is either not quiet or humble is not humble or not rich and vice versa. Everyone who is not generous or wise is both rich and quiet. Everyone who is calm or not strong is both not patient and not old. Everyone who is both funny and not tall is either not old or not happy. Everyone who is not kind is not strong and vice versa. If someone is not humble or curious then john is not patient. Everyone who is either not wise or not generous is both not calm and generous. Alice is patient or not calm. Susan is either funny or curious. Someone is both quiet and curious. Paul is wise or quiet. Paul is both curious and quiet. Alice is both curious and not patient. | Alice is not kind. | contradiction | ((?[X]:((~wise(X)&~funny(X))))=>((~creative(paul)|generous(paul))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((creative(X)|~generous(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((generous(X)&happy(X))=>(~kind(X)&old(X))))&
(((~funny(john)|~tall(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(~strong(X)|rich(X))))&
(((~generous(mary)|creative(mary)))<=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:((~quiet(X)<~>humble(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~generous(X)|wise(X))=>(rich(X)&quiet(X))))&
(![X]:((calm(X)|~strong(X))=>(~patient(X)&~old(X))))&
(![X]:((funny(X)&~tall(X))=>(~old(X)<~>~happy(X))))&
(![X]:(~kind(X)<=>~strong(X)))&
((?[X]:((~humble(X)|curious(X))))=>(~patient(john)))&
(![X]:((~wise(X)<~>~generous(X))=>(~calm(X)&generous(X))))&
((patient(alice)|~calm(alice)))&
((funny(susan)<~>curious(susan)))&
(?[X]:((quiet(X)&curious(X))))&
((wise(paul)|quiet(paul)))&
((curious(paul)&quiet(paul)))&
((curious(alice)&~patient(alice))) | ~kind(alice) | [
"p7",
"p9",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3407942711627682300219890
% SZS output start Proof for 3407942711627682300219890
8. ! [X0] : ((wise(X0) <~> calm(X0)) <=> (rich(X0) | ~strong(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (~rich(X0) | ~humble(X0))) [input p9]
11. ! [X0] : ((wise(X0) | ~generous(X0)) => (quiet(X0) & rich(X0))) [input p10]
12. ! [X0] : ((~strong(X0) | calm(X0)) => (~old(X0) & ~patient(X0))) [input p11]
14. ! [X0] : (~kind(X0) <=> ~strong(X0)) [input p13]
17. ~calm(alice) | patient(alice) [input p16]
23. ~kind(alice) [input hypothesis]
27. ! [X0] : (~kind(X0) => ~strong(X0)) [unused predicate definition removal 14]
34. ! [X0] : ((quiet(X0) & rich(X0)) | (~wise(X0) & generous(X0))) [ennf transformation 11]
35. ! [X0] : ((~old(X0) & ~patient(X0)) | (strong(X0) & ~calm(X0))) [ennf transformation 12]
38. ! [X0] : (~strong(X0) | kind(X0)) [ennf transformation 27]
59. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [nnf transformation 8]
60. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [flattening 59]
66. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 10]
67. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 66]
94. calm(X0) | wise(X0) | strong(X0) [cnf transformation 60]
103. ~rich(X0) | ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 67]
104. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 67]
109. ~wise(X0) | rich(X0) [cnf transformation 34]
111. ~wise(X0) | quiet(X0) [cnf transformation 34]
112. ~calm(X0) | ~patient(X0) [cnf transformation 35]
118. ~strong(X0) | kind(X0) [cnf transformation 38]
125. ~calm(alice) | patient(alice) [cnf transformation 17]
135. ~kind(alice) [cnf transformation 23]
137. ~rich(X0) | ~humble(X0) | ~quiet(X0) [duplicate literal removal 103]
138. ~quiet(X0) | humble(X0) [duplicate literal removal 104]
223. ~rich(X0) | ~quiet(X0) [subsumption resolution 137,138]
236. ~calm(alice) [subsumption resolution 125,112]
272. wise(alice) | strong(alice) [resolution 94,236]
276. 28 <=> strong(alice) [avatar definition]
278. strong(alice) <- (28) [avatar component clause 276]
280. 29 <=> wise(alice) [avatar definition]
282. wise(alice) <- (29) [avatar component clause 280]
283. 28 | 29 [avatar split clause 272,280,276]
284. kind(alice) <- (28) [resolution 278,118]
285. $false <- (28) [subsumption resolution 284,135]
286. ~28 [avatar contradiction clause 285]
291. quiet(alice) <- (29) [resolution 282,111]
292. rich(alice) <- (29) [resolution 282,109]
311. ~quiet(alice) <- (29) [resolution 292,223]
312. $false <- (29) [subsumption resolution 311,291]
313. ~29 [avatar contradiction clause 312]
314. $false [avatar sat refutation 283,286,313]
% SZS output end Proof for 3407942711627682300219890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not kind is not old and vice versa. Everyone who is both brave and patient is wise and vice versa. Everyone who is both not creative and not brave is kind or not humble and vice versa. If susan is either not humble or not quiet then john is both brave and kind and vice versa. Everyone who is either happy or not strong is not happy or patient and vice versa. If alice is not funny then paul is both not happy and not wise and vice versa. Everyone who is both not kind and not strong is not strong and vice versa. If paul is either not patient or wise then someone is generous. Everyone who is generous is both kind and not kind and vice versa. If someone is funny or creative then someone is not strong or not tall. Everyone who is both calm and not tall is both happy and brave. Everyone who is not curious is creative or brave and vice versa. Everyone who is not funny or humble is not brave or not funny and vice versa. If someone is strong then mary is generous and vice versa. Everyone who is either rich or not kind is either not generous or rich. Alice is not tall or not happy. Someone is not humble. Someone is both not wise and creative. Paul is not curious or strong. Susan is not generous. Someone is not tall. Susan is not quiet. Someone is brave. | John is creative. | neutral | (![X]:((~tall(X)|~kind(X))<=>~old(X)))&
(![X]:((brave(X)&patient(X))<=>wise(X)))&
(![X]:((~creative(X)&~brave(X))<=>(kind(X)|~humble(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>((brave(john)&kind(john))))&
(![X]:((happy(X)<~>~strong(X))<=>(~happy(X)|patient(X))))&
((~funny(alice))<=>((~happy(paul)&~wise(paul))))&
(![X]:((~kind(X)&~strong(X))<=>~strong(X)))&
(((~patient(paul)<~>wise(paul)))=>(?[X]:(generous(X))))&
(![X]:(generous(X)<=>(kind(X)&~kind(X))))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((calm(X)&~tall(X))=>(happy(X)&brave(X))))&
(![X]:(~curious(X)<=>(creative(X)|brave(X))))&
(![X]:((~funny(X)|humble(X))<=>(~brave(X)|~funny(X))))&
((?[X]:(strong(X)))<=>(generous(mary)))&
(![X]:((rich(X)<~>~kind(X))=>(~generous(X)<~>rich(X))))&
((~tall(alice)|~happy(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~wise(X)&creative(X))))&
((~curious(paul)|strong(paul)))&
(~generous(susan))&
(?[X]:(~tall(X)))&
(~quiet(susan))&
(?[X]:(brave(X))) | creative(john) | [] | null | 0 |
Everyone who is either not strong or old is both patient and generous and vice versa.
Everyone who is either strong or not rich is generous or brave.
Everyone who is patient is either not strong or quiet and vice versa.
If john is strong or wise then someone is old or not patient and vice versa.
If mary is not wise then mary is not humble and vice versa.
Everyone who is not wise is either not tall or not humble.
Everyone who is both not old and not brave is creative or not tall and vice versa.
Everyone who is strong or creative is both not quiet and funny.
Everyone who is both not patient and not creative is not wise.
If someone is humble or not generous then susan is wise or not calm.
Everyone who is creative is both generous and not patient.
Everyone who is either funny or curious is not creative or not kind and vice versa.
If someone is rich or not strong then john is both strong and not funny and vice versa.
If lucy is old or rich then fred is both tall and brave and vice versa.
If lucy is calm or tall then someone is both strong and brave and vice versa.
Everyone who is not kind or not curious is both kind and not happy and vice versa.
Lucy is not old.
Someone is either happy or not funny.
Someone is either quiet or not old.
Someone is not strong or not tall.
Someone is not quiet or not kind. | Mary is not kind. | contradiction | (![X]:((~strong(X)<~>old(X))<=>(patient(X)&generous(X))))&
(![X]:((strong(X)<~>~rich(X))=>(generous(X)|brave(X))))&
(![X]:(patient(X)<=>(~strong(X)<~>quiet(X))))&
(((strong(john)|wise(john)))<=>(?[X]:((old(X)|~patient(X)))))&
((~wise(mary))<=>(~humble(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~humble(X))))&
(![X]:((~old(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(![X]:((strong(X)|creative(X))=>(~quiet(X)&funny(X))))&
(![X]:((~patient(X)&~creative(X))=>~wise(X)))&
((?[X]:((humble(X)|~generous(X))))=>((wise(susan)|~calm(susan))))&
(![X]:(creative(X)=>(generous(X)&~patient(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((rich(X)|~strong(X))))<=>((strong(john)&~funny(john))))&
(((old(lucy)|rich(lucy)))<=>((tall(fred)&brave(fred))))&
(((calm(lucy)|tall(lucy)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(kind(X)&~happy(X))))&
(~old(lucy))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((~quiet(X)|~kind(X)))) | ~kind(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7194056577652680620233955
% SZS output start Proof for 7194056577652680620233955
16. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~happy(X0) & kind(X0))) [input p15]
22. ~kind(mary) [input hypothesis]
59. ! [X0] : (((~curious(X0) | ~kind(X0)) | (happy(X0) | ~kind(X0))) & ((~happy(X0) & kind(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 16]
60. ! [X0] : ((~curious(X0) | ~kind(X0) | happy(X0) | ~kind(X0)) & ((~happy(X0) & kind(X0)) | (curious(X0) & kind(X0)))) [flattening 59]
126. kind(X0) | kind(X0) [cnf transformation 60]
138. ~kind(mary) [cnf transformation 22]
139. kind(X0) [duplicate literal removal 126]
286. $false [subsumption resolution 138,139]
% SZS output end Proof for 7194056577652680620233955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is wise then someone is either not quiet or brave and vice versa. Everyone who is both quiet and generous is both not brave and not humble. Everyone who is funny is tall and vice versa. Everyone who is both curious and not humble is happy or not tall and vice versa. Everyone who is tall or kind is old. If lucy is not brave then john is old or strong. Everyone who is not old or not strong is both funny and kind and vice versa. Everyone who is either not curious or happy is not calm. Everyone who is not generous is brave or kind and vice versa. Everyone who is strong or calm is quiet and vice versa. Everyone who is not generous is humble. Everyone who is both not rich and generous is not kind and vice versa. Everyone who is not calm is not rich and vice versa. Everyone who is either patient or not quiet is not curious or wise and vice versa. If mary is both not funny and not calm then someone is not happy or happy and vice versa. If paul is not quiet then someone is funny or not creative and vice versa. John is not brave. Lucy is not tall. Someone is either quiet or wise. Alice is either not strong or not rich. Paul is both not creative and curious. Alice is either funny or not patient. | Mary is humble. | contradiction | ((wise(john))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:((quiet(X)&generous(X))=>(~brave(X)&~humble(X))))&
(![X]:(funny(X)<=>tall(X)))&
(![X]:((curious(X)&~humble(X))<=>(happy(X)|~tall(X))))&
(![X]:((tall(X)|kind(X))=>old(X)))&
((~brave(lucy))=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(![X]:((patient(X)<~>~quiet(X))<=>(~curious(X)|wise(X))))&
(((~funny(mary)&~calm(mary)))<=>(?[X]:((~happy(X)|happy(X)))))&
((~quiet(paul))<=>(?[X]:((funny(X)|~creative(X)))))&
(~brave(john))&
(~tall(lucy))&
(?[X]:((quiet(X)<~>wise(X))))&
((~strong(alice)<~>~rich(alice)))&
((~creative(paul)&curious(paul)))&
((funny(alice)<~>~patient(alice))) | humble(mary) | [
"p2",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3116456345590610952240513
% SZS output start Proof for 3116456345590610952240513
3. ! [X0] : (funny(X0) <=> tall(X0)) [input p2]
4. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~tall(X0) | happy(X0))) [input p3]
15. (~calm(mary) & ~funny(mary)) <=> ? [X0] : (happy(X0) | ~happy(X0)) [input p14]
23. humble(mary) [input hypothesis]
35. ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))) [nnf transformation 3]
36. ! [X0] : (((~humble(X0) & curious(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 4]
37. ! [X0] : (((~humble(X0) & curious(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | humble(X0) | ~curious(X0))) [flattening 36]
50. ((~calm(mary) & ~funny(mary)) | ! [X0] : (~happy(X0) & happy(X0))) & (? [X0] : (happy(X0) | ~happy(X0)) | (calm(mary) | funny(mary))) [nnf transformation 15]
51. ((~calm(mary) & ~funny(mary)) | ! [X0] : (~happy(X0) & happy(X0))) & (? [X0] : (happy(X0) | ~happy(X0)) | calm(mary) | funny(mary)) [flattening 50]
52. ((~calm(mary) & ~funny(mary)) | ! [X0] : (~happy(X0) & happy(X0))) & (? [X1] : (happy(X1) | ~happy(X1)) | calm(mary) | funny(mary)) [rectify 51]
53. ? [X1] : (happy(X1) | ~happy(X1)) => (happy(sK1) | ~happy(sK1)) [choice axiom]
54. ((~calm(mary) & ~funny(mary)) | ! [X0] : (~happy(X0) & happy(X0))) & ((happy(sK1) | ~happy(sK1)) | calm(mary) | funny(mary)) [skolemisation 52,53]
71. ~tall(X0) | funny(X0) [cnf transformation 35]
76. ~humble(X0) | tall(X0) [cnf transformation 37]
106. ~funny(mary) | happy(X0) [cnf transformation 54]
107. ~funny(mary) | ~happy(X0) [cnf transformation 54]
123. humble(mary) [cnf transformation 23]
164. 9 <=> ! [X0] : ~happy(X0) [avatar definition]
165. ~happy(X0) <- (9) [avatar component clause 164]
172. 11 <=> ! [X0] : happy(X0) [avatar definition]
173. happy(X0) <- (11) [avatar component clause 172]
176. 12 <=> funny(mary) [avatar definition]
179. 9 | ~12 [avatar split clause 107,176,164]
180. 11 | ~12 [avatar split clause 106,176,172]
232. tall(mary) [resolution 76,123]
233. funny(mary) [resolution 232,71]
236. 12 [avatar split clause 233,176]
237. $false <- (9, 11) [subsumption resolution 165,173]
238. ~9 | ~11 [avatar contradiction clause 237]
239. $false [avatar sat refutation 179,180,236,238]
% SZS output end Proof for 3116456345590610952240513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not wise or curious then someone is either humble or not old and vice versa.
If someone is creative or not curious then mary is not generous and vice versa.
If someone is both generous and not humble then someone is not happy.
Everyone who is not creative is not calm or not tall.
Everyone who is either wise or generous is not wise or not calm and vice versa.
Everyone who is not wise or creative is both not happy and not rich.
Everyone who is either generous or not curious is not calm.
If fred is either not rich or old then paul is either not calm or not kind.
Everyone who is humble is curious or tall and vice versa.
Everyone who is strong is not curious and vice versa.
If john is both not funny and funny then someone is generous.
Everyone who is not wise or funny is not brave or humble and vice versa.
Everyone who is both curious and not patient is either not funny or not rich.
Everyone who is both creative and kind is not patient and vice versa.
If fred is not humble then someone is either not kind or not rich and vice versa.
If mary is either curious or humble then someone is not generous or not happy and vice versa.
Paul is both curious and not generous.
Someone is wise.
Lucy is both rich and generous.
Susan is generous.
Paul is patient or not wise.
Someone is either curious or not generous.
Mary is wise or not quiet.
Susan is both brave and wise. | Fred is not curious. | neutral | (((~wise(john)|curious(john)))<=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:((creative(X)|~curious(X))))<=>(~generous(mary)))&
((?[X]:((generous(X)&~humble(X))))=>(?[X]:(~happy(X))))&
(![X]:(~creative(X)=>(~calm(X)|~tall(X))))&
(![X]:((wise(X)<~>generous(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~rich(X))))&
(![X]:((generous(X)<~>~curious(X))=>~calm(X)))&
(((~rich(fred)<~>old(fred)))=>((~calm(paul)<~>~kind(paul))))&
(![X]:(humble(X)<=>(curious(X)|tall(X))))&
(![X]:(strong(X)<=>~curious(X)))&
(((~funny(john)&funny(john)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~patient(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)&kind(X))<=>~patient(X)))&
((~humble(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~generous(X)|~happy(X)))))&
((curious(paul)&~generous(paul)))&
(?[X]:(wise(X)))&
((rich(lucy)&generous(lucy)))&
(generous(susan))&
((patient(paul)|~wise(paul)))&
(?[X]:((curious(X)<~>~generous(X))))&
((wise(mary)|~quiet(mary)))&
((brave(susan)&wise(susan))) | ~curious(fred) | [] | null | 0 |
If mary is both quiet and not old then susan is kind or not wise and vice versa.
If someone is either not funny or not generous then someone is not tall and vice versa.
Everyone who is both curious and funny is not wise.
If paul is either not brave or happy then lucy is not wise or not creative.
Everyone who is strong is not calm.
If someone is either curious or old then susan is generous or not wise.
Everyone who is both kind and patient is strong or not generous and vice versa.
If someone is funny then someone is either strong or brave.
If paul is both not old and not happy then susan is either wise or not humble.
Everyone who is calm or quiet is both not patient and not funny and vice versa.
Everyone who is not happy is generous and vice versa.
Everyone who is calm is not rich.
Everyone who is either not quiet or strong is strong and vice versa.
If someone is either not humble or not brave then susan is happy and vice versa.
If someone is not generous then someone is creative and vice versa.
If someone is both tall and not funny then alice is curious or not brave.
Someone is humble or not rich.
Lucy is not funny.
Someone is both not old and quiet.
Mary is either creative or quiet.
Someone is either kind or calm.
Paul is either not humble or calm.
Fred is old or not brave.
Mary is wise. | Lucy is quiet. | entailment | (((quiet(mary)&~old(mary)))<=>((kind(susan)|~wise(susan))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)&funny(X))=>~wise(X)))&
(((~brave(paul)<~>happy(paul)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:(strong(X)=>~calm(X)))&
((?[X]:((curious(X)<~>old(X))))=>((generous(susan)|~wise(susan))))&
(![X]:((kind(X)&patient(X))<=>(strong(X)|~generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~old(paul)&~happy(paul)))=>((wise(susan)<~>~humble(susan))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:(calm(X)=>~rich(X)))&
(![X]:((~quiet(X)<~>strong(X))<=>strong(X)))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(happy(susan)))&
((?[X]:(~generous(X)))<=>(?[X]:(creative(X))))&
((?[X]:((tall(X)&~funny(X))))=>((curious(alice)|~brave(alice))))&
(?[X]:((humble(X)|~rich(X))))&
(~funny(lucy))&
(?[X]:((~old(X)&quiet(X))))&
((creative(mary)<~>quiet(mary)))&
(?[X]:((kind(X)<~>calm(X))))&
((~humble(paul)<~>calm(paul)))&
((old(fred)|~brave(fred)))&
(wise(mary)) | quiet(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 735964984422557822740087
% SZS output start Proof for 735964984422557822740087
13. ! [X0] : ((~quiet(X0) <~> strong(X0)) <=> strong(X0)) [input p12]
25. ~quiet(lucy) [input hypothesis]
62. ! [X0] : ((((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~strong(X0)) & (strong(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0))))) [nnf transformation 13]
110. strong(X0) | strong(X0) | quiet(X0) [cnf transformation 62]
113. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 62]
132. ~quiet(lucy) [cnf transformation 25]
133. strong(X0) | quiet(X0) [duplicate literal removal 110]
134. ~strong(X0) | quiet(X0) [duplicate literal removal 113]
234. quiet(X0) [subsumption resolution 133,134]
315. $false [subsumption resolution 132,234]
% SZS output end Proof for 735964984422557822740087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is both rich and not creative and vice versa.
Everyone who is not calm is not patient or strong and vice versa.
Everyone who is either not humble or calm is not calm or creative.
Everyone who is not calm is old or not rich and vice versa.
If lucy is curious or not humble then lucy is not humble or not strong and vice versa.
If someone is both not calm and not rich then alice is either not creative or not humble and vice versa.
Everyone who is not strong is curious and vice versa.
Everyone who is not funny is kind or not creative.
If someone is not strong then someone is both not brave and humble and vice versa.
Everyone who is not tall or calm is happy or not calm and vice versa.
If mary is not kind then susan is either not rich or generous and vice versa.
If mary is not calm then paul is not quiet or not tall.
Everyone who is kind is both strong and not humble and vice versa.
Everyone who is either not brave or brave is not old or generous.
Everyone who is old or not calm is both patient and curious.
If someone is both kind and quiet then mary is both tall and not happy.
Someone is not quiet or not happy.
Someone is not brave or humble.
Alice is rich.
Someone is tall.
Someone is either not kind or not rich.
Someone is either not creative or not generous. | Mary is not humble. | neutral | (![X]:((~generous(X)&~rich(X))<=>(rich(X)&~creative(X))))&
(![X]:(~calm(X)<=>(~patient(X)|strong(X))))&
(![X]:((~humble(X)<~>calm(X))=>(~calm(X)|creative(X))))&
(![X]:(~calm(X)<=>(old(X)|~rich(X))))&
(((curious(lucy)|~humble(lucy)))<=>((~humble(lucy)|~strong(lucy))))&
((?[X]:((~calm(X)&~rich(X))))<=>((~creative(alice)<~>~humble(alice))))&
(![X]:(~strong(X)<=>curious(X)))&
(![X]:(~funny(X)=>(kind(X)|~creative(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~tall(X)|calm(X))<=>(happy(X)|~calm(X))))&
((~kind(mary))<=>((~rich(susan)<~>generous(susan))))&
((~calm(mary))=>((~quiet(paul)|~tall(paul))))&
(![X]:(kind(X)<=>(strong(X)&~humble(X))))&
(![X]:((~brave(X)<~>brave(X))=>(~old(X)|generous(X))))&
(![X]:((old(X)|~calm(X))=>(patient(X)&curious(X))))&
((?[X]:((kind(X)&quiet(X))))=>((tall(mary)&~happy(mary))))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((~brave(X)|humble(X))))&
(rich(alice))&
(?[X]:(tall(X)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((~creative(X)<~>~generous(X)))) | ~humble(mary) | [] | null | 0 |
Everyone who is either humble or brave is both strong and calm and vice versa. If lucy is either not wise or quiet then fred is either funny or not calm. Everyone who is either patient or rich is generous. If susan is both not tall and creative then susan is not strong or brave and vice versa. If someone is both not strong and quiet then mary is both tall and creative. If someone is not calm then susan is either brave or not rich and vice versa. If someone is either not rich or not funny then someone is not curious and vice versa. Everyone who is either brave or not quiet is both not rich and generous and vice versa. Everyone who is happy is humble or wise. If someone is both wise and funny then john is not kind or not humble. If alice is both tall and not wise then someone is not quiet or not funny. Everyone who is either funny or not tall is both not old and not calm. If lucy is not kind or not curious then alice is not rich or patient. If someone is both not quiet and happy then paul is old or not funny and vice versa. If mary is not brave or not old then someone is either rich or generous. If someone is either humble or not calm then alice is both wise and not quiet and vice versa. Susan is not tall or not old. Someone is either curious or funny. Paul is both not old and not strong. Someone is both not brave and not happy. Someone is tall. Someone is wise or calm. John is either wise or not rich. Someone is funny. | Paul is not old. | entailment | (![X]:((humble(X)<~>brave(X))<=>(strong(X)&calm(X))))&
(((~wise(lucy)<~>quiet(lucy)))=>((funny(fred)<~>~calm(fred))))&
(![X]:((patient(X)<~>rich(X))=>generous(X)))&
(((~tall(susan)&creative(susan)))<=>((~strong(susan)|brave(susan))))&
((?[X]:((~strong(X)&quiet(X))))=>((tall(mary)&creative(mary))))&
((?[X]:(~calm(X)))<=>((brave(susan)<~>~rich(susan))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>(?[X]:(~curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(~rich(X)&generous(X))))&
(![X]:(happy(X)=>(humble(X)|wise(X))))&
((?[X]:((wise(X)&funny(X))))=>((~kind(john)|~humble(john))))&
(((tall(alice)&~wise(alice)))=>(?[X]:((~quiet(X)|~funny(X)))))&
(![X]:((funny(X)<~>~tall(X))=>(~old(X)&~calm(X))))&
(((~kind(lucy)|~curious(lucy)))=>((~rich(alice)|patient(alice))))&
((?[X]:((~quiet(X)&happy(X))))<=>((old(paul)|~funny(paul))))&
(((~brave(mary)|~old(mary)))=>(?[X]:((rich(X)<~>generous(X)))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((wise(alice)&~quiet(alice))))&
((~tall(susan)|~old(susan)))&
(?[X]:((curious(X)<~>funny(X))))&
((~old(paul)&~strong(paul)))&
(?[X]:((~brave(X)&~happy(X))))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)|calm(X))))&
((wise(john)<~>~rich(john)))&
(?[X]:(funny(X))) | ~old(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 641060048073519933580023
% SZS output start Proof for 641060048073519933580023
19. ~strong(paul) & ~old(paul) [input p18]
25. old(paul) [input hypothesis]
145. ~old(paul) [cnf transformation 19]
154. old(paul) [cnf transformation 25]
306. 34 <=> old(paul) [avatar definition]
379. ~34 [avatar split clause 145,306]
399. 34 [avatar split clause 154,306]
400. $false [avatar sat refutation 379,399]
% SZS output end Proof for 641060048073519933580023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy is either not humble or old.
If someone is either happy or tall then someone is both not wise and not calm and vice versa.
If alice is either not old or humble then someone is not patient or not quiet.
Everyone who is either happy or not creative is either not calm or not brave and vice versa.
Everyone who is not quiet or not happy is either rich or not generous.
If someone is generous then john is either not generous or wise.
If fred is tall then alice is either brave or happy.
If someone is not old then fred is not kind.
If someone is not wise then lucy is both not rich and tall and vice versa.
If someone is strong or kind then john is not strong.
Everyone who is both not calm and brave is not rich.
If lucy is not funny then susan is patient or curious.
Everyone who is wise or kind is humble or calm and vice versa.
If susan is either not humble or wise then someone is brave.
If someone is both not creative and curious then lucy is both patient and not calm and vice versa.
If someone is either not curious or brave then someone is both not funny and calm.
Susan is both generous and wise.
Someone is either not curious or funny.
Someone is generous or not calm.
Someone is either not calm or not kind.
Someone is not curious or not happy.
Alice is both not wise and not rich.
Susan is either strong or quiet.
Someone is not brave or tall. | Lucy is not tall. | contradiction | (![X]:(~happy(X)=>(~humble(X)<~>old(X))))&
((?[X]:((happy(X)<~>tall(X))))<=>(?[X]:((~wise(X)&~calm(X)))))&
(((~old(alice)<~>humble(alice)))=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((~quiet(X)|~happy(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(generous(X)))=>((~generous(john)<~>wise(john))))&
((tall(fred))=>((brave(alice)<~>happy(alice))))&
((?[X]:(~old(X)))=>(~kind(fred)))&
((?[X]:(~wise(X)))<=>((~rich(lucy)&tall(lucy))))&
((?[X]:((strong(X)|kind(X))))=>(~strong(john)))&
(![X]:((~calm(X)&brave(X))=>~rich(X)))&
((~funny(lucy))=>((patient(susan)|curious(susan))))&
(![X]:((wise(X)|kind(X))<=>(humble(X)|calm(X))))&
(((~humble(susan)<~>wise(susan)))=>(?[X]:(brave(X))))&
((?[X]:((~creative(X)&curious(X))))<=>((patient(lucy)&~calm(lucy))))&
((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((~funny(X)&calm(X)))))&
((generous(susan)&wise(susan)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((generous(X)|~calm(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~wise(alice)&~rich(alice)))&
((strong(susan)<~>quiet(susan)))&
(?[X]:((~brave(X)|tall(X)))) | ~tall(lucy) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8825769888977759731960976
% SZS output start Proof for 8825769888977759731960976
9. ? [X0] : ~wise(X0) <=> (tall(lucy) & ~rich(lucy)) [input p8]
22. ~rich(alice) & ~wise(alice) [input p21]
25. ~tall(lucy) [input hypothesis]
54. (? [X0] : ~wise(X0) | (~tall(lucy) | rich(lucy))) & ((tall(lucy) & ~rich(lucy)) | ! [X0] : wise(X0)) [nnf transformation 9]
55. (? [X0] : ~wise(X0) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X0] : wise(X0)) [flattening 54]
56. (? [X0] : ~wise(X0) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X1] : wise(X1)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. (~wise(sK3) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X1] : wise(X1)) [skolemisation 56,57]
114. tall(lucy) | wise(X1) [cnf transformation 58]
142. ~wise(alice) [cnf transformation 22]
147. ~tall(lucy) [cnf transformation 25]
237. 21 <=> tall(lucy) [avatar definition]
246. 23 <=> ! [X1] : wise(X1) [avatar definition]
247. wise(X1) <- (23) [avatar component clause 246]
248. 23 | 21 [avatar split clause 114,237,246]
388. ~21 [avatar split clause 147,237]
395. $false <- (23) [resolution 247,142]
396. ~23 [avatar contradiction clause 395]
397. $false [avatar sat refutation 248,388,396]
% SZS output end Proof for 8825769888977759731960976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or wise is both funny and not creative and vice versa.
If someone is both strong and wise then someone is either not quiet or quiet.
Everyone who is strong is happy or not rich.
If someone is humble or not old then fred is old and vice versa.
Everyone who is calm or not creative is either not humble or calm.
If someone is both not kind and not calm then someone is either not creative or not patient and vice versa.
If susan is rich then someone is brave or not creative and vice versa.
Everyone who is both happy and old is not strong or calm and vice versa.
Everyone who is creative or funny is calm or not strong.
If fred is both patient and not quiet then someone is either not quiet or not strong and vice versa.
Everyone who is not wise is both not tall and quiet.
If alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
Someone is not generous.
Paul is wise.
Someone is either not calm or not curious.
Fred is either not kind or patient.
Fred is not tall.
Someone is either not brave or calm.
Fred is both not kind and old. | Alice is not creative. | entailment | (![X]:((old(X)|wise(X))<=>(funny(X)&~creative(X))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(strong(X)=>(happy(X)|~rich(X))))&
((?[X]:((humble(X)|~old(X))))<=>(old(fred)))&
(![X]:((calm(X)|~creative(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
((rich(susan))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((happy(X)&old(X))<=>(~strong(X)|calm(X))))&
(![X]:((creative(X)|funny(X))=>(calm(X)|~strong(X))))&
(((patient(fred)&~quiet(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)&quiet(X))))&
(((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
(?[X]:(~generous(X)))&
(wise(paul))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~kind(fred)<~>patient(fred)))&
(~tall(fred))&
(?[X]:((~brave(X)<~>calm(X))))&
((~kind(fred)&old(fred))) | ~creative(alice) | [
"p0",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7415422030569757473726052
% SZS output start Proof for 7415422030569757473726052
1. ! [X0] : ((wise(X0) | old(X0)) <=> (~creative(X0) & funny(X0))) [input p0]
8. ! [X0] : ((old(X0) & happy(X0)) <=> (calm(X0) | ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | creative(X0)) => (~strong(X0) | calm(X0))) [input p8]
24. creative(alice) [input hypothesis]
33. ! [X0] : ((~strong(X0) | calm(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 9]
34. ! [X0] : (~strong(X0) | calm(X0) | (~funny(X0) & ~creative(X0))) [flattening 33]
39. ! [X0] : (((wise(X0) | old(X0)) | (creative(X0) | ~funny(X0))) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((wise(X0) | old(X0) | creative(X0) | ~funny(X0)) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [flattening 39]
59. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ~old(X0) | ~happy(X0))) [flattening 59]
87. ~creative(X0) | ~old(X0) [cnf transformation 40]
112. strong(X0) | old(X0) [cnf transformation 60]
113. ~calm(X0) | old(X0) [cnf transformation 60]
114. ~strong(X0) | calm(X0) | ~creative(X0) [cnf transformation 34]
147. creative(alice) [cnf transformation 24]
375. calm(X0) | ~creative(X0) | old(X0) [resolution 114,112]
376. ~creative(X0) | old(X0) [subsumption resolution 375,113]
377. ~creative(X0) [subsumption resolution 376,87]
378. $false [resolution 377,147]
% SZS output end Proof for 7415422030569757473726052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not humble and happy then someone is not old or tall.
Everyone who is tall is brave.
Everyone who is either wise or kind is both strong and calm.
Everyone who is old or funny is both curious and not strong and vice versa.
Everyone who is not calm is either not old or creative.
If someone is both creative and tall then someone is calm.
Everyone who is not humble or not funny is funny or brave and vice versa.
If someone is either funny or calm then paul is not quiet.
Everyone who is either old or funny is either quiet or generous and vice versa.
Everyone who is either quiet or tall is not tall or quiet.
If someone is quiet or not kind then alice is not brave or not curious and vice versa.
If someone is not curious then someone is not wise or not funny and vice versa.
If john is not rich then someone is wise and vice versa.
Everyone who is either not creative or curious is both not quiet and calm and vice versa.
If fred is not humble then someone is not creative or quiet.
If someone is either curious or not calm then susan is strong.
Someone is rich.
Mary is either not old or not rich.
Lucy is either strong or not quiet.
Mary is either happy or funny.
Mary is not rich or strong.
John is not patient or creative.
Susan is not creative.
Someone is kind. | Paul is quiet. | contradiction | (((~humble(alice)&happy(alice)))=>(?[X]:((~old(X)|tall(X)))))&
(![X]:(tall(X)=>brave(X)))&
(![X]:((wise(X)<~>kind(X))=>(strong(X)&calm(X))))&
(![X]:((old(X)|funny(X))<=>(curious(X)&~strong(X))))&
(![X]:(~calm(X)=>(~old(X)<~>creative(X))))&
((?[X]:((creative(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:((~humble(X)|~funny(X))<=>(funny(X)|brave(X))))&
((?[X]:((funny(X)<~>calm(X))))=>(~quiet(paul)))&
(![X]:((old(X)<~>funny(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((quiet(X)<~>tall(X))=>(~tall(X)|quiet(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~brave(alice)|~curious(alice))))&
((?[X]:(~curious(X)))<=>(?[X]:((~wise(X)|~funny(X)))))&
((~rich(john))<=>(?[X]:(wise(X))))&
(![X]:((~creative(X)<~>curious(X))<=>(~quiet(X)&calm(X))))&
((~humble(fred))=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:((curious(X)<~>~calm(X))))=>(strong(susan)))&
(?[X]:(rich(X)))&
((~old(mary)<~>~rich(mary)))&
((strong(lucy)<~>~quiet(lucy)))&
((happy(mary)<~>funny(mary)))&
((~rich(mary)|strong(mary)))&
((~patient(john)|creative(john)))&
(~creative(susan))&
(?[X]:(kind(X))) | quiet(paul) | [
"p3",
"p4",
"p7",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8893375699880502452909494
% SZS output start Proof for 8893375699880502452909494
4. ! [X0] : ((funny(X0) | old(X0)) <=> (~strong(X0) & curious(X0))) [input p3]
5. ! [X0] : (~calm(X0) => (~old(X0) <~> creative(X0))) [input p4]
8. ? [X0] : (funny(X0) <~> calm(X0)) => ~quiet(paul) [input p7]
12. ? [X0] : ~curious(X0) <=> ? [X0] : (~funny(X0) | ~wise(X0)) [input p11]
14. ! [X0] : ((~creative(X0) <~> curious(X0)) <=> (calm(X0) & ~quiet(X0))) [input p13]
16. ? [X0] : (curious(X0) <~> ~calm(X0)) => strong(susan) [input p15]
25. quiet(paul) [input hypothesis]
27. ? [X0] : ~curious(X0) <=> ? [X1] : (~funny(X1) | ~wise(X1)) [rectify 12]
33. ! [X0] : ((~old(X0) <~> creative(X0)) | calm(X0)) [ennf transformation 5]
35. ~quiet(paul) | ! [X0] : (funny(X0) <=> calm(X0)) [ennf transformation 8]
39. strong(susan) | ! [X0] : (curious(X0) <=> ~calm(X0)) [ennf transformation 16]
43. ! [X0] : (((funny(X0) | old(X0)) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 4]
44. ! [X0] : ((funny(X0) | old(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | (~funny(X0) & ~old(X0)))) [flattening 43]
45. ! [X0] : (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | calm(X0)) [nnf transformation 33]
51. ~quiet(paul) | ! [X0] : ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))) [nnf transformation 35]
59. (? [X0] : ~curious(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X1] : (~funny(X1) | ~wise(X1)) | ! [X0] : curious(X0)) [nnf transformation 27]
60. (? [X0] : ~curious(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X2] : (~funny(X2) | ~wise(X2)) | ! [X3] : curious(X3)) [rectify 59]
61. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
62. ? [X2] : (~funny(X2) | ~wise(X2)) => (~funny(sK4) | ~wise(sK4)) [choice axiom]
63. (~curious(sK3) | ! [X1] : (funny(X1) & wise(X1))) & ((~funny(sK4) | ~wise(sK4)) | ! [X3] : curious(X3)) [skolemisation 60,62,61]
68. ! [X0] : ((((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0))))) [nnf transformation 14]
69. ! [X0] : ((((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0))))) [flattening 68]
72. strong(susan) | ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 39]
86. ~old(X0) | curious(X0) [cnf transformation 44]
87. ~funny(X0) | curious(X0) [cnf transformation 44]
89. ~funny(X0) | ~strong(X0) [cnf transformation 44]
92. ~creative(X0) | old(X0) | calm(X0) [cnf transformation 45]
98. ~quiet(paul) | calm(X0) | ~funny(X0) [cnf transformation 51]
99. ~quiet(paul) | funny(X0) | ~calm(X0) [cnf transformation 51]
116. ~curious(sK3) | funny(X1) [cnf transformation 63]
121. creative(X0) | curious(X0) | calm(X0) [cnf transformation 69]
126. strong(susan) | ~calm(X0) | ~curious(X0) [cnf transformation 72]
138. quiet(paul) [cnf transformation 25]
168. 7 <=> ! [X0] : (funny(X0) | ~calm(X0)) [avatar definition]
169. ~calm(X0) | funny(X0) <- (7) [avatar component clause 168]
171. 8 <=> quiet(paul) [avatar definition]
174. 7 | ~8 [avatar split clause 99,171,168]
176. 9 <=> ! [X0] : (calm(X0) | ~funny(X0)) [avatar definition]
177. ~funny(X0) | calm(X0) <- (9) [avatar component clause 176]
178. 9 | ~8 [avatar split clause 98,171,176]
206. 16 <=> ! [X1] : funny(X1) [avatar definition]
207. funny(X1) <- (16) [avatar component clause 206]
209. 17 <=> curious(sK3) [avatar definition]
211. ~curious(sK3) <- (~17) [avatar component clause 209]
212. 16 | ~17 [avatar split clause 116,209,206]
218. 19 <=> ! [X3] : curious(X3) [avatar definition]
219. curious(X3) <- (19) [avatar component clause 218]
256. 28 <=> ! [X0] : (curious(X0) | calm(X0)) [avatar definition]
257. curious(X0) | calm(X0) <- (28) [avatar component clause 256]
259. 29 <=> strong(susan) [avatar definition]
261. strong(susan) <- (29) [avatar component clause 259]
264. 30 <=> ! [X0] : (~calm(X0) | ~curious(X0)) [avatar definition]
265. ~calm(X0) | ~curious(X0) <- (30) [avatar component clause 264]
266. 30 | 29 [avatar split clause 126,259,264]
302. 8 [avatar split clause 138,171]
389. curious(X0) | calm(X0) | old(X0) | calm(X0) [resolution 121,92]
391. curious(X0) | calm(X0) | old(X0) [duplicate literal removal 389]
393. 48 <=> calm(susan) [avatar definition]
394. ~calm(susan) <- (~48) [avatar component clause 393]
395. calm(susan) <- (48) [avatar component clause 393]
410. curious(X0) | calm(X0) [subsumption resolution 391,86]
411. 28 [avatar split clause 410,256]
431. calm(sK3) <- (~17, 28) [resolution 257,211]
437. funny(susan) <- (7, 48) [resolution 395,169]
443. funny(sK3) <- (7, ~17, 28) [resolution 431,169]
658. ~strong(susan) <- (7, 48) [resolution 437,89]
671. $false <- (7, 29, 48) [subsumption resolution 658,261]
672. ~7 | ~29 | ~48 [avatar contradiction clause 671]
701. curious(sK3) <- (7, ~17, 28) [resolution 443,87]
716. $false <- (7, ~17, 28) [subsumption resolution 701,211]
717. ~7 | 17 | ~28 [avatar contradiction clause 716]
720. calm(X2) <- (9, 16) [resolution 207,177]
723. curious(X5) <- (16) [resolution 207,87]
729. 19 | ~16 [avatar split clause 723,206,218]
744. $false <- (9, 16, ~48) [resolution 720,394]
745. ~9 | ~16 | 48 [avatar contradiction clause 744]
746. ~curious(X0) <- (9, 16, 30) [subsumption resolution 265,720]
747. $false <- (9, 16, 19, 30) [subsumption resolution 746,219]
748. ~9 | ~16 | ~19 | ~30 [avatar contradiction clause 747]
749. $false [avatar sat refutation 174,178,212,266,302,411,672,717,729,745,748]
% SZS output end Proof for 8893375699880502452909494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is old then fred is both not calm and not brave.
Everyone who is brave or not funny is wise or not tall and vice versa.
Everyone who is not humble is either not happy or not wise and vice versa.
If paul is either not quiet or not curious then someone is strong or quiet.
Everyone who is generous or not quiet is either rich or not old.
If someone is either not happy or patient then someone is either creative or not strong.
If alice is not quiet or not calm then someone is not strong and vice versa.
Everyone who is either tall or not happy is not rich or happy and vice versa.
If someone is not curious or not rich then susan is not calm.
If someone is rich then someone is not curious or strong and vice versa.
If someone is not generous then john is both not funny and patient and vice versa.
Everyone who is either not humble or quiet is either not wise or strong and vice versa.
Everyone who is not humble or not happy is both not funny and not curious and vice versa.
If someone is curious or not funny then fred is wise.
If john is both not patient and not curious then someone is both calm and old and vice versa.
Everyone who is not funny or not happy is both not quiet and tall.
John is not happy or not patient.
Susan is both not patient and curious.
Someone is happy or not calm.
Paul is both tall and not rich.
Fred is either tall or curious.
Paul is not quiet or creative.
Lucy is both not curious and humble.
Someone is both not quiet and not creative. | Fred is not wise. | contradiction | ((old(fred))=>((~calm(fred)&~brave(fred))))&
(![X]:((brave(X)|~funny(X))<=>(wise(X)|~tall(X))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~wise(X))))&
(((~quiet(paul)<~>~curious(paul)))=>(?[X]:((strong(X)|quiet(X)))))&
(![X]:((generous(X)|~quiet(X))=>(rich(X)<~>~old(X))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~quiet(alice)|~calm(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(~rich(X)|happy(X))))&
((?[X]:((~curious(X)|~rich(X))))=>(~calm(susan)))&
((?[X]:(rich(X)))<=>(?[X]:((~curious(X)|strong(X)))))&
((?[X]:(~generous(X)))<=>((~funny(john)&patient(john))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~wise(X)<~>strong(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~funny(X)&~curious(X))))&
((?[X]:((curious(X)|~funny(X))))=>(wise(fred)))&
(((~patient(john)&~curious(john)))<=>(?[X]:((calm(X)&old(X)))))&
(![X]:((~funny(X)|~happy(X))=>(~quiet(X)&tall(X))))&
((~happy(john)|~patient(john)))&
((~patient(susan)&curious(susan)))&
(?[X]:((happy(X)|~calm(X))))&
((tall(paul)&~rich(paul)))&
((tall(fred)<~>curious(fred)))&
((~quiet(paul)|creative(paul)))&
((~curious(lucy)&humble(lucy)))&
(?[X]:((~quiet(X)&~creative(X)))) | ~wise(fred) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 645323681197649624145030
% SZS output start Proof for 645323681197649624145030
14. ? [X0] : (~funny(X0) | curious(X0)) => wise(fred) [input p13]
18. curious(susan) & ~patient(susan) [input p17]
25. ~wise(fred) [input hypothesis]
33. wise(fred) | ! [X0] : (funny(X0) & ~curious(X0)) [ennf transformation 14]
126. wise(fred) | ~curious(X0) [cnf transformation 33]
138. curious(susan) [cnf transformation 18]
149. ~wise(fred) [cnf transformation 25]
276. 29 <=> wise(fred) [avatar definition]
281. 30 <=> ! [X0] : ~curious(X0) [avatar definition]
282. ~curious(X0) <- (30) [avatar component clause 281]
283. 30 | 29 [avatar split clause 126,276,281]
324. ~29 [avatar split clause 149,276]
331. $false <- (30) [resolution 282,138]
332. ~30 [avatar contradiction clause 331]
333. $false [avatar sat refutation 283,324,332]
% SZS output end Proof for 645323681197649624145030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and calm is generous.
Everyone who is not tall is both happy and quiet.
Everyone who is not patient is not quiet or not generous.
Everyone who is not strong is both not happy and not rich and vice versa.
If fred is both creative and not happy then someone is either calm or old.
If someone is both not old and old then someone is both humble and not quiet and vice versa.
If susan is not brave or curious then someone is not happy and vice versa.
If lucy is both not kind and not patient then someone is both wise and not wise and vice versa.
If susan is kind or not strong then susan is not wise.
Everyone who is not rich is brave and vice versa.
Everyone who is not wise is either not brave or strong.
Everyone who is both patient and calm is not calm or rich and vice versa.
Everyone who is wise is both not quiet and tall and vice versa.
Everyone who is happy or not tall is either not rich or not strong and vice versa.
If paul is either not strong or curious then someone is not calm or happy.
Someone is either not tall or not kind.
Someone is both not patient and not curious.
Someone is both curious and not patient.
Fred is either kind or not creative.
Someone is humble.
Someone is not old or not wise. | Susan is not rich. | neutral | (![X]:((kind(X)&calm(X))=>generous(X)))&
(![X]:(~tall(X)=>(happy(X)&quiet(X))))&
(![X]:(~patient(X)=>(~quiet(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~happy(X)&~rich(X))))&
(((creative(fred)&~happy(fred)))=>(?[X]:((calm(X)<~>old(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((humble(X)&~quiet(X)))))&
(((~brave(susan)|curious(susan)))<=>(?[X]:(~happy(X))))&
(((~kind(lucy)&~patient(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(((kind(susan)|~strong(susan)))=>(~wise(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:(~wise(X)=>(~brave(X)<~>strong(X))))&
(![X]:((patient(X)&calm(X))<=>(~calm(X)|rich(X))))&
(![X]:(wise(X)<=>(~quiet(X)&tall(X))))&
(![X]:((happy(X)|~tall(X))<=>(~rich(X)<~>~strong(X))))&
(((~strong(paul)<~>curious(paul)))=>(?[X]:((~calm(X)|happy(X)))))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((~patient(X)&~curious(X))))&
(?[X]:((curious(X)&~patient(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:(humble(X)))&
(?[X]:((~old(X)|~wise(X)))) | ~rich(susan) | [] | null | 0 |
If paul is either not rich or rich then fred is not happy or not funny.
Everyone who is either not patient or not happy is both not generous and not happy and vice versa.
If alice is curious or not old then susan is either curious or not brave and vice versa.
Everyone who is not humble is old or curious.
If someone is either not generous or not happy then susan is quiet or not curious and vice versa.
If fred is both not calm and not tall then susan is creative or humble.
Everyone who is either creative or calm is both kind and not tall and vice versa.
Everyone who is both strong and brave is either not strong or old and vice versa.
If paul is either curious or not tall then someone is both not calm and not creative and vice versa.
If someone is patient then lucy is not calm or wise.
Everyone who is either not kind or not rich is both not tall and tall and vice versa.
If susan is either not quiet or not old then someone is not kind.
Everyone who is curious or rich is not rich and vice versa.
Everyone who is not generous is not old or humble.
Everyone who is both old and not kind is old.
Everyone who is either not funny or not happy is not quiet or not generous and vice versa.
Paul is both not happy and curious.
Paul is not quiet.
Someone is both old and not calm.
Paul is either curious or not generous.
Mary is either not brave or not generous.
Susan is not humble.
Mary is generous or not strong. | Fred is not calm. | neutral | (((~rich(paul)<~>rich(paul)))=>((~happy(fred)|~funny(fred))))&
(![X]:((~patient(X)<~>~happy(X))<=>(~generous(X)&~happy(X))))&
(((curious(alice)|~old(alice)))<=>((curious(susan)<~>~brave(susan))))&
(![X]:(~humble(X)=>(old(X)|curious(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>((quiet(susan)|~curious(susan))))&
(((~calm(fred)&~tall(fred)))=>((creative(susan)|humble(susan))))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)&~tall(X))))&
(![X]:((strong(X)&brave(X))<=>(~strong(X)<~>old(X))))&
(((curious(paul)<~>~tall(paul)))<=>(?[X]:((~calm(X)&~creative(X)))))&
((?[X]:(patient(X)))=>((~calm(lucy)|wise(lucy))))&
(![X]:((~kind(X)<~>~rich(X))<=>(~tall(X)&tall(X))))&
(((~quiet(susan)<~>~old(susan)))=>(?[X]:(~kind(X))))&
(![X]:((curious(X)|rich(X))<=>~rich(X)))&
(![X]:(~generous(X)=>(~old(X)|humble(X))))&
(![X]:((old(X)&~kind(X))=>old(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(~quiet(X)|~generous(X))))&
((~happy(paul)&curious(paul)))&
(~quiet(paul))&
(?[X]:((old(X)&~calm(X))))&
((curious(paul)<~>~generous(paul)))&
((~brave(mary)<~>~generous(mary)))&
(~humble(susan))&
((generous(mary)|~strong(mary))) | ~calm(fred) | [] | null | 0 |
Everyone who is not strong is not rich.
Everyone who is patient or kind is humble or not tall.
Everyone who is either not humble or not wise is both calm and curious and vice versa.
Everyone who is both not tall and creative is creative or wise and vice versa.
Everyone who is calm or creative is not brave and vice versa.
Everyone who is not patient is funny.
Everyone who is either not patient or not generous is not funny or funny.
If someone is not funny then someone is both funny and brave.
Everyone who is old is wise.
If someone is either brave or kind then someone is not kind or patient.
If mary is either not quiet or humble then fred is wise.
Everyone who is not happy or happy is both brave and rich.
Everyone who is both not brave and patient is not tall and vice versa.
Everyone who is either brave or not humble is quiet or calm.
If someone is either not curious or generous then susan is either not strong or not generous and vice versa.
If someone is quiet or not happy then someone is not generous and vice versa.
Lucy is both not creative and not kind.
John is kind or not old.
Mary is not happy or happy.
Someone is not humble.
Susan is either not humble or not curious. | Mary is patient. | contradiction | (![X]:(~strong(X)=>~rich(X)))&
(![X]:((patient(X)|kind(X))=>(humble(X)|~tall(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(calm(X)&curious(X))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)|wise(X))))&
(![X]:((calm(X)|creative(X))<=>~brave(X)))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:((~patient(X)<~>~generous(X))=>(~funny(X)|funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(old(X)=>wise(X)))&
((?[X]:((brave(X)<~>kind(X))))=>(?[X]:((~kind(X)|patient(X)))))&
(((~quiet(mary)<~>humble(mary)))=>(wise(fred)))&
(![X]:((~happy(X)|happy(X))=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~strong(susan)<~>~generous(susan))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(~generous(X))))&
((~creative(lucy)&~kind(lucy)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary)))&
(?[X]:(~humble(X)))&
((~humble(susan)<~>~curious(susan))) | patient(mary) | [
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8987857827008457306297597
% SZS output start Proof for 8987857827008457306297597
2. ! [X0] : ((kind(X0) | patient(X0)) => (~tall(X0) | humble(X0))) [input p1]
3. ! [X0] : ((~humble(X0) <~> ~wise(X0)) <=> (curious(X0) & calm(X0))) [input p2]
4. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (wise(X0) | creative(X0))) [input p3]
5. ! [X0] : ((creative(X0) | calm(X0)) <=> ~brave(X0)) [input p4]
12. ! [X0] : ((happy(X0) | ~happy(X0)) => (rich(X0) & brave(X0))) [input p11]
13. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p12]
22. patient(mary) [input hypothesis]
29. ! [X0] : ((~tall(X0) | humble(X0)) | (~kind(X0) & ~patient(X0))) [ennf transformation 2]
30. ! [X0] : (~tall(X0) | humble(X0) | (~kind(X0) & ~patient(X0))) [flattening 29]
37. ! [X0] : ((rich(X0) & brave(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 12]
40. ! [X0] : ((((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))))) [nnf transformation 3]
41. ! [X0] : ((((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))))) [flattening 40]
42. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~creative(X0) | tall(X0))) [flattening 42]
44. ! [X0] : (((creative(X0) | calm(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) & ~calm(X0)))) [nnf transformation 5]
45. ! [X0] : ((creative(X0) | calm(X0) | brave(X0)) & (~brave(X0) | (~creative(X0) & ~calm(X0)))) [flattening 44]
55. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 13]
56. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 55]
71. ~tall(X0) | humble(X0) | ~patient(X0) [cnf transformation 30]
74. ~humble(X0) | calm(X0) | wise(X0) [cnf transformation 41]
81. ~wise(X0) | ~tall(X0) [cnf transformation 43]
84. ~brave(X0) | ~calm(X0) [cnf transformation 45]
96. brave(X0) | happy(X0) [cnf transformation 37]
97. ~happy(X0) | brave(X0) [cnf transformation 37]
101. ~brave(X0) | tall(X0) [cnf transformation 56]
122. patient(mary) [cnf transformation 22]
153. 8 <=> humble(mary) [avatar definition]
154. humble(mary) <- (8) [avatar component clause 153]
167. brave(X0) [subsumption resolution 96,97]
168. tall(X0) [subsumption resolution 101,167]
237. ~calm(X0) [resolution 84,167]
240. ~patient(X1) | humble(X1) [resolution 71,168]
241. humble(mary) [resolution 240,122]
245. calm(mary) | wise(mary) <- (8) [resolution 74,154]
247. wise(mary) <- (8) [subsumption resolution 245,237]
252. ~tall(mary) <- (8) [resolution 247,81]
255. $false <- (8) [subsumption resolution 252,168]
256. ~8 [avatar contradiction clause 255]
257. 8 [avatar split clause 241,153]
258. $false [avatar sat refutation 256,257]
% SZS output end Proof for 8987857827008457306297597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not quiet then susan is not humble. Everyone who is not old or not tall is brave. If someone is not kind then someone is either not old or kind and vice versa. If mary is not rich then someone is either happy or not patient and vice versa. Everyone who is either not strong or creative is funny or not curious and vice versa. If susan is strong then alice is generous and vice versa. Everyone who is not humble or not funny is not rich. If someone is either happy or not tall then someone is humble or not tall. Everyone who is not curious is old. If susan is rich then lucy is brave and vice versa. Everyone who is strong or not old is both not brave and not funny and vice versa. Everyone who is either old or not brave is humble. If someone is not tall or not brave then lucy is creative. Everyone who is either happy or generous is either not old or quiet and vice versa. If susan is either not calm or not funny then john is tall or quiet and vice versa. If someone is either not happy or not generous then alice is calm or not quiet and vice versa. John is not curious. Someone is either not curious or not generous. John is both not brave and not humble. Someone is both not patient and not generous. Paul is kind. Mary is patient or happy. Someone is generous or not curious. | Susan is quiet. | neutral | ((?[X]:((~funny(X)<~>~quiet(X))))=>(~humble(susan)))&
(![X]:((~old(X)|~tall(X))=>brave(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~old(X)<~>kind(X)))))&
((~rich(mary))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>(funny(X)|~curious(X))))&
((strong(susan))<=>(generous(alice)))&
(![X]:((~humble(X)|~funny(X))=>~rich(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:(~curious(X)=>old(X)))&
((rich(susan))<=>(brave(lucy)))&
(![X]:((strong(X)|~old(X))<=>(~brave(X)&~funny(X))))&
(![X]:((old(X)<~>~brave(X))=>humble(X)))&
((?[X]:((~tall(X)|~brave(X))))=>(creative(lucy)))&
(![X]:((happy(X)<~>generous(X))<=>(~old(X)<~>quiet(X))))&
(((~calm(susan)<~>~funny(susan)))<=>((tall(john)|quiet(john))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>((calm(alice)|~quiet(alice))))&
(~curious(john))&
(?[X]:((~curious(X)<~>~generous(X))))&
((~brave(john)&~humble(john)))&
(?[X]:((~patient(X)&~generous(X))))&
(kind(paul))&
((patient(mary)|happy(mary)))&
(?[X]:((generous(X)|~curious(X)))) | quiet(susan) | [] | null | 0 |
Everyone who is not generous or not patient is brave. If someone is quiet then someone is both not strong and strong. Everyone who is not quiet or tall is either strong or rich. If john is funny then alice is rich. Everyone who is either not funny or not old is not tall or tall. Everyone who is both not strong and not calm is not quiet. If susan is both not quiet and creative then someone is both tall and not funny. If someone is tall or not kind then someone is not humble and vice versa. Everyone who is either tall or not brave is not funny or not happy and vice versa. Everyone who is either not funny or strong is both curious and creative and vice versa. Everyone who is not rich or strong is both not wise and patient. Everyone who is brave or humble is either wise or creative. Everyone who is both rich and creative is not rich and vice versa. If lucy is both not wise and curious then someone is both not old and not strong and vice versa. If someone is not old or brave then mary is both happy and creative. Everyone who is rich is either happy or generous and vice versa. Someone is generous. Fred is not creative or not strong. Someone is not wise. Someone is either not tall or wise. | Susan is patient. | entailment | (![X]:((~generous(X)|~patient(X))=>brave(X)))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((~quiet(X)|tall(X))=>(strong(X)<~>rich(X))))&
((funny(john))=>(rich(alice)))&
(![X]:((~funny(X)<~>~old(X))=>(~tall(X)|tall(X))))&
(![X]:((~strong(X)&~calm(X))=>~quiet(X)))&
(((~quiet(susan)&creative(susan)))=>(?[X]:((tall(X)&~funny(X)))))&
((?[X]:((tall(X)|~kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((tall(X)<~>~brave(X))<=>(~funny(X)|~happy(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(curious(X)&creative(X))))&
(![X]:((~rich(X)|strong(X))=>(~wise(X)&patient(X))))&
(![X]:((brave(X)|humble(X))=>(wise(X)<~>creative(X))))&
(![X]:((rich(X)&creative(X))<=>~rich(X)))&
(((~wise(lucy)&curious(lucy)))<=>(?[X]:((~old(X)&~strong(X)))))&
((?[X]:((~old(X)|brave(X))))=>((happy(mary)&creative(mary))))&
(![X]:(rich(X)<=>(happy(X)<~>generous(X))))&
(?[X]:(generous(X)))&
((~creative(fred)|~strong(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~tall(X)<~>wise(X)))) | patient(susan) | [
"p0",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2062493147043543312393592
% SZS output start Proof for 2062493147043543312393592
1. ! [X0] : ((~patient(X0) | ~generous(X0)) => brave(X0)) [input p0]
13. ! [X0] : ((creative(X0) & rich(X0)) <=> ~rich(X0)) [input p12]
15. ? [X0] : (brave(X0) | ~old(X0)) => (creative(mary) & happy(mary)) [input p14]
21. ~patient(susan) [input hypothesis]
25. ! [X0] : (brave(X0) | (patient(X0) & generous(X0))) [ennf transformation 1]
35. (creative(mary) & happy(mary)) | ! [X0] : (~brave(X0) & old(X0)) [ennf transformation 15]
53. ! [X0] : (((creative(X0) & rich(X0)) | rich(X0)) & (~rich(X0) | (~creative(X0) | ~rich(X0)))) [nnf transformation 13]
54. ! [X0] : (((creative(X0) & rich(X0)) | rich(X0)) & (~rich(X0) | ~creative(X0) | ~rich(X0))) [flattening 53]
69. brave(X0) | patient(X0) [cnf transformation 25]
104. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 54]
105. rich(X0) | rich(X0) [cnf transformation 54]
114. creative(mary) | ~brave(X0) [cnf transformation 35]
124. ~patient(susan) [cnf transformation 21]
125. ~rich(X0) | ~creative(X0) [duplicate literal removal 104]
126. rich(X0) [duplicate literal removal 105]
187. ~creative(X0) [subsumption resolution 125,126]
211. ~brave(X0) [subsumption resolution 114,187]
226. patient(X0) [resolution 69,211]
227. $false [resolution 226,124]
% SZS output end Proof for 2062493147043543312393592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is not generous then someone is both kind and not calm and vice versa.
If someone is wise then someone is not brave or not rich.
If someone is both not happy and not kind then lucy is strong and vice versa.
Everyone who is not humble or humble is funny and vice versa.
If fred is funny or happy then someone is either curious or not humble and vice versa.
Everyone who is both brave and tall is both strong and not kind and vice versa.
If alice is not calm then someone is not funny.
Everyone who is not quiet is either not funny or rich and vice versa.
Everyone who is not patient or not happy is calm or not humble.
Everyone who is funny is brave and vice versa.
Everyone who is both not curious and not wise is either happy or not old and vice versa.
Everyone who is either patient or not kind is both not tall and old and vice versa.
If susan is rich or brave then mary is not tall.
If mary is not kind or not happy then someone is both not funny and not rich and vice versa.
If susan is curious or generous then mary is not calm.
Someone is both happy and not strong.
Susan is both curious and not tall.
Paul is tall or not old.
Someone is not curious.
Someone is old.
Alice is either rich or not tall.
Someone is happy.
Fred is both not calm and patient. | Mary is not tall. | entailment | ((~generous(alice))<=>(?[X]:((kind(X)&~calm(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~brave(X)|~rich(X)))))&
((?[X]:((~happy(X)&~kind(X))))<=>(strong(lucy)))&
(![X]:((~humble(X)|humble(X))<=>funny(X)))&
(((funny(fred)|happy(fred)))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(![X]:((brave(X)&tall(X))<=>(strong(X)&~kind(X))))&
((~calm(alice))=>(?[X]:(~funny(X))))&
(![X]:(~quiet(X)<=>(~funny(X)<~>rich(X))))&
(![X]:((~patient(X)|~happy(X))=>(calm(X)|~humble(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~curious(X)&~wise(X))<=>(happy(X)<~>~old(X))))&
(![X]:((patient(X)<~>~kind(X))<=>(~tall(X)&old(X))))&
(((rich(susan)|brave(susan)))=>(~tall(mary)))&
(((~kind(mary)|~happy(mary)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(((curious(susan)|generous(susan)))=>(~calm(mary)))&
(?[X]:((happy(X)&~strong(X))))&
((curious(susan)&~tall(susan)))&
((tall(paul)|~old(paul)))&
(?[X]:(~curious(X)))&
(?[X]:(old(X)))&
((rich(alice)<~>~tall(alice)))&
(?[X]:(happy(X)))&
((~calm(fred)&patient(fred))) | ~tall(mary) | [
"p3",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4203642932842158221880395
% SZS output start Proof for 4203642932842158221880395
4. ! [X0] : ((humble(X0) | ~humble(X0)) <=> funny(X0)) [input p3]
10. ! [X0] : (funny(X0) <=> brave(X0)) [input p9]
13. (brave(susan) | rich(susan)) => ~tall(mary) [input p12]
24. tall(mary) [input hypothesis]
30. ~tall(mary) | (~brave(susan) & ~rich(susan)) [ennf transformation 13]
43. ! [X0] : (((humble(X0) | ~humble(X0)) | ~funny(X0)) & (funny(X0) | (~humble(X0) & humble(X0)))) [nnf transformation 4]
44. ! [X0] : ((humble(X0) | ~humble(X0) | ~funny(X0)) & (funny(X0) | (~humble(X0) & humble(X0)))) [flattening 43]
54. ! [X0] : ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))) [nnf transformation 10]
80. funny(X0) | humble(X0) [cnf transformation 44]
81. funny(X0) | ~humble(X0) [cnf transformation 44]
96. brave(X0) | ~funny(X0) [cnf transformation 54]
111. ~tall(mary) | ~brave(susan) [cnf transformation 30]
131. tall(mary) [cnf transformation 24]
180. funny(X0) [subsumption resolution 80,81]
200. brave(X0) [subsumption resolution 96,180]
201. ~tall(mary) [subsumption resolution 111,200]
254. $false [subsumption resolution 131,201]
% SZS output end Proof for 4203642932842158221880395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and patient is rich or not creative and vice versa.
Everyone who is humble or wise is both not patient and wise.
Everyone who is both not strong and creative is either not curious or not rich.
Everyone who is not kind is either funny or old.
If someone is either not tall or not brave then someone is either tall or generous and vice versa.
Everyone who is either not curious or not rich is either generous or not calm.
If alice is rich then someone is old.
Everyone who is creative or humble is generous and vice versa.
If john is rich then someone is not calm or not curious.
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 not brave or patient is not old and vice versa.
Everyone who is both not tall and not curious is either tall or kind and vice versa.
Someone is both not tall and patient.
Someone is both strong and not calm.
Someone is creative.
Alice is tall or wise.
Someone is either not happy or tall. | John is quiet. | neutral | (![X]:((~patient(X)&patient(X))<=>(rich(X)|~creative(X))))&
(![X]:((humble(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((~strong(X)&creative(X))=>(~curious(X)<~>~rich(X))))&
(![X]:(~kind(X)=>(funny(X)<~>old(X))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(generous(X)<~>~calm(X))))&
((rich(alice))=>(?[X]:(old(X))))&
(![X]:((creative(X)|humble(X))<=>generous(X)))&
((rich(john))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[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]:((~brave(X)|patient(X))<=>~old(X)))&
(![X]:((~tall(X)&~curious(X))<=>(tall(X)<~>kind(X))))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:(creative(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~happy(X)<~>tall(X)))) | quiet(john) | [] | null | 0 |
If john is both not rich and not wise then john is both generous and not happy and vice versa.
Everyone who is not calm or tall is not funny.
If lucy is not curious or not rich then fred is both rich and not wise and vice versa.
If someone is either not old or generous then paul is not funny or wise and vice versa.
If paul is either humble or not funny then someone is both not tall and not creative and vice versa.
Everyone who is quiet is both not quiet and not calm and vice versa.
Everyone who is both rich and not creative is not rich or not tall and vice versa.
If someone is brave then someone is not old or curious and vice versa.
If someone is either not rich or funny then someone is either not strong or not humble.
Everyone who is both not curious and not kind is either not happy or quiet and vice versa.
If alice is not humble then someone is not old.
If someone is not funny or happy then fred is either strong or wise.
Everyone who is both humble and creative is not brave and vice versa.
If someone is either not tall or brave then john is either tall or quiet.
If alice is happy then mary is not humble or not creative.
Everyone who is either generous or not humble is both funny and not curious.
Someone is tall or generous.
Lucy is not kind or not brave.
Fred is not funny or not quiet.
Alice is either curious or creative.
Someone is both kind and creative.
Someone is either humble or not brave.
Someone is either strong or quiet. | Lucy is brave. | neutral | (((~rich(john)&~wise(john)))<=>((generous(john)&~happy(john))))&
(![X]:((~calm(X)|tall(X))=>~funny(X)))&
(((~curious(lucy)|~rich(lucy)))<=>((rich(fred)&~wise(fred))))&
((?[X]:((~old(X)<~>generous(X))))<=>((~funny(paul)|wise(paul))))&
(((humble(paul)<~>~funny(paul)))<=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((rich(X)&~creative(X))<=>(~rich(X)|~tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~old(X)|curious(X)))))&
((?[X]:((~rich(X)<~>funny(X))))=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~kind(X))<=>(~happy(X)<~>quiet(X))))&
((~humble(alice))=>(?[X]:(~old(X))))&
((?[X]:((~funny(X)|happy(X))))=>((strong(fred)<~>wise(fred))))&
(![X]:((humble(X)&creative(X))<=>~brave(X)))&
((?[X]:((~tall(X)<~>brave(X))))=>((tall(john)<~>quiet(john))))&
((happy(alice))=>((~humble(mary)|~creative(mary))))&
(![X]:((generous(X)<~>~humble(X))=>(funny(X)&~curious(X))))&
(?[X]:((tall(X)|generous(X))))&
((~kind(lucy)|~brave(lucy)))&
((~funny(fred)|~quiet(fred)))&
((curious(alice)<~>creative(alice)))&
(?[X]:((kind(X)&creative(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((strong(X)<~>quiet(X)))) | brave(lucy) | [] | null | 0 |
If someone is kind then john is either not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Paul is brave. | contradiction | ((?[X]:(kind(X)))<=>((~quiet(john)<~>humble(john))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | brave(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7382286796688130111680717
% SZS output start Proof for 7382286796688130111680717
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. brave(paul) [input hypothesis]
59. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 59]
112. ~brave(X0) | ~brave(X0) [cnf transformation 60]
124. brave(paul) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
254. $false [subsumption resolution 124,126]
% SZS output end Proof for 7382286796688130111680717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and happy is both not wise and funny and vice versa.
Everyone who is tall is generous or not rich and vice versa.
Everyone who is calm or not generous is either not patient or not funny.
Everyone who is both happy and not kind is not creative or quiet.
Everyone who is either funny or not humble is creative or brave.
Everyone who is tall or brave is either not calm or quiet.
If mary is both not generous and calm then fred is strong or not old.
Everyone who is both quiet and wise is happy or not happy and vice versa.
Everyone who is both patient and strong is both not tall and not humble and vice versa.
Everyone who is both not brave and not calm is either not humble or not happy and vice versa.
Everyone who is not kind is both not humble and wise.
If mary is both not rich and kind then someone is either not tall or not humble.
Everyone who is old is either not tall or strong and vice versa.
If lucy is calm then someone is either tall or brave and vice versa.
Everyone who is happy is quiet or curious and vice versa.
Lucy is not patient.
Someone is strong or not rich.
Someone is quiet. | Mary is not generous. | contradiction | (![X]:((~tall(X)&happy(X))<=>(~wise(X)&funny(X))))&
(![X]:(tall(X)<=>(generous(X)|~rich(X))))&
(![X]:((calm(X)|~generous(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((happy(X)&~kind(X))=>(~creative(X)|quiet(X))))&
(![X]:((funny(X)<~>~humble(X))=>(creative(X)|brave(X))))&
(![X]:((tall(X)|brave(X))=>(~calm(X)<~>quiet(X))))&
(((~generous(mary)&calm(mary)))=>((strong(fred)|~old(fred))))&
(![X]:((quiet(X)&wise(X))<=>(happy(X)|~happy(X))))&
(![X]:((patient(X)&strong(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(~humble(X)&wise(X))))&
(((~rich(mary)&kind(mary)))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(old(X)<=>(~tall(X)<~>strong(X))))&
((calm(lucy))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(quiet(X)|curious(X))))&
(~patient(lucy))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(quiet(X))) | ~generous(mary) | [
"p0",
"p1",
"p5",
"p7",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 848518566989650110269184
% SZS output start Proof for 848518566989650110269184
1. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (funny(X0) & ~wise(X0))) [input p0]
2. ! [X0] : (tall(X0) <=> (~rich(X0) | generous(X0))) [input p1]
6. ! [X0] : ((brave(X0) | tall(X0)) => (~calm(X0) <~> quiet(X0))) [input p5]
8. ! [X0] : ((wise(X0) & quiet(X0)) <=> (~happy(X0) | happy(X0))) [input p7]
10. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : (~kind(X0) => (wise(X0) & ~humble(X0))) [input p10]
12. (kind(mary) & ~rich(mary)) => ? [X0] : (~tall(X0) <~> ~humble(X0)) [input p11]
15. ! [X0] : (happy(X0) <=> (curious(X0) | quiet(X0))) [input p14]
19. ~generous(mary) [input hypothesis]
26. ! [X0] : ((~calm(X0) <~> quiet(X0)) | (~brave(X0) & ~tall(X0))) [ennf transformation 6]
29. ! [X0] : ((wise(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 11]
30. ? [X0] : (~tall(X0) <~> ~humble(X0)) | (~kind(mary) | rich(mary)) [ennf transformation 12]
31. ? [X0] : (~tall(X0) <~> ~humble(X0)) | ~kind(mary) | rich(mary) [flattening 30]
33. ! [X0] : (((happy(X0) & ~tall(X0)) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 1]
34. ! [X0] : (((happy(X0) & ~tall(X0)) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ~happy(X0) | tall(X0))) [flattening 33]
35. ! [X0] : ((tall(X0) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | ~tall(X0))) [nnf transformation 2]
36. ! [X0] : ((tall(X0) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | ~tall(X0))) [flattening 35]
39. ! [X0] : (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~brave(X0) & ~tall(X0))) [nnf transformation 26]
40. ! [X0] : (((wise(X0) & quiet(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (~wise(X0) | ~quiet(X0)))) [nnf transformation 8]
41. ! [X0] : (((wise(X0) & quiet(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ~wise(X0) | ~quiet(X0))) [flattening 40]
44. ! [X0] : (((~calm(X0) & ~brave(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (calm(X0) | brave(X0)))) [nnf transformation 10]
45. ! [X0] : (((~calm(X0) & ~brave(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | calm(X0) | brave(X0))) [flattening 44]
46. ? [X0] : ((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ~kind(mary) | rich(mary) [nnf transformation 31]
47. ? [X0] : ((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) => ((humble(sK0) | tall(sK0)) & (~humble(sK0) | ~tall(sK0))) [choice axiom]
48. ((humble(sK0) | tall(sK0)) & (~humble(sK0) | ~tall(sK0))) | ~kind(mary) | rich(mary) [skolemisation 46,47]
54. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ~happy(X0))) [nnf transformation 15]
55. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ~happy(X0))) [flattening 54]
60. ~wise(X0) | ~happy(X0) | tall(X0) [cnf transformation 34]
64. ~rich(X0) | generous(X0) | ~tall(X0) [cnf transformation 36]
76. ~quiet(X0) | calm(X0) | ~tall(X0) [cnf transformation 39]
80. quiet(X0) | ~happy(X0) [cnf transformation 41]
81. quiet(X0) | happy(X0) [cnf transformation 41]
82. wise(X0) | ~happy(X0) [cnf transformation 41]
83. wise(X0) | happy(X0) [cnf transformation 41]
92. ~calm(X0) | ~happy(X0) | humble(X0) [cnf transformation 45]
94. ~humble(X0) | kind(X0) [cnf transformation 29]
96. ~humble(sK0) | ~tall(sK0) | ~kind(mary) | rich(mary) [cnf transformation 48]
105. happy(X0) | ~quiet(X0) [cnf transformation 55]
110. ~generous(mary) [cnf transformation 19]
112. 1 <=> generous(mary) [avatar definition]
113. ~generous(mary) <- (~1) [avatar component clause 112]
128. wise(X0) [subsumption resolution 82,83]
129. quiet(X0) [subsumption resolution 80,81]
131. 5 <=> rich(mary) [avatar definition]
133. rich(mary) <- (5) [avatar component clause 131]
135. 6 <=> kind(mary) [avatar definition]
137. ~kind(mary) <- (~6) [avatar component clause 135]
139. 7 <=> tall(sK0) [avatar definition]
140. ~tall(sK0) <- (~7) [avatar component clause 139]
143. 8 <=> humble(sK0) [avatar definition]
144. ~humble(sK0) <- (~8) [avatar component clause 143]
147. 5 | ~6 | ~7 | ~8 [avatar split clause 96,143,139,135,131]
170. happy(X0) [subsumption resolution 105,129]
180. ~1 [avatar split clause 110,112]
185. ~happy(X1) | tall(X1) [resolution 60,128]
186. tall(X1) [subsumption resolution 185,170]
208. calm(X1) | ~tall(X1) [resolution 76,129]
209. calm(X1) [subsumption resolution 208,186]
225. ~happy(X0) | humble(X0) [resolution 92,209]
226. humble(X0) [subsumption resolution 225,170]
227. kind(X0) [resolution 226,94]
230. $false <- (~6) [resolution 227,137]
231. 6 [avatar contradiction clause 230]
232. generous(mary) | ~tall(mary) <- (5) [resolution 133,64]
233. ~tall(mary) <- (~1, 5) [subsumption resolution 232,113]
234. $false <- (~1, 5) [subsumption resolution 233,186]
235. 1 | ~5 [avatar contradiction clause 234]
236. $false <- (~8) [subsumption resolution 144,226]
237. 8 [avatar contradiction clause 236]
238. $false <- (~7) [subsumption resolution 140,186]
239. 7 [avatar contradiction clause 238]
240. $false [avatar sat refutation 147,180,231,235,237,239]
% SZS output end Proof for 848518566989650110269184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or quiet is not creative or not humble and vice versa.
If someone is either kind or not calm then susan is both not strong and not humble.
Everyone who is old is both not quiet and not tall and vice versa.
If someone is not wise then someone is both not tall and not strong.
Everyone who is not calm or kind is either wise or strong.
If someone is not calm or not rich then fred is quiet.
If someone is not humble then someone is wise or not kind and vice versa.
If someone is both brave and not brave then paul is calm or curious and vice versa.
If john is both not kind and not creative then someone is funny or not wise and vice versa.
Everyone who is not generous is either creative or not curious and vice versa.
If someone is both strong and happy then john is kind or not brave.
If someone is either funny or not funny then fred is either brave or not quiet and vice versa.
Everyone who is either not kind or rich is both not strong and not humble.
If someone is both not generous and not old then mary is both funny and curious.
If paul is not humble then someone is both not patient and not tall and vice versa.
If someone is both not tall and not brave then someone is either not happy or funny and vice versa.
Someone is either not calm or patient.
Someone is tall or wise.
Someone is either tall or creative.
Someone is not creative or generous.
Alice is both funny and patient.
Someone is not rich.
Someone is both not funny and not quiet.
Susan is wise or not generous. | Fred is not old. | entailment | (![X]:((~generous(X)<~>quiet(X))<=>(~creative(X)|~humble(X))))&
((?[X]:((kind(X)<~>~calm(X))))=>((~strong(susan)&~humble(susan))))&
(![X]:(old(X)<=>(~quiet(X)&~tall(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~calm(X)|kind(X))=>(wise(X)<~>strong(X))))&
((?[X]:((~calm(X)|~rich(X))))=>(quiet(fred)))&
((?[X]:(~humble(X)))<=>(?[X]:((wise(X)|~kind(X)))))&
((?[X]:((brave(X)&~brave(X))))<=>((calm(paul)|curious(paul))))&
(((~kind(john)&~creative(john)))<=>(?[X]:((funny(X)|~wise(X)))))&
(![X]:(~generous(X)<=>(creative(X)<~>~curious(X))))&
((?[X]:((strong(X)&happy(X))))=>((kind(john)|~brave(john))))&
((?[X]:((funny(X)<~>~funny(X))))<=>((brave(fred)<~>~quiet(fred))))&
(![X]:((~kind(X)<~>rich(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~generous(X)&~old(X))))=>((funny(mary)&curious(mary))))&
((~humble(paul))<=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((~tall(X)&~brave(X))))<=>(?[X]:((~happy(X)<~>funny(X)))))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:((tall(X)|wise(X))))&
(?[X]:((tall(X)<~>creative(X))))&
(?[X]:((~creative(X)|generous(X))))&
((funny(alice)&patient(alice)))&
(?[X]:(~rich(X)))&
(?[X]:((~funny(X)&~quiet(X))))&
((wise(susan)|~generous(susan))) | ~old(fred) | [
"p2",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 325423637591485124829982
% SZS output start Proof for 325423637591485124829982
3. ! [X0] : (old(X0) <=> (~tall(X0) & ~quiet(X0))) [input p2]
6. ? [X0] : (~rich(X0) | ~calm(X0)) => quiet(fred) [input p5]
8. ? [X0] : (~brave(X0) & brave(X0)) <=> (curious(paul) | calm(paul)) [input p7]
25. old(fred) [input hypothesis]
29. ! [X0] : (old(X0) => (~tall(X0) & ~quiet(X0))) [unused predicate definition removal 3]
31. ! [X0] : ((~tall(X0) & ~quiet(X0)) | ~old(X0)) [ennf transformation 29]
34. quiet(fred) | ! [X0] : (rich(X0) & calm(X0)) [ennf transformation 6]
51. (? [X0] : (~brave(X0) & brave(X0)) | (~curious(paul) & ~calm(paul))) & ((curious(paul) | calm(paul)) | ! [X0] : (brave(X0) | ~brave(X0))) [nnf transformation 8]
52. (? [X0] : (~brave(X0) & brave(X0)) | (~curious(paul) & ~calm(paul))) & (curious(paul) | calm(paul) | ! [X0] : (brave(X0) | ~brave(X0))) [flattening 51]
53. (? [X0] : (~brave(X0) & brave(X0)) | (~curious(paul) & ~calm(paul))) & (curious(paul) | calm(paul) | ! [X1] : (brave(X1) | ~brave(X1))) [rectify 52]
54. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK3) & brave(sK3)) [choice axiom]
55. ((~brave(sK3) & brave(sK3)) | (~curious(paul) & ~calm(paul))) & (curious(paul) | calm(paul) | ! [X1] : (brave(X1) | ~brave(X1))) [skolemisation 53,54]
100. ~old(X0) | ~quiet(X0) [cnf transformation 31]
108. quiet(fred) | calm(X0) [cnf transformation 34]
114. brave(sK3) | ~calm(paul) [cnf transformation 55]
116. ~brave(sK3) | ~calm(paul) [cnf transformation 55]
163. old(fred) [cnf transformation 25]
203. 9 <=> quiet(fred) [avatar definition]
205. quiet(fred) <- (9) [avatar component clause 203]
208. 10 <=> ! [X0] : calm(X0) [avatar definition]
209. calm(X0) <- (10) [avatar component clause 208]
210. 10 | 9 [avatar split clause 108,203,208]
240. 18 <=> brave(sK3) [avatar definition]
245. 19 <=> calm(paul) [avatar definition]
247. ~calm(paul) <- (~19) [avatar component clause 245]
248. ~19 | ~18 [avatar split clause 116,240,245]
250. ~19 | 18 [avatar split clause 114,240,245]
407. $false <- (10, ~19) [resolution 247,209]
408. ~10 | 19 [avatar contradiction clause 407]
411. ~quiet(fred) [resolution 100,163]
412. $false <- (9) [subsumption resolution 411,205]
413. ~9 [avatar contradiction clause 412]
414. $false [avatar sat refutation 210,248,250,408,413]
% SZS output end Proof for 325423637591485124829982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or kind is not quiet and vice versa.
Everyone who is kind or not generous is either funny or patient and vice versa.
Everyone who is not humble or not curious is not generous or brave and vice versa.
If lucy is brave then alice is both not curious and funny and vice versa.
Everyone who is not funny is both not calm and tall and vice versa.
Everyone who is not rich is either not quiet or not wise.
Everyone who is both happy and not kind is both not curious and not creative.
If someone is either strong or rich then someone is either funny or not quiet.
Everyone who is either generous or brave is not quiet.
Everyone who is not happy is either quiet or not creative.
Everyone who is both not patient and curious is not curious and vice versa.
If mary is rich then alice is either not calm or calm and vice versa.
Everyone who is not wise or generous is funny and vice versa.
Everyone who is generous is both generous and patient and vice versa.
Lucy is quiet or not quiet.
Fred is either not humble or strong.
Paul is quiet. | Paul is tall. | entailment | (![X]:((quiet(X)<~>kind(X))<=>~quiet(X)))&
(![X]:((kind(X)|~generous(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~generous(X)|brave(X))))&
((brave(lucy))<=>((~curious(alice)&funny(alice))))&
(![X]:(~funny(X)<=>(~calm(X)&tall(X))))&
(![X]:(~rich(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((happy(X)&~kind(X))=>(~curious(X)&~creative(X))))&
((?[X]:((strong(X)<~>rich(X))))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>brave(X))=>~quiet(X)))&
(![X]:(~happy(X)=>(quiet(X)<~>~creative(X))))&
(![X]:((~patient(X)&curious(X))<=>~curious(X)))&
((rich(mary))<=>((~calm(alice)<~>calm(alice))))&
(![X]:((~wise(X)|generous(X))<=>funny(X)))&
(![X]:(generous(X)<=>(generous(X)&patient(X))))&
((quiet(lucy)|~quiet(lucy)))&
((~humble(fred)<~>strong(fred)))&
(quiet(paul)) | tall(paul) | [
"p0",
"p1",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 92165301045796233223458
% SZS output start Proof for 92165301045796233223458
1. ! [X0] : ((quiet(X0) <~> kind(X0)) <=> ~quiet(X0)) [input p0]
2. ! [X0] : ((~generous(X0) | kind(X0)) <=> (funny(X0) <~> patient(X0))) [input p1]
5. ! [X0] : (~funny(X0) <=> (tall(X0) & ~calm(X0))) [input p4]
11. ! [X0] : ((curious(X0) & ~patient(X0)) <=> ~curious(X0)) [input p10]
18. ~tall(paul) [input hypothesis]
26. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | quiet(X0)) & (~quiet(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [nnf transformation 1]
27. ! [X0] : (((~generous(X0) | kind(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (generous(X0) & ~kind(X0)))) [nnf transformation 2]
28. ! [X0] : ((~generous(X0) | kind(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (generous(X0) & ~kind(X0)))) [flattening 27]
33. ! [X0] : ((~funny(X0) | (~tall(X0) | calm(X0))) & ((tall(X0) & ~calm(X0)) | funny(X0))) [nnf transformation 5]
34. ! [X0] : ((~funny(X0) | ~tall(X0) | calm(X0)) & ((tall(X0) & ~calm(X0)) | funny(X0))) [flattening 33]
42. ! [X0] : (((curious(X0) & ~patient(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | patient(X0)))) [nnf transformation 11]
43. ! [X0] : (((curious(X0) & ~patient(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | patient(X0))) [flattening 42]
50. ~quiet(X0) | kind(X0) | ~quiet(X0) [cnf transformation 26]
52. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 26]
56. ~patient(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 28]
68. tall(X0) | funny(X0) [cnf transformation 34]
82. ~curious(X0) | ~curious(X0) | patient(X0) [cnf transformation 43]
84. curious(X0) | curious(X0) [cnf transformation 43]
99. ~tall(paul) [cnf transformation 18]
102. ~curious(X0) | patient(X0) [duplicate literal removal 82]
103. curious(X0) [duplicate literal removal 84]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 50]
105. kind(X0) | quiet(X0) [duplicate literal removal 52]
106. kind(X0) [subsumption resolution 104,105]
107. ~patient(X0) | ~funny(X0) [subsumption resolution 56,106]
142. patient(X0) [subsumption resolution 102,103]
163. funny(paul) [resolution 68,99]
164. ~funny(X0) [resolution 107,142]
166. $false [resolution 164,163]
% SZS output end Proof for 92165301045796233223458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then fred is rich.
If john is old or wise then someone is both not funny and not tall and vice versa.
Everyone who is either not patient or not funny is not patient and vice versa.
If someone is curious or not creative then susan is either generous or humble.
Everyone who is either creative or calm is both not old and not creative and vice versa.
Everyone who is humble is either calm or not humble and vice versa.
If susan is either not rich or not kind then susan is not curious or not brave and vice versa.
If someone is creative then someone is either not curious or wise and vice versa.
If someone is both happy and not humble then someone is both not quiet and not brave and vice versa.
If fred is not calm or not old then someone is either curious or not quiet and vice versa.
If someone is kind or creative then lucy is either strong or creative and vice versa.
Everyone who is not rich is either not rich or curious.
Everyone who is happy or funny is both humble and not wise.
If someone is either not old or not tall then paul is both curious and not tall.
Everyone who is both happy and not patient is wise or not patient and vice versa.
Everyone who is patient is not funny or not humble.
Someone is both humble and kind.
Someone is not curious.
Someone is kind.
Someone is happy.
Someone is either rich or not creative.
Mary is humble. | Paul is not wise. | entailment | ((?[X]:(~brave(X)))=>(rich(fred)))&
(((old(john)|wise(john)))<=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:((~patient(X)<~>~funny(X))<=>~patient(X)))&
((?[X]:((curious(X)|~creative(X))))=>((generous(susan)<~>humble(susan))))&
(![X]:((creative(X)<~>calm(X))<=>(~old(X)&~creative(X))))&
(![X]:(humble(X)<=>(calm(X)<~>~humble(X))))&
(((~rich(susan)<~>~kind(susan)))<=>((~curious(susan)|~brave(susan))))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(((~calm(fred)|~old(fred)))<=>(?[X]:((curious(X)<~>~quiet(X)))))&
((?[X]:((kind(X)|creative(X))))<=>((strong(lucy)<~>creative(lucy))))&
(![X]:(~rich(X)=>(~rich(X)<~>curious(X))))&
(![X]:((happy(X)|funny(X))=>(humble(X)&~wise(X))))&
((?[X]:((~old(X)<~>~tall(X))))=>((curious(paul)&~tall(paul))))&
(![X]:((happy(X)&~patient(X))<=>(wise(X)|~patient(X))))&
(![X]:(patient(X)=>(~funny(X)|~humble(X))))&
(?[X]:((humble(X)&kind(X))))&
(?[X]:(~curious(X)))&
(?[X]:(kind(X)))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)<~>~creative(X))))&
(humble(mary)) | ~wise(paul) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2844433016202579910978537
% SZS output start Proof for 2844433016202579910978537
3. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> ~patient(X0)) [input p2]
13. ! [X0] : ((funny(X0) | happy(X0)) => (~wise(X0) & humble(X0))) [input p12]
23. wise(paul) [input hypothesis]
29. ! [X0] : ((~wise(X0) & humble(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 13]
38. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | patient(X0)) & (~patient(X0) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 3]
86. ~patient(X0) | ~patient(X0) | funny(X0) [cnf transformation 38]
88. funny(X0) | patient(X0) | patient(X0) [cnf transformation 38]
134. ~wise(X0) | ~funny(X0) [cnf transformation 29]
153. wise(paul) [cnf transformation 23]
159. ~patient(X0) | funny(X0) [duplicate literal removal 86]
160. funny(X0) | patient(X0) [duplicate literal removal 88]
193. funny(X0) [subsumption resolution 159,160]
335. ~wise(X0) [subsumption resolution 134,193]
367. $false [subsumption resolution 153,335]
% SZS output end Proof for 2844433016202579910978537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich then john is either not calm or generous. If fred is either not generous or brave then paul is humble or rich and vice versa. Everyone who is not creative or humble is strong and vice versa. If lucy is both wise and not rich then alice is either not funny or humble. If lucy is both strong and not creative then susan is either patient or not wise and vice versa. If alice is both not generous and strong then someone is either generous or not brave. Everyone who is not tall or calm is both strong and funny and vice versa. If someone is either not generous or not kind then alice is both not old and not generous and vice versa. Everyone who is both not tall and old is both wise and not quiet. Everyone who is happy or humble is both not tall and patient. If someone is both wise and tall then someone is either quiet or not tall. Everyone who is happy is generous and vice versa. If fred is both old and quiet then someone is both not funny and not quiet and vice versa. If alice is either not happy or not patient then susan is either creative or happy and vice versa. Everyone who is either happy or strong is not patient. If someone is both not kind and tall then alice is both not tall and not strong and vice versa. Susan is both patient and not generous. Someone is not old. Paul is both not tall and not kind. Someone is curious or kind. Alice is both not funny and brave. Lucy is quiet. Someone is not funny or old. | Susan is not tall. | contradiction | ((rich(john))=>((~calm(john)<~>generous(john))))&
(((~generous(fred)<~>brave(fred)))<=>((humble(paul)|rich(paul))))&
(![X]:((~creative(X)|humble(X))<=>strong(X)))&
(((wise(lucy)&~rich(lucy)))=>((~funny(alice)<~>humble(alice))))&
(((strong(lucy)&~creative(lucy)))<=>((patient(susan)<~>~wise(susan))))&
(((~generous(alice)&strong(alice)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((~tall(X)|calm(X))<=>(strong(X)&funny(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((~old(alice)&~generous(alice))))&
(![X]:((~tall(X)&old(X))=>(wise(X)&~quiet(X))))&
(![X]:((happy(X)|humble(X))=>(~tall(X)&patient(X))))&
((?[X]:((wise(X)&tall(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(((old(fred)&quiet(fred)))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~happy(alice)<~>~patient(alice)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((happy(X)<~>strong(X))=>~patient(X)))&
((?[X]:((~kind(X)&tall(X))))<=>((~tall(alice)&~strong(alice))))&
((patient(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((~tall(paul)&~kind(paul)))&
(?[X]:((curious(X)|kind(X))))&
((~funny(alice)&brave(alice)))&
(quiet(lucy))&
(?[X]:((~funny(X)|old(X)))) | ~tall(susan) | [
"p6",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7526909247668194280236509
% SZS output start Proof for 7526909247668194280236509
7. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (funny(X0) & strong(X0))) [input p6]
12. ! [X0] : (happy(X0) <=> generous(X0)) [input p11]
15. ! [X0] : ((happy(X0) <~> strong(X0)) => ~patient(X0)) [input p14]
17. ~generous(susan) & patient(susan) [input p16]
24. ~tall(susan) [input hypothesis]
36. ! [X0] : (~patient(X0) | (happy(X0) <=> strong(X0))) [ennf transformation 15]
48. ! [X0] : (((calm(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [nnf transformation 7]
49. ! [X0] : ((calm(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [flattening 48]
59. ! [X0] : ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))) [nnf transformation 12]
66. ! [X0] : (~patient(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 36]
97. tall(X0) | strong(X0) [cnf transformation 49]
116. ~happy(X0) | generous(X0) [cnf transformation 59]
131. ~patient(X0) | happy(X0) | ~strong(X0) [cnf transformation 66]
136. patient(susan) [cnf transformation 17]
137. ~generous(susan) [cnf transformation 17]
145. ~tall(susan) [cnf transformation 24]
205. 13 <=> patient(susan) [avatar definition]
207. patient(susan) <- (13) [avatar component clause 205]
304. 33 <=> happy(susan) [avatar definition]
305. happy(susan) <- (33) [avatar component clause 304]
338. 13 [avatar split clause 136,205]
352. strong(susan) [resolution 97,145]
408. happy(susan) | ~strong(susan) <- (13) [resolution 131,207]
413. happy(susan) <- (13) [subsumption resolution 408,352]
414. 33 | ~13 [avatar split clause 413,205,304]
421. generous(susan) <- (33) [resolution 305,116]
424. $false <- (33) [subsumption resolution 421,137]
425. ~33 [avatar contradiction clause 424]
426. $false [avatar sat refutation 338,414,425]
% SZS output end Proof for 7526909247668194280236509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or humble is both not happy and wise.
Everyone who is happy or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Everyone who is kind is either kind or not rich.
Everyone who is either brave or not old is both not wise and not calm.
If paul is patient or rich then someone is both not quiet and kind.
Everyone who is either humble or funny is wise and vice versa.
If someone is either not patient or creative then someone is rich or not creative.
John is both not wise and not rich.
Someone is both not brave and not rich.
Paul is not strong or patient.
Someone is creative or patient.
Alice is either not happy or creative.
Lucy is both curious and not funny.
Susan is old.
Alice is not wise. | Lucy is not old. | contradiction | (![X]:((rich(X)|humble(X))=>(~happy(X)&wise(X))))&
(![X]:((happy(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
(![X]:(kind(X)=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~old(X))=>(~wise(X)&~calm(X))))&
(((patient(paul)|rich(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((~wise(john)&~rich(john)))&
(?[X]:((~brave(X)&~rich(X))))&
((~strong(paul)|patient(paul)))&
(?[X]:((creative(X)|patient(X))))&
((~happy(alice)<~>creative(alice)))&
((curious(lucy)&~funny(lucy)))&
(old(susan))&
(~wise(alice)) | ~old(lucy) | [
"p0",
"p1",
"p4",
"p6",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5742376747813573972680663
% SZS output start Proof for 5742376747813573972680663
1. ! [X0] : ((humble(X0) | rich(X0)) => (wise(X0) & ~happy(X0))) [input p0]
2. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~patient(X0) <~> ~curious(X0))) [input p1]
5. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~strong(X0) & ~wise(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (generous(X0) | ~patient(X0))) [input p6]
13. ! [X0] : ((brave(X0) <~> ~old(X0)) => (~calm(X0) & ~wise(X0))) [input p12]
22. ~funny(lucy) & curious(lucy) [input p21]
25. ~old(lucy) [input hypothesis]
29. ! [X0] : ((brave(X0) <~> ~old(X0)) => ~wise(X0)) [pure predicate removal 13]
32. ! [X0] : ((wise(X0) & ~happy(X0)) | (~humble(X0) & ~rich(X0))) [ennf transformation 1]
37. ! [X0] : (~wise(X0) | (brave(X0) <=> ~old(X0))) [ennf transformation 29]
40. ! [X0] : (((~rich(X0) | happy(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | happy(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [flattening 40]
46. ! [X0] : (((brave(X0) | ~humble(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [flattening 46]
50. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ~wise(X0))) [nnf transformation 7]
51. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ~wise(X0))) [flattening 50]
61. ! [X0] : (~wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) [nnf transformation 37]
76. ~rich(X0) | wise(X0) [cnf transformation 32]
79. ~curious(X0) | ~patient(X0) | rich(X0) [cnf transformation 41]
89. ~brave(X0) | ~wise(X0) [cnf transformation 47]
95. patient(X0) | wise(X0) [cnf transformation 51]
111. ~wise(X0) | brave(X0) | old(X0) [cnf transformation 61]
128. curious(lucy) [cnf transformation 22]
132. ~old(lucy) [cnf transformation 25]
216. ~wise(X0) | old(X0) [subsumption resolution 111,89]
299. 32 <=> patient(lucy) [avatar definition]
301. ~patient(lucy) <- (~32) [avatar component clause 299]
312. ~patient(lucy) | rich(lucy) [resolution 79,128]
315. 35 <=> rich(lucy) [avatar definition]
317. rich(lucy) <- (35) [avatar component clause 315]
318. 35 | ~32 [avatar split clause 312,299,315]
319. wise(lucy) <- (~32) [resolution 301,95]
324. old(lucy) <- (~32) [resolution 319,216]
326. $false <- (~32) [subsumption resolution 324,132]
327. 32 [avatar contradiction clause 326]
332. 36 <=> wise(lucy) [avatar definition]
333. wise(lucy) <- (36) [avatar component clause 332]
353. wise(lucy) <- (35) [resolution 317,76]
356. 36 | ~35 [avatar split clause 353,315,332]
368. old(lucy) <- (36) [resolution 333,216]
370. $false <- (36) [subsumption resolution 368,132]
371. ~36 [avatar contradiction clause 370]
372. $false [avatar sat refutation 318,327,356,371]
% SZS output end Proof for 5742376747813573972680663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and old then susan is both brave and quiet and vice versa.
Everyone who is happy or not brave is brave or not old.
Everyone who is not patient is both not generous and patient.
Everyone who is either not strong or curious is humble and vice versa.
Everyone who is both not happy and old is both calm and not generous and vice versa.
Everyone who is funny is either not strong or happy and vice versa.
Everyone who is both wise and curious is not generous or not humble and vice versa.
If someone is both calm and not old then mary is humble and vice versa.
If susan is either not wise or not calm then lucy is either creative or not generous.
Everyone who is generous or not happy is both not curious and not funny.
If someone is rich or not humble then someone is humble or calm.
If john is either not old or wise then susan is not rich or not calm.
Everyone who is either not strong or not patient is either creative or generous.
Everyone who is creative or brave is either not curious or not old and vice versa.
Everyone who is either not tall or not funny is wise and vice versa.
Everyone who is both quiet and not old is quiet and vice versa.
Someone is patient or not patient.
Paul is either not happy or tall.
Someone is both not old and quiet.
Someone is both not calm and not strong.
Someone is brave or rich.
Alice is not rich.
Fred is not calm.
Lucy is either rich or not creative. | Mary is not patient. | contradiction | ((?[X]:((~old(X)&old(X))))<=>((brave(susan)&quiet(susan))))&
(![X]:((happy(X)|~brave(X))=>(brave(X)|~old(X))))&
(![X]:(~patient(X)=>(~generous(X)&patient(X))))&
(![X]:((~strong(X)<~>curious(X))<=>humble(X)))&
(![X]:((~happy(X)&old(X))<=>(calm(X)&~generous(X))))&
(![X]:(funny(X)<=>(~strong(X)<~>happy(X))))&
(![X]:((wise(X)&curious(X))<=>(~generous(X)|~humble(X))))&
((?[X]:((calm(X)&~old(X))))<=>(humble(mary)))&
(((~wise(susan)<~>~calm(susan)))=>((creative(lucy)<~>~generous(lucy))))&
(![X]:((generous(X)|~happy(X))=>(~curious(X)&~funny(X))))&
((?[X]:((rich(X)|~humble(X))))=>(?[X]:((humble(X)|calm(X)))))&
(((~old(john)<~>wise(john)))=>((~rich(susan)|~calm(susan))))&
(![X]:((~strong(X)<~>~patient(X))=>(creative(X)<~>generous(X))))&
(![X]:((creative(X)|brave(X))<=>(~curious(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>wise(X)))&
(![X]:((quiet(X)&~old(X))<=>quiet(X)))&
(?[X]:((patient(X)|~patient(X))))&
((~happy(paul)<~>tall(paul)))&
(?[X]:((~old(X)&quiet(X))))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((brave(X)|rich(X))))&
(~rich(alice))&
(~calm(fred))&
((rich(lucy)<~>~creative(lucy))) | ~patient(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3520393741858318792272180
% SZS output start Proof for 3520393741858318792272180
3. ! [X0] : (~patient(X0) => (patient(X0) & ~generous(X0))) [input p2]
25. ~patient(mary) [input hypothesis]
29. ! [X0] : ((patient(X0) & ~generous(X0)) | patient(X0)) [ennf transformation 3]
79. patient(X0) | patient(X0) [cnf transformation 29]
141. ~patient(mary) [cnf transformation 25]
142. patient(X0) [duplicate literal removal 79]
255. $false [subsumption resolution 141,142]
% SZS output end Proof for 3520393741858318792272180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or old is either quiet or not old.
If paul is either tall or not calm then someone is humble or not quiet.
Everyone who is both generous and strong is both not humble and not happy.
Everyone who is not rich or strong is funny.
Everyone who is both not rich and brave is tall and vice versa.
Everyone who is not strong or kind is either not old or not generous.
Everyone who is either kind or strong is generous or not curious and vice versa.
Everyone who is either quiet or patient is either quiet or creative.
Everyone who is not creative is either old or brave.
If someone is humble then someone is both generous and not kind and vice versa.
Everyone who is old or curious is not tall and vice versa.
If someone is not happy then someone is funny or not humble.
Everyone who is both not creative and creative is both not happy and not calm and vice versa.
Everyone who is either not old or brave is either not creative or not wise.
If someone is not strong then someone is both tall and rich.
If someone is both brave and not happy then someone is humble.
Someone is both not wise and funny.
Alice is not quiet.
Paul is both brave and not rich.
Lucy is not generous or not tall.
Someone is curious or not tall. | Alice is curious. | neutral | (![X]:((~curious(X)<~>old(X))=>(quiet(X)<~>~old(X))))&
(((tall(paul)<~>~calm(paul)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)|strong(X))=>funny(X)))&
(![X]:((~rich(X)&brave(X))<=>tall(X)))&
(![X]:((~strong(X)|kind(X))=>(~old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((quiet(X)<~>patient(X))=>(quiet(X)<~>creative(X))))&
(![X]:(~creative(X)=>(old(X)<~>brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((old(X)|curious(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:((~creative(X)&creative(X))<=>(~happy(X)&~calm(X))))&
(![X]:((~old(X)<~>brave(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((brave(X)&~happy(X))))=>(?[X]:(humble(X))))&
(?[X]:((~wise(X)&funny(X))))&
(~quiet(alice))&
((brave(paul)&~rich(paul)))&
((~generous(lucy)|~tall(lucy)))&
(?[X]:((curious(X)|~tall(X)))) | curious(alice) | [] | null | 0 |
If john is not patient or creative then someone is either not wise or patient and vice versa.
If someone is either not curious or humble then lucy is either old or not happy.
Everyone who is not quiet or patient is either tall or not brave.
If someone is not humble or tall then someone is creative or not creative and vice versa.
Everyone who is not curious is both not wise and patient.
Everyone who is either not quiet or not strong is both kind and happy and vice versa.
Everyone who is both curious and generous is both wise and not generous.
Everyone who is both not patient and not curious is tall or strong.
If someone is creative then someone is either calm or brave and vice versa.
Everyone who is both not generous and not brave is brave and vice versa.
Everyone who is not patient or not funny is both not creative and funny.
Everyone who is curious is both curious and old.
If fred is both funny and creative then alice is not rich.
If someone is curious then someone is not creative.
Everyone who is not strong is either not kind or calm and vice versa.
If fred is not strong or not quiet then mary is not funny or tall and vice versa.
Someone is not quiet.
Someone is either funny or not happy.
Someone is both patient and happy.
Someone is not humble or creative.
Mary is not humble.
Paul is old. | John is not funny. | contradiction | (((~patient(john)|creative(john)))<=>(?[X]:((~wise(X)<~>patient(X)))))&
((?[X]:((~curious(X)<~>humble(X))))=>((old(lucy)<~>~happy(lucy))))&
(![X]:((~quiet(X)|patient(X))=>(tall(X)<~>~brave(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((creative(X)|~creative(X)))))&
(![X]:(~curious(X)=>(~wise(X)&patient(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(kind(X)&happy(X))))&
(![X]:((curious(X)&generous(X))=>(wise(X)&~generous(X))))&
(![X]:((~patient(X)&~curious(X))=>(tall(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((~generous(X)&~brave(X))<=>brave(X)))&
(![X]:((~patient(X)|~funny(X))=>(~creative(X)&funny(X))))&
(![X]:(curious(X)=>(curious(X)&old(X))))&
(((funny(fred)&creative(fred)))=>(~rich(alice)))&
((?[X]:(curious(X)))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)<=>(~kind(X)<~>calm(X))))&
(((~strong(fred)|~quiet(fred)))<=>((~funny(mary)|tall(mary))))&
(?[X]:(~quiet(X)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~humble(X)|creative(X))))&
(~humble(mary))&
(old(paul)) | ~funny(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7126487482269074631541455
% SZS output start Proof for 7126487482269074631541455
11. ! [X0] : ((~funny(X0) | ~patient(X0)) => (funny(X0) & ~creative(X0))) [input p10]
23. ~funny(john) [input hypothesis]
35. ! [X0] : ((funny(X0) & ~creative(X0)) | (funny(X0) & patient(X0))) [ennf transformation 11]
113. funny(X0) | funny(X0) [cnf transformation 35]
133. ~funny(john) [cnf transformation 23]
134. funny(X0) [duplicate literal removal 113]
258. $false [subsumption resolution 133,134]
% SZS output end Proof for 7126487482269074631541455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and strong is both not curious and not funny and vice versa.
Everyone who is both not curious and not happy is kind or calm and vice versa.
If mary is patient or calm then john is either humble or not creative.
If lucy is either patient or not funny then someone is either rich or tall.
Everyone who is not rich or not happy is not quiet or not generous and vice versa.
If someone is not humble or rich then someone is both not tall and humble and vice versa.
Everyone who is both not rich and curious is kind or not strong.
Everyone who is not rich is humble or not happy and vice versa.
Everyone who is not kind is not quiet and vice versa.
If someone is patient or funny then someone is calm or kind and vice versa.
If paul is not rich then someone is not wise and vice versa.
Everyone who is not tall is not curious or patient and vice versa.
Everyone who is not calm or curious is both not patient and patient and vice versa.
If someone is happy or not funny then susan is either humble or not creative.
If mary is humble then paul is wise or humble and vice versa.
If alice is not happy then lucy is not generous and vice versa.
Someone is either rich or not generous.
Susan is old.
Mary is both quiet and not old.
Susan is either humble or not humble.
Someone is either rich or not rich.
Someone is both patient and brave. | Alice is funny. | entailment | (![X]:((rich(X)&strong(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~curious(X)&~happy(X))<=>(kind(X)|calm(X))))&
(((patient(mary)|calm(mary)))=>((humble(john)<~>~creative(john))))&
(((patient(lucy)<~>~funny(lucy)))=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((~rich(X)|~happy(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~humble(X)|rich(X))))<=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:((~rich(X)&curious(X))=>(kind(X)|~strong(X))))&
(![X]:(~rich(X)<=>(humble(X)|~happy(X))))&
(![X]:(~kind(X)<=>~quiet(X)))&
((?[X]:((patient(X)|funny(X))))<=>(?[X]:((calm(X)|kind(X)))))&
((~rich(paul))<=>(?[X]:(~wise(X))))&
(![X]:(~tall(X)<=>(~curious(X)|patient(X))))&
(![X]:((~calm(X)|curious(X))<=>(~patient(X)&patient(X))))&
((?[X]:((happy(X)|~funny(X))))=>((humble(susan)<~>~creative(susan))))&
((humble(mary))<=>((wise(paul)|humble(paul))))&
((~happy(alice))<=>(~generous(lucy)))&
(?[X]:((rich(X)<~>~generous(X))))&
(old(susan))&
((quiet(mary)&~old(mary)))&
((humble(susan)<~>~humble(susan)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((patient(X)&brave(X)))) | funny(alice) | [
"p0",
"p1",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7503662646229381823323325
% SZS output start Proof for 7503662646229381823323325
1. ! [X0] : ((strong(X0) & rich(X0)) <=> (~funny(X0) & ~curious(X0))) [input p0]
2. ! [X0] : ((~happy(X0) & ~curious(X0)) <=> (calm(X0) | kind(X0))) [input p1]
8. ! [X0] : (~rich(X0) <=> (~happy(X0) | humble(X0))) [input p7]
13. ! [X0] : ((curious(X0) | ~calm(X0)) <=> (patient(X0) & ~patient(X0))) [input p12]
23. ~funny(alice) [input hypothesis]
32. ! [X0] : (((strong(X0) & rich(X0)) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & rich(X0)) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | ~strong(X0) | ~rich(X0))) [flattening 32]
34. ! [X0] : (((~happy(X0) & ~curious(X0)) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | (happy(X0) | curious(X0)))) [nnf transformation 2]
35. ! [X0] : (((~happy(X0) & ~curious(X0)) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | happy(X0) | curious(X0))) [flattening 34]
47. ! [X0] : ((~rich(X0) | (happy(X0) & ~humble(X0))) & ((~happy(X0) | humble(X0)) | rich(X0))) [nnf transformation 8]
48. ! [X0] : ((~rich(X0) | (happy(X0) & ~humble(X0))) & (~happy(X0) | humble(X0) | rich(X0))) [flattening 47]
61. ! [X0] : (((curious(X0) | ~calm(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~curious(X0) & calm(X0)))) [nnf transformation 13]
62. ! [X0] : ((curious(X0) | ~calm(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~curious(X0) & calm(X0)))) [flattening 61]
78. funny(X0) | rich(X0) | curious(X0) [cnf transformation 33]
84. ~calm(X0) | ~happy(X0) [cnf transformation 35]
105. ~rich(X0) | happy(X0) [cnf transformation 48]
117. ~patient(X0) | calm(X0) [cnf transformation 62]
118. ~patient(X0) | ~curious(X0) [cnf transformation 62]
119. patient(X0) | calm(X0) [cnf transformation 62]
120. ~curious(X0) | patient(X0) [cnf transformation 62]
141. ~funny(alice) [cnf transformation 23]
259. ~curious(X0) [subsumption resolution 118,120]
260. calm(X0) [subsumption resolution 117,119]
274. 30 <=> ! [X0] : ~happy(X0) [avatar definition]
275. ~happy(X0) <- (30) [avatar component clause 274]
317. ~happy(X0) [resolution 84,260]
318. 30 [avatar split clause 317,274]
336. rich(alice) | curious(alice) [resolution 78,141]
338. rich(alice) [subsumption resolution 336,259]
339. happy(alice) [resolution 338,105]
342. $false <- (30) [subsumption resolution 339,275]
343. ~30 [avatar contradiction clause 342]
346. $false [avatar sat refutation 318,343]
% SZS output end Proof for 7503662646229381823323325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not funny then someone is not brave and vice versa. Everyone who is either not wise or not old is generous or not strong. Everyone who is not curious or not rich is either not strong or not patient and vice versa. Everyone who is funny is brave or not generous and vice versa. If someone is not rich then lucy is not curious. If paul is happy then alice is calm or curious and vice versa. If someone is either not curious or kind then someone is either curious or calm. Everyone who is both not quiet and rich is both happy and kind. Everyone who is happy or old is both not quiet and not strong and vice versa. Everyone who is either not happy or not kind is funny and vice versa. If paul is either tall or not curious then paul is both brave and not strong and vice versa. Everyone who is both not happy and curious is generous or curious and vice versa. If paul is either not funny or tall then john is not calm and vice versa. If someone is both curious and not curious then paul is both not humble and tall and vice versa. If paul is not funny or not patient then someone is both quiet and funny and vice versa. If someone is both not creative and happy then mary is either curious or creative. Someone is both not old and not humble. Lucy is both not wise and patient. Someone is either kind or calm. John is both not generous and rich. Lucy is not brave. Someone is either rich or not generous. Someone is both not wise and calm. | Mary is wise. | neutral | ((?[X]:((tall(X)&~funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~wise(X)<~>~old(X))=>(generous(X)|~strong(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(brave(X)|~generous(X))))&
((?[X]:(~rich(X)))=>(~curious(lucy)))&
((happy(paul))<=>((calm(alice)|curious(alice))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((~quiet(X)&rich(X))=>(happy(X)&kind(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~happy(X)<~>~kind(X))<=>funny(X)))&
(((tall(paul)<~>~curious(paul)))<=>((brave(paul)&~strong(paul))))&
(![X]:((~happy(X)&curious(X))<=>(generous(X)|curious(X))))&
(((~funny(paul)<~>tall(paul)))<=>(~calm(john)))&
((?[X]:((curious(X)&~curious(X))))<=>((~humble(paul)&tall(paul))))&
(((~funny(paul)|~patient(paul)))<=>(?[X]:((quiet(X)&funny(X)))))&
((?[X]:((~creative(X)&happy(X))))=>((curious(mary)<~>creative(mary))))&
(?[X]:((~old(X)&~humble(X))))&
((~wise(lucy)&patient(lucy)))&
(?[X]:((kind(X)<~>calm(X))))&
((~generous(john)&rich(john)))&
(~brave(lucy))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~wise(X)&calm(X)))) | wise(mary) | [] | null | 0 |
Everyone who is kind or not wise is either calm or happy and vice versa. Everyone who is wise is either not brave or tall. If someone is not calm then someone is not humble. Everyone who is not generous is both curious and brave and vice versa. Everyone who is either not patient or generous is not brave and vice versa. Everyone who is creative is not funny or humble and vice versa. If someone is both humble and rich then someone is old and vice versa. If mary is funny then someone is not calm or kind. Everyone who is both not strong and not patient is both not funny and not generous and vice versa. If paul is not generous or wise then someone is not calm or generous and vice versa. Everyone who is both curious and brave is both not curious and tall. If alice is both not rich and not humble then someone is not calm or not old. If someone is both not strong and wise then lucy is kind and vice versa. If john is either kind or calm then someone is brave or funny. If someone is not humble then someone is not old. If someone is not brave or happy then someone is not wise and vice versa. Someone is not happy. John is not old. Someone is both strong and not curious. Someone is either not kind or tall. Paul is both not patient and funny. Someone is not strong or rich. Paul is generous. Someone is both not calm and creative. | Paul is tall. | entailment | (![X]:((kind(X)|~wise(X))<=>(calm(X)<~>happy(X))))&
(![X]:(wise(X)=>(~brave(X)<~>tall(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:(~generous(X)<=>(curious(X)&brave(X))))&
(![X]:((~patient(X)<~>generous(X))<=>~brave(X)))&
(![X]:(creative(X)<=>(~funny(X)|humble(X))))&
((?[X]:((humble(X)&rich(X))))<=>(?[X]:(old(X))))&
((funny(mary))=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((~strong(X)&~patient(X))<=>(~funny(X)&~generous(X))))&
(((~generous(paul)|wise(paul)))<=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:((curious(X)&brave(X))=>(~curious(X)&tall(X))))&
(((~rich(alice)&~humble(alice)))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~strong(X)&wise(X))))<=>(kind(lucy)))&
(((kind(john)<~>calm(john)))=>(?[X]:((brave(X)|funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:(~old(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(~wise(X))))&
(?[X]:(~happy(X)))&
(~old(john))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~kind(X)<~>tall(X))))&
((~patient(paul)&funny(paul)))&
(?[X]:((~strong(X)|rich(X))))&
(generous(paul))&
(?[X]:((~calm(X)&creative(X)))) | tall(paul) | [
"p1",
"p3",
"p4",
"p9",
"p10",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2189767897941465947704253
% SZS output start Proof for 2189767897941465947704253
2. ! [X0] : (wise(X0) => (~brave(X0) <~> tall(X0))) [input p1]
4. ! [X0] : (~generous(X0) <=> (brave(X0) & curious(X0))) [input p3]
5. ! [X0] : ((~patient(X0) <~> generous(X0)) <=> ~brave(X0)) [input p4]
10. (wise(paul) | ~generous(paul)) <=> ? [X0] : (generous(X0) | ~calm(X0)) [input p9]
11. ! [X0] : ((brave(X0) & curious(X0)) => (tall(X0) & ~curious(X0))) [input p10]
21. funny(paul) & ~patient(paul) [input p20]
23. generous(paul) [input p22]
25. ~tall(paul) [input hypothesis]
31. ! [X0] : ((~brave(X0) <~> tall(X0)) | ~wise(X0)) [ennf transformation 2]
36. ! [X0] : ((tall(X0) & ~curious(X0)) | (~brave(X0) | ~curious(X0))) [ennf transformation 11]
37. ! [X0] : ((tall(X0) & ~curious(X0)) | ~brave(X0) | ~curious(X0)) [flattening 36]
44. ! [X0] : (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | ~wise(X0)) [nnf transformation 31]
48. ! [X0] : ((~generous(X0) | (~brave(X0) | ~curious(X0))) & ((brave(X0) & curious(X0)) | generous(X0))) [nnf transformation 4]
49. ! [X0] : ((~generous(X0) | ~brave(X0) | ~curious(X0)) & ((brave(X0) & curious(X0)) | generous(X0))) [flattening 48]
50. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | brave(X0)) & (~brave(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [nnf transformation 5]
60. ((wise(paul) | ~generous(paul)) | ! [X0] : (~generous(X0) & calm(X0))) & (? [X0] : (generous(X0) | ~calm(X0)) | (~wise(paul) & generous(paul))) [nnf transformation 10]
61. (wise(paul) | ~generous(paul) | ! [X0] : (~generous(X0) & calm(X0))) & (? [X0] : (generous(X0) | ~calm(X0)) | (~wise(paul) & generous(paul))) [flattening 60]
62. (wise(paul) | ~generous(paul) | ! [X0] : (~generous(X0) & calm(X0))) & (? [X1] : (generous(X1) | ~calm(X1)) | (~wise(paul) & generous(paul))) [rectify 61]
63. ? [X1] : (generous(X1) | ~calm(X1)) => (generous(sK4) | ~calm(sK4)) [choice axiom]
64. (wise(paul) | ~generous(paul) | ! [X0] : (~generous(X0) & calm(X0))) & ((generous(sK4) | ~calm(sK4)) | (~wise(paul) & generous(paul))) [skolemisation 62,63]
99. ~brave(X0) | tall(X0) | ~wise(X0) [cnf transformation 44]
102. curious(X0) | generous(X0) [cnf transformation 49]
103. generous(X0) | brave(X0) [cnf transformation 49]
108. ~generous(X0) | patient(X0) | brave(X0) [cnf transformation 50]
121. wise(paul) | ~generous(paul) | ~generous(X0) [cnf transformation 64]
122. ~curious(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 37]
140. ~patient(paul) [cnf transformation 21]
143. generous(paul) [cnf transformation 23]
146. ~tall(paul) [cnf transformation 25]
147. ~curious(X0) | ~brave(X0) [duplicate literal removal 122]
156. patient(X0) | brave(X0) [subsumption resolution 108,103]
195. 11 <=> ! [X0] : ~generous(X0) [avatar definition]
196. ~generous(X0) <- (11) [avatar component clause 195]
198. 12 <=> generous(paul) [avatar definition]
202. 13 <=> wise(paul) [avatar definition]
205. 11 | ~12 | 13 [avatar split clause 121,202,198,195]
321. 12 [avatar split clause 143,198]
323. ~brave(X0) | generous(X0) [resolution 147,102]
324. generous(X0) [subsumption resolution 323,103]
325. brave(paul) [resolution 156,140]
358. tall(paul) | ~wise(paul) [resolution 99,325]
359. ~wise(paul) [subsumption resolution 358,146]
362. ~13 [avatar split clause 359,202]
363. $false <- (11) [subsumption resolution 196,324]
364. ~11 [avatar contradiction clause 363]
365. $false [avatar sat refutation 205,321,362,364]
% SZS output end Proof for 2189767897941465947704253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both rich and not brave and vice versa.
If someone is not calm then lucy is either not humble or not calm.
Everyone who is not patient is not generous.
Everyone who is not kind or tall is creative.
If someone is tall or creative then mary is kind or not wise and vice versa.
Everyone who is either funny or creative is not funny.
Everyone who is creative or rich is not generous or not strong.
Everyone who is rich is quiet or not funny and vice versa.
Everyone who is not happy or not patient is not tall.
If lucy is either not funny or curious then someone is either not funny or not old and vice versa.
If someone is either not generous or not tall then susan is wise.
Everyone who is not wise is both not quiet and not old and vice versa.
If paul is either not funny or quiet then susan is both not quiet and old.
If susan is not patient then lucy is either funny or not quiet.
Everyone who is both old and not humble is both quiet and brave.
If susan is both kind and not humble then someone is strong or not calm.
Someone is not brave or not quiet.
Someone is not humble or not brave.
Someone is either brave or kind.
Someone is both quiet and not humble.
Someone is either curious or quiet.
Someone is both not quiet and kind.
Someone is both humble and creative.
Someone is both not tall and not humble. | Susan is not quiet. | neutral | (![X]:(~wise(X)<=>(rich(X)&~brave(X))))&
((?[X]:(~calm(X)))=>((~humble(lucy)<~>~calm(lucy))))&
(![X]:(~patient(X)=>~generous(X)))&
(![X]:((~kind(X)|tall(X))=>creative(X)))&
((?[X]:((tall(X)|creative(X))))<=>((kind(mary)|~wise(mary))))&
(![X]:((funny(X)<~>creative(X))=>~funny(X)))&
(![X]:((creative(X)|rich(X))=>(~generous(X)|~strong(X))))&
(![X]:(rich(X)<=>(quiet(X)|~funny(X))))&
(![X]:((~happy(X)|~patient(X))=>~tall(X)))&
(((~funny(lucy)<~>curious(lucy)))<=>(?[X]:((~funny(X)<~>~old(X)))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(wise(susan)))&
(![X]:(~wise(X)<=>(~quiet(X)&~old(X))))&
(((~funny(paul)<~>quiet(paul)))=>((~quiet(susan)&old(susan))))&
((~patient(susan))=>((funny(lucy)<~>~quiet(lucy))))&
(![X]:((old(X)&~humble(X))=>(quiet(X)&brave(X))))&
(((kind(susan)&~humble(susan)))=>(?[X]:((strong(X)|~calm(X)))))&
(?[X]:((~brave(X)|~quiet(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~tall(X)&~humble(X)))) | ~quiet(susan) | [] | null | 0 |
Everyone who is not tall or happy is both curious and not funny.
If john is both creative and tall then lucy is not rich or rich and vice versa.
Everyone who is both strong and patient is either quiet or not quiet and vice versa.
If someone is either not rich or old then someone is both curious and not patient.
If mary is calm then someone is either quiet or wise and vice versa.
If lucy is either humble or not happy then john is not kind or not humble.
Everyone who is either not generous or not tall is both not happy and funny and vice versa.
If someone is not quiet then someone is tall or not strong and vice versa.
Everyone who is not curious or rich is not brave.
If someone is either not humble or not brave then someone is kind or not strong.
Everyone who is both not strong and not calm is either not old or quiet.
Everyone who is both creative and not happy is both not humble and funny and vice versa.
Everyone who is either funny or not quiet is curious or not calm and vice versa.
Everyone who is calm or not humble is not kind and vice versa.
Everyone who is not calm is quiet or not quiet and vice versa.
If lucy is not strong or not curious then fred is both not generous and patient and vice versa.
Alice is either strong or not quiet.
Someone is both not curious and not creative.
Someone is strong.
Someone is either quiet or not rich.
Lucy is both funny and not old.
Someone is not kind.
John is both not rich and humble. | Alice is generous. | contradiction | (![X]:((~tall(X)|happy(X))=>(curious(X)&~funny(X))))&
(((creative(john)&tall(john)))<=>((~rich(lucy)|rich(lucy))))&
(![X]:((strong(X)&patient(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~rich(X)<~>old(X))))=>(?[X]:((curious(X)&~patient(X)))))&
((calm(mary))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(((humble(lucy)<~>~happy(lucy)))=>((~kind(john)|~humble(john))))&
(![X]:((~generous(X)<~>~tall(X))<=>(~happy(X)&funny(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:((~curious(X)|rich(X))=>~brave(X)))&
((?[X]:((~humble(X)<~>~brave(X))))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~strong(X)&~calm(X))=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)&~happy(X))<=>(~humble(X)&funny(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(curious(X)|~calm(X))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(((~strong(lucy)|~curious(lucy)))<=>((~generous(fred)&patient(fred))))&
((strong(alice)<~>~quiet(alice)))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((funny(lucy)&~old(lucy)))&
(?[X]:(~kind(X)))&
((~rich(john)&humble(john))) | generous(alice) | [
"p0",
"p2",
"p6",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7583926693909119708220916
% SZS output start Proof for 7583926693909119708220916
1. ! [X0] : ((happy(X0) | ~tall(X0)) => (~funny(X0) & curious(X0))) [input p0]
3. ! [X0] : ((patient(X0) & strong(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p2]
7. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (funny(X0) & ~happy(X0))) [input p6]
13. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> (~calm(X0) | curious(X0))) [input p12]
15. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p14]
17. strong(alice) <~> ~quiet(alice) [input p16]
24. generous(alice) [input hypothesis]
28. ! [X0] : ((~funny(X0) & curious(X0)) | (~happy(X0) & tall(X0))) [ennf transformation 1]
38. ! [X0] : (((patient(X0) & strong(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (~patient(X0) | ~strong(X0)))) [nnf transformation 3]
39. ! [X0] : (((patient(X0) & strong(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | ~patient(X0) | ~strong(X0))) [flattening 38]
49. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~funny(X0) | happy(X0))) & ((funny(X0) & ~happy(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 7]
50. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | ~funny(X0) | happy(X0)) & ((funny(X0) & ~happy(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [flattening 49]
63. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 13]
64. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [flattening 63]
67. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 15]
68. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 67]
71. (quiet(alice) | ~strong(alice)) & (~quiet(alice) | strong(alice)) [nnf transformation 17]
83. ~funny(X0) | tall(X0) [cnf transformation 28]
84. ~funny(X0) | ~happy(X0) [cnf transformation 28]
92. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 39]
93. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 39]
110. ~tall(X0) | ~generous(X0) | ~funny(X0) | happy(X0) [cnf transformation 50]
128. ~quiet(X0) | funny(X0) | calm(X0) [cnf transformation 64]
135. ~calm(X0) | ~quiet(X0) [cnf transformation 68]
136. ~calm(X0) | quiet(X0) [cnf transformation 68]
143. quiet(alice) | ~strong(alice) [cnf transformation 71]
154. generous(alice) [cnf transformation 24]
155. strong(X0) | ~quiet(X0) [duplicate literal removal 92]
156. quiet(X0) | strong(X0) [duplicate literal removal 93]
176. strong(X0) [subsumption resolution 155,156]
219. ~generous(X0) | ~funny(X0) | happy(X0) [subsumption resolution 110,83]
220. ~generous(X0) | ~funny(X0) [subsumption resolution 219,84]
253. ~calm(X0) [subsumption resolution 135,136]
266. quiet(alice) [subsumption resolution 143,176]
303. ~funny(alice) [resolution 220,154]
369. funny(alice) | calm(alice) [resolution 128,266]
372. calm(alice) [subsumption resolution 369,303]
373. $false [subsumption resolution 372,253]
% SZS output end Proof for 7583926693909119708220916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not happy then alice is not strong or quiet. If fred is not wise or calm then lucy is happy or wise and vice versa. Everyone who is rich or humble is both curious and tall and vice versa. Everyone who is both kind and patient is both not happy and funny and vice versa. Everyone who is not brave or old is both brave and not strong and vice versa. If john is both not creative and not tall then someone is either strong or quiet. Everyone who is not humble is kind or curious. Everyone who is patient or rich is not generous and vice versa. Everyone who is not calm is both not happy and not old and vice versa. If someone is both not strong and not creative then mary is either not curious or not quiet and vice versa. Everyone who is either tall or old is not kind. Everyone who is happy or not funny is either rich or quiet and vice versa. Everyone who is humble is wise and vice versa. If someone is curious or strong then someone is either humble or not humble and vice versa. Everyone who is both strong and not generous is either tall or not patient. If susan is both old and creative then lucy is both strong and not creative and vice versa. Fred is not happy or kind. Mary is not curious. Lucy is either not brave or kind. Mary is not patient. John is wise or strong. Someone is tall or not rich. Someone is either not patient or generous. Alice is either strong or not funny. | Alice is humble. | neutral | ((~happy(susan))=>((~strong(alice)|quiet(alice))))&
(((~wise(fred)|calm(fred)))<=>((happy(lucy)|wise(lucy))))&
(![X]:((rich(X)|humble(X))<=>(curious(X)&tall(X))))&
(![X]:((kind(X)&patient(X))<=>(~happy(X)&funny(X))))&
(![X]:((~brave(X)|old(X))<=>(brave(X)&~strong(X))))&
(((~creative(john)&~tall(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(kind(X)|curious(X))))&
(![X]:((patient(X)|rich(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~happy(X)&~old(X))))&
((?[X]:((~strong(X)&~creative(X))))<=>((~curious(mary)<~>~quiet(mary))))&
(![X]:((tall(X)<~>old(X))=>~kind(X)))&
(![X]:((happy(X)|~funny(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(humble(X)<=>wise(X)))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((strong(X)&~generous(X))=>(tall(X)<~>~patient(X))))&
(((old(susan)&creative(susan)))<=>((strong(lucy)&~creative(lucy))))&
((~happy(fred)|kind(fred)))&
(~curious(mary))&
((~brave(lucy)<~>kind(lucy)))&
(~patient(mary))&
((wise(john)|strong(john)))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((strong(alice)<~>~funny(alice))) | humble(alice) | [] | null | 0 |
If someone is either not old or not curious then john is both happy and not curious and vice versa. If someone is not curious or rich then someone is rich or wise. Everyone who is rich or creative is both happy and not strong and vice versa. If fred is both funny and not tall then someone is either brave or kind and vice versa. Everyone who is both calm and not happy is not happy and vice versa. If susan is either not old or old then alice is not funny or strong and vice versa. If someone is both tall and calm then paul is either humble or curious. If paul is rich or not tall then someone is rich. Everyone who is generous or wise is both not quiet and not wise and vice versa. Everyone who is not generous is either strong or not funny. If fred is not creative then someone is either old or not brave. Everyone who is not rich or not patient is not funny or calm. If someone is both tall and brave then susan is either not brave or patient and vice versa. If john is either humble or wise then someone is rich or kind and vice versa. Everyone who is either calm or not quiet is not patient and vice versa. Everyone who is both not curious and calm is curious or rich and vice versa. Someone is not humble. Lucy is both not quiet and rich. Susan is not funny. Susan is either not patient or calm. | Lucy is happy. | entailment | ((?[X]:((~old(X)<~>~curious(X))))<=>((happy(john)&~curious(john))))&
((?[X]:((~curious(X)|rich(X))))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((rich(X)|creative(X))<=>(happy(X)&~strong(X))))&
(((funny(fred)&~tall(fred)))<=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((calm(X)&~happy(X))<=>~happy(X)))&
(((~old(susan)<~>old(susan)))<=>((~funny(alice)|strong(alice))))&
((?[X]:((tall(X)&calm(X))))=>((humble(paul)<~>curious(paul))))&
(((rich(paul)|~tall(paul)))=>(?[X]:(rich(X))))&
(![X]:((generous(X)|wise(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(~generous(X)=>(strong(X)<~>~funny(X))))&
((~creative(fred))=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~patient(X))=>(~funny(X)|calm(X))))&
((?[X]:((tall(X)&brave(X))))<=>((~brave(susan)<~>patient(susan))))&
(((humble(john)<~>wise(john)))<=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>~patient(X)))&
(![X]:((~curious(X)&calm(X))<=>(curious(X)|rich(X))))&
(?[X]:(~humble(X)))&
((~quiet(lucy)&rich(lucy)))&
(~funny(susan))&
((~patient(susan)<~>calm(susan))) | happy(lucy) | [
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 533820477458289039206878
% SZS output start Proof for 533820477458289039206878
3. ! [X0] : ((creative(X0) | rich(X0)) <=> (~strong(X0) & happy(X0))) [input p2]
18. rich(lucy) & ~quiet(lucy) [input p17]
21. ~happy(lucy) [input hypothesis]
38. ! [X0] : (((creative(X0) | rich(X0)) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | (~creative(X0) & ~rich(X0)))) [nnf transformation 3]
39. ! [X0] : ((creative(X0) | rich(X0) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | (~creative(X0) & ~rich(X0)))) [flattening 38]
80. ~rich(X0) | happy(X0) [cnf transformation 39]
138. rich(lucy) [cnf transformation 18]
142. ~happy(lucy) [cnf transformation 21]
335. happy(lucy) [resolution 80,138]
338. $false [subsumption resolution 335,142]
% SZS output end Proof for 533820477458289039206878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny or brave then someone is rich or brave and vice versa. Everyone who is both kind and wise is both kind and not old. Everyone who is creative is curious and vice versa. If mary is humble or not curious then someone is not calm. Everyone who is strong or not quiet is both not creative and happy. Everyone who is wise is either not strong or not old. Everyone who is happy is both not curious and not calm. Everyone who is not funny is either not strong or not kind and vice versa. Everyone who is funny is either creative or happy and vice versa. Everyone who is both not happy and patient is both old and not brave. If someone is either curious or not creative then someone is both not patient and tall. If someone is either not humble or not patient then someone is both patient and happy and vice versa. Everyone who is not kind is both humble and strong and vice versa. If someone is either not quiet or not happy then fred is both not curious and not creative and vice versa. Everyone who is calm is strong or not rich. If alice is both strong and not curious then paul is either not wise or curious and vice versa. John is humble. Lucy is not wise. Alice is both not happy and not curious. Someone is both quiet and old. Someone is tall or wise. Fred is both not wise and not humble. | Alice is not funny. | entailment | (((funny(lucy)|brave(lucy)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)&~old(X))))&
(![X]:(creative(X)<=>curious(X)))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(![X]:(happy(X)=>(~curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((~happy(X)&patient(X))=>(old(X)&~brave(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:(~kind(X)<=>(humble(X)&strong(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((~curious(fred)&~creative(fred))))&
(![X]:(calm(X)=>(strong(X)|~rich(X))))&
(((strong(alice)&~curious(alice)))<=>((~wise(paul)<~>curious(paul))))&
(humble(john))&
(~wise(lucy))&
((~happy(alice)&~curious(alice)))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((tall(X)|wise(X))))&
((~wise(fred)&~humble(fred))) | ~funny(alice) | [
"p4",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9183233715973779532944052
% SZS output start Proof for 9183233715973779532944052
5. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> ~kind(X0))) [input p7]
13. ! [X0] : (~kind(X0) <=> (strong(X0) & humble(X0))) [input p12]
19. ~curious(alice) & ~happy(alice) [input p18]
23. funny(alice) [input hypothesis]
33. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 5]
46. ! [X0] : ((~funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 8]
57. ! [X0] : ((~kind(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | kind(X0))) [nnf transformation 13]
58. ! [X0] : ((~kind(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | kind(X0))) [flattening 57]
78. ~strong(X0) | happy(X0) [cnf transformation 33]
85. ~kind(X0) | ~funny(X0) | strong(X0) [cnf transformation 46]
102. strong(X0) | kind(X0) [cnf transformation 58]
118. ~happy(alice) [cnf transformation 19]
124. funny(alice) [cnf transformation 23]
243. 26 <=> strong(alice) [avatar definition]
244. ~strong(alice) <- (~26) [avatar component clause 243]
245. strong(alice) <- (26) [avatar component clause 243]
257. kind(alice) <- (~26) [resolution 102,244]
289. ~funny(alice) | strong(alice) <- (~26) [resolution 85,257]
300. strong(alice) <- (~26) [subsumption resolution 289,124]
301. $false <- (~26) [subsumption resolution 300,244]
302. 26 [avatar contradiction clause 301]
314. happy(alice) <- (26) [resolution 245,78]
316. $false <- (26) [subsumption resolution 314,118]
317. ~26 [avatar contradiction clause 316]
318. $false [avatar sat refutation 302,317]
% SZS output end Proof for 9183233715973779532944052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either calm or strong then someone is both not kind and not wise and vice versa. Everyone who is both curious and not humble is not tall. If someone is either not funny or old then someone is either not patient or wise and vice versa. Everyone who is both humble and not humble is not curious or creative and vice versa. If someone is patient or not curious then someone is not funny and vice versa. If someone is either not old or humble then mary is not funny and vice versa. If someone is both curious and brave then susan is patient or not quiet. If someone is tall then someone is either strong or generous and vice versa. Everyone who is both not strong and not brave is curious or not curious. Everyone who is not patient or not generous is not curious or not creative and vice versa. Everyone who is both not kind and not calm is both not tall and not strong. If alice is not creative then john is creative or quiet and vice versa. Everyone who is patient is strong and vice versa. If john is patient or strong then fred is rich or not humble and vice versa. If someone is both not brave and not wise then someone is not old. Paul is generous. Susan is not quiet or funny. Mary is not happy. Lucy is not humble. Someone is not creative or quiet. Fred is kind. John is kind or not humble. Susan is either quiet or not wise. | Lucy is tall. | contradiction | (((calm(paul)<~>strong(paul)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((curious(X)&~humble(X))=>~tall(X)))&
((?[X]:((~funny(X)<~>old(X))))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((humble(X)&~humble(X))<=>(~curious(X)|creative(X))))&
((?[X]:((patient(X)|~curious(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>(~funny(mary)))&
((?[X]:((curious(X)&brave(X))))=>((patient(susan)|~quiet(susan))))&
((?[X]:(tall(X)))<=>(?[X]:((strong(X)<~>generous(X)))))&
(![X]:((~strong(X)&~brave(X))=>(curious(X)|~curious(X))))&
(![X]:((~patient(X)|~generous(X))<=>(~curious(X)|~creative(X))))&
(![X]:((~kind(X)&~calm(X))=>(~tall(X)&~strong(X))))&
((~creative(alice))<=>((creative(john)|quiet(john))))&
(![X]:(patient(X)<=>strong(X)))&
(((patient(john)|strong(john)))<=>((rich(fred)|~humble(fred))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:(~old(X))))&
(generous(paul))&
((~quiet(susan)|funny(susan)))&
(~happy(mary))&
(~humble(lucy))&
(?[X]:((~creative(X)|quiet(X))))&
(kind(fred))&
((kind(john)|~humble(john)))&
((quiet(susan)<~>~wise(susan))) | tall(lucy) | [
"p1",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1964805499604633532919977
% SZS output start Proof for 1964805499604633532919977
2. ! [X0] : ((~humble(X0) & curious(X0)) => ~tall(X0)) [input p1]
4. ! [X0] : ((~humble(X0) & humble(X0)) <=> (creative(X0) | ~curious(X0))) [input p3]
19. ~humble(lucy) [input p18]
24. tall(lucy) [input hypothesis]
30. ! [X0] : (~tall(X0) | (humble(X0) | ~curious(X0))) [ennf transformation 2]
31. ! [X0] : (~tall(X0) | humble(X0) | ~curious(X0)) [flattening 30]
48. ! [X0] : (((~humble(X0) & humble(X0)) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | (humble(X0) | ~humble(X0)))) [nnf transformation 4]
49. ! [X0] : (((~humble(X0) & humble(X0)) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | humble(X0) | ~humble(X0))) [flattening 48]
83. ~tall(X0) | humble(X0) | ~curious(X0) [cnf transformation 31]
93. humble(X0) | curious(X0) [cnf transformation 49]
95. ~humble(X0) | curious(X0) [cnf transformation 49]
128. ~humble(lucy) [cnf transformation 19]
134. tall(lucy) [cnf transformation 24]
197. curious(X0) [subsumption resolution 93,95]
349. humble(lucy) | ~curious(lucy) [resolution 83,134]
351. ~curious(lucy) [subsumption resolution 349,128]
352. $false [subsumption resolution 351,197]
% SZS output end Proof for 1964805499604633532919977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not funny is strong or patient. If someone is either brave or not rich then mary is not humble or strong. If mary is not curious or calm then paul is not wise and vice versa. If someone is both creative and wise then mary is either wise or curious and vice versa. Everyone who is not happy or not rich is kind and vice versa. If fred is both happy and not patient then someone is wise. Everyone who is generous is not generous or not happy and vice versa. Everyone who is either not happy or quiet is not tall or brave and vice versa. Everyone who is generous or not curious is both not curious and not calm and vice versa. If someone is both wise and tall then alice is patient or not humble. If someone is both not happy and calm then alice is both not funny and not humble. If susan is not curious or calm then paul is both kind and not patient and vice versa. Everyone who is not rich or rich is rich or generous. Everyone who is not rich is either not wise or rich and vice versa. If someone is not humble then someone is both curious and humble. Fred is both humble and not funny. Paul is both not brave and strong. Susan is kind. Someone is tall. Someone is kind. Someone is not funny. | Susan is not calm. | entailment | (![X]:((old(X)|~funny(X))=>(strong(X)|patient(X))))&
((?[X]:((brave(X)<~>~rich(X))))=>((~humble(mary)|strong(mary))))&
(((~curious(mary)|calm(mary)))<=>(~wise(paul)))&
((?[X]:((creative(X)&wise(X))))<=>((wise(mary)<~>curious(mary))))&
(![X]:((~happy(X)|~rich(X))<=>kind(X)))&
(((happy(fred)&~patient(fred)))=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(~generous(X)|~happy(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(~tall(X)|brave(X))))&
(![X]:((generous(X)|~curious(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((wise(X)&tall(X))))=>((patient(alice)|~humble(alice))))&
((?[X]:((~happy(X)&calm(X))))=>((~funny(alice)&~humble(alice))))&
(((~curious(susan)|calm(susan)))<=>((kind(paul)&~patient(paul))))&
(![X]:((~rich(X)|rich(X))=>(rich(X)|generous(X))))&
(![X]:(~rich(X)<=>(~wise(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((curious(X)&humble(X)))))&
((humble(fred)&~funny(fred)))&
((~brave(paul)&strong(paul)))&
(kind(susan))&
(?[X]:(tall(X)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X))) | ~calm(susan) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 563841191096910562383291
% SZS output start Proof for 563841191096910562383291
7. ! [X0] : (generous(X0) <=> (~happy(X0) | ~generous(X0))) [input p6]
9. ! [X0] : ((~curious(X0) | generous(X0)) <=> (~calm(X0) & ~curious(X0))) [input p8]
22. calm(susan) [input hypothesis]
48. ! [X0] : ((generous(X0) | (happy(X0) & generous(X0))) & ((~happy(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 7]
49. ! [X0] : ((generous(X0) | (happy(X0) & generous(X0))) & (~happy(X0) | ~generous(X0) | ~generous(X0))) [flattening 48]
52. ! [X0] : (((~curious(X0) | generous(X0)) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | (curious(X0) & ~generous(X0)))) [nnf transformation 9]
53. ! [X0] : ((~curious(X0) | generous(X0) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | (curious(X0) & ~generous(X0)))) [flattening 52]
78. generous(X0) | generous(X0) [cnf transformation 49]
88. ~calm(X0) | ~generous(X0) [cnf transformation 53]
111. calm(susan) [cnf transformation 22]
116. generous(X0) [duplicate literal removal 78]
170. ~calm(X0) [subsumption resolution 88,116]
197. $false [subsumption resolution 111,170]
% SZS output end Proof for 563841191096910562383291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is not humble. Everyone who is both quiet and humble is either rich or tall. Everyone who is either not patient or brave is both not calm and patient. If fred is not happy or not curious then someone is both not kind and not calm and vice versa. If lucy is either not strong or strong then someone is both humble and quiet. If lucy is either not humble or creative then someone is both happy and curious. If someone is both not funny and not tall then paul is not patient. If someone is either not generous or not brave then susan is tall and vice versa. If someone is not old then someone is not curious or not patient and vice versa. Everyone who is both wise and patient is not brave or not humble and vice versa. If alice is both tall and curious then someone is either happy or not tall and vice versa. Everyone who is not wise or not humble is either rich or quiet and vice versa. Everyone who is both generous and not brave is strong. If susan is either not generous or not calm then susan is not creative or kind. If someone is not kind then paul is both funny and calm. Everyone who is both brave and not rich is either humble or not brave and vice versa. Someone is happy or not strong. Someone is either not brave or not funny. Someone is both not humble and not strong. Mary is not patient or not generous. Alice is brave. Lucy is not creative. Fred is both not curious and generous. | Mary is patient. | neutral | (![X]:((kind(X)&creative(X))=>~humble(X)))&
(![X]:((quiet(X)&humble(X))=>(rich(X)<~>tall(X))))&
(![X]:((~patient(X)<~>brave(X))=>(~calm(X)&patient(X))))&
(((~happy(fred)|~curious(fred)))<=>(?[X]:((~kind(X)&~calm(X)))))&
(((~strong(lucy)<~>strong(lucy)))=>(?[X]:((humble(X)&quiet(X)))))&
(((~humble(lucy)<~>creative(lucy)))=>(?[X]:((happy(X)&curious(X)))))&
((?[X]:((~funny(X)&~tall(X))))=>(~patient(paul)))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(tall(susan)))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((wise(X)&patient(X))<=>(~brave(X)|~humble(X))))&
(((tall(alice)&curious(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((generous(X)&~brave(X))=>strong(X)))&
(((~generous(susan)<~>~calm(susan)))=>((~creative(susan)|kind(susan))))&
((?[X]:(~kind(X)))=>((funny(paul)&calm(paul))))&
(![X]:((brave(X)&~rich(X))<=>(humble(X)<~>~brave(X))))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~patient(mary)|~generous(mary)))&
(brave(alice))&
(~creative(lucy))&
((~curious(fred)&generous(fred))) | patient(mary) | [] | null | 0 |
Everyone who is both curious and wise is happy.
If john is either quiet or not rich then mary is not wise or creative and vice versa.
Everyone who is brave or old is both not happy and not old.
If john is either wise or not calm then susan is calm.
Everyone who is funny is either rich or not tall.
Everyone who is humble or calm is rich or not wise and vice versa.
If someone is humble then lucy is not quiet and vice versa.
Everyone who is patient is both generous and wise and vice versa.
Everyone who is old or not strong is either kind or curious.
Everyone who is not rich or not generous is both not funny and rich.
Everyone who is both strong and not generous is both funny and rich.
If alice is either creative or strong then paul is either not strong or not rich and vice versa.
Everyone who is rich or patient is not happy.
Everyone who is either not curious or not happy is brave or humble and vice versa.
Everyone who is rich or not old is strong or not funny and vice versa.
Susan is either old or not generous.
John is either not old or happy.
Mary is either not patient or happy.
Someone is both not old and not happy.
John is either rich or kind.
Lucy is both not funny and creative.
Someone is either wise or not wise. | Paul is happy. | contradiction | (![X]:((curious(X)&wise(X))=>happy(X)))&
(((quiet(john)<~>~rich(john)))<=>((~wise(mary)|creative(mary))))&
(![X]:((brave(X)|old(X))=>(~happy(X)&~old(X))))&
(((wise(john)<~>~calm(john)))=>(calm(susan)))&
(![X]:(funny(X)=>(rich(X)<~>~tall(X))))&
(![X]:((humble(X)|calm(X))<=>(rich(X)|~wise(X))))&
((?[X]:(humble(X)))<=>(~quiet(lucy)))&
(![X]:(patient(X)<=>(generous(X)&wise(X))))&
(![X]:((old(X)|~strong(X))=>(kind(X)<~>curious(X))))&
(![X]:((~rich(X)|~generous(X))=>(~funny(X)&rich(X))))&
(![X]:((strong(X)&~generous(X))=>(funny(X)&rich(X))))&
(((creative(alice)<~>strong(alice)))<=>((~strong(paul)<~>~rich(paul))))&
(![X]:((rich(X)|patient(X))=>~happy(X)))&
(![X]:((~curious(X)<~>~happy(X))<=>(brave(X)|humble(X))))&
(![X]:((rich(X)|~old(X))<=>(strong(X)|~funny(X))))&
((old(susan)<~>~generous(susan)))&
((~old(john)<~>happy(john)))&
((~patient(mary)<~>happy(mary)))&
(?[X]:((~old(X)&~happy(X))))&
((rich(john)<~>kind(john)))&
((~funny(lucy)&creative(lucy)))&
(?[X]:((wise(X)<~>~wise(X)))) | happy(paul) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4024612029352578876224710
% SZS output start Proof for 4024612029352578876224710
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (rich(X0) & ~funny(X0))) [input p9]
13. ! [X0] : ((patient(X0) | rich(X0)) => ~happy(X0)) [input p12]
23. happy(paul) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~funny(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
33. ! [X0] : (~happy(X0) | (~patient(X0) & ~rich(X0))) [ennf transformation 13]
91. rich(X0) | rich(X0) [cnf transformation 30]
103. ~happy(X0) | ~rich(X0) [cnf transformation 33]
129. happy(paul) [cnf transformation 23]
130. rich(X0) [duplicate literal removal 91]
202. ~happy(X0) [subsumption resolution 103,130]
210. $false [subsumption resolution 129,202]
% SZS output end Proof for 4024612029352578876224710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is kind.
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
If fred is curious or not kind then lucy is both old and quiet.
Everyone who is strong or not happy is not rich or not quiet.
Everyone who is calm is not strong.
Everyone who is brave is either happy or old and vice versa.
Everyone who is generous is kind and vice versa.
Someone is either not rich or humble.
Lucy is quiet.
Paul is kind or not creative.
Mary is either quiet or not funny.
Someone is not funny.
Mary is quiet.
Someone is either not humble or not patient. | Fred is old. | neutral | (![X]:(~wise(X)=>kind(X)))&
(((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
(((curious(fred)|~kind(fred)))=>((old(lucy)&quiet(lucy))))&
(![X]:((strong(X)|~happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:(brave(X)<=>(happy(X)<~>old(X))))&
(![X]:(generous(X)<=>kind(X)))&
(?[X]:((~rich(X)<~>humble(X))))&
(quiet(lucy))&
((kind(paul)|~creative(paul)))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:(~funny(X)))&
(quiet(mary))&
(?[X]:((~humble(X)<~>~patient(X)))) | old(fred) | [] | null | 0 |
Everyone who is generous is either not generous or humble and vice versa.
Everyone who is tall or humble is either not calm or generous and vice versa.
Everyone who is strong is quiet.
If someone is not generous or not funny then paul is either not strong or not creative.
If mary is rich or not wise then susan is either not rich or not funny and vice versa.
Everyone who is both curious and not old is not quiet and vice versa.
If fred is either not wise or humble then alice is not kind or not happy and vice versa.
If fred is strong then someone is either not kind or wise and vice versa.
Everyone who is both not generous and not curious is humble or wise and vice versa.
Everyone who is both wise and not wise is both old and funny.
Everyone who is both not rich and funny is not wise or happy.
If someone is generous then someone is brave and vice versa.
Everyone who is not old is both not strong and not kind.
If alice is both not tall and not funny then someone is not patient and vice versa.
If someone is rich then lucy is both rich and not wise and vice versa.
If paul is either not kind or happy then paul is either brave or not patient and vice versa.
Paul is both not funny and not calm.
John is not tall.
Someone is funny or not tall.
Someone is both tall and not rich.
Alice is old or not calm.
Someone is wise or quiet.
Someone is both not tall and not calm. | Alice is happy. | neutral | (![X]:(generous(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((tall(X)|humble(X))<=>(~calm(X)<~>generous(X))))&
(![X]:(strong(X)=>quiet(X)))&
((?[X]:((~generous(X)|~funny(X))))=>((~strong(paul)<~>~creative(paul))))&
(((rich(mary)|~wise(mary)))<=>((~rich(susan)<~>~funny(susan))))&
(![X]:((curious(X)&~old(X))<=>~quiet(X)))&
(((~wise(fred)<~>humble(fred)))<=>((~kind(alice)|~happy(alice))))&
((strong(fred))<=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:((~generous(X)&~curious(X))<=>(humble(X)|wise(X))))&
(![X]:((wise(X)&~wise(X))=>(old(X)&funny(X))))&
(![X]:((~rich(X)&funny(X))=>(~wise(X)|happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:(brave(X))))&
(![X]:(~old(X)=>(~strong(X)&~kind(X))))&
(((~tall(alice)&~funny(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:(rich(X)))<=>((rich(lucy)&~wise(lucy))))&
(((~kind(paul)<~>happy(paul)))<=>((brave(paul)<~>~patient(paul))))&
((~funny(paul)&~calm(paul)))&
(~tall(john))&
(?[X]:((funny(X)|~tall(X))))&
(?[X]:((tall(X)&~rich(X))))&
((old(alice)|~calm(alice)))&
(?[X]:((wise(X)|quiet(X))))&
(?[X]:((~tall(X)&~calm(X)))) | happy(alice) | [] | null | 0 |
Everyone who is either not creative or not old is both patient and creative and vice versa.
Everyone who is not quiet or humble is both not strong and rich.
Everyone who is not happy or creative is both not creative and not brave.
Everyone who is both quiet and not tall is both not funny and not creative and vice versa.
If someone is not quiet then someone is both not patient and strong and vice versa.
Everyone who is calm or not calm is both not wise and not brave and vice versa.
If someone is not rich then fred is not strong.
Everyone who is happy or funny is either old or creative.
Everyone who is either not calm or not quiet is either not funny or patient and vice versa.
If fred is brave or generous then someone is not kind.
If someone is both not humble and strong then paul is wise or kind.
Everyone who is wise is not tall or not happy.
Everyone who is both generous and strong is both not old and funny and vice versa.
If someone is either happy or curious then someone is either not funny or humble.
If someone is curious or not curious then alice is either funny or not rich and vice versa.
Everyone who is quiet is both not brave and not kind and vice versa.
Lucy is either creative or not brave.
Someone is not old.
Someone is both quiet and not kind.
Someone is strong or humble. | Lucy is not humble. | neutral | (![X]:((~creative(X)<~>~old(X))<=>(patient(X)&creative(X))))&
(![X]:((~quiet(X)|humble(X))=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((calm(X)|~calm(X))<=>(~wise(X)&~brave(X))))&
((?[X]:(~rich(X)))=>(~strong(fred)))&
(![X]:((happy(X)|funny(X))=>(old(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~funny(X)<~>patient(X))))&
(((brave(fred)|generous(fred)))=>(?[X]:(~kind(X))))&
((?[X]:((~humble(X)&strong(X))))=>((wise(paul)|kind(paul))))&
(![X]:(wise(X)=>(~tall(X)|~happy(X))))&
(![X]:((generous(X)&strong(X))<=>(~old(X)&funny(X))))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((~funny(X)<~>humble(X)))))&
((?[X]:((curious(X)|~curious(X))))<=>((funny(alice)<~>~rich(alice))))&
(![X]:(quiet(X)<=>(~brave(X)&~kind(X))))&
((creative(lucy)<~>~brave(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((strong(X)|humble(X)))) | ~humble(lucy) | [] | null | 0 |
If lucy is either not tall or humble then paul is funny or not quiet and vice versa.
Everyone who is either not generous or not wise is either curious or brave and vice versa.
Everyone who is not quiet or not kind is both not brave and not creative.
Everyone who is both funny and old is humble.
If someone is both patient and not quiet then someone is either humble or not generous and vice versa.
Everyone who is both not happy and tall is either humble or tall and vice versa.
If susan is not calm then mary is quiet or rich and vice versa.
Everyone who is patient is both brave and wise and vice versa.
Everyone who is brave is curious.
Everyone who is both not patient and quiet is both curious and not humble.
Everyone who is creative or not funny is calm.
If mary is tall or not curious then someone is not patient and vice versa.
If someone is brave or calm then someone is either brave or curious and vice versa.
If paul is either not wise or not creative then susan is either creative or not kind and vice versa.
Everyone who is both not quiet and not funny is not curious and vice versa.
Everyone who is both funny and not old is both not kind and funny.
Someone is either creative or brave.
Someone is both funny and not calm.
Paul is quiet or not curious.
Paul is both rich and old.
Someone is not quiet or not humble.
Someone is both patient and not old. | Lucy is not generous. | neutral | (((~tall(lucy)<~>humble(lucy)))<=>((funny(paul)|~quiet(paul))))&
(![X]:((~generous(X)<~>~wise(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((funny(X)&old(X))=>humble(X)))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~happy(X)&tall(X))<=>(humble(X)<~>tall(X))))&
((~calm(susan))<=>((quiet(mary)|rich(mary))))&
(![X]:(patient(X)<=>(brave(X)&wise(X))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((~patient(X)&quiet(X))=>(curious(X)&~humble(X))))&
(![X]:((creative(X)|~funny(X))=>calm(X)))&
(((tall(mary)|~curious(mary)))<=>(?[X]:(~patient(X))))&
((?[X]:((brave(X)|calm(X))))<=>(?[X]:((brave(X)<~>curious(X)))))&
(((~wise(paul)<~>~creative(paul)))<=>((creative(susan)<~>~kind(susan))))&
(![X]:((~quiet(X)&~funny(X))<=>~curious(X)))&
(![X]:((funny(X)&~old(X))=>(~kind(X)&funny(X))))&
(?[X]:((creative(X)<~>brave(X))))&
(?[X]:((funny(X)&~calm(X))))&
((quiet(paul)|~curious(paul)))&
((rich(paul)&old(paul)))&
(?[X]:((~quiet(X)|~humble(X))))&
(?[X]:((patient(X)&~old(X)))) | ~generous(lucy) | [] | null | 0 |
If someone is both tall and wise then someone is not quiet.
If someone is patient or tall then someone is both not tall and not strong.
Everyone who is not wise or not patient is either old or humble.
Everyone who is not kind is either humble or not creative and vice versa.
Everyone who is either not old or not brave is curious or tall.
Everyone who is either not humble or happy is both not brave and not wise and vice versa.
If fred is not strong then mary is both curious and not tall and vice versa.
If someone is not patient then mary is both old and not wise and vice versa.
Everyone who is both not old and humble is funny.
Everyone who is funny is both creative and not humble and vice versa.
Everyone who is rich or not wise is either not wise or funny and vice versa.
Everyone who is not rich or not calm is both wise and not funny and vice versa.
Everyone who is either tall or not funny is either not rich or strong and vice versa.
Everyone who is either not rich or patient is either not rich or not wise and vice versa.
Everyone who is not generous or not wise is either not generous or kind.
Someone is not brave or not rich.
Paul is either happy or not tall.
Paul is not curious or curious.
Alice is tall or strong.
Paul is either kind or tall.
Alice is rich. | Paul is not tall. | contradiction | ((?[X]:((tall(X)&wise(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((patient(X)|tall(X))))=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~wise(X)|~patient(X))=>(old(X)<~>humble(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)<~>~brave(X))=>(curious(X)|tall(X))))&
(![X]:((~humble(X)<~>happy(X))<=>(~brave(X)&~wise(X))))&
((~strong(fred))<=>((curious(mary)&~tall(mary))))&
((?[X]:(~patient(X)))<=>((old(mary)&~wise(mary))))&
(![X]:((~old(X)&humble(X))=>funny(X)))&
(![X]:(funny(X)<=>(creative(X)&~humble(X))))&
(![X]:((rich(X)|~wise(X))<=>(~wise(X)<~>funny(X))))&
(![X]:((~rich(X)|~calm(X))<=>(wise(X)&~funny(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~generous(X)|~wise(X))=>(~generous(X)<~>kind(X))))&
(?[X]:((~brave(X)|~rich(X))))&
((happy(paul)<~>~tall(paul)))&
((~curious(paul)|curious(paul)))&
((tall(alice)|strong(alice)))&
((kind(paul)<~>tall(paul)))&
(rich(alice)) | ~tall(paul) | [
"p2",
"p3",
"p5",
"p8",
"p9",
"p10",
"p11",
"p13",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4623669438327674989840171
% SZS output start Proof for 4623669438327674989840171
3. ! [X0] : ((~patient(X0) | ~wise(X0)) => (old(X0) <~> humble(X0))) [input p2]
4. ! [X0] : (~kind(X0) <=> (humble(X0) <~> ~creative(X0))) [input p3]
6. ! [X0] : ((~humble(X0) <~> happy(X0)) <=> (~wise(X0) & ~brave(X0))) [input p5]
9. ! [X0] : ((humble(X0) & ~old(X0)) => funny(X0)) [input p8]
10. ! [X0] : (funny(X0) <=> (~humble(X0) & creative(X0))) [input p9]
11. ! [X0] : ((~wise(X0) | rich(X0)) <=> (~wise(X0) <~> funny(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~funny(X0) & wise(X0))) [input p11]
14. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p13]
17. happy(paul) <~> ~tall(paul) [input p16]
20. kind(paul) <~> tall(paul) [input p19]
22. ~tall(paul) [input hypothesis]
27. ! [X0] : ((old(X0) <~> humble(X0)) | (patient(X0) & wise(X0))) [ennf transformation 3]
30. ! [X0] : (funny(X0) | (~humble(X0) | old(X0))) [ennf transformation 9]
31. ! [X0] : (funny(X0) | ~humble(X0) | old(X0)) [flattening 30]
36. ! [X0] : (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (patient(X0) & wise(X0))) [nnf transformation 27]
37. ! [X0] : ((~kind(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | kind(X0))) [nnf transformation 4]
39. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [nnf transformation 6]
40. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [flattening 39]
48. ! [X0] : ((funny(X0) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | ~funny(X0))) [nnf transformation 10]
49. ! [X0] : ((funny(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~funny(X0))) [flattening 48]
50. ! [X0] : (((~wise(X0) | rich(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (wise(X0) & ~rich(X0)))) [nnf transformation 11]
51. ! [X0] : ((~wise(X0) | rich(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (wise(X0) & ~rich(X0)))) [flattening 50]
52. ! [X0] : (((~calm(X0) | ~rich(X0)) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | (calm(X0) & rich(X0)))) [nnf transformation 12]
53. ! [X0] : ((~calm(X0) | ~rich(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | (calm(X0) & rich(X0)))) [flattening 52]
55. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 14]
59. (tall(paul) | ~happy(paul)) & (~tall(paul) | happy(paul)) [nnf transformation 17]
60. (~tall(paul) | ~kind(paul)) & (tall(paul) | kind(paul)) [nnf transformation 20]
65. humble(X0) | old(X0) | wise(X0) [cnf transformation 36]
67. ~humble(X0) | ~old(X0) | wise(X0) [cnf transformation 36]
68. ~humble(X0) | ~old(X0) | patient(X0) [cnf transformation 36]
72. ~kind(X0) | humble(X0) | creative(X0) [cnf transformation 37]
77. ~wise(X0) | happy(X0) | humble(X0) [cnf transformation 40]
87. ~humble(X0) | funny(X0) | old(X0) [cnf transformation 31]
89. ~funny(X0) | ~humble(X0) [cnf transformation 49]
90. ~creative(X0) | humble(X0) | funny(X0) [cnf transformation 49]
94. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 51]
97. rich(X0) | wise(X0) [cnf transformation 53]
111. ~wise(X0) | ~rich(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 55]
116. ~patient(X0) | rich(X0) | ~wise(X0) | rich(X0) [cnf transformation 55]
124. tall(paul) | ~happy(paul) [cnf transformation 59]
127. tall(paul) | kind(paul) [cnf transformation 60]
130. ~tall(paul) [cnf transformation 22]
132. ~wise(X0) | ~rich(X0) | ~patient(X0) [duplicate literal removal 111]
135. ~patient(X0) | rich(X0) | ~wise(X0) [duplicate literal removal 116]
136. ~funny(X0) | wise(X0) [duplicate literal removal 94]
193. ~patient(X0) | rich(X0) [subsumption resolution 135,97]
195. ~patient(X0) | ~wise(X0) [subsumption resolution 132,193]
206. 14 <=> happy(paul) [avatar definition]
208. ~happy(paul) <- (~14) [avatar component clause 206]
210. 15 <=> tall(paul) [avatar definition]
213. ~14 | 15 [avatar split clause 124,210,206]
225. 18 <=> kind(paul) [avatar definition]
226. kind(paul) <- (18) [avatar component clause 225]
229. 18 | 15 [avatar split clause 127,210,225]
230. ~15 [avatar split clause 130,210]
244. humble(paul) | creative(paul) <- (18) [resolution 72,226]
246. 19 <=> creative(paul) [avatar definition]
248. creative(paul) <- (19) [avatar component clause 246]
250. 20 <=> humble(paul) [avatar definition]
251. ~humble(paul) <- (~20) [avatar component clause 250]
252. humble(paul) <- (20) [avatar component clause 250]
253. 19 | 20 | ~18 [avatar split clause 244,225,250,246]
259. old(paul) | wise(paul) <- (~20) [resolution 251,65]
261. 21 <=> patient(paul) [avatar definition]
263. patient(paul) <- (21) [avatar component clause 261]
265. 22 <=> old(paul) [avatar definition]
266. ~old(paul) <- (~22) [avatar component clause 265]
270. 23 <=> wise(paul) [avatar definition]
272. wise(paul) <- (23) [avatar component clause 270]
273. 23 | 22 | 20 [avatar split clause 259,250,265,270]
295. ~old(paul) | patient(paul) <- (20) [resolution 252,68]
296. ~old(paul) | wise(paul) <- (20) [resolution 252,67]
297. 21 | ~22 | ~20 [avatar split clause 295,250,265,261]
298. 23 | ~22 | ~20 [avatar split clause 296,250,265,270]
301. funny(paul) | old(paul) <- (20) [resolution 87,252]
305. funny(paul) <- (20, ~22) [subsumption resolution 301,266]
363. ~humble(paul) <- (20, ~22) [resolution 305,89]
367. $false <- (20, ~22) [subsumption resolution 363,252]
368. ~20 | 22 [avatar contradiction clause 367]
372. humble(paul) | funny(paul) <- (19) [resolution 248,90]
375. funny(paul) <- (19, ~20) [subsumption resolution 372,251]
382. wise(paul) <- (19, ~20) [resolution 375,136]
386. 23 | ~19 | 20 [avatar split clause 382,250,246,270]
388. happy(paul) | humble(paul) <- (23) [resolution 272,77]
389. humble(paul) <- (~14, 23) [subsumption resolution 388,208]
392. 20 | 14 | ~23 [avatar split clause 389,270,206,250]
414. ~wise(paul) <- (21) [resolution 263,195]
416. $false <- (21, 23) [subsumption resolution 414,272]
417. ~21 | ~23 [avatar contradiction clause 416]
418. $false [avatar sat refutation 213,229,230,253,273,297,298,368,386,392,417]
% SZS output end Proof for 4623669438327674989840171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not creative or not tall then lucy is either happy or kind.
Everyone who is both patient and not wise is not brave or calm and vice versa.
If paul is either rich or not rich then someone is not happy or wise.
Everyone who is both funny and not creative is not generous or happy and vice versa.
Everyone who is calm or humble is both patient and strong.
Everyone who is not brave is both not calm and not humble and vice versa.
Everyone who is not wise is not calm or not curious.
Everyone who is either not patient or calm is either funny or not brave.
If someone is not funny then someone is not calm or strong.
Everyone who is not patient is creative.
Everyone who is either not curious or not happy is not humble or not creative and vice versa.
Everyone who is either not old or calm is either patient or strong and vice versa.
If lucy is strong then someone is kind and vice versa.
If someone is brave or rich then alice is curious or not tall and vice versa.
If mary is either not generous or not happy then someone is either not curious or not kind and vice versa.
Everyone who is not generous is not old or calm.
Mary is either not wise or not quiet.
Someone is either quiet or generous.
Someone is either not happy or happy.
Someone is not funny.
Someone is patient or not patient.
Lucy is not calm or strong.
Someone is either not creative or curious.
Someone is not old. | Alice is not tall. | neutral | (((~creative(john)|~tall(john)))=>((happy(lucy)<~>kind(lucy))))&
(![X]:((patient(X)&~wise(X))<=>(~brave(X)|calm(X))))&
(((rich(paul)<~>~rich(paul)))=>(?[X]:((~happy(X)|wise(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~generous(X)|happy(X))))&
(![X]:((calm(X)|humble(X))=>(patient(X)&strong(X))))&
(![X]:(~brave(X)<=>(~calm(X)&~humble(X))))&
(![X]:(~wise(X)=>(~calm(X)|~curious(X))))&
(![X]:((~patient(X)<~>calm(X))=>(funny(X)<~>~brave(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)|strong(X)))))&
(![X]:(~patient(X)=>creative(X)))&
(![X]:((~curious(X)<~>~happy(X))<=>(~humble(X)|~creative(X))))&
(![X]:((~old(X)<~>calm(X))<=>(patient(X)<~>strong(X))))&
((strong(lucy))<=>(?[X]:(kind(X))))&
((?[X]:((brave(X)|rich(X))))<=>((curious(alice)|~tall(alice))))&
(((~generous(mary)<~>~happy(mary)))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:(~generous(X)=>(~old(X)|calm(X))))&
((~wise(mary)<~>~quiet(mary)))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:((~happy(X)<~>happy(X))))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)|~patient(X))))&
((~calm(lucy)|strong(lucy)))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:(~old(X))) | ~tall(alice) | [] | null | 0 |
Everyone who is kind or old is not brave or not strong and vice versa.
If john is either funny or not patient then mary is both not quiet and not tall.
If someone is either not wise or old then someone is not tall and vice versa.
Everyone who is not tall is both not brave and not patient.
Everyone who is not humble is either not quiet or brave.
Everyone who is quiet is both funny and not kind and vice versa.
If someone is not strong then someone is both not strong and creative.
Everyone who is both patient and not strong is not kind or creative and vice versa.
Everyone who is not funny is either brave or old.
If someone is either old or not kind then john is both tall and calm and vice versa.
Everyone who is brave or wise is both not funny and strong and vice versa.
Everyone who is either creative or not generous is rich.
If someone is both strong and not brave then someone is either not wise or old.
If mary is either wise or brave then someone is either rich or happy.
Everyone who is either not rich or not quiet is both not wise and not tall.
If mary is both not patient and not kind then susan is either not kind or not curious and vice versa.
Someone is tall or not wise.
Someone is not kind or not happy.
Someone is both patient and quiet.
Someone is both not patient and not quiet.
Someone is either calm or curious.
Someone is either kind or humble.
Fred is tall.
Someone is not rich or not patient. | John is not kind. | neutral | (![X]:((kind(X)|old(X))<=>(~brave(X)|~strong(X))))&
(((funny(john)<~>~patient(john)))=>((~quiet(mary)&~tall(mary))))&
((?[X]:((~wise(X)<~>old(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~tall(X)=>(~brave(X)&~patient(X))))&
(![X]:(~humble(X)=>(~quiet(X)<~>brave(X))))&
(![X]:(quiet(X)<=>(funny(X)&~kind(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~strong(X)&creative(X)))))&
(![X]:((patient(X)&~strong(X))<=>(~kind(X)|creative(X))))&
(![X]:(~funny(X)=>(brave(X)<~>old(X))))&
((?[X]:((old(X)<~>~kind(X))))<=>((tall(john)&calm(john))))&
(![X]:((brave(X)|wise(X))<=>(~funny(X)&strong(X))))&
(![X]:((creative(X)<~>~generous(X))=>rich(X)))&
((?[X]:((strong(X)&~brave(X))))=>(?[X]:((~wise(X)<~>old(X)))))&
(((wise(mary)<~>brave(mary)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~rich(X)<~>~quiet(X))=>(~wise(X)&~tall(X))))&
(((~patient(mary)&~kind(mary)))<=>((~kind(susan)<~>~curious(susan))))&
(?[X]:((tall(X)|~wise(X))))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:((patient(X)&quiet(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:((kind(X)<~>humble(X))))&
(tall(fred))&
(?[X]:((~rich(X)|~patient(X)))) | ~kind(john) | [] | null | 0 |
If someone is either not kind or tall then lucy is either wise or brave and vice versa. If someone is not brave then paul is either generous or not patient. Everyone who is both not tall and funny is both not creative and tall and vice versa. If fred is patient then paul is both generous and not calm and vice versa. If someone is calm or not strong then john is either not generous or not brave and vice versa. Everyone who is either strong or generous is both funny and not curious. Everyone who is both generous and humble is not curious or tall and vice versa. Everyone who is both strong and not happy is not quiet or humble. If someone is not kind or creative then john is wise and vice versa. If someone is humble or kind then lucy is both not humble and not wise. Everyone who is calm or humble is either not strong or generous. Everyone who is not quiet is both not happy and not wise and vice versa. Everyone who is tall is both not humble and not patient. Everyone who is either strong or calm is not kind or patient. If someone is both old and calm then someone is not funny. Everyone who is generous is either generous or old and vice versa. Mary is both rich and not curious. Someone is not strong. Someone is both not happy and patient. John is not kind. Paul is old or not humble. Paul is not kind or not tall. Alice is strong. Mary is both calm and wise. | Lucy is not wise. | entailment | ((?[X]:((~kind(X)<~>tall(X))))<=>((wise(lucy)<~>brave(lucy))))&
((?[X]:(~brave(X)))=>((generous(paul)<~>~patient(paul))))&
(![X]:((~tall(X)&funny(X))<=>(~creative(X)&tall(X))))&
((patient(fred))<=>((generous(paul)&~calm(paul))))&
((?[X]:((calm(X)|~strong(X))))<=>((~generous(john)<~>~brave(john))))&
(![X]:((strong(X)<~>generous(X))=>(funny(X)&~curious(X))))&
(![X]:((generous(X)&humble(X))<=>(~curious(X)|tall(X))))&
(![X]:((strong(X)&~happy(X))=>(~quiet(X)|humble(X))))&
((?[X]:((~kind(X)|creative(X))))<=>(wise(john)))&
((?[X]:((humble(X)|kind(X))))=>((~humble(lucy)&~wise(lucy))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)<~>generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)&~wise(X))))&
(![X]:(tall(X)=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:(generous(X)<=>(generous(X)<~>old(X))))&
((rich(mary)&~curious(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)&patient(X))))&
(~kind(john))&
((old(paul)|~humble(paul)))&
((~kind(paul)|~tall(paul)))&
(strong(alice))&
((calm(mary)&wise(mary))) | ~wise(lucy) | [
"p6",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8619117819656501437292470
% SZS output start Proof for 8619117819656501437292470
7. ! [X0] : ((humble(X0) & generous(X0)) <=> (tall(X0) | ~curious(X0))) [input p6]
10. ? [X0] : (kind(X0) | humble(X0)) => (~wise(lucy) & ~humble(lucy)) [input p9]
17. ~curious(mary) & rich(mary) [input p16]
25. wise(lucy) [input hypothesis]
28. ~curious(mary) [pure predicate removal 17]
33. (~wise(lucy) & ~humble(lucy)) | ! [X0] : (~kind(X0) & ~humble(X0)) [ennf transformation 10]
54. ! [X0] : (((humble(X0) & generous(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 7]
55. ! [X0] : (((humble(X0) & generous(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | ~humble(X0) | ~generous(X0))) [flattening 54]
100. humble(X0) | curious(X0) [cnf transformation 55]
108. ~wise(lucy) | ~humble(X0) [cnf transformation 33]
125. ~curious(mary) [cnf transformation 28]
135. wise(lucy) [cnf transformation 25]
145. 2 <=> wise(lucy) [avatar definition]
248. 24 <=> ! [X0] : ~humble(X0) [avatar definition]
249. ~humble(X0) <- (24) [avatar component clause 248]
250. 24 | ~2 [avatar split clause 108,145,248]
268. 2 [avatar split clause 135,145]
270. curious(X0) <- (24) [resolution 100,249]
272. $false <- (24) [resolution 270,125]
273. ~24 [avatar contradiction clause 272]
274. $false [avatar sat refutation 250,268,273]
% SZS output end Proof for 8619117819656501437292470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not kind or not strong then someone is generous. Everyone who is not generous or not creative is both not funny and not curious. If someone is both not creative and kind then paul is not happy or not funny. Everyone who is not wise or brave is calm and vice versa. If someone is not generous then susan is both kind and patient. If someone is happy or generous then fred is creative. If mary is either not wise or brave then someone is both not brave and not tall and vice versa. Everyone who is not old or curious is either humble or generous. Everyone who is both not calm and humble is either not wise or calm. If fred is both strong and creative then fred is not curious or humble. If lucy is either not tall or not humble then mary is both happy and not wise and vice versa. Everyone who is either curious or quiet is either wise or calm. If fred is not creative or calm then lucy is both not happy and not strong and vice versa. If fred is both wise and not calm then fred is happy or not patient and vice versa. If paul is either curious or not brave then someone is not creative or rich. Everyone who is either not strong or quiet is both not curious and not humble. Someone is not calm. Someone is not generous. Someone is both tall and generous. Mary is creative or not generous. Someone is both not brave and not humble. Lucy is humble. Fred is wise or not curious. Someone is both not funny and not humble. | Lucy is not calm. | contradiction | (((~kind(alice)<~>~strong(alice)))=>(?[X]:(generous(X))))&
(![X]:((~generous(X)|~creative(X))=>(~funny(X)&~curious(X))))&
((?[X]:((~creative(X)&kind(X))))=>((~happy(paul)|~funny(paul))))&
(![X]:((~wise(X)|brave(X))<=>calm(X)))&
((?[X]:(~generous(X)))=>((kind(susan)&patient(susan))))&
((?[X]:((happy(X)|generous(X))))=>(creative(fred)))&
(((~wise(mary)<~>brave(mary)))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((~old(X)|curious(X))=>(humble(X)<~>generous(X))))&
(![X]:((~calm(X)&humble(X))=>(~wise(X)<~>calm(X))))&
(((strong(fred)&creative(fred)))=>((~curious(fred)|humble(fred))))&
(((~tall(lucy)<~>~humble(lucy)))<=>((happy(mary)&~wise(mary))))&
(![X]:((curious(X)<~>quiet(X))=>(wise(X)<~>calm(X))))&
(((~creative(fred)|calm(fred)))<=>((~happy(lucy)&~strong(lucy))))&
(((wise(fred)&~calm(fred)))<=>((happy(fred)|~patient(fred))))&
(((curious(paul)<~>~brave(paul)))=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>(~curious(X)&~humble(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~generous(X)))&
(?[X]:((tall(X)&generous(X))))&
((creative(mary)|~generous(mary)))&
(?[X]:((~brave(X)&~humble(X))))&
(humble(lucy))&
((wise(fred)|~curious(fred)))&
(?[X]:((~funny(X)&~humble(X)))) | ~calm(lucy) | [
"p3",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2399316986061189031563809
% SZS output start Proof for 2399316986061189031563809
4. ! [X0] : ((brave(X0) | ~wise(X0)) <=> calm(X0)) [input p3]
9. ! [X0] : ((humble(X0) & ~calm(X0)) => (~wise(X0) <~> calm(X0))) [input p8]
22. humble(lucy) [input p21]
25. ~calm(lucy) [input hypothesis]
36. ! [X0] : ((~wise(X0) <~> calm(X0)) | (~humble(X0) | calm(X0))) [ennf transformation 9]
37. ! [X0] : ((~wise(X0) <~> calm(X0)) | ~humble(X0) | calm(X0)) [flattening 36]
45. ! [X0] : (((brave(X0) | ~wise(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 4]
46. ! [X0] : ((brave(X0) | ~wise(X0) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [flattening 45]
52. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~humble(X0) | calm(X0)) [nnf transformation 37]
75. calm(X0) | wise(X0) [cnf transformation 46]
90. calm(X0) | ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 52]
124. humble(lucy) [cnf transformation 22]
127. ~calm(lucy) [cnf transformation 25]
128. calm(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 90]
194. ~humble(X0) | calm(X0) [subsumption resolution 128,75]
215. 19 <=> humble(lucy) [avatar definition]
217. humble(lucy) <- (19) [avatar component clause 215]
268. 19 [avatar split clause 124,215]
275. calm(lucy) <- (19) [resolution 194,217]
276. $false <- (19) [subsumption resolution 275,127]
277. ~19 [avatar contradiction clause 276]
278. $false [avatar sat refutation 268,277]
% SZS output end Proof for 2399316986061189031563809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 not brave. | 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))) | ~brave(lucy) | [
"p1",
"p2",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 521380715350201999270447
% SZS output start Proof for 521380715350201999270447
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]
9. ! [X0] : ((kind(X0) | old(X0)) <=> (creative(X0) & old(X0))) [input p8]
16. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p15]
23. ~brave(lucy) [input hypothesis]
27. ! [X0] : (~generous(X0) | (tall(X0) & ~old(X0))) [ennf transformation 2]
28. ! [X0] : ((brave(X0) & ~creative(X0)) | (patient(X0) <=> ~kind(X0))) [ennf transformation 4]
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]
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]
71. ~old(X0) | ~generous(X0) [cnf transformation 27]
74. ~patient(X0) | kind(X0) [cnf transformation 40]
79. brave(X0) | patient(X0) | kind(X0) [cnf transformation 41]
96. ~kind(X0) | old(X0) [cnf transformation 47]
98. ~kind(X0) | creative(X0) [cnf transformation 47]
129. ~creative(X0) | generous(X0) [cnf transformation 34]
137. ~brave(lucy) [cnf transformation 23]
166. brave(X0) | kind(X0) [subsumption resolution 79,74]
269. 26 <=> brave(lucy) [avatar definition]
270. ~brave(lucy) <- (~26) [avatar component clause 269]
277. ~26 [avatar split clause 137,269]
292. kind(lucy) <- (~26) [resolution 166,270]
295. creative(lucy) <- (~26) [resolution 292,98]
296. old(lucy) <- (~26) [resolution 292,96]
301. generous(lucy) <- (~26) [resolution 295,129]
314. ~generous(lucy) <- (~26) [resolution 296,71]
315. $false <- (~26) [subsumption resolution 314,301]
316. 26 [avatar contradiction clause 315]
317. $false [avatar sat refutation 277,316]
% SZS output end Proof for 521380715350201999270447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both strong and not strong and vice versa. If someone is calm or old then paul is not generous and vice versa. Everyone who is generous or creative is both curious and not kind. Everyone who is old is both not calm and not humble. Everyone who is tall or brave is happy or old. Everyone who is either not creative or not funny is not patient. Everyone who is either brave or not quiet is both not brave and strong. Everyone who is not brave is either wise or not old and vice versa. Everyone who is both not humble and not patient is either not wise or not funny and vice versa. If susan is not strong then someone is humble or not rich. Everyone who is not quiet is not brave or not curious and vice versa. If paul is either kind or not tall then mary is either not brave or tall and vice versa. Everyone who is tall is curious or old. Everyone who is not humble is either humble or happy and vice versa. If paul is curious or not strong then someone is not quiet and vice versa. If lucy is either not tall or not curious then fred is either not humble or not old. Lucy is not generous. Someone is generous. Paul is both not kind and not quiet. Fred is wise. Lucy is not brave. Someone is creative. Someone is funny. | Lucy is not patient. | entailment | ((?[X]:(patient(X)))<=>(?[X]:((strong(X)&~strong(X)))))&
((?[X]:((calm(X)|old(X))))<=>(~generous(paul)))&
(![X]:((generous(X)|creative(X))=>(curious(X)&~kind(X))))&
(![X]:(old(X)=>(~calm(X)&~humble(X))))&
(![X]:((tall(X)|brave(X))=>(happy(X)|old(X))))&
(![X]:((~creative(X)<~>~funny(X))=>~patient(X)))&
(![X]:((brave(X)<~>~quiet(X))=>(~brave(X)&strong(X))))&
(![X]:(~brave(X)<=>(wise(X)<~>~old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~wise(X)<~>~funny(X))))&
((~strong(susan))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~brave(X)|~curious(X))))&
(((kind(paul)<~>~tall(paul)))<=>((~brave(mary)<~>tall(mary))))&
(![X]:(tall(X)=>(curious(X)|old(X))))&
(![X]:(~humble(X)<=>(humble(X)<~>happy(X))))&
(((curious(paul)|~strong(paul)))<=>(?[X]:(~quiet(X))))&
(((~tall(lucy)<~>~curious(lucy)))=>((~humble(fred)<~>~old(fred))))&
(~generous(lucy))&
(?[X]:(generous(X)))&
((~kind(paul)&~quiet(paul)))&
(wise(fred))&
(~brave(lucy))&
(?[X]:(creative(X)))&
(?[X]:(funny(X))) | ~patient(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 312969292157157456238611
% SZS output start Proof for 312969292157157456238611
1. ? [X0] : patient(X0) <=> ? [X0] : (~strong(X0) & strong(X0)) [input p0]
24. patient(lucy) [input hypothesis]
25. ? [X0] : patient(X0) <=> ? [X1] : (~strong(X1) & strong(X1)) [rectify 1]
36. (? [X0] : patient(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ~patient(X0)) [nnf transformation 25]
37. (? [X0] : patient(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X2] : (~strong(X2) & strong(X2)) | ! [X3] : ~patient(X3)) [rectify 36]
38. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
39. ? [X2] : (~strong(X2) & strong(X2)) => (~strong(sK1) & strong(sK1)) [choice axiom]
40. (patient(sK0) | ! [X1] : (strong(X1) | ~strong(X1))) & ((~strong(sK1) & strong(sK1)) | ! [X3] : ~patient(X3)) [skolemisation 37,39,38]
66. strong(sK1) | ~patient(X3) [cnf transformation 40]
67. ~strong(sK1) | ~patient(X3) [cnf transformation 40]
127. patient(lucy) [cnf transformation 24]
132. 1 <=> ! [X3] : ~patient(X3) [avatar definition]
133. ~patient(X3) <- (1) [avatar component clause 132]
135. 2 <=> strong(sK1) [avatar definition]
138. 1 | ~2 [avatar split clause 67,135,132]
139. 1 | 2 [avatar split clause 66,135,132]
217. $false <- (1) [resolution 133,127]
218. ~1 [avatar contradiction clause 217]
219. $false [avatar sat refutation 138,139,218]
% SZS output end Proof for 312969292157157456238611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old is not quiet and vice versa.
If susan is not quiet then mary is either creative or not strong and vice versa.
Everyone who is not old is patient.
If alice is either old or not patient then someone is not strong and vice versa.
If someone is either not patient or not rich then someone is not rich and vice versa.
Everyone who is either not quiet or not funny is both not creative and humble.
Everyone who is either tall or calm is not wise or not funny.
Everyone who is both not funny and kind is not quiet.
Everyone who is kind or patient is both happy and not humble.
Everyone who is patient or not strong is not tall or quiet and vice versa.
Everyone who is either not happy or not old is both happy and not strong and vice versa.
If alice is either calm or creative then someone is not creative and vice versa.
Everyone who is not kind or rich is both old and not creative.
If paul is both calm and not patient then someone is both curious and not rich and vice versa.
Everyone who is either not wise or not humble is rich and vice versa.
Fred is either old or not kind.
Fred is not generous or brave.
Someone is both wise and strong.
John is not calm or patient.
John is calm or old.
Someone is rich or not humble. | Alice is old. | entailment | (![X]:((happy(X)<~>~old(X))<=>~quiet(X)))&
((~quiet(susan))<=>((creative(mary)<~>~strong(mary))))&
(![X]:(~old(X)=>patient(X)))&
(((old(alice)<~>~patient(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~creative(X)&humble(X))))&
(![X]:((tall(X)<~>calm(X))=>(~wise(X)|~funny(X))))&
(![X]:((~funny(X)&kind(X))=>~quiet(X)))&
(![X]:((kind(X)|patient(X))=>(happy(X)&~humble(X))))&
(![X]:((patient(X)|~strong(X))<=>(~tall(X)|quiet(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(happy(X)&~strong(X))))&
(((calm(alice)<~>creative(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)|rich(X))=>(old(X)&~creative(X))))&
(((calm(paul)&~patient(paul)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((~wise(X)<~>~humble(X))<=>rich(X)))&
((old(fred)<~>~kind(fred)))&
((~generous(fred)|brave(fred)))&
(?[X]:((wise(X)&strong(X))))&
((~calm(john)|patient(john)))&
((calm(john)|old(john)))&
(?[X]:((rich(X)|~humble(X)))) | old(alice) | [
"p2",
"p3",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 792187614063198738876792
% SZS output start Proof for 792187614063198738876792
3. ! [X0] : (~old(X0) => patient(X0)) [input p2]
4. (old(alice) <~> ~patient(alice)) <=> ? [X0] : ~strong(X0) [input p3]
9. ! [X0] : ((patient(X0) | kind(X0)) => (~humble(X0) & happy(X0))) [input p8]
11. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> (~strong(X0) & happy(X0))) [input p10]
22. ~old(alice) [input hypothesis]
25. ! [X0] : (patient(X0) | old(X0)) [ennf transformation 3]
31. ! [X0] : ((~humble(X0) & happy(X0)) | (~patient(X0) & ~kind(X0))) [ennf transformation 9]
35. (((patient(alice) | ~old(alice)) & (~patient(alice) | old(alice))) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ((old(alice) | patient(alice)) & (~patient(alice) | ~old(alice)))) [nnf transformation 4]
36. (((patient(alice) | ~old(alice)) & (~patient(alice) | old(alice))) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ((old(alice) | patient(alice)) & (~patient(alice) | ~old(alice)))) [rectify 35]
37. ? [X1] : ~strong(X1) => ~strong(sK0) [choice axiom]
38. (((patient(alice) | ~old(alice)) & (~patient(alice) | old(alice))) | ! [X0] : strong(X0)) & (~strong(sK0) | ((old(alice) | patient(alice)) & (~patient(alice) | ~old(alice)))) [skolemisation 36,37]
48. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 11]
49. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [flattening 48]
73. patient(X0) | old(X0) [cnf transformation 25]
76. ~patient(alice) | old(alice) | strong(X0) [cnf transformation 38]
90. ~patient(X0) | happy(X0) [cnf transformation 31]
97. happy(X0) | ~old(X0) | happy(X0) [cnf transformation 49]
100. ~strong(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
126. ~old(alice) [cnf transformation 22]
127. ~old(X0) | happy(X0) [duplicate literal removal 97]
147. 4 <=> ! [X0] : strong(X0) [avatar definition]
148. strong(X0) <- (4) [avatar component clause 147]
154. old(alice) | strong(X0) [subsumption resolution 76,73]
156. 6 <=> old(alice) [avatar definition]
157. ~old(alice) <- (~6) [avatar component clause 156]
159. 4 | 6 [avatar split clause 154,156,147]
257. ~6 [avatar split clause 126,156]
267. happy(X0) | old(X0) [resolution 90,73]
268. happy(X0) [subsumption resolution 267,127]
351. ~happy(X0) | old(X0) <- (4) [resolution 100,148]
352. old(X0) <- (4) [subsumption resolution 351,268]
353. $false <- (4, ~6) [resolution 352,157]
356. ~4 | 6 [avatar contradiction clause 353]
357. $false [avatar sat refutation 159,257,356]
% SZS output end Proof for 792187614063198738876792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or curious is calm or creative.
Everyone who is both not tall and old is either funny or not calm and vice versa.
Everyone who is either not quiet or not calm is patient and vice versa.
Everyone who is both generous and not curious is not curious or patient and vice versa.
Everyone who is not tall or creative is either not funny or kind and vice versa.
If someone is not rich then paul is both creative and quiet and vice versa.
If someone is brave or old then lucy is quiet or not happy and vice versa.
Everyone who is both not humble and humble is wise or not funny.
Everyone who is not wise or happy is both not calm and humble and vice versa.
Everyone who is quiet or creative is generous.
Everyone who is both not happy and quiet is creative and vice versa.
Everyone who is happy is not humble or not funny and vice versa.
Everyone who is not old is either wise or not humble and vice versa.
If someone is curious then mary is not patient.
If lucy is not creative then someone is not brave and vice versa.
If someone is either strong or rich then mary is not tall or not curious.
Paul is not curious or brave.
Mary is not creative or calm.
Mary is not creative or old.
Susan is brave or not kind.
John is not quiet or tall.
Someone is rich.
Someone is either not wise or rich. | Paul is not kind. | contradiction | (![X]:((old(X)<~>curious(X))=>(calm(X)|creative(X))))&
(![X]:((~tall(X)&old(X))<=>(funny(X)<~>~calm(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>patient(X)))&
(![X]:((generous(X)&~curious(X))<=>(~curious(X)|patient(X))))&
(![X]:((~tall(X)|creative(X))<=>(~funny(X)<~>kind(X))))&
((?[X]:(~rich(X)))<=>((creative(paul)&quiet(paul))))&
((?[X]:((brave(X)|old(X))))<=>((quiet(lucy)|~happy(lucy))))&
(![X]:((~humble(X)&humble(X))=>(wise(X)|~funny(X))))&
(![X]:((~wise(X)|happy(X))<=>(~calm(X)&humble(X))))&
(![X]:((quiet(X)|creative(X))=>generous(X)))&
(![X]:((~happy(X)&quiet(X))<=>creative(X)))&
(![X]:(happy(X)<=>(~humble(X)|~funny(X))))&
(![X]:(~old(X)<=>(wise(X)<~>~humble(X))))&
((?[X]:(curious(X)))=>(~patient(mary)))&
((~creative(lucy))<=>(?[X]:(~brave(X))))&
((?[X]:((strong(X)<~>rich(X))))=>((~tall(mary)|~curious(mary))))&
((~curious(paul)|brave(paul)))&
((~creative(mary)|calm(mary)))&
((~creative(mary)|old(mary)))&
((brave(susan)|~kind(susan)))&
((~quiet(john)|tall(john)))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>rich(X)))) | ~kind(paul) | [
"p1",
"p4",
"p5",
"p8",
"p10",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3499779383985649039144107
% SZS output start Proof for 3499779383985649039144107
2. ! [X0] : ((old(X0) & ~tall(X0)) <=> (funny(X0) <~> ~calm(X0))) [input p1]
5. ! [X0] : ((creative(X0) | ~tall(X0)) <=> (~funny(X0) <~> kind(X0))) [input p4]
6. ? [X0] : ~rich(X0) <=> (quiet(paul) & creative(paul)) [input p5]
9. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (humble(X0) & ~calm(X0))) [input p8]
11. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : (happy(X0) <=> (~funny(X0) | ~humble(X0))) [input p11]
13. ! [X0] : (~old(X0) <=> (wise(X0) <~> ~humble(X0))) [input p12]
23. ? [X0] : (~wise(X0) <~> rich(X0)) [input p22]
24. ~kind(paul) [input hypothesis]
34. ! [X0] : (((old(X0) & ~tall(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) & (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | (~old(X0) | tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((old(X0) & ~tall(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) & (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ~old(X0) | tall(X0))) [flattening 34]
39. ! [X0] : (((creative(X0) | ~tall(X0)) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) & (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (~creative(X0) & tall(X0)))) [nnf transformation 5]
40. ! [X0] : ((creative(X0) | ~tall(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) & (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (~creative(X0) & tall(X0)))) [flattening 39]
41. (? [X0] : ~rich(X0) | (~quiet(paul) | ~creative(paul))) & ((quiet(paul) & creative(paul)) | ! [X0] : rich(X0)) [nnf transformation 6]
42. (? [X0] : ~rich(X0) | ~quiet(paul) | ~creative(paul)) & ((quiet(paul) & creative(paul)) | ! [X0] : rich(X0)) [flattening 41]
43. (? [X0] : ~rich(X0) | ~quiet(paul) | ~creative(paul)) & ((quiet(paul) & creative(paul)) | ! [X1] : rich(X1)) [rectify 42]
44. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
45. (~rich(sK0) | ~quiet(paul) | ~creative(paul)) & ((quiet(paul) & creative(paul)) | ! [X1] : rich(X1)) [skolemisation 43,44]
51. ! [X0] : (((happy(X0) | ~wise(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~happy(X0) & wise(X0)))) [nnf transformation 9]
52. ! [X0] : ((happy(X0) | ~wise(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~happy(X0) & wise(X0)))) [flattening 51]
53. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~creative(X0)) & (creative(X0) | (~quiet(X0) | happy(X0)))) [nnf transformation 11]
54. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~creative(X0)) & (creative(X0) | ~quiet(X0) | happy(X0))) [flattening 53]
55. ! [X0] : ((happy(X0) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | ~happy(X0))) [nnf transformation 12]
56. ! [X0] : ((happy(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | ~happy(X0))) [flattening 55]
57. ! [X0] : ((~old(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | old(X0))) [nnf transformation 13]
65. ? [X0] : ((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) [nnf transformation 23]
66. ? [X0] : ((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) => ((~rich(sK4) | wise(sK4)) & (rich(sK4) | ~wise(sK4))) [choice axiom]
67. (~rich(sK4) | wise(sK4)) & (rich(sK4) | ~wise(sK4)) [skolemisation 65,66]
74. ~funny(X0) | ~calm(X0) | old(X0) [cnf transformation 35]
75. funny(X0) | old(X0) | calm(X0) [cnf transformation 35]
86. ~funny(X0) | kind(X0) | ~creative(X0) [cnf transformation 40]
91. creative(paul) | rich(X1) [cnf transformation 45]
100. ~happy(X0) | ~calm(X0) [cnf transformation 52]
102. ~happy(X0) | humble(X0) [cnf transformation 52]
103. ~wise(X0) | happy(X0) | ~humble(X0) | calm(X0) [cnf transformation 52]
107. ~happy(X0) | ~creative(X0) [cnf transformation 54]
109. ~funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 56]
110. happy(X0) | humble(X0) [cnf transformation 56]
111. happy(X0) | funny(X0) [cnf transformation 56]
114. ~old(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 57]
128. ~rich(sK4) | wise(sK4) [cnf transformation 67]
129. ~kind(paul) [cnf transformation 24]
131. 1 <=> creative(paul) [avatar definition]
132. creative(paul) <- (1) [avatar component clause 131]
144. 4 <=> ! [X1] : rich(X1) [avatar definition]
145. rich(X1) <- (4) [avatar component clause 144]
147. 4 | 1 [avatar split clause 91,131,144]
174. humble(X0) [subsumption resolution 110,102]
175. ~happy(X0) | ~funny(X0) [subsumption resolution 109,174]
176. ~wise(X0) | ~old(X0) [subsumption resolution 114,174]
257. 29 <=> wise(sK4) [avatar definition]
259. wise(sK4) <- (29) [avatar component clause 257]
261. 30 <=> rich(sK4) [avatar definition]
263. ~rich(sK4) <- (~30) [avatar component clause 261]
264. 29 | ~30 [avatar split clause 128,261,257]
268. $false <- (4, ~30) [resolution 263,145]
269. ~4 | 30 [avatar contradiction clause 268]
271. ~creative(X0) | funny(X0) [resolution 111,107]
273. ~calm(X2) | funny(X2) [resolution 111,100]
316. 34 <=> calm(sK4) [avatar definition]
318. calm(sK4) <- (34) [avatar component clause 316]
320. 35 <=> happy(sK4) [avatar definition]
322. happy(sK4) <- (35) [avatar component clause 320]
341. happy(sK4) | ~humble(sK4) | calm(sK4) <- (29) [resolution 259,103]
356. happy(sK4) | calm(sK4) <- (29) [subsumption resolution 341,174]
357. 34 | 35 | ~29 [avatar split clause 356,257,320,316]
358. ~funny(sK4) <- (35) [resolution 322,175]
362. old(sK4) | calm(sK4) <- (35) [resolution 358,75]
367. funny(paul) <- (1) [resolution 132,271]
421. kind(paul) | ~creative(paul) <- (1) [resolution 367,86]
425. ~creative(paul) <- (1) [subsumption resolution 421,129]
426. $false <- (1) [subsumption resolution 425,132]
427. ~1 [avatar contradiction clause 426]
439. 45 <=> old(sK4) [avatar definition]
440. ~old(sK4) <- (~45) [avatar component clause 439]
442. 34 | 45 | ~35 [avatar split clause 362,320,439,316]
445. ~old(sK4) <- (29) [resolution 259,176]
446. ~45 | ~29 [avatar split clause 445,257,439]
449. funny(sK4) <- (34) [resolution 318,273]
501. ~calm(sK4) | old(sK4) <- (34) [resolution 449,74]
504. old(sK4) <- (34) [subsumption resolution 501,318]
505. $false <- (34, ~45) [subsumption resolution 504,440]
506. ~34 | 45 [avatar contradiction clause 505]
508. $false [avatar sat refutation 147,264,269,357,427,442,446,506]
% SZS output end Proof for 3499779383985649039144107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is patient then john is kind or not patient.
If alice is patient then susan is not funny or quiet and vice versa.
Everyone who is humble or not curious is either not generous or not wise and vice versa.
If someone is both wise and not brave then lucy is patient or rich.
Everyone who is not quiet is either calm or not calm.
If susan is not rich then lucy is not calm or not patient.
Everyone who is not kind or not rich is not strong or tall and vice versa.
Everyone who is both not curious and wise is both curious and not tall and vice versa.
If alice is brave then susan is either happy or not rich and vice versa.
Everyone who is curious or not old is not generous or not tall and vice versa.
Everyone who is both brave and not happy is either not happy or not wise and vice versa.
If someone is either rich or not patient then john is both not tall and happy.
If someone is either not quiet or wise then susan is old and vice versa.
Everyone who is not wise or not old is both not brave and wise and vice versa.
Everyone who is not humble is both calm and not creative and vice versa.
If susan is rich or not patient then mary is not humble or not wise and vice versa.
Mary is both humble and wise.
Mary is either calm or not humble.
Lucy is either calm or not quiet.
Susan is both not brave and patient.
Someone is brave or generous.
Someone is both not kind and calm. | Mary is not quiet. | entailment | ((patient(paul))=>((kind(john)|~patient(john))))&
((patient(alice))<=>((~funny(susan)|quiet(susan))))&
(![X]:((humble(X)|~curious(X))<=>(~generous(X)<~>~wise(X))))&
((?[X]:((wise(X)&~brave(X))))=>((patient(lucy)|rich(lucy))))&
(![X]:(~quiet(X)=>(calm(X)<~>~calm(X))))&
((~rich(susan))=>((~calm(lucy)|~patient(lucy))))&
(![X]:((~kind(X)|~rich(X))<=>(~strong(X)|tall(X))))&
(![X]:((~curious(X)&wise(X))<=>(curious(X)&~tall(X))))&
((brave(alice))<=>((happy(susan)<~>~rich(susan))))&
(![X]:((curious(X)|~old(X))<=>(~generous(X)|~tall(X))))&
(![X]:((brave(X)&~happy(X))<=>(~happy(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~patient(X))))=>((~tall(john)&happy(john))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(old(susan)))&
(![X]:((~wise(X)|~old(X))<=>(~brave(X)&wise(X))))&
(![X]:(~humble(X)<=>(calm(X)&~creative(X))))&
(((rich(susan)|~patient(susan)))<=>((~humble(mary)|~wise(mary))))&
((humble(mary)&wise(mary)))&
((calm(mary)<~>~humble(mary)))&
((calm(lucy)<~>~quiet(lucy)))&
((~brave(susan)&patient(susan)))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((~kind(X)&calm(X)))) | ~quiet(mary) | [
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5079296833495927944898740
% SZS output start Proof for 5079296833495927944898740
13. ? [X0] : (~quiet(X0) <~> wise(X0)) <=> old(susan) [input p12]
14. ! [X0] : ((~old(X0) | ~wise(X0)) <=> (wise(X0) & ~brave(X0))) [input p13]
20. patient(susan) & ~brave(susan) [input p19]
23. quiet(mary) [input hypothesis]
47. (? [X0] : ((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~old(susan)) & (old(susan) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) [nnf transformation 13]
48. (? [X0] : ((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~old(susan)) & (old(susan) | ! [X1] : ((~quiet(X1) | ~wise(X1)) & (wise(X1) | quiet(X1)))) [rectify 47]
49. ? [X0] : ((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) => ((~wise(sK0) | quiet(sK0)) & (wise(sK0) | ~quiet(sK0))) [choice axiom]
50. (((~wise(sK0) | quiet(sK0)) & (wise(sK0) | ~quiet(sK0))) | ~old(susan)) & (old(susan) | ! [X1] : ((~quiet(X1) | ~wise(X1)) & (wise(X1) | quiet(X1)))) [skolemisation 48,49]
51. ! [X0] : (((~old(X0) | ~wise(X0)) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | (old(X0) & wise(X0)))) [nnf transformation 14]
52. ! [X0] : ((~old(X0) | ~wise(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | (old(X0) & wise(X0)))) [flattening 51]
104. old(susan) | ~quiet(X1) | ~wise(X1) [cnf transformation 50]
109. wise(X0) | wise(X0) [cnf transformation 52]
111. ~old(X0) | ~wise(X0) | ~wise(X0) | brave(X0) [cnf transformation 52]
125. ~brave(susan) [cnf transformation 20]
130. quiet(mary) [cnf transformation 23]
131. wise(X0) [duplicate literal removal 109]
132. ~old(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 111]
220. 18 <=> old(susan) [avatar definition]
221. old(susan) <- (18) [avatar component clause 220]
234. 21 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
235. ~quiet(X1) | ~wise(X1) <- (21) [avatar component clause 234]
236. 21 | 18 [avatar split clause 104,220,234]
329. ~wise(susan) | brave(susan) <- (18) [resolution 132,221]
332. brave(susan) <- (18) [subsumption resolution 329,131]
333. $false <- (18) [subsumption resolution 332,125]
334. ~18 [avatar contradiction clause 333]
335. ~quiet(X1) <- (21) [subsumption resolution 235,131]
337. $false <- (21) [resolution 335,130]
340. ~21 [avatar contradiction clause 337]
341. $false [avatar sat refutation 236,334,340]
% SZS output end Proof for 5079296833495927944898740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and calm then paul is both not wise and not rich and vice versa.
Everyone who is both not wise and generous is brave or not funny and vice versa.
Everyone who is not tall is quiet or not happy and vice versa.
If paul is rich then mary is both wise and not kind.
Everyone who is not happy is generous and vice versa.
If someone is not strong or not brave then someone is both curious and not calm and vice versa.
Everyone who is either not brave or kind is either wise or old and vice versa.
If someone is calm then lucy is both quiet and creative.
Everyone who is either not old or humble is both quiet and curious.
Everyone who is curious is wise or not happy.
Everyone who is quiet or not patient is both old and strong.
Everyone who is rich is either tall or not curious and vice versa.
Everyone who is not humble is kind.
Everyone who is creative or rich is quiet and vice versa.
Everyone who is both old and not brave is not wise or brave and vice versa.
If someone is either funny or strong then john is either not rich or not kind and vice versa.
Fred is either patient or not tall.
Someone is funny or not generous.
Someone is either kind or happy.
Someone is both strong and not happy. | Paul is not happy. | neutral | ((?[X]:((~strong(X)&calm(X))))<=>((~wise(paul)&~rich(paul))))&
(![X]:((~wise(X)&generous(X))<=>(brave(X)|~funny(X))))&
(![X]:(~tall(X)<=>(quiet(X)|~happy(X))))&
((rich(paul))=>((wise(mary)&~kind(mary))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((strong(X)&~happy(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is happy or not rich is not wise.
If john is both creative and not strong then mary is both not kind and quiet.
Everyone who is rich or quiet is both creative and happy and vice versa.
Everyone who is both happy and not creative is both not kind and not wise and vice versa.
If someone is either humble or not happy then someone is not generous and vice versa.
Everyone who is both creative and patient is not humble or not curious.
If alice is not old or curious then someone is not tall and vice versa.
If alice is patient then mary is not happy and vice versa.
Everyone who is wise is not patient or not funny.
Everyone who is generous or not brave is not calm or not creative and vice versa.
If susan is funny or not old then someone is both tall and not kind and vice versa.
If paul is either not humble or not generous then someone is creative and vice versa.
If mary is not wise or not happy then someone is not happy or happy and vice versa.
Everyone who is both not calm and not quiet is either strong or wise and vice versa.
Fred is funny.
Someone is not brave.
Someone is either quiet or not generous.
Susan is quiet or not patient.
Lucy is wise or quiet.
Someone is both brave and quiet. | Lucy is kind. | entailment | (![X]:((happy(X)|~rich(X))=>~wise(X)))&
(((creative(john)&~strong(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((rich(X)|quiet(X))<=>(creative(X)&happy(X))))&
(![X]:((happy(X)&~creative(X))<=>(~kind(X)&~wise(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)&patient(X))=>(~humble(X)|~curious(X))))&
(((~old(alice)|curious(alice)))<=>(?[X]:(~tall(X))))&
((patient(alice))<=>(~happy(mary)))&
(![X]:(wise(X)=>(~patient(X)|~funny(X))))&
(![X]:((generous(X)|~brave(X))<=>(~calm(X)|~creative(X))))&
(((funny(susan)|~old(susan)))<=>(?[X]:((tall(X)&~kind(X)))))&
(((~humble(paul)<~>~generous(paul)))<=>(?[X]:(creative(X))))&
(((~wise(mary)|~happy(mary)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(strong(X)<~>wise(X))))&
(funny(fred))&
(?[X]:(~brave(X)))&
(?[X]:((quiet(X)<~>~generous(X))))&
((quiet(susan)|~patient(susan)))&
((wise(lucy)|quiet(lucy)))&
(?[X]:((brave(X)&quiet(X)))) | kind(lucy) | [
"p0",
"p2",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2039403496793492911842223
% SZS output start Proof for 2039403496793492911842223
1. ! [X0] : ((~rich(X0) | happy(X0)) => ~wise(X0)) [input p0]
3. ! [X0] : ((quiet(X0) | rich(X0)) <=> (happy(X0) & creative(X0))) [input p2]
4. ! [X0] : ((~creative(X0) & happy(X0)) <=> (~wise(X0) & ~kind(X0))) [input p3]
19. quiet(lucy) | wise(lucy) [input p18]
21. ~kind(lucy) [input hypothesis]
23. ! [X0] : (~wise(X0) | (rich(X0) & ~happy(X0))) [ennf transformation 1]
30. ! [X0] : (((quiet(X0) | rich(X0)) | (~happy(X0) | ~creative(X0))) & ((happy(X0) & creative(X0)) | (~quiet(X0) & ~rich(X0)))) [nnf transformation 3]
31. ! [X0] : ((quiet(X0) | rich(X0) | ~happy(X0) | ~creative(X0)) & ((happy(X0) & creative(X0)) | (~quiet(X0) & ~rich(X0)))) [flattening 30]
32. ! [X0] : (((~creative(X0) & happy(X0)) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 4]
33. ! [X0] : (((~creative(X0) & happy(X0)) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | creative(X0) | ~happy(X0))) [flattening 32]
70. ~wise(X0) | ~happy(X0) [cnf transformation 23]
71. ~wise(X0) | rich(X0) [cnf transformation 23]
75. ~quiet(X0) | creative(X0) [cnf transformation 31]
76. ~rich(X0) | happy(X0) [cnf transformation 31]
82. ~creative(X0) | wise(X0) | kind(X0) [cnf transformation 33]
122. quiet(lucy) | wise(lucy) [cnf transformation 19]
125. ~kind(lucy) [cnf transformation 21]
260. 30 <=> wise(lucy) [avatar definition]
261. ~wise(lucy) <- (~30) [avatar component clause 260]
262. wise(lucy) <- (30) [avatar component clause 260]
264. 31 <=> quiet(lucy) [avatar definition]
266. quiet(lucy) <- (31) [avatar component clause 264]
267. 30 | 31 [avatar split clause 122,264,260]
268. ~happy(lucy) <- (30) [resolution 70,262]
269. rich(lucy) <- (30) [resolution 71,262]
274. happy(lucy) <- (30) [resolution 76,269]
275. $false <- (30) [subsumption resolution 274,268]
276. ~30 [avatar contradiction clause 275]
277. creative(lucy) <- (31) [resolution 266,75]
284. wise(lucy) | kind(lucy) <- (31) [resolution 82,277]
303. kind(lucy) <- (~30, 31) [subsumption resolution 284,261]
304. $false <- (~30, 31) [subsumption resolution 303,125]
305. 30 | ~31 [avatar contradiction clause 304]
306. $false [avatar sat refutation 267,276,305]
% SZS output end Proof for 2039403496793492911842223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then lucy is both not creative and not brave and vice versa.
Everyone who is both not humble and old is strong.
If someone is funny or not tall then someone is both not happy and not rich and vice versa.
If someone is both not calm and curious then john is both not rich and not curious.
If someone is kind or curious then lucy is either not kind or not generous and vice versa.
Everyone who is not creative is not tall and vice versa.
Everyone who is either not tall or brave is not calm or not generous.
If fred is both wise and kind then someone is both creative and not funny and vice versa.
Everyone who is not quiet is not strong or strong.
If someone is both not strong and generous then someone is both wise and not old.
If lucy is both not quiet and not rich then fred is not funny and vice versa.
Everyone who is patient or not generous is both not humble and not curious.
If mary is both not strong and creative then fred is happy.
Everyone who is either not curious or happy is both generous and not strong and vice versa.
Everyone who is happy or not calm is both not tall and not brave.
If someone is not creative then someone is calm.
John is brave.
Someone is either generous or not generous.
Someone is patient or humble.
Alice is either funny or tall.
Someone is not old.
Fred is not patient or patient.
Someone is both rich and kind.
Someone is either not strong or not creative. | Fred is humble. | neutral | ((?[X]:(~kind(X)))<=>((~creative(lucy)&~brave(lucy))))&
(![X]:((~humble(X)&old(X))=>strong(X)))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((~happy(X)&~rich(X)))))&
((?[X]:((~calm(X)&curious(X))))=>((~rich(john)&~curious(john))))&
((?[X]:((kind(X)|curious(X))))<=>((~kind(lucy)<~>~generous(lucy))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~tall(X)<~>brave(X))=>(~calm(X)|~generous(X))))&
(((wise(fred)&kind(fred)))<=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:(~quiet(X)=>(~strong(X)|strong(X))))&
((?[X]:((~strong(X)&generous(X))))=>(?[X]:((wise(X)&~old(X)))))&
(((~quiet(lucy)&~rich(lucy)))<=>(~funny(fred)))&
(![X]:((patient(X)|~generous(X))=>(~humble(X)&~curious(X))))&
(((~strong(mary)&creative(mary)))=>(happy(fred)))&
(![X]:((~curious(X)<~>happy(X))<=>(generous(X)&~strong(X))))&
(![X]:((happy(X)|~calm(X))=>(~tall(X)&~brave(X))))&
((?[X]:(~creative(X)))=>(?[X]:(calm(X))))&
(brave(john))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((patient(X)|humble(X))))&
((funny(alice)<~>tall(alice)))&
(?[X]:(~old(X)))&
((~patient(fred)|patient(fred)))&
(?[X]:((rich(X)&kind(X))))&
(?[X]:((~strong(X)<~>~creative(X)))) | humble(fred) | [] | null | 0 |
Everyone who is patient or not tall is both kind and calm. If someone is not funny or not calm then susan is both curious and kind. Everyone who is both not humble and creative is happy. Everyone who is creative or not calm is old. If susan is curious or kind then someone is not old or happy and vice versa. If paul is brave then mary is either happy or not quiet and vice versa. If someone is not old then someone is both not funny and not patient and vice versa. Everyone who is either not happy or not creative is either creative or quiet and vice versa. Everyone who is creative or old is both not calm and patient. Everyone who is both not happy and not old is not funny and vice versa. Everyone who is either not tall or happy is either patient or not curious and vice versa. If someone is not generous or not humble then lucy is not patient or not rich. If fred is either kind or not quiet then someone is either curious or rich. Everyone who is not rich or wise is either calm or not happy and vice versa. If someone is creative or not patient then paul is not patient. Someone is both funny and generous. Lucy is not creative. Mary is rich or wise. Lucy is both not strong and not happy. Mary is happy. Someone is both not creative and humble. | Susan is not patient. | neutral | (![X]:((patient(X)|~tall(X))=>(kind(X)&calm(X))))&
((?[X]:((~funny(X)|~calm(X))))=>((curious(susan)&kind(susan))))&
(![X]:((~humble(X)&creative(X))=>happy(X)))&
(![X]:((creative(X)|~calm(X))=>old(X)))&
(((curious(susan)|kind(susan)))<=>(?[X]:((~old(X)|happy(X)))))&
((brave(paul))<=>((happy(mary)<~>~quiet(mary))))&
((?[X]:(~old(X)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((~happy(X)<~>~creative(X))<=>(creative(X)<~>quiet(X))))&
(![X]:((creative(X)|old(X))=>(~calm(X)&patient(X))))&
(![X]:((~happy(X)&~old(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>happy(X))<=>(patient(X)<~>~curious(X))))&
((?[X]:((~generous(X)|~humble(X))))=>((~patient(lucy)|~rich(lucy))))&
(((kind(fred)<~>~quiet(fred)))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((~rich(X)|wise(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:((creative(X)|~patient(X))))=>(~patient(paul)))&
(?[X]:((funny(X)&generous(X))))&
(~creative(lucy))&
((rich(mary)|wise(mary)))&
((~strong(lucy)&~happy(lucy)))&
(happy(mary))&
(?[X]:((~creative(X)&humble(X)))) | ~patient(susan) | [] | null | 0 |
Everyone who is not funny is not tall or happy.
Everyone who is not rich or not quiet is either wise or not curious.
If someone is both strong and old then alice is calm and vice versa.
Everyone who is either not patient or funny is both not old and humble and vice versa.
If alice is not kind or funny then susan is creative.
Everyone who is both generous and not wise is both not tall and brave and vice versa.
Everyone who is either not creative or not kind is not calm or patient.
If someone is not generous or wise then paul is old and vice versa.
If someone is both not rich and not calm then someone is both not rich and happy.
If someone is both kind and not humble then someone is brave or calm.
Everyone who is generous is both not patient and funny and vice versa.
Everyone who is either not rich or curious is curious or not generous.
Everyone who is not curious or not generous is both not tall and not kind.
Everyone who is both not strong and not humble is not kind.
Everyone who is not old or brave is curious.
Everyone who is both not calm and brave is patient and vice versa.
Alice is not wise or not funny.
Someone is not generous or not brave.
Alice is old.
Someone is not old or not humble.
Alice is either kind or old.
Someone is not kind.
John is either wise or creative. | Alice is brave. | entailment | (![X]:(~funny(X)=>(~tall(X)|happy(X))))&
(![X]:((~rich(X)|~quiet(X))=>(wise(X)<~>~curious(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(alice)))&
(![X]:((~patient(X)<~>funny(X))<=>(~old(X)&humble(X))))&
(((~kind(alice)|funny(alice)))=>(creative(susan)))&
(![X]:((generous(X)&~wise(X))<=>(~tall(X)&brave(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(~calm(X)|patient(X))))&
((?[X]:((~generous(X)|wise(X))))<=>(old(paul)))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((~rich(X)&happy(X)))))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:(generous(X)<=>(~patient(X)&funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>(curious(X)|~generous(X))))&
(![X]:((~curious(X)|~generous(X))=>(~tall(X)&~kind(X))))&
(![X]:((~strong(X)&~humble(X))=>~kind(X)))&
(![X]:((~old(X)|brave(X))=>curious(X)))&
(![X]:((~calm(X)&brave(X))<=>patient(X)))&
((~wise(alice)|~funny(alice)))&
(?[X]:((~generous(X)|~brave(X))))&
(old(alice))&
(?[X]:((~old(X)|~humble(X))))&
((kind(alice)<~>old(alice)))&
(?[X]:(~kind(X)))&
((wise(john)<~>creative(john))) | brave(alice) | [
"p3",
"p5",
"p10",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 558839706138412535824140
% SZS output start Proof for 558839706138412535824140
4. ! [X0] : ((~patient(X0) <~> funny(X0)) <=> (humble(X0) & ~old(X0))) [input p3]
6. ! [X0] : ((~wise(X0) & generous(X0)) <=> (brave(X0) & ~tall(X0))) [input p5]
11. ! [X0] : (generous(X0) <=> (funny(X0) & ~patient(X0))) [input p10]
16. ! [X0] : ((brave(X0) & ~calm(X0)) <=> patient(X0)) [input p15]
17. ~funny(alice) | ~wise(alice) [input p16]
19. old(alice) [input p18]
24. ~brave(alice) [input hypothesis]
47. ! [X0] : ((((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0))))) [nnf transformation 4]
48. ! [X0] : ((((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0))))) [flattening 47]
49. ! [X0] : (((~wise(X0) & generous(X0)) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | (wise(X0) | ~generous(X0)))) [nnf transformation 6]
50. ! [X0] : (((~wise(X0) & generous(X0)) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | wise(X0) | ~generous(X0))) [flattening 49]
62. ! [X0] : ((generous(X0) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | ~generous(X0))) [nnf transformation 11]
63. ! [X0] : ((generous(X0) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | ~generous(X0))) [flattening 62]
65. ! [X0] : (((brave(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | (~brave(X0) | calm(X0)))) [nnf transformation 16]
66. ! [X0] : (((brave(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | ~brave(X0) | calm(X0))) [flattening 65]
80. ~old(X0) | funny(X0) | patient(X0) [cnf transformation 48]
89. ~generous(X0) | wise(X0) | brave(X0) [cnf transformation 50]
101. ~funny(X0) | generous(X0) | patient(X0) [cnf transformation 63]
113. ~patient(X0) | brave(X0) [cnf transformation 66]
114. ~funny(alice) | ~wise(alice) [cnf transformation 17]
116. old(alice) [cnf transformation 19]
123. ~brave(alice) [cnf transformation 24]
144. 5 <=> funny(alice) [avatar definition]
145. funny(alice) <- (5) [avatar component clause 144]
199. 18 <=> wise(alice) [avatar definition]
201. ~wise(alice) <- (~18) [avatar component clause 199]
202. ~18 | ~5 [avatar split clause 114,144,199]
246. funny(alice) | patient(alice) [resolution 80,116]
250. 27 <=> patient(alice) [avatar definition]
252. patient(alice) <- (27) [avatar component clause 250]
253. 27 | 5 [avatar split clause 246,144,250]
293. generous(alice) | patient(alice) <- (5) [resolution 101,145]
295. 32 <=> generous(alice) [avatar definition]
297. generous(alice) <- (32) [avatar component clause 295]
298. 27 | 32 | ~5 [avatar split clause 293,144,295,250]
301. brave(alice) <- (27) [resolution 252,113]
307. $false <- (27) [subsumption resolution 301,123]
308. ~27 [avatar contradiction clause 307]
310. wise(alice) | brave(alice) <- (32) [resolution 297,89]
314. brave(alice) <- (~18, 32) [subsumption resolution 310,201]
315. $false <- (~18, 32) [subsumption resolution 314,123]
316. 18 | ~32 [avatar contradiction clause 315]
318. $false [avatar sat refutation 202,253,298,308,316]
% SZS output end Proof for 558839706138412535824140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or creative is not old and vice versa.
Everyone who is not creative is brave.
Everyone who is not humble or not creative is both not kind and humble and vice versa.
Everyone who is either not tall or happy is both happy and rich and vice versa.
Everyone who is both not happy and generous is either not strong or not calm and vice versa.
If mary is either generous or not old then mary is both humble and not quiet and vice versa.
If john is not creative then lucy is brave or not rich and vice versa.
If someone is not brave or not humble then paul is rich or not old and vice versa.
Everyone who is either not humble or wise is not rich or tall and vice versa.
Everyone who is creative is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Someone is humble or not curious.
Someone is not funny.
Someone is not humble or tall.
Someone is either quiet or not patient. | Mary is creative. | entailment | (![X]:((humble(X)|creative(X))<=>~old(X)))&
(![X]:(~creative(X)=>brave(X)))&
(![X]:((~humble(X)|~creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&generous(X))<=>(~strong(X)<~>~calm(X))))&
(((generous(mary)<~>~old(mary)))<=>((humble(mary)&~quiet(mary))))&
((~creative(john))<=>((brave(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((~humble(X)<~>wise(X))<=>(~rich(X)|tall(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | creative(mary) | [
"p0",
"p2",
"p5",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 345679846944536967143795
% SZS output start Proof for 345679846944536967143795
1. ! [X0] : ((creative(X0) | humble(X0)) <=> ~old(X0)) [input p0]
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (humble(X0) & ~kind(X0))) [input p2]
6. (generous(mary) <~> ~old(mary)) <=> (~quiet(mary) & humble(mary)) [input p5]
11. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (~wise(X0) | strong(X0))) [input p10]
14. ! [X0] : ((~patient(X0) <~> patient(X0)) => (strong(X0) | creative(X0))) [input p13]
16. ! [X0] : ((~happy(X0) | generous(X0)) => ~humble(X0)) [input p15]
21. ~creative(mary) [input hypothesis]
24. ! [X0] : ((strong(X0) | creative(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 14]
25. ! [X0] : (strong(X0) | creative(X0) | (~patient(X0) <=> patient(X0))) [flattening 24]
28. ! [X0] : (~humble(X0) | (happy(X0) & ~generous(X0))) [ennf transformation 16]
29. ! [X0] : (((creative(X0) | humble(X0)) | old(X0)) & (~old(X0) | (~creative(X0) & ~humble(X0)))) [nnf transformation 1]
30. ! [X0] : ((creative(X0) | humble(X0) | old(X0)) & (~old(X0) | (~creative(X0) & ~humble(X0)))) [flattening 29]
31. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
32. ! [X0] : ((~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [flattening 31]
37. (((old(mary) | ~generous(mary)) & (~old(mary) | generous(mary))) | (quiet(mary) | ~humble(mary))) & ((~quiet(mary) & humble(mary)) | ((generous(mary) | old(mary)) & (~old(mary) | ~generous(mary)))) [nnf transformation 6]
38. (((old(mary) | ~generous(mary)) & (~old(mary) | generous(mary))) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ((generous(mary) | old(mary)) & (~old(mary) | ~generous(mary)))) [flattening 37]
49. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 11]
50. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | calm(X0) | ~quiet(X0))) [flattening 49]
55. ! [X0] : (strong(X0) | creative(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 25]
67. ~old(X0) | ~humble(X0) [cnf transformation 30]
73. humble(X0) | humble(X0) [cnf transformation 32]
91. ~quiet(mary) | generous(mary) | old(mary) [cnf transformation 38]
112. ~strong(X0) | quiet(X0) [cnf transformation 50]
124. strong(X0) | creative(X0) | patient(X0) | patient(X0) [cnf transformation 55]
125. strong(X0) | creative(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 55]
128. ~humble(X0) | ~generous(X0) [cnf transformation 28]
135. ~creative(mary) [cnf transformation 21]
136. strong(X0) | creative(X0) | patient(X0) [duplicate literal removal 124]
137. strong(X0) | creative(X0) | ~patient(X0) [duplicate literal removal 125]
140. humble(X0) [duplicate literal removal 73]
144. 1 <=> quiet(mary) [avatar definition]
145. ~quiet(mary) <- (~1) [avatar component clause 144]
148. 2 <=> generous(mary) [avatar definition]
149. generous(mary) <- (2) [avatar component clause 148]
152. 3 <=> old(mary) [avatar definition]
154. old(mary) <- (3) [avatar component clause 152]
156. 3 | 2 | ~1 [avatar split clause 91,144,148,152]
212. strong(X0) | creative(X0) [subsumption resolution 136,137]
232. ~generous(X0) [subsumption resolution 128,140]
250. quiet(X0) | creative(X0) [resolution 212,112]
255. creative(mary) <- (~1) [resolution 250,145]
257. $false <- (~1) [subsumption resolution 255,135]
258. 1 [avatar contradiction clause 257]
260. ~humble(mary) <- (3) [resolution 154,67]
261. $false <- (3) [subsumption resolution 260,140]
262. ~3 [avatar contradiction clause 261]
263. $false <- (2) [subsumption resolution 149,232]
264. ~2 [avatar contradiction clause 263]
265. $false [avatar sat refutation 156,258,262,264]
% SZS output end Proof for 345679846944536967143795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is funny and vice versa.
Everyone who is either not humble or humble is either not patient or kind and vice versa.
Everyone who is tall or not tall is either not wise or curious and vice versa.
If paul is either generous or not rich then fred is patient and vice versa.
If alice is both not wise and not patient then someone is not happy or not curious.
Everyone who is either not generous or not strong is strong or not tall and vice versa.
If alice is not funny or not patient then fred is humble or patient.
Everyone who is not tall is not creative or patient.
Everyone who is not quiet or not calm is either not creative or rich.
If john is both not patient and not brave then john is not quiet or patient and vice versa.
Everyone who is either not generous or tall is either happy or rich and vice versa.
Everyone who is not strong or not kind is both not quiet and rich and vice versa.
Everyone who is both curious and not patient is not rich.
Everyone who is not patient or not funny is both old and not patient.
Everyone who is both patient and not generous is either not kind or not funny.
Paul is either quiet or not strong.
Someone is both wise and not humble.
Someone is either not funny or not brave.
Susan is both happy and generous.
Alice is calm or not curious. | Alice is creative. | entailment | (![X]:(old(X)<=>funny(X)))&
(![X]:((~humble(X)<~>humble(X))<=>(~patient(X)<~>kind(X))))&
(![X]:((tall(X)|~tall(X))<=>(~wise(X)<~>curious(X))))&
(((generous(paul)<~>~rich(paul)))<=>(patient(fred)))&
(((~wise(alice)&~patient(alice)))=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:((~generous(X)<~>~strong(X))<=>(strong(X)|~tall(X))))&
(((~funny(alice)|~patient(alice)))=>((humble(fred)|patient(fred))))&
(![X]:(~tall(X)=>(~creative(X)|patient(X))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)<~>rich(X))))&
(((~patient(john)&~brave(john)))<=>((~quiet(john)|patient(john))))&
(![X]:((~generous(X)<~>tall(X))<=>(happy(X)<~>rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>(~quiet(X)&rich(X))))&
(![X]:((curious(X)&~patient(X))=>~rich(X)))&
(![X]:((~patient(X)|~funny(X))=>(old(X)&~patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~kind(X)<~>~funny(X))))&
((quiet(paul)<~>~strong(paul)))&
(?[X]:((wise(X)&~humble(X))))&
(?[X]:((~funny(X)<~>~brave(X))))&
((happy(susan)&generous(susan)))&
((calm(alice)|~curious(alice))) | creative(alice) | [
"p0",
"p1",
"p5",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4267895302563587351326697
% SZS output start Proof for 4267895302563587351326697
1. ! [X0] : (old(X0) <=> funny(X0)) [input p0]
2. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~patient(X0) <~> kind(X0))) [input p1]
6. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> (~tall(X0) | strong(X0))) [input p5]
9. ! [X0] : ((~calm(X0) | ~quiet(X0)) => (~creative(X0) <~> rich(X0))) [input p8]
12. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (rich(X0) & ~quiet(X0))) [input p11]
14. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p13]
15. ! [X0] : ((~generous(X0) & patient(X0)) => (~kind(X0) <~> ~funny(X0))) [input p14]
21. ~creative(alice) [input hypothesis]
22. ! [X0] : (old(X0) => funny(X0)) [unused predicate definition removal 1]
23. ! [X0] : (~quiet(X0) => (~creative(X0) <~> rich(X0))) [pure predicate removal 9]
25. ! [X0] : (funny(X0) | ~old(X0)) [ennf transformation 22]
32. ! [X0] : ((~creative(X0) <~> rich(X0)) | quiet(X0)) [ennf transformation 23]
35. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 14]
36. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | (generous(X0) | ~patient(X0))) [ennf transformation 15]
37. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | generous(X0) | ~patient(X0)) [flattening 36]
38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0)))) & (((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 2]
44. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 6]
45. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [flattening 44]
46. ! [X0] : (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | quiet(X0)) [nnf transformation 32]
50. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 12]
51. ! [X0] : ((~kind(X0) | ~strong(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [flattening 50]
52. ! [X0] : (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | generous(X0) | ~patient(X0)) [nnf transformation 37]
59. ~old(X0) | funny(X0) [cnf transformation 25]
62. ~kind(X0) | patient(X0) | humble(X0) | humble(X0) [cnf transformation 38]
63. ~kind(X0) | patient(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38]
80. ~tall(X0) | strong(X0) | ~generous(X0) | strong(X0) [cnf transformation 45]
81. ~strong(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 45]
82. ~strong(X0) | ~generous(X0) | tall(X0) [cnf transformation 45]
89. ~rich(X0) | creative(X0) | quiet(X0) [cnf transformation 46]
103. ~quiet(X0) | strong(X0) [cnf transformation 51]
104. ~quiet(X0) | kind(X0) [cnf transformation 51]
105. strong(X0) | rich(X0) [cnf transformation 51]
106. rich(X0) | kind(X0) [cnf transformation 51]
110. old(X0) | funny(X0) [cnf transformation 35]
113. ~funny(X0) | ~kind(X0) | generous(X0) | ~patient(X0) [cnf transformation 52]
123. ~creative(alice) [cnf transformation 21]
126. ~tall(X0) | strong(X0) | ~generous(X0) [duplicate literal removal 80]
127. ~strong(X0) | ~generous(X0) [duplicate literal removal 81]
130. ~kind(X0) | patient(X0) | humble(X0) [duplicate literal removal 62]
131. ~kind(X0) | patient(X0) | ~humble(X0) [duplicate literal removal 63]
132. ~kind(X0) | patient(X0) [subsumption resolution 130,131]
169. ~generous(X0) | ~tall(X0) [subsumption resolution 126,127]
201. funny(X0) [subsumption resolution 110,59]
202. ~kind(X0) | generous(X0) | ~patient(X0) [subsumption resolution 113,201]
203. ~kind(X0) | generous(X0) [subsumption resolution 202,132]
224. ~generous(X0) | rich(X0) [resolution 127,105]
253. creative(X0) | quiet(X0) | kind(X0) [resolution 89,106]
257. creative(X0) | kind(X0) [subsumption resolution 253,104]
352. kind(alice) [resolution 257,123]
357. generous(alice) [resolution 352,203]
375. rich(alice) [resolution 357,224]
376. ~tall(alice) [resolution 357,169]
406. creative(alice) | quiet(alice) [resolution 375,89]
408. quiet(alice) [subsumption resolution 406,123]
440. strong(alice) [resolution 408,103]
450. ~generous(alice) | tall(alice) [resolution 440,82]
452. tall(alice) [subsumption resolution 450,357]
453. $false [subsumption resolution 452,376]
% SZS output end Proof for 4267895302563587351326697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or calm is both not funny and not patient.
Everyone who is generous or curious is old.
Everyone who is not wise is both tall and creative and vice versa.
If someone is either not humble or tall then susan is both curious and not generous.
If john is not funny or not kind then someone is either calm or creative and vice versa.
Everyone who is rich or not creative is either not happy or not humble.
If paul is happy then someone is not quiet or old and vice versa.
If someone is old then alice is both not patient and not rich and vice versa.
Everyone who is either rich or wise is either not tall or not happy and vice versa.
Everyone who is either not kind or strong is both rich and quiet.
If someone is both curious and funny then someone is either calm or not old.
Everyone who is either tall or not humble is calm or not generous.
If someone is not strong or not funny then john is both not curious and not funny and vice versa.
Everyone who is strong is not rich and vice versa.
If mary is both not calm and not curious then mary is patient or calm and vice versa.
If lucy is either not old or not funny then john is not generous and vice versa.
Alice is calm.
Susan is either strong or not happy.
Someone is not rich.
Lucy is either wise or not kind.
Someone is not kind.
Mary is both not quiet and not calm.
Mary is either not humble or not happy.
John is not generous or strong. | John is not rich. | neutral | (![X]:((humble(X)<~>calm(X))=>(~funny(X)&~patient(X))))&
(![X]:((generous(X)|curious(X))=>old(X)))&
(![X]:(~wise(X)<=>(tall(X)&creative(X))))&
((?[X]:((~humble(X)<~>tall(X))))=>((curious(susan)&~generous(susan))))&
(((~funny(john)|~kind(john)))<=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((rich(X)|~creative(X))=>(~happy(X)<~>~humble(X))))&
((happy(paul))<=>(?[X]:((~quiet(X)|old(X)))))&
((?[X]:(old(X)))<=>((~patient(alice)&~rich(alice))))&
(![X]:((rich(X)<~>wise(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&quiet(X))))&
((?[X]:((curious(X)&funny(X))))=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:((tall(X)<~>~humble(X))=>(calm(X)|~generous(X))))&
((?[X]:((~strong(X)|~funny(X))))<=>((~curious(john)&~funny(john))))&
(![X]:(strong(X)<=>~rich(X)))&
(((~calm(mary)&~curious(mary)))<=>((patient(mary)|calm(mary))))&
(((~old(lucy)<~>~funny(lucy)))<=>(~generous(john)))&
(calm(alice))&
((strong(susan)<~>~happy(susan)))&
(?[X]:(~rich(X)))&
((wise(lucy)<~>~kind(lucy)))&
(?[X]:(~kind(X)))&
((~quiet(mary)&~calm(mary)))&
((~humble(mary)<~>~happy(mary)))&
((~generous(john)|strong(john))) | ~rich(john) | [] | null | 0 |
If alice is wise or quiet then mary is rich and vice versa.
Everyone who is either curious or funny is both not happy and not humble and vice versa.
If lucy is rich then someone is either patient or old and vice versa.
If susan is both not funny and not humble then john is both happy and not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Mary is curious or not funny.
Someone is not quiet.
John is both wise and not patient.
Paul is either not creative or not kind.
Mary is both not patient and kind.
Someone is not happy or not generous.
Fred is both strong and humble. | Paul is not brave. | contradiction | (((wise(alice)|quiet(alice)))<=>(rich(mary)))&
(![X]:((curious(X)<~>funny(X))<=>(~happy(X)&~humble(X))))&
((rich(lucy))<=>(?[X]:((patient(X)<~>old(X)))))&
(((~funny(susan)&~humble(susan)))<=>((happy(john)&~kind(john))))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
((curious(mary)|~funny(mary)))&
(?[X]:(~quiet(X)))&
((wise(john)&~patient(john)))&
((~creative(paul)<~>~kind(paul)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
((strong(fred)&humble(fred))) | ~brave(paul) | [
"p2",
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3979672106170346043933352
% SZS output start Proof for 3979672106170346043933352
3. rich(lucy) <=> ? [X0] : (patient(X0) <~> old(X0)) [input p2]
8. ? [X0] : (generous(X0) | ~old(X0)) <=> (kind(paul) & brave(paul)) [input p7]
11. ! [X0] : (old(X0) <=> ~rich(X0)) [input p10]
19. ~patient(john) & wise(john) [input p18]
24. ~brave(paul) [input hypothesis]
33. (rich(lucy) | ! [X0] : ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (? [X0] : ((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~rich(lucy)) [nnf transformation 3]
34. (rich(lucy) | ! [X0] : ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (? [X1] : ((~old(X1) | ~patient(X1)) & (old(X1) | patient(X1))) | ~rich(lucy)) [rectify 33]
35. ? [X1] : ((~old(X1) | ~patient(X1)) & (old(X1) | patient(X1))) => ((~old(sK0) | ~patient(sK0)) & (old(sK0) | patient(sK0))) [choice axiom]
36. (rich(lucy) | ! [X0] : ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(sK0) | ~patient(sK0)) & (old(sK0) | patient(sK0))) | ~rich(lucy)) [skolemisation 34,35]
47. (? [X0] : (generous(X0) | ~old(X0)) | (~kind(paul) | ~brave(paul))) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [nnf transformation 8]
48. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [flattening 47]
49. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [rectify 48]
50. ? [X0] : (generous(X0) | ~old(X0)) => (generous(sK2) | ~old(sK2)) [choice axiom]
51. ((generous(sK2) | ~old(sK2)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [skolemisation 49,50]
61. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 11]
97. rich(lucy) | patient(X0) | ~old(X0) [cnf transformation 36]
115. brave(paul) | old(X1) [cnf transformation 51]
127. ~old(X0) | ~rich(X0) [cnf transformation 61]
157. ~patient(john) [cnf transformation 19]
165. ~brave(paul) [cnf transformation 24]
182. 4 <=> ! [X0] : (patient(X0) | ~old(X0)) [avatar definition]
183. patient(X0) | ~old(X0) <- (4) [avatar component clause 182]
185. 5 <=> rich(lucy) [avatar definition]
187. rich(lucy) <- (5) [avatar component clause 185]
188. 4 | 5 [avatar split clause 97,185,182]
236. 16 <=> brave(paul) [avatar definition]
257. 21 <=> ! [X1] : old(X1) [avatar definition]
258. old(X1) <- (21) [avatar component clause 257]
261. 21 | 16 [avatar split clause 115,236,257]
407. ~16 [avatar split clause 165,236]
416. patient(X0) <- (4, 21) [subsumption resolution 183,258]
425. $false <- (4, 21) [resolution 416,157]
428. ~4 | ~21 [avatar contradiction clause 425]
432. ~rich(X0) <- (21) [resolution 127,258]
433. $false <- (5, 21) [resolution 432,187]
434. ~5 | ~21 [avatar contradiction clause 433]
435. $false [avatar sat refutation 188,261,407,428,434]
% SZS output end Proof for 3979672106170346043933352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not wise then someone is either not kind or not creative and vice versa.
Everyone who is either calm or generous is either humble or not generous.
If lucy is not quiet or not calm then paul is not kind.
Everyone who is both humble and not kind is either creative or kind.
Everyone who is either strong or tall is either generous or brave.
Everyone who is not wise is either not happy or creative and vice versa.
If lucy is generous or not generous then fred is not wise or not generous and vice versa.
Everyone who is either not wise or wise is either kind or tall and vice versa.
Everyone who is either wise or not brave is not creative or not wise and vice versa.
If someone is either creative or happy then someone is not happy and vice versa.
If someone is not funny or not happy then john is not old or happy and vice versa.
Everyone who is not calm or not old is both wise and tall.
If someone is both strong and not patient then john is either not quiet or not creative and vice versa.
If fred is either funny or not creative then someone is both not calm and funny.
If alice is kind or funny then fred is either not curious or not tall.
Everyone who is not quiet or not patient is both not strong and not funny and vice versa.
Susan is not tall.
Lucy is both quiet and not patient.
Fred is not funny or not brave.
Fred is brave.
Susan is both humble and generous.
Someone is either humble or not wise.
Someone is quiet or not patient.
Alice is not creative. | Susan is old. | entailment | ((?[X]:((~happy(X)|~wise(X))))<=>(?[X]:((~kind(X)<~>~creative(X)))))&
(![X]:((calm(X)<~>generous(X))=>(humble(X)<~>~generous(X))))&
(((~quiet(lucy)|~calm(lucy)))=>(~kind(paul)))&
(![X]:((humble(X)&~kind(X))=>(creative(X)<~>kind(X))))&
(![X]:((strong(X)<~>tall(X))=>(generous(X)<~>brave(X))))&
(![X]:(~wise(X)<=>(~happy(X)<~>creative(X))))&
(((generous(lucy)|~generous(lucy)))<=>((~wise(fred)|~generous(fred))))&
(![X]:((~wise(X)<~>wise(X))<=>(kind(X)<~>tall(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(~creative(X)|~wise(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~funny(X)|~happy(X))))<=>((~old(john)|happy(john))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:((~calm(X)&funny(X)))))&
(((kind(alice)|funny(alice)))=>((~curious(fred)<~>~tall(fred))))&
(![X]:((~quiet(X)|~patient(X))<=>(~strong(X)&~funny(X))))&
(~tall(susan))&
((quiet(lucy)&~patient(lucy)))&
((~funny(fred)|~brave(fred)))&
(brave(fred))&
((humble(susan)&generous(susan)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((quiet(X)|~patient(X))))&
(~creative(alice)) | old(susan) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5948496913280538391951747
% SZS output start Proof for 5948496913280538391951747
12. ! [X0] : ((~old(X0) | ~calm(X0)) => (tall(X0) & wise(X0))) [input p11]
17. ~tall(susan) [input p16]
25. ~old(susan) [input hypothesis]
33. ! [X0] : ((tall(X0) & wise(X0)) | (old(X0) & calm(X0))) [ennf transformation 12]
126. old(X0) | tall(X0) [cnf transformation 33]
146. ~tall(susan) [cnf transformation 17]
157. ~old(susan) [cnf transformation 25]
378. tall(susan) [resolution 126,157]
380. $false [subsumption resolution 378,146]
% SZS output end Proof for 5948496913280538391951747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not quiet is either not old or patient and vice versa. If susan is quiet then alice is both not quiet and not strong and vice versa. Everyone who is not creative or not quiet is kind or not quiet and vice versa. If fred is happy then someone is happy and vice versa. Everyone who is both not patient and creative is both calm and not old. If mary is humble then lucy is patient or rich and vice versa. If someone is either not old or not kind then someone is funny and vice versa. If someone is not old or not funny then mary is both kind and rich and vice versa. Everyone who is either not brave or old is not wise or quiet and vice versa. Everyone who is either generous or kind is both not rich and not brave. Everyone who is both not calm and creative is not funny. If someone is humble or tall then someone is creative. Everyone who is not patient is either not quiet or creative and vice versa. If alice is tall or wise then susan is creative or not strong. Everyone who is both tall and not strong is strong and vice versa. If john is both not old and calm then someone is either not curious or not old. Someone is either tall or not generous. Susan is either patient or rich. Susan is both not kind and not patient. Paul is both not brave and not quiet. Alice is both generous and not curious. Mary is not old. | Alice is not rich. | neutral | (![X]:((strong(X)&~quiet(X))<=>(~old(X)<~>patient(X))))&
((quiet(susan))<=>((~quiet(alice)&~strong(alice))))&
(![X]:((~creative(X)|~quiet(X))<=>(kind(X)|~quiet(X))))&
((happy(fred))<=>(?[X]:(happy(X))))&
(![X]:((~patient(X)&creative(X))=>(calm(X)&~old(X))))&
((humble(mary))<=>((patient(lucy)|rich(lucy))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~old(X)|~funny(X))))<=>((kind(mary)&rich(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(~wise(X)|quiet(X))))&
(![X]:((generous(X)<~>kind(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)&creative(X))=>~funny(X)))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>creative(X))))&
(((tall(alice)|wise(alice)))=>((creative(susan)|~strong(susan))))&
(![X]:((tall(X)&~strong(X))<=>strong(X)))&
(((~old(john)&calm(john)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(susan)<~>rich(susan)))&
((~kind(susan)&~patient(susan)))&
((~brave(paul)&~quiet(paul)))&
((generous(alice)&~curious(alice)))&
(~old(mary)) | ~rich(alice) | [] | null | 0 |
If someone is both rich and not kind then someone is either not patient or calm and vice versa.
Everyone who is not happy is both not creative and not curious.
If someone is both not rich and not strong then someone is either not creative or not calm.
If someone is both not quiet and generous then someone is not generous.
Everyone who is kind is strong.
If someone is both not kind and not patient then someone is both not funny and humble.
If paul is calm then alice is both not generous and curious and vice versa.
Everyone who is kind or quiet is either creative or old.
Everyone who is either quiet or not curious is funny and vice versa.
If susan is not creative then someone is not brave.
Everyone who is calm or not humble is wise.
If someone is kind then alice is either quiet or not kind.
Everyone who is not old is not brave.
Everyone who is humble or not brave is both not happy and happy.
Everyone who is not brave or happy is not patient or strong and vice versa.
Everyone who is both old and calm is either kind or not patient and vice versa.
Someone is either quiet or curious.
Someone is patient or tall.
Someone is not funny.
Lucy is not quiet or old.
Someone is either not tall or not quiet. | Alice is not old. | contradiction | ((?[X]:((rich(X)&~kind(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(~happy(X)=>(~creative(X)&~curious(X))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((~creative(X)<~>~calm(X)))))&
((?[X]:((~quiet(X)&generous(X))))=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>strong(X)))&
((?[X]:((~kind(X)&~patient(X))))=>(?[X]:((~funny(X)&humble(X)))))&
((calm(paul))<=>((~generous(alice)&curious(alice))))&
(![X]:((kind(X)|quiet(X))=>(creative(X)<~>old(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>funny(X)))&
((~creative(susan))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|~humble(X))=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:(~funny(X)))&
((~quiet(lucy)|old(lucy)))&
(?[X]:((~tall(X)<~>~quiet(X)))) | ~old(alice) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8587977611460508578802432
% SZS output start Proof for 8587977611460508578802432
13. ! [X0] : (~old(X0) => ~brave(X0)) [input p12]
14. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p13]
22. ~old(alice) [input hypothesis]
38. ! [X0] : (~brave(X0) | old(X0)) [ennf transformation 13]
39. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 14]
102. ~brave(X0) | old(X0) [cnf transformation 38]
104. ~happy(X0) | brave(X0) [cnf transformation 39]
106. happy(X0) | brave(X0) [cnf transformation 39]
124. ~old(alice) [cnf transformation 22]
227. brave(X0) [subsumption resolution 104,106]
272. old(X0) [resolution 102,227]
273. $false [resolution 272,124]
% SZS output end Proof for 8587977611460508578802432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not creative or not curious. If someone is kind then someone is either wise or not quiet and vice versa. If someone is both not calm and old then someone is not creative or not old. Everyone who is both quiet and not calm is either calm or not strong. If lucy is not happy then susan is not wise or strong. Everyone who is not funny or creative is kind and vice versa. Everyone who is both tall and strong is not kind or generous and vice versa. If fred is either wise or not patient then mary is either brave or calm and vice versa. If susan is patient or not funny then paul is either not rich or humble and vice versa. Everyone who is not calm or not funny is patient and vice versa. If susan is both not curious and funny then someone is either not patient or old. If mary is both curious and not kind then someone is not rich or not old. If fred is generous then alice is tall or curious and vice versa. Everyone who is not happy or not calm is strong. If mary is either generous or not curious then someone is not quiet and vice versa. If someone is either not creative or funny then someone is either not calm or creative and vice versa. Someone is either quiet or generous. John is quiet. Mary is creative or not curious. Susan is not tall. Susan is patient or quiet. Someone is both funny and patient. Mary is either strong or not generous. Someone is creative or not rich. | Mary is happy. | entailment | (![X]:(kind(X)=>(~creative(X)|~curious(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
((?[X]:((~calm(X)&old(X))))=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:((quiet(X)&~calm(X))=>(calm(X)<~>~strong(X))))&
((~happy(lucy))=>((~wise(susan)|strong(susan))))&
(![X]:((~funny(X)|creative(X))<=>kind(X)))&
(![X]:((tall(X)&strong(X))<=>(~kind(X)|generous(X))))&
(((wise(fred)<~>~patient(fred)))<=>((brave(mary)<~>calm(mary))))&
(((patient(susan)|~funny(susan)))<=>((~rich(paul)<~>humble(paul))))&
(![X]:((~calm(X)|~funny(X))<=>patient(X)))&
(((~curious(susan)&funny(susan)))=>(?[X]:((~patient(X)<~>old(X)))))&
(((curious(mary)&~kind(mary)))=>(?[X]:((~rich(X)|~old(X)))))&
((generous(fred))<=>((tall(alice)|curious(alice))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
(((generous(mary)<~>~curious(mary)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>funny(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(?[X]:((quiet(X)<~>generous(X))))&
(quiet(john))&
((creative(mary)|~curious(mary)))&
(~tall(susan))&
((patient(susan)|quiet(susan)))&
(?[X]:((funny(X)&patient(X))))&
((strong(mary)<~>~generous(mary)))&
(?[X]:((creative(X)|~rich(X)))) | happy(mary) | [
"p0",
"p3",
"p5",
"p9",
"p13",
"p14",
"p18",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 245779429597675115041562
% SZS output start Proof for 245779429597675115041562
1. ! [X0] : (kind(X0) => (~curious(X0) | ~creative(X0))) [input p0]
4. ! [X0] : ((~calm(X0) & quiet(X0)) => (calm(X0) <~> ~strong(X0))) [input p3]
6. ! [X0] : ((creative(X0) | ~funny(X0)) <=> kind(X0)) [input p5]
10. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> patient(X0)) [input p9]
14. ! [X0] : ((~calm(X0) | ~happy(X0)) => strong(X0)) [input p13]
15. (generous(mary) <~> ~curious(mary)) <=> ? [X0] : ~quiet(X0) [input p14]
19. ~curious(mary) | creative(mary) [input p18]
22. ? [X0] : (patient(X0) & funny(X0)) [input p21]
23. strong(mary) <~> ~generous(mary) [input p22]
25. ~happy(mary) [input hypothesis]
29. ! [X0] : ((~curious(X0) | ~creative(X0)) | ~kind(X0)) [ennf transformation 1]
30. ! [X0] : (~curious(X0) | ~creative(X0) | ~kind(X0)) [flattening 29]
32. ! [X0] : ((calm(X0) <~> ~strong(X0)) | (calm(X0) | ~quiet(X0))) [ennf transformation 4]
33. ! [X0] : ((calm(X0) <~> ~strong(X0)) | calm(X0) | ~quiet(X0)) [flattening 32]
40. ! [X0] : (strong(X0) | (calm(X0) & happy(X0))) [ennf transformation 14]
49. ! [X0] : (((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | calm(X0) | ~quiet(X0)) [nnf transformation 33]
50. ! [X0] : (((creative(X0) | ~funny(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) & funny(X0)))) [nnf transformation 6]
51. ! [X0] : ((creative(X0) | ~funny(X0) | ~kind(X0)) & (kind(X0) | (~creative(X0) & funny(X0)))) [flattening 50]
57. ! [X0] : (((~funny(X0) | ~calm(X0)) | ~patient(X0)) & (patient(X0) | (funny(X0) & calm(X0)))) [nnf transformation 10]
58. ! [X0] : ((~funny(X0) | ~calm(X0) | ~patient(X0)) & (patient(X0) | (funny(X0) & calm(X0)))) [flattening 57]
66. (((curious(mary) | ~generous(mary)) & (~curious(mary) | generous(mary))) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ((generous(mary) | curious(mary)) & (~curious(mary) | ~generous(mary)))) [nnf transformation 15]
67. (((curious(mary) | ~generous(mary)) & (~curious(mary) | generous(mary))) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ((generous(mary) | curious(mary)) & (~curious(mary) | ~generous(mary)))) [rectify 66]
68. ? [X1] : ~quiet(X1) => ~quiet(sK5) [choice axiom]
69. (((curious(mary) | ~generous(mary)) & (~curious(mary) | generous(mary))) | ! [X0] : quiet(X0)) & (~quiet(sK5) | ((generous(mary) | curious(mary)) & (~curious(mary) | ~generous(mary)))) [skolemisation 67,68]
78. ? [X0] : (patient(X0) & funny(X0)) => (patient(sK9) & funny(sK9)) [choice axiom]
79. patient(sK9) & funny(sK9) [skolemisation 22,78]
80. (generous(mary) | ~strong(mary)) & (~generous(mary) | strong(mary)) [nnf transformation 23]
83. ~curious(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 30]
89. ~strong(X0) | calm(X0) | calm(X0) | ~quiet(X0) [cnf transformation 49]
93. ~creative(X0) | kind(X0) [cnf transformation 51]
116. ~patient(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 58]
123. happy(X0) | strong(X0) [cnf transformation 40]
124. strong(X0) | calm(X0) [cnf transformation 40]
128. curious(mary) | ~generous(mary) | quiet(X0) [cnf transformation 69]
140. ~curious(mary) | creative(mary) [cnf transformation 19]
143. funny(sK9) [cnf transformation 79]
144. patient(sK9) [cnf transformation 79]
146. generous(mary) | ~strong(mary) [cnf transformation 80]
148. ~happy(mary) [cnf transformation 25]
149. ~strong(X0) | calm(X0) | ~quiet(X0) [duplicate literal removal 89]
261. 24 <=> curious(mary) [avatar definition]
262. curious(mary) <- (24) [avatar component clause 261]
265. 25 <=> kind(mary) [avatar definition]
267. kind(mary) <- (25) [avatar component clause 265]
293. 31 <=> ! [X0] : quiet(X0) [avatar definition]
294. quiet(X0) <- (31) [avatar component clause 293]
296. 32 <=> generous(mary) [avatar definition]
299. 31 | ~32 | 24 [avatar split clause 128,261,296,293]
354. 44 <=> creative(mary) [avatar definition]
356. creative(mary) <- (44) [avatar component clause 354]
357. 44 | ~24 [avatar split clause 140,261,354]
364. 46 <=> strong(mary) [avatar definition]
367. ~46 | 32 [avatar split clause 146,296,364]
385. strong(mary) [resolution 123,148]
388. 46 [avatar split clause 385,364]
415. kind(mary) <- (44) [resolution 356,93]
418. 25 | ~44 [avatar split clause 415,354,265]
425. ~creative(mary) | ~kind(mary) <- (24) [resolution 83,262]
426. ~kind(mary) <- (24, 44) [subsumption resolution 425,356]
427. $false <- (24, 25, 44) [subsumption resolution 426,267]
428. ~24 | ~25 | ~44 [avatar contradiction clause 427]
463. ~calm(sK9) | ~funny(sK9) [resolution 116,144]
467. ~calm(sK9) [subsumption resolution 463,143]
469. calm(X0) | ~quiet(X0) | calm(X0) [resolution 149,124]
473. calm(X0) | ~quiet(X0) [duplicate literal removal 469]
474. calm(X0) <- (31) [subsumption resolution 473,294]
494. $false <- (31) [resolution 474,467]
497. ~31 [avatar contradiction clause 494]
499. $false [avatar sat refutation 299,357,367,388,418,428,497]
% SZS output end Proof for 245779429597675115041562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and generous is not calm. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. If someone is either calm or curious then someone is both curious and not creative and vice versa. If someone is quiet or old then fred is not funny or not creative and vice versa. If someone is either curious or funny then someone is calm and vice versa. Fred is patient or brave. Someone is strong or not funny. Fred is both generous and funny. Alice is not funny or creative. Someone is either humble or not wise. Someone is not curious or not funny. Someone is generous. | Fred is not funny. | contradiction | (![X]:((~quiet(X)&generous(X))=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((quiet(X)|old(X))))<=>((~funny(fred)|~creative(fred))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
((patient(fred)|brave(fred)))&
(?[X]:((strong(X)|~funny(X))))&
((generous(fred)&funny(fred)))&
((~funny(alice)|creative(alice)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:(generous(X))) | ~funny(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3543943549242537554881676
% SZS output start Proof for 3543943549242537554881676
19. funny(fred) & generous(fred) [input p18]
24. ~funny(fred) [input hypothesis]
132. funny(fred) [cnf transformation 19]
138. ~funny(fred) [cnf transformation 24]
236. 22 <=> funny(fred) [avatar definition]
282. 22 [avatar split clause 132,236]
311. ~22 [avatar split clause 138,236]
312. $false [avatar sat refutation 282,311]
% SZS output end Proof for 3543943549242537554881676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old is not wise or not tall and vice versa.
Everyone who is not tall is happy or not humble.
Everyone who is either not tall or humble is either strong or not quiet.
Everyone who is both not brave and not generous is strong or rich.
Everyone who is not old is both calm and rich.
Everyone who is not tall is either creative or not humble and vice versa.
If paul is not calm or not quiet then alice is either not funny or strong.
Everyone who is not funny or wise is not tall or not strong and vice versa.
If someone is either curious or not funny then someone is curious or happy.
If someone is either tall or calm then paul is both generous and not calm and vice versa.
Everyone who is brave or not humble is both wise and patient and vice versa.
If someone is either tall or wise then susan is not calm.
Everyone who is both not patient and not wise is curious or not curious.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
Someone is either funny or happy.
Paul is both not tall and not generous.
Paul is either old or generous.
Alice is both kind and not wise.
Someone is not generous.
Someone is not patient.
Someone is either old or wise.
Alice is not curious. | Alice is not brave. | entailment | (![X]:((happy(X)|old(X))<=>(~wise(X)|~tall(X))))&
(![X]:(~tall(X)=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>humble(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(strong(X)|rich(X))))&
(![X]:(~old(X)=>(calm(X)&rich(X))))&
(![X]:(~tall(X)<=>(creative(X)<~>~humble(X))))&
(((~calm(paul)|~quiet(paul)))=>((~funny(alice)<~>strong(alice))))&
(![X]:((~funny(X)|wise(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((curious(X)|happy(X)))))&
((?[X]:((tall(X)<~>calm(X))))<=>((generous(paul)&~calm(paul))))&
(![X]:((brave(X)|~humble(X))<=>(wise(X)&patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(~calm(susan)))&
(![X]:((~patient(X)&~wise(X))=>(curious(X)|~curious(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
(?[X]:((funny(X)<~>happy(X))))&
((~tall(paul)&~generous(paul)))&
((old(paul)<~>generous(paul)))&
((kind(alice)&~wise(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)<~>wise(X))))&
(~curious(alice)) | ~brave(alice) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4461725085651326314833659
% SZS output start Proof for 4461725085651326314833659
11. ! [X0] : ((~humble(X0) | brave(X0)) <=> (patient(X0) & wise(X0))) [input p10]
20. ~wise(alice) & kind(alice) [input p19]
25. brave(alice) [input hypothesis]
28. ~wise(alice) [pure predicate removal 20]
56. ! [X0] : (((~humble(X0) | brave(X0)) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | (humble(X0) & ~brave(X0)))) [nnf transformation 11]
57. ! [X0] : ((~humble(X0) | brave(X0) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | (humble(X0) & ~brave(X0)))) [flattening 56]
104. ~brave(X0) | wise(X0) [cnf transformation 57]
126. ~wise(alice) [cnf transformation 28]
132. brave(alice) [cnf transformation 25]
254. wise(alice) [resolution 104,132]
255. $false [subsumption resolution 254,126]
% SZS output end Proof for 4461725085651326314833659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or humble is patient.
Everyone who is either not rich or creative is either rich or not tall.
If someone is either not wise or strong then fred is either not brave or not rich.
If paul is not quiet or not creative then someone is wise or not patient and vice versa.
Everyone who is either quiet or not quiet is either not brave or tall.
Everyone who is both brave and not humble is not kind or tall and vice versa.
Everyone who is both generous and humble is both not humble and not old and vice versa.
Everyone who is both wise and quiet is either calm or not creative and vice versa.
If someone is patient then fred is both humble and not kind.
If someone is either not rich or wise then someone is not funny.
If someone is either not brave or rich then mary is both not patient and not kind.
Everyone who is not curious or curious is either not strong or generous and vice versa.
If someone is either quiet or kind then paul is both curious and not old.
If mary is not strong or happy then someone is not tall or not happy.
If john is not brave or not happy then someone is funny.
Everyone who is not funny is not kind and vice versa.
John is not creative.
Someone is not creative or happy.
Someone is generous or curious.
Susan is funny.
Paul is not curious.
Fred is not strong. | Fred is rich. | neutral | (![X]:((strong(X)<~>humble(X))=>patient(X)))&
(![X]:((~rich(X)<~>creative(X))=>(rich(X)<~>~tall(X))))&
((?[X]:((~wise(X)<~>strong(X))))=>((~brave(fred)<~>~rich(fred))))&
(((~quiet(paul)|~creative(paul)))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((brave(X)&~humble(X))<=>(~kind(X)|tall(X))))&
(![X]:((generous(X)&humble(X))<=>(~humble(X)&~old(X))))&
(![X]:((wise(X)&quiet(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(patient(X)))=>((humble(fred)&~kind(fred))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>rich(X))))=>((~patient(mary)&~kind(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>((curious(paul)&~old(paul))))&
(((~strong(mary)|happy(mary)))=>(?[X]:((~tall(X)|~happy(X)))))&
(((~brave(john)|~happy(john)))=>(?[X]:(funny(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(~creative(john))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((generous(X)|curious(X))))&
(funny(susan))&
(~curious(paul))&
(~strong(fred)) | rich(fred) | [] | null | 0 |
Everyone who is strong or not curious is kind and vice versa.
Everyone who is not strong is wise and vice versa.
If someone is not happy or not patient then someone is not creative.
If someone is brave then lucy is either happy or not kind.
If someone is both creative and not brave then someone is old or strong.
Everyone who is either funny or curious is both happy and rich and vice versa.
Everyone who is either not funny or not old is either strong or not strong and vice versa.
Everyone who is rich is both kind and funny and vice versa.
If mary is creative then mary is quiet or curious.
Everyone who is calm is not creative or wise.
Everyone who is both not kind and funny is not brave or not old and vice versa.
Everyone who is either calm or not humble is both not quiet and strong and vice versa.
If someone is not strong or calm then fred is both not happy and funny.
Everyone who is not calm or wise is both happy and not wise and vice versa.
If alice is both funny and tall then someone is either happy or not strong.
Someone is not happy or creative.
Someone is either generous or not patient.
Susan is brave or not funny.
John is not creative.
Someone is tall.
John is humble.
Someone is either happy or not generous. | Fred is curious. | contradiction | (![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:(~strong(X)<=>wise(X)))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:(brave(X)))=>((happy(lucy)<~>~kind(lucy))))&
((?[X]:((creative(X)&~brave(X))))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(happy(X)&rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(rich(X)<=>(kind(X)&funny(X))))&
((creative(mary))=>((quiet(mary)|curious(mary))))&
(![X]:(calm(X)=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)&funny(X))<=>(~brave(X)|~old(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~strong(X)|calm(X))))=>((~happy(fred)&funny(fred))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~wise(X))))&
(((funny(alice)&tall(alice)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
((brave(susan)|~funny(susan)))&
(~creative(john))&
(?[X]:(tall(X)))&
(humble(john))&
(?[X]:((happy(X)<~>~generous(X)))) | curious(fred) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3164171969224015810865006
% SZS output start Proof for 3164171969224015810865006
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p0]
2. ! [X0] : (~strong(X0) <=> wise(X0)) [input p1]
6. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (rich(X0) & happy(X0))) [input p5]
7. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p6]
8. ! [X0] : (rich(X0) <=> (funny(X0) & kind(X0))) [input p7]
11. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (~old(X0) | ~brave(X0))) [input p10]
14. ! [X0] : ((wise(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
23. curious(fred) [input hypothesis]
36. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 36]
38. ! [X0] : ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))) [nnf transformation 2]
46. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 46]
48. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 7]
49. ! [X0] : ((rich(X0) | (~funny(X0) | ~kind(X0))) & ((funny(X0) & kind(X0)) | ~rich(X0))) [nnf transformation 8]
50. ! [X0] : ((rich(X0) | ~funny(X0) | ~kind(X0)) & ((funny(X0) & kind(X0)) | ~rich(X0))) [flattening 49]
51. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | (~funny(X0) | kind(X0)))) [nnf transformation 11]
52. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ~funny(X0) | kind(X0))) [flattening 51]
55. ! [X0] : (((wise(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [flattening 55]
70. ~strong(X0) | kind(X0) [cnf transformation 37]
73. wise(X0) | strong(X0) [cnf transformation 38]
83. ~curious(X0) | funny(X0) | rich(X0) [cnf transformation 47]
90. ~old(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
91. ~old(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 48]
95. ~rich(X0) | funny(X0) [cnf transformation 50]
101. ~kind(X0) | old(X0) [cnf transformation 52]
117. ~wise(X0) | ~wise(X0) [cnf transformation 56]
130. curious(fred) [cnf transformation 23]
131. ~wise(X0) [duplicate literal removal 117]
133. ~old(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 90]
134. ~old(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 91]
175. ~funny(X0) | ~old(X0) [subsumption resolution 133,134]
193. 14 <=> funny(fred) [avatar definition]
194. ~funny(fred) <- (~14) [avatar component clause 193]
195. funny(fred) <- (14) [avatar component clause 193]
198. 15 <=> ! [X0] : strong(X0) [avatar definition]
199. strong(X0) <- (15) [avatar component clause 198]
256. strong(X0) [resolution 73,131]
257. 15 [avatar split clause 256,198]
258. kind(X0) <- (15) [resolution 199,70]
266. old(X0) <- (15) [resolution 101,258]
270. ~old(fred) <- (14) [resolution 175,195]
273. $false <- (14, 15) [subsumption resolution 270,266]
274. ~14 | ~15 [avatar contradiction clause 273]
293. funny(fred) | rich(fred) [resolution 83,130]
294. rich(fred) <- (~14) [subsumption resolution 293,194]
295. funny(fred) <- (~14) [resolution 294,95]
297. $false <- (~14) [subsumption resolution 295,194]
298. 14 [avatar contradiction clause 297]
299. $false [avatar sat refutation 257,274,298]
% SZS output end Proof for 3164171969224015810865006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not curious is rich and vice versa. Everyone who is curious is both not brave and brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. If someone is curious or not wise then someone is not rich. Everyone who is not curious is creative or not patient and vice versa. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. Lucy is either not curious or brave. Susan is either funny or not calm. Fred is not kind. Paul is tall or brave. | Lucy is not generous. | neutral | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(~brave(X)&brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul))) | ~generous(lucy) | [] | null | 0 |
Everyone who is not old is both rich and not strong and vice versa.
Everyone who is both not rich and curious is either not kind or not humble and vice versa.
Everyone who is both calm and not rich is both quiet and rich and vice versa.
If susan is not kind or humble then lucy is both not calm and not creative and vice versa.
If someone is not happy then lucy is both happy and wise and vice versa.
If paul is quiet or not wise then someone is not strong.
Everyone who is either not kind or rich is not old or not wise and vice versa.
Everyone who is brave is not brave.
Everyone who is quiet or not old is either not rich or not wise and vice versa.
Everyone who is not quiet or wise is both not rich and not kind and vice versa.
If fred is not happy then susan is not wise or calm.
If mary is not curious or not generous then someone is both not wise and not brave and vice versa.
If mary is either not funny or not humble then mary is not old or strong.
Everyone who is either not humble or not rich is both curious and not patient.
Everyone who is not brave or calm is not humble or not old.
If someone is both creative and calm then mary is either not curious or humble.
Someone is both not tall and not patient.
John is not generous.
Alice is not quiet or not rich.
John is both not patient and not tall. | John is not curious. | entailment | (![X]:(~old(X)<=>(rich(X)&~strong(X))))&
(![X]:((~rich(X)&curious(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((calm(X)&~rich(X))<=>(quiet(X)&rich(X))))&
(((~kind(susan)|humble(susan)))<=>((~calm(lucy)&~creative(lucy))))&
((?[X]:(~happy(X)))<=>((happy(lucy)&wise(lucy))))&
(((quiet(paul)|~wise(paul)))=>(?[X]:(~strong(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~old(X)|~wise(X))))&
(![X]:(brave(X)=>~brave(X)))&
(![X]:((quiet(X)|~old(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~rich(X)&~kind(X))))&
((~happy(fred))=>((~wise(susan)|calm(susan))))&
(((~curious(mary)|~generous(mary)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(((~funny(mary)<~>~humble(mary)))=>((~old(mary)|strong(mary))))&
(![X]:((~humble(X)<~>~rich(X))=>(curious(X)&~patient(X))))&
(![X]:((~brave(X)|calm(X))=>(~humble(X)|~old(X))))&
((?[X]:((creative(X)&calm(X))))=>((~curious(mary)<~>humble(mary))))&
(?[X]:((~tall(X)&~patient(X))))&
(~generous(john))&
((~quiet(alice)|~rich(alice)))&
((~patient(john)&~tall(john))) | ~curious(john) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8567001918441169948175637
% SZS output start Proof for 8567001918441169948175637
1. ! [X0] : (~old(X0) <=> (~strong(X0) & rich(X0))) [input p0]
2. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p1]
3. ! [X0] : ((~rich(X0) & calm(X0)) <=> (rich(X0) & quiet(X0))) [input p2]
7. ! [X0] : ((~kind(X0) <~> rich(X0)) <=> (~wise(X0) | ~old(X0))) [input p6]
8. ! [X0] : (brave(X0) => ~brave(X0)) [input p7]
10. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (~kind(X0) & ~rich(X0))) [input p9]
15. ! [X0] : ((calm(X0) | ~brave(X0)) => (~old(X0) | ~humble(X0))) [input p14]
21. curious(john) [input hypothesis]
28. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 8]
34. ! [X0] : ((~old(X0) | ~humble(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 15]
35. ! [X0] : (~old(X0) | ~humble(X0) | (~calm(X0) & brave(X0))) [flattening 34]
37. ! [X0] : ((~old(X0) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | old(X0))) [nnf transformation 1]
38. ! [X0] : ((~old(X0) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | old(X0))) [flattening 37]
39. ! [X0] : (((curious(X0) & ~rich(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~curious(X0) | rich(X0)))) [nnf transformation 2]
40. ! [X0] : (((curious(X0) & ~rich(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | ~curious(X0) | rich(X0))) [flattening 39]
41. ! [X0] : (((~rich(X0) & calm(X0)) | (~rich(X0) | ~quiet(X0))) & ((rich(X0) & quiet(X0)) | (rich(X0) | ~calm(X0)))) [nnf transformation 3]
42. ! [X0] : (((~rich(X0) & calm(X0)) | ~rich(X0) | ~quiet(X0)) & ((rich(X0) & quiet(X0)) | rich(X0) | ~calm(X0))) [flattening 41]
52. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [flattening 52]
56. ! [X0] : (((wise(X0) | ~quiet(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | ~quiet(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [flattening 56]
66. rich(X0) | old(X0) [cnf transformation 38]
70. ~curious(X0) | kind(X0) | humble(X0) | rich(X0) [cnf transformation 40]
78. ~rich(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 42]
92. ~kind(X0) | rich(X0) | wise(X0) [cnf transformation 53]
95. ~brave(X0) | ~brave(X0) [cnf transformation 28]
102. ~rich(X0) | quiet(X0) [cnf transformation 57]
105. ~wise(X0) | ~kind(X0) [cnf transformation 57]
117. ~old(X0) | ~humble(X0) | brave(X0) [cnf transformation 35]
123. curious(john) [cnf transformation 21]
124. ~brave(X0) [duplicate literal removal 95]
126. ~quiet(X0) | ~rich(X0) [duplicate literal removal 78]
186. ~rich(X0) [subsumption resolution 102,126]
238. ~humble(X0) | ~old(X0) [subsumption resolution 117,124]
243. old(X0) [resolution 66,186]
264. kind(john) | humble(john) | rich(john) [resolution 70,123]
265. kind(john) | humble(john) [subsumption resolution 264,186]
267. 24 <=> humble(john) [avatar definition]
269. humble(john) <- (24) [avatar component clause 267]
271. 25 <=> kind(john) [avatar definition]
273. kind(john) <- (25) [avatar component clause 271]
274. 24 | 25 [avatar split clause 265,271,267]
278. ~old(john) <- (24) [resolution 269,238]
283. $false <- (24) [subsumption resolution 278,243]
284. ~24 [avatar contradiction clause 283]
285. rich(john) | wise(john) <- (25) [resolution 273,92]
289. wise(john) <- (25) [subsumption resolution 285,186]
296. ~kind(john) <- (25) [resolution 289,105]
298. $false <- (25) [subsumption resolution 296,273]
299. ~25 [avatar contradiction clause 298]
300. $false [avatar sat refutation 274,284,299]
% SZS output end Proof for 8567001918441169948175637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not creative then fred is either quiet or creative.
Everyone who is both creative and not happy is not tall or not old.
Everyone who is either not patient or not wise is either not generous or brave and vice versa.
If fred is tall or not brave then someone is both not strong and quiet.
Everyone who is either curious or not generous is either happy or creative and vice versa.
If mary is not strong then someone is either creative or not tall and vice versa.
If someone is tall then someone is not curious or happy.
If paul is both not wise and not curious then someone is not old and vice versa.
If someone is calm then someone is funny or not curious.
Everyone who is rich is both tall and humble.
Everyone who is either not kind or not happy is both not happy and humble and vice versa.
Everyone who is not patient or not humble is both funny and not calm and vice versa.
Everyone who is kind or not creative is either not tall or not patient and vice versa.
If someone is either humble or generous then alice is either patient or curious and vice versa.
Everyone who is both not strong and strong is both not happy and not strong and vice versa.
If someone is happy or quiet then someone is strong and vice versa.
Someone is either not old or not generous.
John is not creative.
Someone is both not kind and curious.
Someone is not patient.
Someone is brave or calm.
Lucy is either tall or not kind.
Fred is both not brave and humble. | Paul is curious. | neutral | ((?[X]:((strong(X)|~creative(X))))=>((quiet(fred)<~>creative(fred))))&
(![X]:((creative(X)&~happy(X))=>(~tall(X)|~old(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(~generous(X)<~>brave(X))))&
(((tall(fred)|~brave(fred)))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(happy(X)<~>creative(X))))&
((~strong(mary))<=>(?[X]:((creative(X)<~>~tall(X)))))&
((?[X]:(tall(X)))=>(?[X]:((~curious(X)|happy(X)))))&
(((~wise(paul)&~curious(paul)))<=>(?[X]:(~old(X))))&
((?[X]:(calm(X)))=>(?[X]:((funny(X)|~curious(X)))))&
(![X]:(rich(X)=>(tall(X)&humble(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>(~happy(X)&humble(X))))&
(![X]:((~patient(X)|~humble(X))<=>(funny(X)&~calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~tall(X)<~>~patient(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>((patient(alice)<~>curious(alice))))&
(![X]:((~strong(X)&strong(X))<=>(~happy(X)&~strong(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:(strong(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
(~creative(john))&
(?[X]:((~kind(X)&curious(X))))&
(?[X]:(~patient(X)))&
(?[X]:((brave(X)|calm(X))))&
((tall(lucy)<~>~kind(lucy)))&
((~brave(fred)&humble(fred))) | curious(paul) | [] | null | 0 |
Everyone who is either not funny or creative is not patient or not strong.
If alice is either quiet or generous then someone is kind or quiet.
Everyone who is wise or kind is both not calm and tall.
If someone is old or kind then someone is both kind and not rich and vice versa.
Everyone who is not wise is either generous or not humble and vice versa.
If susan is both strong and not calm then lucy is either kind or not brave.
Everyone who is both creative and not kind is both humble and not old and vice versa.
Everyone who is both humble and not strong is either tall or not old.
If lucy is not patient or not wise then someone is either not brave or not old.
Everyone who is calm is wise and vice versa.
Everyone who is curious is either old or not brave and vice versa.
Everyone who is either quiet or not calm is either not funny or not calm.
Everyone who is not generous or old is not calm.
If lucy is not strong then lucy is generous or creative and vice versa.
If alice is both generous and not patient then someone is both not funny and not patient and vice versa.
If someone is either wise or rich then lucy is either strong or tall.
Someone is either humble or quiet.
Someone is not calm or funny.
Paul is both not creative and not patient.
Someone is either not rich or wise.
Paul is either not humble or happy.
Lucy is both not calm and not old. | Alice is quiet. | neutral | (![X]:((~funny(X)<~>creative(X))=>(~patient(X)|~strong(X))))&
(((quiet(alice)<~>generous(alice)))=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((wise(X)|kind(X))=>(~calm(X)&tall(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:(~wise(X)<=>(generous(X)<~>~humble(X))))&
(((strong(susan)&~calm(susan)))=>((kind(lucy)<~>~brave(lucy))))&
(![X]:((creative(X)&~kind(X))<=>(humble(X)&~old(X))))&
(![X]:((humble(X)&~strong(X))=>(tall(X)<~>~old(X))))&
(((~patient(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:(curious(X)<=>(old(X)<~>~brave(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((~generous(X)|old(X))=>~calm(X)))&
((~strong(lucy))<=>((generous(lucy)|creative(lucy))))&
(((generous(alice)&~patient(alice)))<=>(?[X]:((~funny(X)&~patient(X)))))&
((?[X]:((wise(X)<~>rich(X))))=>((strong(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((~calm(X)|funny(X))))&
((~creative(paul)&~patient(paul)))&
(?[X]:((~rich(X)<~>wise(X))))&
((~humble(paul)<~>happy(paul)))&
((~calm(lucy)&~old(lucy))) | quiet(alice) | [] | null | 0 |
If lucy is brave then someone is curious.
Everyone who is both funny and curious is curious or not funny and vice versa.
If alice is rich or not rich then mary is old or not happy.
Everyone who is not quiet or old is either curious or not generous and vice versa.
If mary is generous then alice is not happy or funny.
Everyone who is either not generous or patient is not generous or tall.
If fred is patient or rich then lucy is either not kind or quiet.
If susan is either humble or not funny then mary is funny and vice versa.
If someone is not happy or funny then someone is not calm and vice versa.
Everyone who is either not humble or not curious is both tall and not old.
If someone is old then fred is kind.
Everyone who is wise or calm is both patient and not kind.
If someone is either happy or brave then lucy is funny.
If mary is both not rich and not kind then someone is rich or curious.
If fred is either kind or not rich then someone is both not rich and wise and vice versa.
Everyone who is either patient or curious is not patient or quiet and vice versa.
Alice is rich.
Someone is not calm.
Someone is not humble or not funny.
Fred is humble.
Someone is not happy.
Alice is curious.
Someone is both not wise and not tall.
Someone is funny. | Fred is patient. | neutral | ((brave(lucy))=>(?[X]:(curious(X))))&
(![X]:((funny(X)&curious(X))<=>(curious(X)|~funny(X))))&
(((rich(alice)|~rich(alice)))=>((old(mary)|~happy(mary))))&
(![X]:((~quiet(X)|old(X))<=>(curious(X)<~>~generous(X))))&
((generous(mary))=>((~happy(alice)|funny(alice))))&
(![X]:((~generous(X)<~>patient(X))=>(~generous(X)|tall(X))))&
(((patient(fred)|rich(fred)))=>((~kind(lucy)<~>quiet(lucy))))&
(((humble(susan)<~>~funny(susan)))<=>(funny(mary)))&
((?[X]:((~happy(X)|funny(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~humble(X)<~>~curious(X))=>(tall(X)&~old(X))))&
((?[X]:(old(X)))=>(kind(fred)))&
(![X]:((wise(X)|calm(X))=>(patient(X)&~kind(X))))&
((?[X]:((happy(X)<~>brave(X))))=>(funny(lucy)))&
(((~rich(mary)&~kind(mary)))=>(?[X]:((rich(X)|curious(X)))))&
(((kind(fred)<~>~rich(fred)))<=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((patient(X)<~>curious(X))<=>(~patient(X)|quiet(X))))&
(rich(alice))&
(?[X]:(~calm(X)))&
(?[X]:((~humble(X)|~funny(X))))&
(humble(fred))&
(?[X]:(~happy(X)))&
(curious(alice))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:(funny(X))) | patient(fred) | [] | null | 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.