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 someone is not rich then someone is not happy or quiet.
Everyone who is both not funny and not tall is both happy and not old.
Everyone who is both quiet and not humble is not happy or old and vice versa.
Everyone who is both curious and rich is not wise and vice versa.
If alice is quiet or happy then alice is tall.
Everyone who is curious or humble is creative or old and vice versa.
If someone is not happy or old then mary is not strong or calm and vice versa.
Everyone who is either patient or not brave is both creative and not rich and vice versa.
If alice is both patient and not kind then lucy is kind.
If paul is both not funny and not strong then someone is both not brave and creative and vice versa.
Everyone who is both happy and rich is not generous or not old and vice versa.
If john is rich or not strong then paul is both not generous and rich and vice versa.
If someone is generous or not old then susan is funny or brave.
Everyone who is not strong is both not creative and not kind and vice versa.
Everyone who is both not kind and curious is either creative or kind and vice versa.
If someone is either generous or old then someone is not calm or not happy.
Alice is both not generous and patient.
Someone is not calm.
Susan is old.
Someone is both creative and curious.
Lucy is both not generous and not curious.
Someone is not wise or creative.
Someone is humble. | Lucy is not rich. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((~funny(X)&~tall(X))=>(happy(X)&~old(X))))&
(![X]:((quiet(X)&~humble(X))<=>(~happy(X)|old(X))))&
(![X]:((curious(X)&rich(X))<=>~wise(X)))&
(((quiet(alice)|happy(alice)))=>(tall(alice)))&
(![X]:((curious(X)|humble(X))<=>(creative(X)|old(X))))&
((?[X]:((~happy(X)|old(X))))<=>((~strong(mary)|calm(mary))))&
(![X]:((patient(X)<~>~brave(X))<=>(creative(X)&~rich(X))))&
(((patient(alice)&~kind(alice)))=>(kind(lucy)))&
(((~funny(paul)&~strong(paul)))<=>(?[X]:((~brave(X)&creative(X)))))&
(![X]:((happy(X)&rich(X))<=>(~generous(X)|~old(X))))&
(((rich(john)|~strong(john)))<=>((~generous(paul)&rich(paul))))&
((?[X]:((generous(X)|~old(X))))=>((funny(susan)|brave(susan))))&
(![X]:(~strong(X)<=>(~creative(X)&~kind(X))))&
(![X]:((~kind(X)&curious(X))<=>(creative(X)<~>kind(X))))&
((?[X]:((generous(X)<~>old(X))))=>(?[X]:((~calm(X)|~happy(X)))))&
((~generous(alice)&patient(alice)))&
(?[X]:(~calm(X)))&
(old(susan))&
(?[X]:((creative(X)&curious(X))))&
((~generous(lucy)&~curious(lucy)))&
(?[X]:((~wise(X)|creative(X))))&
(?[X]:(humble(X))) | ~rich(lucy) | [
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4748770068859007391702593
% SZS output start Proof for 4748770068859007391702593
11. ! [X0] : ((rich(X0) & happy(X0)) <=> (~old(X0) | ~generous(X0))) [input p10]
21. ~curious(lucy) & ~generous(lucy) [input p20]
24. ~rich(lucy) [input hypothesis]
56. ! [X0] : (((rich(X0) & happy(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~rich(X0) | ~happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((rich(X0) & happy(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~rich(X0) | ~happy(X0))) [flattening 56]
106. generous(X0) | rich(X0) [cnf transformation 57]
132. ~generous(lucy) [cnf transformation 21]
136. ~rich(lucy) [cnf transformation 24]
290. rich(lucy) [resolution 106,132]
291. $false [subsumption resolution 290,136]
% SZS output end Proof for 4748770068859007391702593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or happy is either not calm or not brave.
If alice is not tall or not rich then someone is either rich or not humble.
If someone is either not kind or kind then someone is either kind or not tall and vice versa.
If someone is kind then someone is not strong and vice versa.
Everyone who is either rich or not generous is patient and vice versa.
If someone is both tall and not kind then someone is either funny or patient.
If paul is not generous then mary is either not wise or not generous.
Everyone who is not brave or curious is both quiet and not calm.
If someone is tall or creative then fred is either not generous or not kind.
Everyone who is not old is both creative and funny and vice versa.
Everyone who is not generous is rich and vice versa.
If lucy is both humble and not creative then someone is not humble and vice versa.
Everyone who is calm is curious or funny.
If john is both calm and happy then fred is not kind or curious and vice versa.
Everyone who is both not creative and funny is calm and vice versa.
If someone is happy or rich then fred is both not generous and kind and vice versa.
John is both kind and not patient.
Someone is both quiet and calm.
Alice is not humble or funny.
John is either funny or not humble.
Someone is kind. | Paul is patient. | contradiction | (![X]:((~kind(X)<~>happy(X))=>(~calm(X)<~>~brave(X))))&
(((~tall(alice)|~rich(alice)))=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:((kind(X)<~>~tall(X)))))&
((?[X]:(kind(X)))<=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~generous(X))<=>patient(X)))&
((?[X]:((tall(X)&~kind(X))))=>(?[X]:((funny(X)<~>patient(X)))))&
((~generous(paul))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~brave(X)|curious(X))=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|creative(X))))=>((~generous(fred)<~>~kind(fred))))&
(![X]:(~old(X)<=>(creative(X)&funny(X))))&
(![X]:(~generous(X)<=>rich(X)))&
(((humble(lucy)&~creative(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:(calm(X)=>(curious(X)|funny(X))))&
(((calm(john)&happy(john)))<=>((~kind(fred)|curious(fred))))&
(![X]:((~creative(X)&funny(X))<=>calm(X)))&
((?[X]:((happy(X)|rich(X))))<=>((~generous(fred)&kind(fred))))&
((kind(john)&~patient(john)))&
(?[X]:((quiet(X)&calm(X))))&
((~humble(alice)|funny(alice)))&
((funny(john)<~>~humble(john)))&
(?[X]:(kind(X))) | patient(paul) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8872530277515017480520980
% SZS output start Proof for 8872530277515017480520980
5. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> patient(X0)) [input p4]
11. ! [X0] : (~generous(X0) <=> rich(X0)) [input p10]
22. patient(paul) [input hypothesis]
50. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ~patient(X0)) & (patient(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 5]
57. ! [X0] : ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0))) [nnf transformation 11]
97. ~patient(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
98. ~patient(X0) | ~rich(X0) | generous(X0) [cnf transformation 50]
109. generous(X0) | rich(X0) [cnf transformation 57]
110. ~generous(X0) | ~rich(X0) [cnf transformation 57]
135. patient(paul) [cnf transformation 22]
205. 15 <=> generous(paul) [avatar definition]
206. ~generous(paul) <- (~15) [avatar component clause 205]
322. rich(paul) | ~generous(paul) [resolution 97,135]
328. ~generous(paul) [subsumption resolution 322,110]
329. ~15 [avatar split clause 328,205]
330. rich(paul) <- (~15) [resolution 206,109]
332. ~rich(paul) | generous(paul) [resolution 98,135]
335. generous(paul) <- (~15) [subsumption resolution 332,330]
336. $false <- (~15) [subsumption resolution 335,206]
337. 15 [avatar contradiction clause 336]
338. $false [avatar sat refutation 329,337]
% SZS output end Proof for 8872530277515017480520980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is either quiet or not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
Susan is both not curious and old.
Someone is curious.
Fred is either not calm or not rich.
Someone is generous.
Someone is both quiet and not happy.
Someone is either curious or humble. | Paul is not old. | neutral | (![X]:((~rich(X)&~generous(X))<=>(quiet(X)<~>~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
((~curious(susan)&old(susan)))&
(?[X]:(curious(X)))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is both tall and not kind is either strong or not tall and vice versa.
Everyone who is both calm and not creative is either rich or not funny and vice versa.
If someone is quiet then paul is both rich and wise and vice versa.
If susan is humble then alice is creative or not strong and vice versa.
If someone is patient then someone is old or not patient.
Everyone who is funny is brave or not creative and vice versa.
If someone is either not creative or not patient then john is both curious and old and vice versa.
Everyone who is both not wise and humble is either not wise or patient.
Everyone who is either not wise or brave is either patient or generous and vice versa.
Everyone who is either not tall or not happy is either funny or strong and vice versa.
If someone is either curious or creative then lucy is both curious and not brave and vice versa.
Everyone who is humble is not humble.
Everyone who is both patient and not calm is old and vice versa.
If someone is either curious or not tall then john is not happy and vice versa.
Everyone who is rich or kind is both not quiet and strong and vice versa.
If mary is funny or creative then mary is not curious or not creative.
Someone is either not strong or brave.
Someone is both old and wise.
Fred is quiet or not kind.
Someone is both not brave and tall.
John is either not quiet or not rich.
Alice is not rich or quiet.
Alice is patient or curious.
Fred is wise or not brave. | Alice is creative. | contradiction | (![X]:((tall(X)&~kind(X))<=>(strong(X)<~>~tall(X))))&
(![X]:((calm(X)&~creative(X))<=>(rich(X)<~>~funny(X))))&
((?[X]:(quiet(X)))<=>((rich(paul)&wise(paul))))&
((humble(susan))<=>((creative(alice)|~strong(alice))))&
((?[X]:(patient(X)))=>(?[X]:((old(X)|~patient(X)))))&
(![X]:(funny(X)<=>(brave(X)|~creative(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((curious(john)&old(john))))&
(![X]:((~wise(X)&humble(X))=>(~wise(X)<~>patient(X))))&
(![X]:((~wise(X)<~>brave(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>((curious(lucy)&~brave(lucy))))&
(![X]:(humble(X)=>~humble(X)))&
(![X]:((patient(X)&~calm(X))<=>old(X)))&
((?[X]:((curious(X)<~>~tall(X))))<=>(~happy(john)))&
(![X]:((rich(X)|kind(X))<=>(~quiet(X)&strong(X))))&
(((funny(mary)|creative(mary)))=>((~curious(mary)|~creative(mary))))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((old(X)&wise(X))))&
((quiet(fred)|~kind(fred)))&
(?[X]:((~brave(X)&tall(X))))&
((~quiet(john)<~>~rich(john)))&
((~rich(alice)|quiet(alice)))&
((patient(alice)|curious(alice)))&
((wise(fred)|~brave(fred))) | creative(alice) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8600855458743788119213886
% SZS output start Proof for 8600855458743788119213886
4. humble(susan) <=> (~strong(alice) | creative(alice)) [input p3]
12. ! [X0] : (humble(X0) => ~humble(X0)) [input p11]
25. creative(alice) [input hypothesis]
30. ! [X0] : (~humble(X0) | ~humble(X0)) [ennf transformation 12]
42. (humble(susan) | (strong(alice) & ~creative(alice))) & ((~strong(alice) | creative(alice)) | ~humble(susan)) [nnf transformation 4]
43. (humble(susan) | (strong(alice) & ~creative(alice))) & (~strong(alice) | creative(alice) | ~humble(susan)) [flattening 42]
94. humble(susan) | ~creative(alice) [cnf transformation 43]
130. ~humble(X0) | ~humble(X0) [cnf transformation 30]
157. creative(alice) [cnf transformation 25]
159. ~humble(X0) [duplicate literal removal 130]
187. 6 <=> humble(susan) [avatar definition]
189. humble(susan) <- (6) [avatar component clause 187]
192. 7 <=> creative(alice) [avatar definition]
195. ~7 | 6 [avatar split clause 94,187,192]
337. 7 [avatar split clause 157,192]
338. $false <- (6) [subsumption resolution 189,159]
339. ~6 [avatar contradiction clause 338]
340. $false [avatar sat refutation 195,337,339]
% SZS output end Proof for 8600855458743788119213886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not strong is both not brave and kind and vice versa.
If someone is kind or humble then someone is old.
Everyone who is both happy and curious is either not humble or calm.
Everyone who is quiet or happy is both not generous and tall.
Everyone who is either brave or curious is either not happy or kind.
If someone is not patient then alice is both not creative and not calm and vice versa.
If alice is either not brave or quiet then someone is either not generous or not patient.
Everyone who is not kind or calm is not kind or kind.
Everyone who is both kind and not old is either not quiet or curious.
Everyone who is both curious and not happy is strong and vice versa.
If someone is both not generous and patient then someone is either funny or generous and vice versa.
Everyone who is both generous and not rich is not happy or not brave and vice versa.
If mary is both humble and not strong then paul is either not generous or rich and vice versa.
Everyone who is patient or curious is either calm or not funny.
If someone is rich or curious then alice is both old and not rich.
If someone is not quiet then someone is wise.
Mary is patient or tall.
Lucy is either wise or not strong.
Someone is either not creative or not patient.
John is either not rich or kind.
Alice is wise.
Someone is not funny or not humble.
Fred is not quiet.
Someone is not humble. | John is not funny. | contradiction | (![X]:((tall(X)&~strong(X))<=>(~brave(X)&kind(X))))&
((?[X]:((kind(X)|humble(X))))=>(?[X]:(old(X))))&
(![X]:((happy(X)&curious(X))=>(~humble(X)<~>calm(X))))&
(![X]:((quiet(X)|happy(X))=>(~generous(X)&tall(X))))&
(![X]:((brave(X)<~>curious(X))=>(~happy(X)<~>kind(X))))&
((?[X]:(~patient(X)))<=>((~creative(alice)&~calm(alice))))&
(((~brave(alice)<~>quiet(alice)))=>(?[X]:((~generous(X)<~>~patient(X)))))&
(![X]:((~kind(X)|calm(X))=>(~kind(X)|kind(X))))&
(![X]:((kind(X)&~old(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((curious(X)&~happy(X))<=>strong(X)))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~happy(X)|~brave(X))))&
(((humble(mary)&~strong(mary)))<=>((~generous(paul)<~>rich(paul))))&
(![X]:((patient(X)|curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((rich(X)|curious(X))))=>((old(alice)&~rich(alice))))&
((?[X]:(~quiet(X)))=>(?[X]:(wise(X))))&
((patient(mary)|tall(mary)))&
((wise(lucy)<~>~strong(lucy)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~rich(john)<~>kind(john)))&
(wise(alice))&
(?[X]:((~funny(X)|~humble(X))))&
(~quiet(fred))&
(?[X]:(~humble(X))) | ~funny(john) | [
"p0",
"p3",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8555211754324755505515834
% SZS output start Proof for 8555211754324755505515834
1. ! [X0] : ((~strong(X0) & tall(X0)) <=> (kind(X0) & ~brave(X0))) [input p0]
4. ! [X0] : ((happy(X0) | quiet(X0)) => (tall(X0) & ~generous(X0))) [input p3]
10. ! [X0] : ((~happy(X0) & curious(X0)) <=> strong(X0)) [input p9]
11. ? [X0] : (patient(X0) & ~generous(X0)) <=> ? [X0] : (funny(X0) <~> generous(X0)) [input p10]
12. ! [X0] : ((~rich(X0) & generous(X0)) <=> (~brave(X0) | ~happy(X0))) [input p11]
25. ~funny(john) [input hypothesis]
27. ? [X0] : (patient(X0) & ~generous(X0)) <=> ? [X1] : (funny(X1) <~> generous(X1)) [rectify 11]
34. ! [X0] : ((tall(X0) & ~generous(X0)) | (~happy(X0) & ~quiet(X0))) [ennf transformation 4]
42. ! [X0] : (((~strong(X0) & tall(X0)) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | (strong(X0) | ~tall(X0)))) [nnf transformation 1]
43. ! [X0] : (((~strong(X0) & tall(X0)) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | strong(X0) | ~tall(X0))) [flattening 42]
54. ! [X0] : (((~happy(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | (happy(X0) | ~curious(X0)))) [nnf transformation 10]
55. ! [X0] : (((~happy(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | happy(X0) | ~curious(X0))) [flattening 54]
56. (? [X0] : (patient(X0) & ~generous(X0)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (? [X1] : ((~generous(X1) | ~funny(X1)) & (generous(X1) | funny(X1))) | ! [X0] : (~patient(X0) | generous(X0))) [nnf transformation 27]
57. (? [X0] : (patient(X0) & ~generous(X0)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (? [X2] : ((~generous(X2) | ~funny(X2)) & (generous(X2) | funny(X2))) | ! [X3] : (~patient(X3) | generous(X3))) [rectify 56]
58. ? [X0] : (patient(X0) & ~generous(X0)) => (patient(sK2) & ~generous(sK2)) [choice axiom]
59. ? [X2] : ((~generous(X2) | ~funny(X2)) & (generous(X2) | funny(X2))) => ((~generous(sK3) | ~funny(sK3)) & (generous(sK3) | funny(sK3))) [choice axiom]
60. ((patient(sK2) & ~generous(sK2)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (((~generous(sK3) | ~funny(sK3)) & (generous(sK3) | funny(sK3))) | ! [X3] : (~patient(X3) | generous(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((~rich(X0) & generous(X0)) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | (rich(X0) | ~generous(X0)))) [nnf transformation 12]
62. ! [X0] : (((~rich(X0) & generous(X0)) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | rich(X0) | ~generous(X0))) [flattening 61]
78. ~brave(X0) | strong(X0) | ~tall(X0) [cnf transformation 43]
87. ~happy(X0) | tall(X0) [cnf transformation 34]
103. ~happy(X0) | ~strong(X0) [cnf transformation 55]
107. ~generous(sK2) | funny(X1) | ~generous(X1) [cnf transformation 60]
111. generous(X0) | happy(X0) [cnf transformation 62]
112. generous(X0) | brave(X0) [cnf transformation 62]
139. ~funny(john) [cnf transformation 25]
180. 9 <=> ! [X1] : (funny(X1) | ~generous(X1)) [avatar definition]
181. ~generous(X1) | funny(X1) <- (9) [avatar component clause 180]
192. 12 <=> generous(sK2) [avatar definition]
194. ~generous(sK2) <- (~12) [avatar component clause 192]
195. 9 | ~12 [avatar split clause 107,192,180]
303. happy(sK2) <- (~12) [resolution 111,194]
307. brave(sK2) <- (~12) [resolution 112,194]
311. ~strong(sK2) <- (~12) [resolution 303,103]
312. tall(sK2) <- (~12) [resolution 303,87]
321. funny(X0) | brave(X0) <- (9) [resolution 181,112]
322. funny(X1) | happy(X1) <- (9) [resolution 181,111]
326. strong(sK2) | ~tall(sK2) <- (~12) [resolution 78,307]
328. ~tall(sK2) <- (~12) [subsumption resolution 326,311]
329. $false <- (~12) [subsumption resolution 328,312]
330. 12 [avatar contradiction clause 329]
474. brave(john) <- (9) [resolution 321,139]
476. strong(john) | ~tall(john) <- (9) [resolution 474,78]
478. 54 <=> tall(john) [avatar definition]
480. ~tall(john) <- (~54) [avatar component clause 478]
482. 55 <=> strong(john) [avatar definition]
485. ~54 | 55 | ~9 [avatar split clause 476,180,482,478]
489. happy(john) <- (9) [resolution 322,139]
503. ~strong(john) <- (9) [resolution 489,103]
504. tall(john) <- (9) [resolution 489,87]
507. ~55 | ~9 [avatar split clause 503,180,482]
508. $false <- (9, ~54) [subsumption resolution 504,480]
509. ~9 | 54 [avatar contradiction clause 508]
510. $false [avatar sat refutation 195,330,485,507,509]
% SZS output end Proof for 8555211754324755505515834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not generous or not patient then someone is either wise or not tall and vice versa.
Everyone who is brave or not patient is not generous.
Everyone who is not patient or not rich is both happy and not old and vice versa.
Everyone who is both not rich and not brave is not wise or rich.
If paul is kind then paul is either kind or not old.
Everyone who is not patient or rich is either not patient or not calm and vice versa.
If john is either not funny or not wise then someone is both not generous and not rich and vice versa.
Everyone who is not quiet or rich is either not patient or not rich and vice versa.
If someone is either not rich or not calm then someone is strong.
Everyone who is not kind or quiet is either tall or creative and vice versa.
Everyone who is not calm is both not old and not generous and vice versa.
Everyone who is both not old and quiet is both generous and not tall.
If someone is not rich or patient then susan is either not generous or not rich and vice versa.
Everyone who is both generous and brave is both wise and curious.
Everyone who is either humble or not old is both old and not quiet and vice versa.
Mary is not tall or curious.
Alice is old or humble.
Someone is both not rich and not curious.
Someone is either not quiet or strong.
Someone is both kind and not rich. | Paul is not rich. | entailment | (((~generous(susan)<~>~patient(susan)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((brave(X)|~patient(X))=>~generous(X)))&
(![X]:((~patient(X)|~rich(X))<=>(happy(X)&~old(X))))&
(![X]:((~rich(X)&~brave(X))=>(~wise(X)|rich(X))))&
((kind(paul))=>((kind(paul)<~>~old(paul))))&
(![X]:((~patient(X)|rich(X))<=>(~patient(X)<~>~calm(X))))&
(((~funny(john)<~>~wise(john)))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~quiet(X)|rich(X))<=>(~patient(X)<~>~rich(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>(?[X]:(strong(X))))&
(![X]:((~kind(X)|quiet(X))<=>(tall(X)<~>creative(X))))&
(![X]:(~calm(X)<=>(~old(X)&~generous(X))))&
(![X]:((~old(X)&quiet(X))=>(generous(X)&~tall(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((~generous(susan)<~>~rich(susan))))&
(![X]:((generous(X)&brave(X))=>(wise(X)&curious(X))))&
(![X]:((humble(X)<~>~old(X))<=>(old(X)&~quiet(X))))&
((~tall(mary)|curious(mary)))&
((old(alice)|humble(alice)))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((kind(X)&~rich(X)))) | ~rich(paul) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4118088752108356216773417
% SZS output start Proof for 4118088752108356216773417
2. ! [X0] : ((~patient(X0) | brave(X0)) => ~generous(X0)) [input p1]
3. ! [X0] : ((~rich(X0) | ~patient(X0)) <=> (~old(X0) & happy(X0))) [input p2]
6. ! [X0] : ((rich(X0) | ~patient(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p5]
8. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p7]
11. ! [X0] : (~calm(X0) <=> (~generous(X0) & ~old(X0))) [input p10]
21. rich(paul) [input hypothesis]
23. ! [X0] : (~generous(X0) | (patient(X0) & ~brave(X0))) [ennf transformation 2]
36. ! [X0] : (((~rich(X0) | ~patient(X0)) | (old(X0) | ~happy(X0))) & ((~old(X0) & happy(X0)) | (rich(X0) & patient(X0)))) [nnf transformation 3]
37. ! [X0] : ((~rich(X0) | ~patient(X0) | old(X0) | ~happy(X0)) & ((~old(X0) & happy(X0)) | (rich(X0) & patient(X0)))) [flattening 36]
39. ! [X0] : (((rich(X0) | ~patient(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~rich(X0) & patient(X0)))) [nnf transformation 6]
40. ! [X0] : ((rich(X0) | ~patient(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~rich(X0) & patient(X0)))) [flattening 39]
45. ! [X0] : (((rich(X0) | ~quiet(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (~rich(X0) & quiet(X0)))) [nnf transformation 8]
46. ! [X0] : ((rich(X0) | ~quiet(X0) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (~rich(X0) & quiet(X0)))) [flattening 45]
53. ! [X0] : ((~calm(X0) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | calm(X0))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | calm(X0))) [flattening 53]
77. ~generous(X0) | patient(X0) [cnf transformation 23]
80. ~old(X0) | patient(X0) [cnf transformation 37]
88. calm(X0) | patient(X0) | patient(X0) [cnf transformation 40]
99. ~rich(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 46]
114. ~calm(X0) | generous(X0) | old(X0) [cnf transformation 54]
139. rich(paul) [cnf transformation 21]
142. ~rich(X0) | ~patient(X0) [duplicate literal removal 99]
144. calm(X0) | patient(X0) [duplicate literal removal 88]
268. ~patient(paul) [resolution 142,139]
301. generous(X0) | old(X0) | patient(X0) [resolution 114,144]
312. old(X0) | patient(X0) [subsumption resolution 301,77]
313. patient(X0) [subsumption resolution 312,80]
321. $false [resolution 313,268]
% SZS output end Proof for 4118088752108356216773417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not curious or strong then someone is both calm and not kind and vice versa.
If someone is either tall or strong then someone is humble and vice versa.
Everyone who is not quiet or kind is happy or calm.
Everyone who is both not old and happy is both not curious and not creative and vice versa.
Everyone who is kind or tall is either wise or happy.
Everyone who is not humble or funny is either not strong or not calm.
Everyone who is wise is not humble or kind and vice versa.
If mary is both not humble and patient then alice is generous or not patient and vice versa.
Everyone who is both generous and rich is not generous.
If someone is not generous then someone is either wise or not strong and vice versa.
If fred is either not calm or wise then lucy is not strong.
Everyone who is both old and patient is either not tall or patient and vice versa.
If someone is not calm or not happy then john is both curious and not patient.
Everyone who is both not brave and not old is old.
Everyone who is old or not rich is both not tall and rich.
Everyone who is both not generous and not humble is not tall or tall and vice versa.
Someone is either happy or not happy.
Alice is both patient and not old.
John is either old or not old.
Someone is both not kind and quiet.
Mary is not humble.
Someone is not patient or tall. | Mary is not patient. | entailment | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(happy(X)|calm(X))))&
(![X]:((~old(X)&happy(X))<=>(~curious(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))=>(wise(X)<~>happy(X))))&
(![X]:((~humble(X)|funny(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~humble(X)|kind(X))))&
(((~humble(mary)&patient(mary)))<=>((generous(alice)|~patient(alice))))&
(![X]:((generous(X)&rich(X))=>~generous(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
((patient(alice)&~old(alice)))&
((old(john)<~>~old(john)))&
(?[X]:((~kind(X)&quiet(X))))&
(~humble(mary))&
(?[X]:((~patient(X)|tall(X)))) | ~patient(mary) | [
"p7",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6966118470833318112372318
% SZS output start Proof for 6966118470833318112372318
8. (patient(mary) & ~humble(mary)) <=> (~patient(alice) | generous(alice)) [input p7]
16. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (tall(X0) | ~tall(X0))) [input p15]
18. ~old(alice) & patient(alice) [input p17]
21. ~humble(mary) [input p20]
23. patient(mary) [input hypothesis]
54. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & ((~patient(alice) | generous(alice)) | (~patient(mary) | humble(mary))) [nnf transformation 8]
55. ((patient(mary) & ~humble(mary)) | (patient(alice) & ~generous(alice))) & (~patient(alice) | generous(alice) | ~patient(mary) | humble(mary)) [flattening 54]
64. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 16]
65. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | humble(X0) | generous(X0))) [flattening 64]
98. ~patient(alice) | generous(alice) | ~patient(mary) | humble(mary) [cnf transformation 55]
125. ~generous(X0) | tall(X0) [cnf transformation 65]
126. ~generous(X0) | ~tall(X0) [cnf transformation 65]
131. patient(alice) [cnf transformation 18]
136. ~humble(mary) [cnf transformation 21]
138. patient(mary) [cnf transformation 23]
194. 12 <=> patient(alice) [avatar definition]
198. 13 <=> patient(mary) [avatar definition]
203. 14 <=> generous(alice) [avatar definition]
204. generous(alice) <- (14) [avatar component clause 203]
208. 15 <=> humble(mary) [avatar definition]
213. 15 | ~13 | 14 | ~12 [avatar split clause 98,194,203,198,208]
275. ~generous(X0) [subsumption resolution 125,126]
276. 12 [avatar split clause 131,194]
277. ~15 [avatar split clause 136,208]
279. 13 [avatar split clause 138,198]
280. $false <- (14) [subsumption resolution 204,275]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 213,276,277,279,281]
% SZS output end Proof for 6966118470833318112372318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not humble or not happy then fred is not brave or not funny. If fred is quiet then john is either rich or not generous. If john is generous then someone is old or not rich. Everyone who is both quiet and curious is not patient and vice versa. Everyone who is not funny or happy is not generous. If someone is quiet or not humble then someone is funny and vice versa. Everyone who is happy or not curious is not brave or creative and vice versa. Everyone who is both wise and creative is both not rich and curious and vice versa. Everyone who is either brave or not quiet is generous and vice versa. Everyone who is not wise or not curious is both tall and not quiet and vice versa. Everyone who is both not humble and kind is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Everyone who is either not generous or patient is curious and vice versa. Everyone who is both calm and quiet is both not patient and not brave and vice versa. Susan is either tall or not brave. Paul is kind or not humble. Alice is both humble and not strong. Someone is curious. Someone is both calm and not funny. Someone is creative. | Lucy is not happy. | contradiction | (((~humble(lucy)<~>~happy(lucy)))=>((~brave(fred)|~funny(fred))))&
((quiet(fred))=>((rich(john)<~>~generous(john))))&
((generous(john))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>~patient(X)))&
(![X]:((~funny(X)|happy(X))=>~generous(X)))&
((?[X]:((quiet(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)|~curious(X))<=>(~brave(X)|creative(X))))&
(![X]:((wise(X)&creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((~wise(X)|~curious(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~old(X))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>patient(X))<=>curious(X)))&
(![X]:((calm(X)&quiet(X))<=>(~patient(X)&~brave(X))))&
((tall(susan)<~>~brave(susan)))&
((kind(paul)|~humble(paul)))&
((humble(alice)&~strong(alice)))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:(creative(X))) | ~happy(lucy) | [
"p3",
"p4",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9024806141240165689680645
% SZS output start Proof for 9024806141240165689680645
4. ! [X0] : ((curious(X0) & quiet(X0)) <=> ~patient(X0)) [input p3]
5. ! [X0] : ((happy(X0) | ~funny(X0)) => ~generous(X0)) [input p4]
7. ! [X0] : ((~curious(X0) | happy(X0)) <=> (creative(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((brave(X0) <~> ~quiet(X0)) <=> generous(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> (~quiet(X0) & tall(X0))) [input p9]
11. ! [X0] : ((kind(X0) & ~humble(X0)) <=> (~old(X0) | patient(X0))) [input p10]
12. ! [X0] : ((strong(X0) | quiet(X0)) <=> (~humble(X0) <~> ~brave(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (rich(X0) <~> ~old(X0))) [input p12]
14. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p13]
15. ! [X0] : ((~generous(X0) <~> patient(X0)) <=> curious(X0)) [input p14]
23. ~happy(lucy) [input hypothesis]
29. ! [X0] : (~generous(X0) | (~happy(X0) & funny(X0))) [ennf transformation 5]
30. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 14]
35. ! [X0] : (((curious(X0) & quiet(X0)) | patient(X0)) & (~patient(X0) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 4]
36. ! [X0] : (((curious(X0) & quiet(X0)) | patient(X0)) & (~patient(X0) | ~curious(X0) | ~quiet(X0))) [flattening 35]
42. ! [X0] : (((~curious(X0) | happy(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (curious(X0) & ~happy(X0)))) [nnf transformation 7]
43. ! [X0] : ((~curious(X0) | happy(X0) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | (curious(X0) & ~happy(X0)))) [flattening 42]
46. ! [X0] : ((((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ~generous(X0)) & (generous(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))))) [nnf transformation 9]
47. ! [X0] : (((~curious(X0) | ~wise(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (curious(X0) & wise(X0)))) [nnf transformation 10]
48. ! [X0] : ((~curious(X0) | ~wise(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (curious(X0) & wise(X0)))) [flattening 47]
49. ! [X0] : (((kind(X0) & ~humble(X0)) | (old(X0) & ~patient(X0))) & ((~old(X0) | patient(X0)) | (~kind(X0) | humble(X0)))) [nnf transformation 11]
50. ! [X0] : (((kind(X0) & ~humble(X0)) | (old(X0) & ~patient(X0))) & (~old(X0) | patient(X0) | ~kind(X0) | humble(X0))) [flattening 49]
51. ! [X0] : (((strong(X0) | quiet(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (~strong(X0) & ~quiet(X0)))) [nnf transformation 12]
52. ! [X0] : ((strong(X0) | quiet(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (~strong(X0) & ~quiet(X0)))) [flattening 51]
53. ! [X0] : ((tall(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0))) [nnf transformation 13]
54. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 30]
55. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | ~curious(X0)) & (curious(X0) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [nnf transformation 15]
70. ~patient(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 36]
71. patient(X0) | quiet(X0) [cnf transformation 36]
72. patient(X0) | curious(X0) [cnf transformation 36]
74. ~generous(X0) | ~happy(X0) [cnf transformation 29]
80. ~curious(X0) | happy(X0) | brave(X0) [cnf transformation 43]
86. ~quiet(X0) | generous(X0) | ~brave(X0) [cnf transformation 46]
89. ~generous(X0) | ~brave(X0) | quiet(X0) [cnf transformation 46]
91. tall(X0) | curious(X0) [cnf transformation 48]
98. ~patient(X0) | kind(X0) [cnf transformation 50]
99. kind(X0) | old(X0) [cnf transformation 50]
100. ~quiet(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 52]
102. ~quiet(X0) | humble(X0) | brave(X0) [cnf transformation 52]
106. ~tall(X0) | rich(X0) | ~old(X0) [cnf transformation 53]
107. ~tall(X0) | ~rich(X0) | old(X0) [cnf transformation 53]
110. ~kind(X0) | ~old(X0) | ~rich(X0) [cnf transformation 54]
111. rich(X0) | old(X0) | ~kind(X0) [cnf transformation 54]
114. patient(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 55]
115. ~patient(X0) | generous(X0) | ~curious(X0) [cnf transformation 55]
129. ~happy(lucy) [cnf transformation 23]
131. 1 <=> happy(lucy) [avatar definition]
132. ~happy(lucy) <- (~1) [avatar component clause 131]
184. 13 <=> ! [X3] : humble(X3) [avatar definition]
185. humble(X3) <- (13) [avatar component clause 184]
195. old(X0) | rich(X0) [subsumption resolution 111,99]
196. ~generous(X0) | patient(X0) [subsumption resolution 114,72]
217. ~1 [avatar split clause 129,131]
223. kind(X0) | curious(X0) [resolution 98,72]
355. rich(X0) | ~old(X0) | curious(X0) [resolution 106,91]
358. curious(X0) | rich(X0) [subsumption resolution 355,195]
360. ~rich(X0) | old(X0) | curious(X0) [resolution 107,91]
363. curious(X0) | old(X0) [subsumption resolution 360,358]
376. ~old(X0) | ~rich(X0) | curious(X0) [resolution 110,223]
378. ~old(X0) | curious(X0) [subsumption resolution 376,358]
379. curious(X0) [subsumption resolution 378,363]
382. brave(X2) | happy(X2) [resolution 379,80]
389. generous(X1) | ~curious(X1) | quiet(X1) [resolution 115,71]
390. generous(X1) | quiet(X1) [subsumption resolution 389,379]
535. quiet(X0) | ~brave(X0) | quiet(X0) [resolution 390,89]
539. ~happy(X4) | quiet(X4) [resolution 390,74]
541. ~brave(X0) | quiet(X0) [duplicate literal removal 535]
714. happy(X0) | quiet(X0) [resolution 382,541]
724. quiet(X0) [subsumption resolution 714,539]
733. brave(X0) | humble(X0) [resolution 724,102]
734. ~brave(X1) | ~humble(X1) [resolution 724,100]
735. ~brave(X2) | generous(X2) [resolution 724,86]
778. ~humble(X1) | happy(X1) [resolution 734,382]
790. generous(X0) | humble(X0) [resolution 735,733]
806. patient(X3) | humble(X3) [resolution 790,196]
849. humble(X1) | ~curious(X1) | ~quiet(X1) [resolution 806,70]
853. humble(X1) | ~quiet(X1) [subsumption resolution 849,379]
854. humble(X1) [subsumption resolution 853,724]
855. 13 [avatar split clause 854,184]
856. happy(X0) <- (13) [resolution 185,778]
874. $false <- (~1, 13) [resolution 856,132]
875. 1 | ~13 [avatar contradiction clause 874]
876. $false [avatar sat refutation 217,855,875]
% SZS output end Proof for 9024806141240165689680645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and generous is not creative and vice versa.
If someone is rich then susan is either not humble or not generous.
Everyone who is both strong and brave is strong or not brave.
If mary is rich then someone is patient.
If someone is both rich and not tall then john is either not strong or not creative.
Everyone who is not happy is not tall or not rich.
Everyone who is not quiet or happy is both tall and old.
If someone is generous or not quiet then someone is rich or creative and vice versa.
Everyone who is not quiet or not brave is not generous and vice versa.
If someone is not humble then alice is happy or not patient and vice versa.
Everyone who is either creative or not old is not happy or rich and vice versa.
Everyone who is quiet or wise is not quiet.
Everyone who is either kind or not happy is either not calm or strong.
Everyone who is both not curious and not brave is both humble and not quiet and vice versa.
If paul is not generous then someone is not happy and vice versa.
Someone is curious.
Someone is both not funny and rich.
John is not happy.
Someone is both strong and happy.
Fred is either rich or brave.
Someone is both not generous and strong.
Susan is patient. | Fred is not funny. | neutral | (![X]:((funny(X)&generous(X))<=>~creative(X)))&
((?[X]:(rich(X)))=>((~humble(susan)<~>~generous(susan))))&
(![X]:((strong(X)&brave(X))=>(strong(X)|~brave(X))))&
((rich(mary))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~tall(X))))=>((~strong(john)<~>~creative(john))))&
(![X]:(~happy(X)=>(~tall(X)|~rich(X))))&
(![X]:((~quiet(X)|happy(X))=>(tall(X)&old(X))))&
((?[X]:((generous(X)|~quiet(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>~generous(X)))&
((?[X]:(~humble(X)))<=>((happy(alice)|~patient(alice))))&
(![X]:((creative(X)<~>~old(X))<=>(~happy(X)|rich(X))))&
(![X]:((quiet(X)|wise(X))=>~quiet(X)))&
(![X]:((kind(X)<~>~happy(X))=>(~calm(X)<~>strong(X))))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)&~quiet(X))))&
((~generous(paul))<=>(?[X]:(~happy(X))))&
(?[X]:(curious(X)))&
(?[X]:((~funny(X)&rich(X))))&
(~happy(john))&
(?[X]:((strong(X)&happy(X))))&
((rich(fred)<~>brave(fred)))&
(?[X]:((~generous(X)&strong(X))))&
(patient(susan)) | ~funny(fred) | [] | null | 0 |
Everyone who is not funny or not creative is both creative and not kind.
If someone is generous or not calm then someone is creative or not curious.
If fred is not tall then john is either curious or funny.
Everyone who is either not patient or not strong is curious and vice versa.
If susan is rich then someone is either rich or not rich.
If mary is both tall and not tall then john is calm.
Everyone who is either rich or strong is creative and vice versa.
Everyone who is funny or not tall is either not happy or not kind.
Everyone who is not curious is strong or not calm and vice versa.
If someone is either not strong or curious then someone is both kind and not brave and vice versa.
If someone is both not happy and calm then mary is not creative or kind and vice versa.
If someone is either not funny or humble then someone is generous.
If john is either tall or not patient then someone is both not quiet and funny and vice versa.
Everyone who is strong is not generous or humble.
If fred is funny then alice is strong.
Everyone who is happy is not funny and vice versa.
Someone is not curious.
Lucy is either not old or curious.
Someone is either not happy or not funny.
Someone is either not creative or not wise.
Someone is either old or not strong.
Fred is both happy and generous.
Someone is not old.
Someone is either brave or not kind. | Fred is not funny. | entailment | (![X]:((~funny(X)|~creative(X))=>(creative(X)&~kind(X))))&
((?[X]:((generous(X)|~calm(X))))=>(?[X]:((creative(X)|~curious(X)))))&
((~tall(fred))=>((curious(john)<~>funny(john))))&
(![X]:((~patient(X)<~>~strong(X))<=>curious(X)))&
((rich(susan))=>(?[X]:((rich(X)<~>~rich(X)))))&
(((tall(mary)&~tall(mary)))=>(calm(john)))&
(![X]:((rich(X)<~>strong(X))<=>creative(X)))&
(![X]:((funny(X)|~tall(X))=>(~happy(X)<~>~kind(X))))&
(![X]:(~curious(X)<=>(strong(X)|~calm(X))))&
((?[X]:((~strong(X)<~>curious(X))))<=>(?[X]:((kind(X)&~brave(X)))))&
((?[X]:((~happy(X)&calm(X))))<=>((~creative(mary)|kind(mary))))&
((?[X]:((~funny(X)<~>humble(X))))=>(?[X]:(generous(X))))&
(((tall(john)<~>~patient(john)))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:(strong(X)=>(~generous(X)|humble(X))))&
((funny(fred))=>(strong(alice)))&
(![X]:(happy(X)<=>~funny(X)))&
(?[X]:(~curious(X)))&
((~old(lucy)<~>curious(lucy)))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((old(X)<~>~strong(X))))&
((happy(fred)&generous(fred)))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)<~>~kind(X)))) | ~funny(fred) | [
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2383613328953434683575795
% SZS output start Proof for 2383613328953434683575795
16. ! [X0] : (happy(X0) <=> ~funny(X0)) [input p15]
22. generous(fred) & happy(fred) [input p21]
25. funny(fred) [input hypothesis]
70. ! [X0] : ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))) [nnf transformation 16]
135. ~happy(X0) | ~funny(X0) [cnf transformation 70]
146. happy(fred) [cnf transformation 22]
151. funny(fred) [cnf transformation 25]
255. 22 <=> funny(fred) [avatar definition]
256. funny(fred) <- (22) [avatar component clause 255]
294. 22 [avatar split clause 151,255]
299. ~funny(fred) [resolution 135,146]
300. $false <- (22) [subsumption resolution 299,256]
301. ~22 [avatar contradiction clause 300]
302. $false [avatar sat refutation 294,301]
% SZS output end Proof for 2383613328953434683575795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or strong is not rich.
If someone is both curious and not generous then someone is either not strong or calm.
If someone is both strong and wise then someone is both curious and not funny.
Everyone who is either not kind or happy is creative or not wise and vice versa.
If susan is quiet then someone is both not funny and not patient.
If someone is not strong then alice is either not calm or wise and vice versa.
If someone is both not calm and happy then someone is either strong or quiet and vice versa.
Everyone who is not generous is not calm or not strong and vice versa.
If someone is generous then someone is not funny or not happy and vice versa.
If paul is old or not brave then susan is calm and vice versa.
If lucy is quiet or not humble then paul is either not wise or not quiet.
If mary is funny or tall then someone is not funny and vice versa.
Everyone who is either not wise or wise is not calm or rich and vice versa.
Everyone who is both patient and generous is generous or humble.
Everyone who is either not calm or wise is wise and vice versa.
If fred is both not patient and patient then alice is either creative or not wise and vice versa.
Mary is old.
Fred is quiet or not calm.
Paul is generous or rich.
Paul is not rich or not curious.
Someone is either not kind or creative. | Fred is not generous. | contradiction | (![X]:((calm(X)<~>strong(X))=>~rich(X)))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~kind(X)<~>happy(X))<=>(creative(X)|~wise(X))))&
((quiet(susan))=>(?[X]:((~funny(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((~calm(alice)<~>wise(alice))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(((old(paul)|~brave(paul)))<=>(calm(susan)))&
(((quiet(lucy)|~humble(lucy)))=>((~wise(paul)<~>~quiet(paul))))&
(((funny(mary)|tall(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~calm(X)|rich(X))))&
(![X]:((patient(X)&generous(X))=>(generous(X)|humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>wise(X)))&
(((~patient(fred)&patient(fred)))<=>((creative(alice)<~>~wise(alice))))&
(old(mary))&
((quiet(fred)|~calm(fred)))&
((generous(paul)|rich(paul)))&
((~rich(paul)|~curious(paul)))&
(?[X]:((~kind(X)<~>creative(X)))) | ~generous(fred) | [
"p0",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7296984912602704007155949
% SZS output start Proof for 7296984912602704007155949
1. ! [X0] : ((calm(X0) <~> strong(X0)) => ~rich(X0)) [input p0]
8. ! [X0] : (~generous(X0) <=> (~strong(X0) | ~calm(X0))) [input p7]
13. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) | ~calm(X0))) [input p12]
15. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> wise(X0)) [input p14]
22. ~generous(fred) [input hypothesis]
29. ! [X0] : (~rich(X0) | (calm(X0) <=> strong(X0))) [ennf transformation 1]
34. ! [X0] : (~rich(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) [nnf transformation 29]
55. ! [X0] : ((~generous(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | generous(X0))) [nnf transformation 8]
56. ! [X0] : ((~generous(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | generous(X0))) [flattening 55]
70. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 13]
71. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 70]
72. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~wise(X0)) & (wise(X0) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 15]
78. ~rich(X0) | strong(X0) | ~calm(X0) [cnf transformation 34]
102. ~strong(X0) | ~calm(X0) | generous(X0) [cnf transformation 56]
116. rich(X0) | ~calm(X0) | wise(X0) | wise(X0) [cnf transformation 71]
117. rich(X0) | ~calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 71]
122. wise(X0) | wise(X0) | calm(X0) [cnf transformation 72]
125. ~wise(X0) | calm(X0) | ~wise(X0) [cnf transformation 72]
138. ~generous(fred) [cnf transformation 22]
139. wise(X0) | calm(X0) [duplicate literal removal 122]
140. ~wise(X0) | calm(X0) [duplicate literal removal 125]
141. rich(X0) | ~calm(X0) | wise(X0) [duplicate literal removal 116]
142. rich(X0) | ~calm(X0) | ~wise(X0) [duplicate literal removal 117]
198. 13 <=> ! [X1] : strong(X1) [avatar definition]
199. strong(X1) <- (13) [avatar component clause 198]
301. ~calm(X0) | rich(X0) [subsumption resolution 141,142]
302. calm(X0) [subsumption resolution 139,140]
359. rich(X0) [resolution 301,302]
362. strong(X0) | ~calm(X0) [resolution 359,78]
364. strong(X0) [subsumption resolution 362,302]
365. 13 [avatar split clause 364,198]
409. ~calm(X0) | generous(X0) <- (13) [resolution 102,199]
413. generous(X0) <- (13) [subsumption resolution 409,302]
414. $false <- (13) [resolution 413,138]
417. ~13 [avatar contradiction clause 414]
418. $false [avatar sat refutation 365,417]
% SZS output end Proof for 7296984912602704007155949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is old or humble.
Everyone who is both not rich and not strong is either humble or not quiet and vice versa.
Everyone who is both not quiet and not patient is generous and vice versa.
If someone is not generous then lucy is both not brave and funny and vice versa.
If fred is either humble or not happy then someone is not old and vice versa.
If susan is calm then someone is either not wise or not rich and vice versa.
Everyone who is both strong and patient is not brave and vice versa.
If mary is creative then someone is happy or generous.
Everyone who is old is either not calm or happy.
Everyone who is both tall and not generous is either wise or old.
Everyone who is tall is either not patient or not generous and vice versa.
Everyone who is both not wise and not brave is both not strong and rich.
Everyone who is both not creative and generous is either old or not generous.
Everyone who is kind or not calm is humble or quiet and vice versa.
If john is strong or not humble then someone is either not humble or not quiet.
If someone is either patient or humble then lucy is not tall or not creative and vice versa.
Someone is both calm and not funny.
Susan is humble.
Someone is not wise.
Someone is not brave.
Lucy is not kind or not calm.
Someone is either not kind or rich.
Someone is either not generous or not tall.
Someone is either not humble or humble. | Fred is not happy. | neutral | (![X]:(creative(X)=>(old(X)|humble(X))))&
(![X]:((~rich(X)&~strong(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~patient(X))<=>generous(X)))&
((?[X]:(~generous(X)))<=>((~brave(lucy)&funny(lucy))))&
(((humble(fred)<~>~happy(fred)))<=>(?[X]:(~old(X))))&
((calm(susan))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:((strong(X)&patient(X))<=>~brave(X)))&
((creative(mary))=>(?[X]:((happy(X)|generous(X)))))&
(![X]:(old(X)=>(~calm(X)<~>happy(X))))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>old(X))))&
(![X]:(tall(X)<=>(~patient(X)<~>~generous(X))))&
(![X]:((~wise(X)&~brave(X))=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)&generous(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)|~calm(X))<=>(humble(X)|quiet(X))))&
(((strong(john)|~humble(john)))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
((?[X]:((patient(X)<~>humble(X))))<=>((~tall(lucy)|~creative(lucy))))&
(?[X]:((calm(X)&~funny(X))))&
(humble(susan))&
(?[X]:(~wise(X)))&
(?[X]:(~brave(X)))&
((~kind(lucy)|~calm(lucy)))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((~humble(X)<~>humble(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is both kind and tall is calm.
If someone is curious or funny then susan is happy or not wise and vice versa.
Everyone who is both wise and humble is both not creative and not humble.
Everyone who is wise is old or happy.
Everyone who is kind or happy is either not rich or not curious.
Everyone who is either brave or not quiet is not funny and vice versa.
If paul is both not old and not funny then someone is brave or generous.
Everyone who is wise or calm is not rich or patient.
Everyone who is not curious is not strong or strong.
If paul is either strong or calm then someone is generous.
If john is not old then someone is either quiet or calm and vice versa.
Everyone who is not patient or calm is quiet or not rich.
Everyone who is both not kind and not patient is both old and not old and vice versa.
Everyone who is not funny or not rich is not generous and vice versa.
Everyone who is strong is either not old or not generous.
If lucy is either not wise or not funny then someone is not calm and vice versa.
John is either not kind or funny.
Someone is both not quiet and generous.
John is either strong or tall.
Alice is not curious.
Someone is both quiet and happy.
Someone is both not tall and generous. | Alice is not tall. | neutral | (![X]:((kind(X)&tall(X))=>calm(X)))&
((?[X]:((curious(X)|funny(X))))<=>((happy(susan)|~wise(susan))))&
(![X]:((wise(X)&humble(X))=>(~creative(X)&~humble(X))))&
(![X]:(wise(X)=>(old(X)|happy(X))))&
(![X]:((kind(X)|happy(X))=>(~rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>~funny(X)))&
(((~old(paul)&~funny(paul)))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:((wise(X)|calm(X))=>(~rich(X)|patient(X))))&
(![X]:(~curious(X)=>(~strong(X)|strong(X))))&
(((strong(paul)<~>calm(paul)))=>(?[X]:(generous(X))))&
((~old(john))<=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:((~patient(X)|calm(X))=>(quiet(X)|~rich(X))))&
(![X]:((~kind(X)&~patient(X))<=>(old(X)&~old(X))))&
(![X]:((~funny(X)|~rich(X))<=>~generous(X)))&
(![X]:(strong(X)=>(~old(X)<~>~generous(X))))&
(((~wise(lucy)<~>~funny(lucy)))<=>(?[X]:(~calm(X))))&
((~kind(john)<~>funny(john)))&
(?[X]:((~quiet(X)&generous(X))))&
((strong(john)<~>tall(john)))&
(~curious(alice))&
(?[X]:((quiet(X)&happy(X))))&
(?[X]:((~tall(X)&generous(X)))) | ~tall(alice) | [] | null | 0 |
Everyone who is either old or not wise is either quiet or generous.
Everyone who is not generous is not humble or not tall and vice versa.
Everyone who is either creative or not curious is both not brave and not patient and vice versa.
Everyone who is both funny and not calm is not happy or kind and vice versa.
Everyone who is both not brave and rich is not wise and vice versa.
Everyone who is both kind and patient is both strong and not brave and vice versa.
If someone is either not strong or curious then someone is funny and vice versa.
Everyone who is not happy is either tall or not wise.
Everyone who is either humble or not tall is kind and vice versa.
Everyone who is either not calm or humble is either not patient or not quiet.
Everyone who is either tall or funny is both generous and quiet and vice versa.
Everyone who is either not wise or not brave is either brave or not tall and vice versa.
If john is not rich or not creative then someone is both rich and creative.
If john is not wise or happy then john is either not old or happy.
Everyone who is funny or quiet is both rich and old.
If someone is either tall or not strong then someone is either brave or not patient.
Paul is calm or funny.
Someone is either old or not brave.
Paul is not curious.
Someone is strong or old.
Susan is both generous and not quiet.
Alice is either curious or creative.
Someone is either tall or old. | John is not old. | contradiction | (![X]:((old(X)<~>~wise(X))=>(quiet(X)<~>generous(X))))&
(![X]:(~generous(X)<=>(~humble(X)|~tall(X))))&
(![X]:((creative(X)<~>~curious(X))<=>(~brave(X)&~patient(X))))&
(![X]:((funny(X)&~calm(X))<=>(~happy(X)|kind(X))))&
(![X]:((~brave(X)&rich(X))<=>~wise(X)))&
(![X]:((kind(X)&patient(X))<=>(strong(X)&~brave(X))))&
((?[X]:((~strong(X)<~>curious(X))))<=>(?[X]:(funny(X))))&
(![X]:(~happy(X)=>(tall(X)<~>~wise(X))))&
(![X]:((humble(X)<~>~tall(X))<=>kind(X)))&
(![X]:((~calm(X)<~>humble(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>funny(X))<=>(generous(X)&quiet(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)<~>~tall(X))))&
(((~rich(john)|~creative(john)))=>(?[X]:((rich(X)&creative(X)))))&
(((~wise(john)|happy(john)))=>((~old(john)<~>happy(john))))&
(![X]:((funny(X)|quiet(X))=>(rich(X)&old(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>(?[X]:((brave(X)<~>~patient(X)))))&
((calm(paul)|funny(paul)))&
(?[X]:((old(X)<~>~brave(X))))&
(~curious(paul))&
(?[X]:((strong(X)|old(X))))&
((generous(susan)&~quiet(susan)))&
((curious(alice)<~>creative(alice)))&
(?[X]:((tall(X)<~>old(X)))) | ~old(john) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 85114121463041689654844
% SZS output start Proof for 85114121463041689654844
4. ! [X0] : ((~calm(X0) & funny(X0)) <=> (kind(X0) | ~happy(X0))) [input p3]
14. (happy(john) | ~wise(john)) => (~old(john) <~> happy(john)) [input p13]
15. ! [X0] : ((quiet(X0) | funny(X0)) => (old(X0) & rich(X0))) [input p14]
24. ~old(john) [input hypothesis]
31. (~old(john) <~> happy(john)) | (~happy(john) & wise(john)) [ennf transformation 14]
32. ! [X0] : ((old(X0) & rich(X0)) | (~quiet(X0) & ~funny(X0))) [ennf transformation 15]
39. ! [X0] : (((~calm(X0) & funny(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (calm(X0) | ~funny(X0)))) [nnf transformation 4]
40. ! [X0] : (((~calm(X0) & funny(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | calm(X0) | ~funny(X0))) [flattening 39]
58. ((~happy(john) | old(john)) & (happy(john) | ~old(john))) | (~happy(john) & wise(john)) [nnf transformation 31]
86. happy(X0) | funny(X0) [cnf transformation 40]
132. ~happy(john) | old(john) | ~happy(john) [cnf transformation 58]
135. ~funny(X0) | old(X0) [cnf transformation 32]
152. ~old(john) [cnf transformation 24]
153. ~happy(john) | old(john) [duplicate literal removal 132]
209. 11 <=> old(john) [avatar definition]
210. ~old(john) <- (~11) [avatar component clause 209]
213. 12 <=> happy(john) [avatar definition]
215. ~happy(john) <- (~12) [avatar component clause 213]
216. 11 | ~12 [avatar split clause 153,213,209]
289. ~11 [avatar split clause 152,209]
292. funny(john) <- (~12) [resolution 86,215]
297. old(john) <- (~12) [resolution 135,292]
298. $false <- (~11, ~12) [subsumption resolution 297,210]
299. 11 | 12 [avatar contradiction clause 298]
300. $false [avatar sat refutation 216,289,299]
% SZS output end Proof for 85114121463041689654844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or wise is not tall or quiet. If susan is either quiet or not strong then paul is both not old and not patient. Everyone who is either not strong or not tall is either not calm or not strong. Everyone who is strong is either not old or humble. Everyone who is not creative or not humble is both not old and not tall. If someone is not brave or not strong then fred is patient or tall. Everyone who is either wise or strong is not calm and vice versa. Everyone who is either strong or not strong is both not creative and curious and vice versa. If paul is not generous or tall then paul is not happy or not quiet and vice versa. Everyone who is funny is not funny or not calm and vice versa. Everyone who is not brave is creative or tall and vice versa. Everyone who is funny is both happy and not quiet and vice versa. Everyone who is both not rich and creative is either humble or not funny and vice versa. If paul is not wise then someone is both not humble and not tall. Everyone who is both generous and brave is both not calm and rich and vice versa. If someone is rich then someone is both happy and funny and vice versa. Someone is both not calm and not strong. Fred is either tall or not wise. Susan is not tall. Lucy is either rich or not humble. Someone is both not quiet and not wise. | Fred is quiet. | contradiction | (![X]:((~generous(X)<~>wise(X))=>(~tall(X)|quiet(X))))&
(((quiet(susan)<~>~strong(susan)))=>((~old(paul)&~patient(paul))))&
(![X]:((~strong(X)<~>~tall(X))=>(~calm(X)<~>~strong(X))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
(?[X]:((~calm(X)&~strong(X))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X)))) | quiet(fred) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6412340881252076817696482
% SZS output start Proof for 6412340881252076817696482
10. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p9]
12. ! [X0] : (funny(X0) <=> (~quiet(X0) & happy(X0))) [input p11]
22. quiet(fred) [input hypothesis]
42. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 10]
43. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 42]
46. ! [X0] : ((funny(X0) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 12]
47. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [flattening 46]
98. funny(X0) | funny(X0) [cnf transformation 43]
104. ~quiet(X0) | ~funny(X0) [cnf transformation 47]
130. quiet(fred) [cnf transformation 22]
132. funny(X0) [duplicate literal removal 98]
199. ~quiet(X0) [subsumption resolution 104,132]
223. $false [subsumption resolution 130,199]
% SZS output end Proof for 6412340881252076817696482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is quiet then mary is both brave and not quiet and vice versa.
Everyone who is old is both not kind and strong.
If someone is old or not quiet then someone is brave or not happy and vice versa.
Everyone who is both kind and not happy is not funny and vice versa.
If someone is either humble or funny then lucy is brave or not strong and vice versa.
If fred is not funny then someone is both patient and curious and vice versa.
Everyone who is strong or rich is either kind or not curious.
If someone is both happy and not wise then fred is not tall.
If mary is both not quiet and not generous then someone is not tall or strong.
Everyone who is creative or curious is tall.
If someone is kind or generous then someone is both not calm and not patient and vice versa.
If lucy is wise then susan is creative.
Everyone who is either not funny or humble is both not happy and not brave and vice versa.
Everyone who is not tall is both brave and rich.
Everyone who is kind or not calm is tall or not kind and vice versa.
Everyone who is old is both old and not tall.
Someone is either not generous or not wise.
Someone is rich or strong.
Someone is not quiet.
Someone is funny or not brave.
Someone is either not brave or funny.
Someone is both curious and not kind.
Susan is strong or kind.
Susan is both quiet and not wise. | Fred is not rich. | neutral | ((quiet(susan))<=>((brave(mary)&~quiet(mary))))&
(![X]:(old(X)=>(~kind(X)&strong(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((kind(X)&~happy(X))<=>~funny(X)))&
((?[X]:((humble(X)<~>funny(X))))<=>((brave(lucy)|~strong(lucy))))&
((~funny(fred))<=>(?[X]:((patient(X)&curious(X)))))&
(![X]:((strong(X)|rich(X))=>(kind(X)<~>~curious(X))))&
((?[X]:((happy(X)&~wise(X))))=>(~tall(fred)))&
(((~quiet(mary)&~generous(mary)))=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((creative(X)|curious(X))=>tall(X)))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~calm(X)&~patient(X)))))&
((wise(lucy))=>(creative(susan)))&
(![X]:((~funny(X)<~>humble(X))<=>(~happy(X)&~brave(X))))&
(![X]:(~tall(X)=>(brave(X)&rich(X))))&
(![X]:((kind(X)|~calm(X))<=>(tall(X)|~kind(X))))&
(![X]:(old(X)=>(old(X)&~tall(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((curious(X)&~kind(X))))&
((strong(susan)|kind(susan)))&
((quiet(susan)&~wise(susan))) | ~rich(fred) | [] | null | 0 |
Everyone who is not funny is brave and vice versa.
If someone is not kind or old then someone is creative.
Everyone who is both kind and not kind is either not brave or curious.
Everyone who is both patient and not happy is either quiet or happy and vice versa.
If fred is either quiet or old then paul is both happy and wise and vice versa.
Everyone who is generous is either curious or wise and vice versa.
If someone is both not patient and not rich then fred is patient or not funny and vice versa.
If someone is either curious or not kind then lucy is both not humble and not brave and vice versa.
If paul is both funny and not strong then mary is kind or not curious.
Everyone who is either quiet or not patient is wise and vice versa.
Everyone who is both humble and curious is not humble or not patient and vice versa.
If someone is both not curious and not old then john is not patient and vice versa.
If someone is both not wise and tall then someone is tall and vice versa.
If lucy is creative or not creative then someone is either calm or not kind and vice versa.
If susan is either not brave or quiet then alice is quiet or not old and vice versa.
Everyone who is not funny is creative.
Fred is funny or not tall.
Paul is happy.
Lucy is either not generous or patient.
Mary is both not quiet and not patient.
Someone is not wise.
Alice is tall.
Someone is either old or not rich. | Lucy is humble. | entailment | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:((kind(X)&~kind(X))=>(~brave(X)<~>curious(X))))&
(![X]:((patient(X)&~happy(X))<=>(quiet(X)<~>happy(X))))&
(((quiet(fred)<~>old(fred)))<=>((happy(paul)&wise(paul))))&
(![X]:(generous(X)<=>(curious(X)<~>wise(X))))&
((?[X]:((~patient(X)&~rich(X))))<=>((patient(fred)|~funny(fred))))&
((?[X]:((curious(X)<~>~kind(X))))<=>((~humble(lucy)&~brave(lucy))))&
(((funny(paul)&~strong(paul)))=>((kind(mary)|~curious(mary))))&
(![X]:((quiet(X)<~>~patient(X))<=>wise(X)))&
(![X]:((humble(X)&curious(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~curious(X)&~old(X))))<=>(~patient(john)))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(((~brave(susan)<~>quiet(susan)))<=>((quiet(alice)|~old(alice))))&
(![X]:(~funny(X)=>creative(X)))&
((funny(fred)|~tall(fred)))&
(happy(paul))&
((~generous(lucy)<~>patient(lucy)))&
((~quiet(mary)&~patient(mary)))&
(?[X]:(~wise(X)))&
(tall(alice))&
(?[X]:((old(X)<~>~rich(X)))) | humble(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7232069379290740007348786
% SZS output start Proof for 7232069379290740007348786
11. ! [X0] : ((curious(X0) & humble(X0)) <=> (~patient(X0) | ~humble(X0))) [input p10]
24. ~humble(lucy) [input hypothesis]
53. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 11]
54. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 53]
115. humble(X0) | humble(X0) [cnf transformation 54]
148. ~humble(lucy) [cnf transformation 24]
150. humble(X0) [duplicate literal removal 115]
346. $false [subsumption resolution 148,150]
% SZS output end Proof for 7232069379290740007348786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or not creative then someone is not rich. Everyone who is both not wise and not rich is funny and vice versa. Everyone who is either generous or not old is both not humble and old. If mary is either not strong or not generous then paul is either generous or wise. If john is not generous or wise then someone is both not quiet and not strong and vice versa. Everyone who is both kind and not quiet is both not kind and funny. Everyone who is either old or not curious is strong. If paul is both not strong and generous then john is not strong or not wise and vice versa. Everyone who is either calm or not calm is both not tall and curious and vice versa. If paul is both kind and not quiet then someone is not rich and vice versa. If fred is either tall or not calm then someone is both old and not tall and vice versa. Everyone who is both not quiet and strong is both not curious and not brave. Everyone who is creative is both not calm and not patient and vice versa. Everyone who is generous is kind or not humble and vice versa. Everyone who is both brave and funny is patient or not wise. Everyone who is rich is either generous or calm and vice versa. Someone is both humble and strong. Someone is old or kind. Alice is strong. Mary is curious or quiet. John is either not calm or wise. Someone is happy. Someone is either not funny or not quiet. Mary is wise or not tall. | Fred is rich. | entailment | (((~wise(mary)|~creative(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(![X]:((brave(X)&funny(X))=>(patient(X)|~wise(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((old(X)|kind(X))))&
(strong(alice))&
((curious(mary)|quiet(mary)))&
((~calm(john)<~>wise(john)))&
(?[X]:(happy(X)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((wise(mary)|~tall(mary))) | rich(fred) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 872736760208677547398105
% SZS output start Proof for 872736760208677547398105
6. ! [X0] : ((~quiet(X0) & kind(X0)) => (funny(X0) & ~kind(X0))) [input p5]
10. (~quiet(paul) & kind(paul)) <=> ? [X0] : ~rich(X0) [input p9]
25. ~rich(fred) [input hypothesis]
34. ! [X0] : ((funny(X0) & ~kind(X0)) | (quiet(X0) | ~kind(X0))) [ennf transformation 6]
35. ! [X0] : ((funny(X0) & ~kind(X0)) | quiet(X0) | ~kind(X0)) [flattening 34]
56. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (quiet(paul) | ~kind(paul))) [nnf transformation 10]
57. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | quiet(paul) | ~kind(paul)) [flattening 56]
58. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | quiet(paul) | ~kind(paul)) [rectify 57]
59. ? [X1] : ~rich(X1) => ~rich(sK2) [choice axiom]
60. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (~rich(sK2) | quiet(paul) | ~kind(paul)) [skolemisation 58,59]
94. ~kind(X0) | quiet(X0) | ~kind(X0) [cnf transformation 35]
110. kind(paul) | rich(X0) [cnf transformation 60]
111. ~quiet(paul) | rich(X0) [cnf transformation 60]
137. ~rich(fred) [cnf transformation 25]
142. ~kind(X0) | quiet(X0) [duplicate literal removal 94]
218. 15 <=> ! [X0] : rich(X0) [avatar definition]
219. rich(X0) <- (15) [avatar component clause 218]
221. 16 <=> quiet(paul) [avatar definition]
223. ~quiet(paul) <- (~16) [avatar component clause 221]
224. 15 | ~16 [avatar split clause 111,221,218]
226. 17 <=> kind(paul) [avatar definition]
228. kind(paul) <- (17) [avatar component clause 226]
229. 15 | 17 [avatar split clause 110,226,218]
282. quiet(paul) <- (17) [resolution 142,228]
283. $false <- (~16, 17) [subsumption resolution 282,223]
284. 16 | ~17 [avatar contradiction clause 283]
285. $false <- (15) [resolution 219,137]
288. ~15 [avatar contradiction clause 285]
289. $false [avatar sat refutation 224,229,284,288]
% SZS output end Proof for 872736760208677547398105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both old and not wise then mary is both rich and not calm and vice versa.
Everyone who is either not old or not happy is not brave and vice versa.
Everyone who is calm or strong is both quiet and curious and vice versa.
Everyone who is both not strong and not kind is not happy or quiet.
Everyone who is both quiet and not tall is generous or calm.
Everyone who is calm is either not funny or not old and vice versa.
Everyone who is patient or humble is either funny or humble.
Everyone who is both calm and not quiet is both not brave and not strong and vice versa.
Everyone who is old is not quiet and vice versa.
Everyone who is old is not curious or not calm and vice versa.
Everyone who is not wise is either happy or not curious and vice versa.
Everyone who is calm or not humble is happy or not curious.
Everyone who is both creative and not brave is both not brave and not patient.
Everyone who is either not rich or not old is humble.
Everyone who is brave or not wise is both quiet and strong.
If someone is both not generous and creative then lucy is rich or not old and vice versa.
Someone is not calm or not kind.
John is tall or creative.
Someone is calm.
Susan is happy or not creative.
Mary is either not curious or curious.
Someone is kind.
Paul is calm or kind.
Alice is tall. | Lucy is not humble. | entailment | (((old(john)&~wise(john)))<=>((rich(mary)&~calm(mary))))&
(![X]:((~old(X)<~>~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|strong(X))<=>(quiet(X)&curious(X))))&
(![X]:((~strong(X)&~kind(X))=>(~happy(X)|quiet(X))))&
(![X]:((quiet(X)&~tall(X))=>(generous(X)|calm(X))))&
(![X]:(calm(X)<=>(~funny(X)<~>~old(X))))&
(![X]:((patient(X)|humble(X))=>(funny(X)<~>humble(X))))&
(![X]:((calm(X)&~quiet(X))<=>(~brave(X)&~strong(X))))&
(![X]:(old(X)<=>~quiet(X)))&
(![X]:(old(X)<=>(~curious(X)|~calm(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((calm(X)|~humble(X))=>(happy(X)|~curious(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)<~>~old(X))=>humble(X)))&
(![X]:((brave(X)|~wise(X))=>(quiet(X)&strong(X))))&
((?[X]:((~generous(X)&creative(X))))<=>((rich(lucy)|~old(lucy))))&
(?[X]:((~calm(X)|~kind(X))))&
((tall(john)|creative(john)))&
(?[X]:(calm(X)))&
((happy(susan)|~creative(susan)))&
((~curious(mary)<~>curious(mary)))&
(?[X]:(kind(X)))&
((calm(paul)|kind(paul)))&
(tall(alice)) | ~humble(lucy) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 502828034746268937449647
% SZS output start Proof for 502828034746268937449647
3. ! [X0] : ((strong(X0) | calm(X0)) <=> (curious(X0) & quiet(X0))) [input p2]
6. ! [X0] : (calm(X0) <=> (~funny(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : ((humble(X0) | patient(X0)) => (funny(X0) <~> humble(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) & calm(X0)) <=> (~strong(X0) & ~brave(X0))) [input p7]
9. ! [X0] : (old(X0) <=> ~quiet(X0)) [input p8]
10. ! [X0] : (old(X0) <=> (~calm(X0) | ~curious(X0))) [input p9]
15. ! [X0] : ((~wise(X0) | brave(X0)) => (strong(X0) & quiet(X0))) [input p14]
25. humble(lucy) [input hypothesis]
26. ! [X0] : (humble(X0) => (funny(X0) <~> humble(X0))) [pure predicate removal 7]
33. ! [X0] : ((funny(X0) <~> humble(X0)) | ~humble(X0)) [ennf transformation 26]
39. ! [X0] : ((strong(X0) & quiet(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 15]
43. ! [X0] : (((strong(X0) | calm(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((strong(X0) | calm(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : ((calm(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ~calm(X0))) [nnf transformation 6]
46. ! [X0] : (((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | ~humble(X0)) [nnf transformation 33]
47. ! [X0] : (((~quiet(X0) & calm(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (quiet(X0) | ~calm(X0)))) [nnf transformation 8]
48. ! [X0] : (((~quiet(X0) & calm(X0)) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | quiet(X0) | ~calm(X0))) [flattening 47]
49. ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))) [nnf transformation 9]
50. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & ((~calm(X0) | ~curious(X0)) | ~old(X0))) [nnf transformation 10]
51. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & (~calm(X0) | ~curious(X0) | ~old(X0))) [flattening 50]
74. ~calm(X0) | quiet(X0) [cnf transformation 44]
75. ~strong(X0) | quiet(X0) [cnf transformation 44]
81. ~calm(X0) | funny(X0) | old(X0) [cnf transformation 45]
85. ~humble(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 46]
88. strong(X0) | calm(X0) | brave(X0) [cnf transformation 48]
90. ~quiet(X0) | ~old(X0) [cnf transformation 49]
94. calm(X0) | old(X0) [cnf transformation 51]
104. ~brave(X0) | quiet(X0) [cnf transformation 39]
120. humble(lucy) [cnf transformation 25]
121. ~humble(X0) | ~funny(X0) [duplicate literal removal 85]
209. ~funny(lucy) [resolution 121,120]
228. funny(X0) | old(X0) | old(X0) [resolution 81,94]
229. funny(X0) | old(X0) [duplicate literal removal 228]
241. calm(X1) | brave(X1) | quiet(X1) [resolution 88,75]
243. calm(X1) | quiet(X1) [subsumption resolution 241,104]
244. quiet(X1) [subsumption resolution 243,74]
245. ~old(X0) [resolution 244,90]
292. old(lucy) [resolution 229,209]
298. $false [subsumption resolution 292,245]
% SZS output end Proof for 502828034746268937449647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not happy then lucy is both not quiet and not brave. If someone is both strong and not patient then alice is both not curious and funny. Everyone who is either not creative or not humble is patient or kind. Everyone who is either not quiet or creative is either patient or happy. Everyone who is not kind or not old is either not humble or not old. Everyone who is either kind or old is not humble or not calm. Everyone who is calm or not quiet is strong or patient and vice versa. If alice is curious or not humble then someone is strong or not patient and vice versa. Everyone who is both not patient and quiet is not rich or not wise and vice versa. Everyone who is either not rich or not funny is both calm and not funny and vice versa. If someone is either rich or calm then fred is happy and vice versa. Everyone who is both not generous and not rich is curious and vice versa. If fred is either not kind or quiet then someone is both rich and old and vice versa. Everyone who is not patient is either not humble or rich and vice versa. Everyone who is creative is both kind and not brave. If someone is not funny or strong then someone is both not strong and rich and vice versa. Someone is not creative. Paul is not creative or not calm. Someone is humble or funny. Alice is both creative and quiet. Someone is both calm and generous. Alice is not tall or not humble. Someone is funny. Someone is generous. | Fred is kind. | neutral | ((?[X]:((~strong(X)&~happy(X))))=>((~quiet(lucy)&~brave(lucy))))&
((?[X]:((strong(X)&~patient(X))))=>((~curious(alice)&funny(alice))))&
(![X]:((~creative(X)<~>~humble(X))=>(patient(X)|kind(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(patient(X)<~>happy(X))))&
(![X]:((~kind(X)|~old(X))=>(~humble(X)<~>~old(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|~calm(X))))&
(![X]:((calm(X)|~quiet(X))<=>(strong(X)|patient(X))))&
(((curious(alice)|~humble(alice)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
(((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:(~patient(X)<=>(~humble(X)<~>rich(X))))&
(![X]:(creative(X)=>(kind(X)&~brave(X))))&
((?[X]:((~funny(X)|strong(X))))<=>(?[X]:((~strong(X)&rich(X)))))&
(?[X]:(~creative(X)))&
((~creative(paul)|~calm(paul)))&
(?[X]:((humble(X)|funny(X))))&
((creative(alice)&quiet(alice)))&
(?[X]:((calm(X)&generous(X))))&
((~tall(alice)|~humble(alice)))&
(?[X]:(funny(X)))&
(?[X]:(generous(X))) | kind(fred) | [] | null | 0 |
If someone is both not patient and happy then alice is both not kind and not funny. Everyone who is both not brave and funny is creative or not strong and vice versa. Everyone who is both not wise and curious is not strong and vice versa. Everyone who is either rich or creative is funny. If someone is quiet then someone is not curious and vice versa. If someone is both calm and not quiet then someone is both not funny and calm and vice versa. If someone is not creative or not old then alice is either funny or not curious. Everyone who is generous is not quiet or not creative and vice versa. If fred is curious then lucy is not patient or calm and vice versa. Everyone who is not old or not wise is generous. If lucy is either happy or old then someone is both not strong and not curious and vice versa. Everyone who is both not calm and generous is either happy or not creative. Everyone who is not kind or kind is kind or not kind. If alice is calm or strong then someone is both kind and patient and vice versa. Everyone who is quiet or calm is old and vice versa. If someone is not rich or not curious then fred is either kind or not brave. Paul is either not brave or brave. John is both not rich and calm. Fred is rich. Paul is either tall or not humble. Susan is not old or humble. Susan is wise. Paul is not tall. | Fred is funny. | entailment | ((?[X]:((~patient(X)&happy(X))))=>((~kind(alice)&~funny(alice))))&
(![X]:((~brave(X)&funny(X))<=>(creative(X)|~strong(X))))&
(![X]:((~wise(X)&curious(X))<=>~strong(X)))&
(![X]:((rich(X)<~>creative(X))=>funny(X)))&
((?[X]:(quiet(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((~creative(X)|~old(X))))=>((funny(alice)<~>~curious(alice))))&
(![X]:(generous(X)<=>(~quiet(X)|~creative(X))))&
((curious(fred))<=>((~patient(lucy)|calm(lucy))))&
(![X]:((~old(X)|~wise(X))=>generous(X)))&
(((happy(lucy)<~>old(lucy)))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~calm(X)&generous(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~kind(X)|kind(X))=>(kind(X)|~kind(X))))&
(((calm(alice)|strong(alice)))<=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((quiet(X)|calm(X))<=>old(X)))&
((?[X]:((~rich(X)|~curious(X))))=>((kind(fred)<~>~brave(fred))))&
((~brave(paul)<~>brave(paul)))&
((~rich(john)&calm(john)))&
(rich(fred))&
((tall(paul)<~>~humble(paul)))&
((~old(susan)|humble(susan)))&
(wise(susan))&
(~tall(paul)) | funny(fred) | [
"p1",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8947401486338882628550188
% SZS output start Proof for 8947401486338882628550188
2. ! [X0] : ((funny(X0) & ~brave(X0)) <=> (~strong(X0) | creative(X0))) [input p1]
4. ! [X0] : ((rich(X0) <~> creative(X0)) => funny(X0)) [input p3]
19. rich(fred) [input p18]
24. ~funny(fred) [input hypothesis]
28. ! [X0] : (funny(X0) | (rich(X0) <=> creative(X0))) [ennf transformation 4]
36. ! [X0] : (((funny(X0) & ~brave(X0)) | (strong(X0) & ~creative(X0))) & ((~strong(X0) | creative(X0)) | (~funny(X0) | brave(X0)))) [nnf transformation 2]
37. ! [X0] : (((funny(X0) & ~brave(X0)) | (strong(X0) & ~creative(X0))) & (~strong(X0) | creative(X0) | ~funny(X0) | brave(X0))) [flattening 36]
40. ! [X0] : (funny(X0) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) [nnf transformation 28]
76. ~creative(X0) | funny(X0) [cnf transformation 37]
81. funny(X0) | creative(X0) | ~rich(X0) [cnf transformation 40]
127. rich(fred) [cnf transformation 19]
133. ~funny(fred) [cnf transformation 24]
149. ~rich(X0) | funny(X0) [subsumption resolution 81,76]
328. funny(fred) [resolution 149,127]
329. $false [subsumption resolution 328,133]
% SZS output end Proof for 8947401486338882628550188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or old is both not curious and not humble.
If susan is either strong or not happy then someone is either happy or generous and vice versa.
Everyone who is both not rich and generous is both not tall and patient.
Everyone who is not tall is both funny and not calm.
Everyone who is both not funny and not humble is not brave or creative and vice versa.
If susan is both not humble and not happy then fred is either brave or not brave.
If susan is not funny then alice is not kind or happy.
If someone is not calm then susan is either generous or tall.
Everyone who is calm or not generous is both not creative and patient and vice versa.
Everyone who is both not old and kind is tall or not old and vice versa.
Everyone who is both rich and not old is old or not quiet.
Everyone who is happy or funny is both creative and kind.
If lucy is both not funny and not tall then someone is either not curious or not wise.
Everyone who is both not curious and creative is both not quiet and not generous.
Everyone who is either not tall or old is humble.
If alice is quiet or strong then someone is either calm or not tall.
Someone is happy or rich.
Susan is either humble or rich.
Someone is not rich or patient.
Someone is wise or not strong. | Susan is strong. | neutral | (![X]:((patient(X)<~>old(X))=>(~curious(X)&~humble(X))))&
(((strong(susan)<~>~happy(susan)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:((~rich(X)&generous(X))=>(~tall(X)&patient(X))))&
(![X]:(~tall(X)=>(funny(X)&~calm(X))))&
(![X]:((~funny(X)&~humble(X))<=>(~brave(X)|creative(X))))&
(((~humble(susan)&~happy(susan)))=>((brave(fred)<~>~brave(fred))))&
((~funny(susan))=>((~kind(alice)|happy(alice))))&
((?[X]:(~calm(X)))=>((generous(susan)<~>tall(susan))))&
(![X]:((calm(X)|~generous(X))<=>(~creative(X)&patient(X))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)|~old(X))))&
(![X]:((rich(X)&~old(X))=>(old(X)|~quiet(X))))&
(![X]:((happy(X)|funny(X))=>(creative(X)&kind(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~curious(X)&creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>humble(X)))&
(((quiet(alice)|strong(alice)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(?[X]:((happy(X)|rich(X))))&
((humble(susan)<~>rich(susan)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((wise(X)|~strong(X)))) | strong(susan) | [] | null | 0 |
Everyone who is both calm and quiet is both not happy and curious and vice versa. Everyone who is not generous is not calm and vice versa. If alice is both not funny and humble then lucy is both old and not tall and vice versa. Everyone who is either not patient or brave is both humble and not happy and vice versa. Everyone who is tall or not creative is either not brave or not creative. Everyone who is not quiet or not curious is happy and vice versa. If paul is both funny and rich then fred is not rich. Everyone who is both not strong and happy is both not creative and not kind and vice versa. Everyone who is funny or creative is not wise and vice versa. Everyone who is brave or funny is rich or not tall and vice versa. Everyone who is either not creative or not quiet is either happy or not kind and vice versa. Everyone who is not funny is either not humble or not strong and vice versa. If paul is calm then mary is humble or kind. Everyone who is funny or not humble is either happy or not brave and vice versa. Everyone who is both quiet and wise is both old and not quiet and vice versa. If alice is not wise then someone is either not kind or not rich. Mary is both not humble and strong. Someone is curious. Someone is both not old and not strong. Someone is either generous or not kind. Fred is not happy or not creative. Susan is both not tall and not creative. Someone is either not quiet or creative. Someone is not humble. | Alice is not creative. | neutral | (![X]:((calm(X)&quiet(X))<=>(~happy(X)&curious(X))))&
(![X]:(~generous(X)<=>~calm(X)))&
(((~funny(alice)&humble(alice)))<=>((old(lucy)&~tall(lucy))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)|~creative(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~curious(X))<=>happy(X)))&
(((funny(paul)&rich(paul)))=>(~rich(fred)))&
(![X]:((~strong(X)&happy(X))<=>(~creative(X)&~kind(X))))&
(![X]:((funny(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
(![X]:((quiet(X)&wise(X))<=>(old(X)&~quiet(X))))&
((~wise(alice))=>(?[X]:((~kind(X)<~>~rich(X)))))&
((~humble(mary)&strong(mary)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred)))&
((~tall(susan)&~creative(susan)))&
(?[X]:((~quiet(X)<~>creative(X))))&
(?[X]:(~humble(X))) | ~creative(alice) | [] | null | 0 |
If someone is funny then paul is both brave and not quiet.
If john is creative or not rich then fred is either not quiet or quiet and vice versa.
If someone is both not creative and happy then fred is either generous or not curious and vice versa.
Everyone who is either patient or not old is either not kind or not brave and vice versa.
If someone is generous then mary is funny and vice versa.
If someone is not kind then someone is both not brave and calm and vice versa.
If someone is both not brave and not happy then mary is either not rich or not curious and vice versa.
Everyone who is not tall or happy is both tall and not quiet and vice versa.
Everyone who is either wise or not tall is both not patient and strong and vice versa.
Everyone who is funny or patient is both not rich and rich.
Everyone who is either curious or not strong is not humble or generous.
If someone is not happy or not creative then alice is not tall or quiet and vice versa.
Everyone who is both patient and brave is either kind or not brave and vice versa.
If paul is both not tall and calm then john is both curious and not kind and vice versa.
If someone is not creative or not rich then someone is strong or not wise.
Mary is not rich or not strong.
Someone is old or not quiet.
John is both not old and tall.
Mary is not creative.
Someone is either not brave or not patient.
Someone is not brave or quiet.
Someone is not patient.
Someone is either not patient or not quiet. | Alice is happy. | contradiction | ((?[X]:(funny(X)))=>((brave(paul)&~quiet(paul))))&
(((creative(john)|~rich(john)))<=>((~quiet(fred)<~>quiet(fred))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
((?[X]:(~kind(X)))<=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~rich(mary)<~>~curious(mary))))&
(![X]:((~tall(X)|happy(X))<=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)|patient(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~humble(X)|generous(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~tall(alice)|quiet(alice))))&
(![X]:((patient(X)&brave(X))<=>(kind(X)<~>~brave(X))))&
(((~tall(paul)&calm(paul)))<=>((curious(john)&~kind(john))))&
((?[X]:((~creative(X)|~rich(X))))=>(?[X]:((strong(X)|~wise(X)))))&
((~rich(mary)|~strong(mary)))&
(?[X]:((old(X)|~quiet(X))))&
((~old(john)&tall(john)))&
(~creative(mary))&
(?[X]:((~brave(X)<~>~patient(X))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)<~>~quiet(X)))) | happy(alice) | [
"p7",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3741633665293018616187210
% SZS output start Proof for 3741633665293018616187210
8. ! [X0] : ((happy(X0) | ~tall(X0)) <=> (~quiet(X0) & tall(X0))) [input p7]
12. ? [X0] : (~creative(X0) | ~happy(X0)) <=> (quiet(alice) | ~tall(alice)) [input p11]
19. ~creative(mary) [input p18]
24. happy(alice) [input hypothesis]
51. ! [X0] : (((happy(X0) | ~tall(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (~happy(X0) & tall(X0)))) [nnf transformation 8]
52. ! [X0] : ((happy(X0) | ~tall(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (~happy(X0) & tall(X0)))) [flattening 51]
55. (? [X0] : (~creative(X0) | ~happy(X0)) | (~quiet(alice) & tall(alice))) & ((quiet(alice) | ~tall(alice)) | ! [X0] : (creative(X0) & happy(X0))) [nnf transformation 12]
56. (? [X0] : (~creative(X0) | ~happy(X0)) | (~quiet(alice) & tall(alice))) & (quiet(alice) | ~tall(alice) | ! [X0] : (creative(X0) & happy(X0))) [flattening 55]
57. (? [X0] : (~creative(X0) | ~happy(X0)) | (~quiet(alice) & tall(alice))) & (quiet(alice) | ~tall(alice) | ! [X1] : (creative(X1) & happy(X1))) [rectify 56]
58. ? [X0] : (~creative(X0) | ~happy(X0)) => (~creative(sK5) | ~happy(sK5)) [choice axiom]
59. ((~creative(sK5) | ~happy(sK5)) | (~quiet(alice) & tall(alice))) & (quiet(alice) | ~tall(alice) | ! [X1] : (creative(X1) & happy(X1))) [skolemisation 57,58]
112. tall(X0) | tall(X0) [cnf transformation 52]
115. ~happy(X0) | ~quiet(X0) [cnf transformation 52]
128. quiet(alice) | ~tall(alice) | creative(X1) [cnf transformation 59]
147. ~creative(mary) [cnf transformation 19]
154. happy(alice) [cnf transformation 24]
157. tall(X0) [duplicate literal removal 112]
279. 25 <=> quiet(alice) [avatar definition]
291. quiet(alice) | creative(X1) [subsumption resolution 128,157]
293. 28 <=> ! [X1] : creative(X1) [avatar definition]
294. creative(X1) <- (28) [avatar component clause 293]
295. 28 | 25 [avatar split clause 291,279,293]
352. ~quiet(alice) [resolution 115,154]
356. ~25 [avatar split clause 352,279]
357. $false <- (28) [resolution 294,147]
360. ~28 [avatar contradiction clause 357]
361. $false [avatar sat refutation 295,356,360]
% SZS output end Proof for 3741633665293018616187210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble is both not creative and not generous.
Everyone who is not happy is funny or strong and vice versa.
If paul is either happy or not wise then paul is patient.
If someone is not happy then someone is both not generous and humble.
Everyone who is both not tall and calm is both not curious and not brave and vice versa.
If someone is either not generous or not funny then someone is either not patient or patient and vice versa.
Everyone who is not funny is not tall and vice versa.
Everyone who is either curious or not creative is either not strong or calm.
If fred is either happy or old then alice is not curious or strong and vice versa.
Everyone who is creative is not tall.
If someone is wise or not rich then someone is either not funny or not humble and vice versa.
If alice is old or tall then lucy is tall or not wise and vice versa.
Everyone who is old or not old is rich or not wise.
If someone is quiet then fred is either not rich or calm and vice versa.
Everyone who is both quiet and kind is curious or not curious and vice versa.
Everyone who is not strong is either not funny or kind.
Lucy is both wise and not happy.
Lucy is both funny and not happy.
Fred is rich.
Lucy is not humble.
Fred is not creative.
Someone is either not wise or generous.
Someone is either not wise or not generous.
Someone is not generous or not tall. | Fred is not calm. | contradiction | (![X]:((~creative(X)|~humble(X))=>(~creative(X)&~generous(X))))&
(![X]:(~happy(X)<=>(funny(X)|strong(X))))&
(((happy(paul)<~>~wise(paul)))=>(patient(paul)))&
((?[X]:(~happy(X)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)&~brave(X))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((curious(X)<~>~creative(X))=>(~strong(X)<~>calm(X))))&
(((happy(fred)<~>old(fred)))<=>((~curious(alice)|strong(alice))))&
(![X]:(creative(X)=>~tall(X)))&
((?[X]:((wise(X)|~rich(X))))<=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((old(alice)|tall(alice)))<=>((tall(lucy)|~wise(lucy))))&
(![X]:((old(X)|~old(X))=>(rich(X)|~wise(X))))&
((?[X]:(quiet(X)))<=>((~rich(fred)<~>calm(fred))))&
(![X]:((quiet(X)&kind(X))<=>(curious(X)|~curious(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>kind(X))))&
((wise(lucy)&~happy(lucy)))&
((funny(lucy)&~happy(lucy)))&
(rich(fred))&
(~humble(lucy))&
(~creative(fred))&
(?[X]:((~wise(X)<~>generous(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~generous(X)|~tall(X)))) | ~calm(fred) | [
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7800911755288560058174397
% SZS output start Proof for 7800911755288560058174397
14. ? [X0] : quiet(X0) <=> (~rich(fred) <~> calm(fred)) [input p13]
15. ! [X0] : ((kind(X0) & quiet(X0)) <=> (~curious(X0) | curious(X0))) [input p14]
19. rich(fred) [input p18]
25. ~calm(fred) [input hypothesis]
61. (? [X0] : quiet(X0) | ((~rich(fred) | ~calm(fred)) & (calm(fred) | rich(fred)))) & (((~calm(fred) | rich(fred)) & (calm(fred) | ~rich(fred))) | ! [X0] : ~quiet(X0)) [nnf transformation 14]
62. (? [X0] : quiet(X0) | ((~rich(fred) | ~calm(fred)) & (calm(fred) | rich(fred)))) & (((~calm(fred) | rich(fred)) & (calm(fred) | ~rich(fred))) | ! [X1] : ~quiet(X1)) [rectify 61]
63. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
64. (quiet(sK5) | ((~rich(fred) | ~calm(fred)) & (calm(fred) | rich(fred)))) & (((~calm(fred) | rich(fred)) & (calm(fred) | ~rich(fred))) | ! [X1] : ~quiet(X1)) [skolemisation 62,63]
65. ! [X0] : (((kind(X0) & quiet(X0)) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 15]
66. ! [X0] : (((kind(X0) & quiet(X0)) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~kind(X0) | ~quiet(X0))) [flattening 65]
124. calm(fred) | ~rich(fred) | ~quiet(X1) [cnf transformation 64]
129. quiet(X0) | ~curious(X0) [cnf transformation 66]
130. quiet(X0) | curious(X0) [cnf transformation 66]
139. rich(fred) [cnf transformation 19]
147. ~calm(fred) [cnf transformation 25]
275. 27 <=> calm(fred) [avatar definition]
279. 28 <=> rich(fred) [avatar definition]
289. 30 <=> ! [X1] : ~quiet(X1) [avatar definition]
290. ~quiet(X1) <- (30) [avatar component clause 289]
292. 30 | ~28 | 27 [avatar split clause 124,275,279,289]
294. quiet(X0) [subsumption resolution 129,130]
297. 28 [avatar split clause 139,279]
327. ~27 [avatar split clause 147,275]
328. $false <- (30) [subsumption resolution 290,294]
329. ~30 [avatar contradiction clause 328]
330. $false [avatar sat refutation 292,297,327,329]
% SZS output end Proof for 7800911755288560058174397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then susan is funny or tall and vice versa. Everyone who is strong or not quiet is not quiet. Everyone who is either not old or not quiet is both not rich and wise. Everyone who is strong or not happy is both rich and patient. Everyone who is not kind or not tall is not happy and vice versa. Everyone who is not funny is not old and vice versa. If lucy is both generous and not happy then lucy is rich or patient and vice versa. Everyone who is not strong or not funny is not creative and vice versa. If someone is not curious or calm then mary is patient or not humble. If mary is both not humble and old then lucy is quiet or rich. Everyone who is either quiet or brave is not humble or wise and vice versa. If alice is either generous or rich then john is either tall or rich and vice versa. If someone is strong then someone is not rich. Everyone who is both not old and not tall is happy. If susan is funny or not rich then someone is either quiet or funny. Everyone who is generous or patient is not patient and vice versa. Someone is either not patient or not kind. Mary is either tall or not kind. Someone is either not rich or not kind. Someone is not brave or tall. Someone is not funny or humble. Someone is creative or not old. | Lucy is not calm. | neutral | ((?[X]:((curious(X)|~curious(X))))<=>((funny(susan)|tall(susan))))&
(![X]:((strong(X)|~quiet(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~quiet(X))=>(~rich(X)&wise(X))))&
(![X]:((strong(X)|~happy(X))=>(rich(X)&patient(X))))&
(![X]:((~kind(X)|~tall(X))<=>~happy(X)))&
(![X]:(~funny(X)<=>~old(X)))&
(((generous(lucy)&~happy(lucy)))<=>((rich(lucy)|patient(lucy))))&
(![X]:((~strong(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~curious(X)|calm(X))))=>((patient(mary)|~humble(mary))))&
(((~humble(mary)&old(mary)))=>((quiet(lucy)|rich(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(~humble(X)|wise(X))))&
(((generous(alice)<~>rich(alice)))<=>((tall(john)<~>rich(john))))&
((?[X]:(strong(X)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&~tall(X))=>happy(X)))&
(((funny(susan)|~rich(susan)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((generous(X)|patient(X))<=>~patient(X)))&
(?[X]:((~patient(X)<~>~kind(X))))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((creative(X)|~old(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is both brave and wise is both not kind and patient. If someone is quiet then someone is both creative and not funny. Everyone who is curious or funny is both curious and not creative and vice versa. If susan is tall then alice is both quiet and tall and vice versa. If someone is not patient or strong then someone is both not patient and not strong and vice versa. Everyone who is happy or not tall is quiet or not quiet. If someone is both quiet and not creative then someone is brave or not happy and vice versa. Everyone who is either brave or humble is both not calm and happy and vice versa. Everyone who is both not creative and curious is not old or happy and vice versa. Everyone who is either creative or funny is funny and vice versa. Everyone who is either not rich or creative is both not patient and not humble and vice versa. If john is not wise or generous then someone is both not funny and not kind. If someone is not old or not curious then fred is either strong or not rich. If alice is both not tall and not humble then susan is either humble or not quiet and vice versa. Everyone who is not humble is either funny or not creative. Everyone who is humble or not quiet is not strong or rich and vice versa. Someone is not patient or not kind. Someone is either strong or kind. Alice is both not creative and strong. Fred is either wise or not rich. Mary is either rich or not brave. | Alice is old. | neutral | (![X]:((brave(X)&wise(X))=>(~kind(X)&patient(X))))&
((?[X]:(quiet(X)))=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((curious(X)|funny(X))<=>(curious(X)&~creative(X))))&
((tall(susan))<=>((quiet(alice)&tall(alice))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:((happy(X)|~tall(X))=>(quiet(X)|~quiet(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))<=>(~old(X)|happy(X))))&
(![X]:((creative(X)<~>funny(X))<=>funny(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)&~humble(X))))&
(((~wise(john)|generous(john)))=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~old(X)|~curious(X))))=>((strong(fred)<~>~rich(fred))))&
(((~tall(alice)&~humble(alice)))<=>((humble(susan)<~>~quiet(susan))))&
(![X]:(~humble(X)=>(funny(X)<~>~creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~strong(X)|rich(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>kind(X))))&
((~creative(alice)&strong(alice)))&
((wise(fred)<~>~rich(fred)))&
((rich(mary)<~>~brave(mary))) | old(alice) | [] | null | 0 |
If someone is curious or strong then lucy is patient or quiet and vice versa.
Everyone who is either brave or not wise is either not generous or not curious and vice versa.
If lucy is both tall and wise then lucy is both not patient and generous.
Everyone who is strong or not curious is curious or not creative and vice versa.
Everyone who is either creative or not old is either strong or humble and vice versa.
If lucy is humble then someone is either not kind or creative and vice versa.
Everyone who is either not strong or curious is either not curious or wise and vice versa.
If susan is not funny or creative then paul is calm and vice versa.
If someone is not brave or not kind then alice is not quiet and vice versa.
If alice is either patient or brave then someone is both patient and quiet.
Everyone who is not quiet is either creative or patient.
Everyone who is not generous is both funny and strong and vice versa.
Everyone who is curious or strong is either not brave or not tall and vice versa.
If alice is not kind then someone is creative or brave.
If someone is not rich or happy then mary is not happy or not calm.
If susan is not wise then mary is both not calm and brave.
Susan is rich or curious.
Lucy is curious or kind.
Someone is quiet.
Someone is either not rich or generous.
Mary is old or not old.
Someone is either humble or generous.
Susan is both tall and not creative.
Susan is both funny and quiet. | Susan is curious. | contradiction | ((?[X]:((curious(X)|strong(X))))<=>((patient(lucy)|quiet(lucy))))&
(![X]:((brave(X)<~>~wise(X))<=>(~generous(X)<~>~curious(X))))&
(((tall(lucy)&wise(lucy)))=>((~patient(lucy)&generous(lucy))))&
(![X]:((strong(X)|~curious(X))<=>(curious(X)|~creative(X))))&
(![X]:((creative(X)<~>~old(X))<=>(strong(X)<~>humble(X))))&
((humble(lucy))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:((~strong(X)<~>curious(X))<=>(~curious(X)<~>wise(X))))&
(((~funny(susan)|creative(susan)))<=>(calm(paul)))&
((?[X]:((~brave(X)|~kind(X))))<=>(~quiet(alice)))&
(((patient(alice)<~>brave(alice)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:(~quiet(X)=>(creative(X)<~>patient(X))))&
(![X]:(~generous(X)<=>(funny(X)&strong(X))))&
(![X]:((curious(X)|strong(X))<=>(~brave(X)<~>~tall(X))))&
((~kind(alice))=>(?[X]:((creative(X)|brave(X)))))&
((?[X]:((~rich(X)|happy(X))))=>((~happy(mary)|~calm(mary))))&
((~wise(susan))=>((~calm(mary)&brave(mary))))&
((rich(susan)|curious(susan)))&
((curious(lucy)|kind(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)<~>generous(X))))&
((old(mary)|~old(mary)))&
(?[X]:((humble(X)<~>generous(X))))&
((tall(susan)&~creative(susan)))&
((funny(susan)&quiet(susan))) | curious(susan) | [
"p1",
"p3",
"p6",
"p11",
"p12",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6697157831211308858978469
% SZS output start Proof for 6697157831211308858978469
2. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : ((~curious(X0) | strong(X0)) <=> (~creative(X0) | curious(X0))) [input p3]
7. ! [X0] : ((~strong(X0) <~> curious(X0)) <=> (~curious(X0) <~> wise(X0))) [input p6]
12. ! [X0] : (~generous(X0) <=> (strong(X0) & funny(X0))) [input p11]
13. ! [X0] : ((strong(X0) | curious(X0)) <=> (~brave(X0) <~> ~tall(X0))) [input p12]
23. ~creative(susan) & tall(susan) [input p22]
24. quiet(susan) & funny(susan) [input p23]
25. curious(susan) [input hypothesis]
38. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 2]
39. ! [X0] : (((~curious(X0) | strong(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (curious(X0) & ~strong(X0)))) [nnf transformation 4]
40. ! [X0] : ((~curious(X0) | strong(X0) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | (curious(X0) & ~strong(X0)))) [flattening 39]
46. ! [X0] : ((((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0))))) [nnf transformation 7]
57. ! [X0] : ((~generous(X0) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | generous(X0))) [nnf transformation 12]
58. ! [X0] : ((~generous(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | generous(X0))) [flattening 57]
59. ! [X0] : (((strong(X0) | curious(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) & (((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (~strong(X0) & ~curious(X0)))) [nnf transformation 13]
60. ! [X0] : ((strong(X0) | curious(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) & (((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (~strong(X0) & ~curious(X0)))) [flattening 59]
79. ~wise(X0) | brave(X0) | ~curious(X0) | generous(X0) [cnf transformation 38]
87. ~curious(X0) | strong(X0) | ~curious(X0) [cnf transformation 40]
102. wise(X0) | ~curious(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 46]
105. curious(X0) | ~strong(X0) | wise(X0) | curious(X0) [cnf transformation 46]
123. ~funny(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 58]
124. ~tall(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 60]
141. tall(susan) [cnf transformation 23]
143. funny(susan) [cnf transformation 24]
145. curious(susan) [cnf transformation 25]
146. wise(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 102]
148. ~strong(X0) | curious(X0) | wise(X0) [duplicate literal removal 105]
151. ~curious(X0) | strong(X0) [duplicate literal removal 87]
215. ~strong(X0) | wise(X0) [subsumption resolution 146,148]
221. 16 <=> funny(susan) [avatar definition]
222. funny(susan) <- (16) [avatar component clause 221]
288. 30 <=> wise(susan) [avatar definition]
290. wise(susan) <- (30) [avatar component clause 288]
306. 34 <=> curious(susan) [avatar definition]
308. curious(susan) <- (34) [avatar component clause 306]
340. 16 [avatar split clause 143,221]
341. 34 [avatar split clause 145,306]
345. strong(susan) <- (34) [resolution 151,308]
349. wise(susan) <- (34) [resolution 215,345]
397. ~strong(susan) | ~generous(susan) <- (16) [resolution 123,222]
399. ~generous(susan) <- (16, 34) [subsumption resolution 397,345]
401. ~brave(susan) | ~curious(susan) [resolution 124,141]
402. ~brave(susan) <- (34) [subsumption resolution 401,308]
526. brave(susan) | ~curious(susan) | generous(susan) <- (30) [resolution 79,290]
528. ~curious(susan) | generous(susan) <- (30, 34) [subsumption resolution 526,402]
529. generous(susan) <- (30, 34) [subsumption resolution 528,308]
530. $false <- (16, 30, 34) [subsumption resolution 529,399]
531. ~16 | ~30 | ~34 [avatar contradiction clause 530]
538. 30 | ~34 [avatar split clause 349,306,288]
539. $false [avatar sat refutation 340,341,531,538]
% SZS output end Proof for 6697157831211308858978469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not quiet is old.
If paul is brave or generous then lucy is either not funny or wise.
If paul is both funny and tall then paul is either brave or happy and vice versa.
Everyone who is not funny or creative is not rich or not brave.
Everyone who is either not kind or calm is both not creative and old and vice versa.
If lucy is calm then paul is not kind or not wise and vice versa.
Everyone who is generous is calm.
If someone is patient or curious then susan is both generous and not patient.
If susan is not calm or creative then fred is not patient or not humble and vice versa.
If someone is strong then someone is patient.
Everyone who is not wise is both not creative and tall and vice versa.
Everyone who is either not rich or kind is either creative or not brave.
If susan is either not rich or not old then alice is wise and vice versa.
Everyone who is not wise is not curious or not rich.
Everyone who is not curious is not patient or generous.
Everyone who is not rich or brave is both curious and patient and vice versa.
Someone is not rich or tall.
Alice is either not funny or not strong.
Lucy is either funny or old.
Mary is not curious.
Someone is either tall or not wise.
Alice is not old or quiet.
Alice is curious. | Susan is strong. | neutral | (![X]:((~calm(X)<~>~quiet(X))=>old(X)))&
(((brave(paul)|generous(paul)))=>((~funny(lucy)<~>wise(lucy))))&
(((funny(paul)&tall(paul)))<=>((brave(paul)<~>happy(paul))))&
(![X]:((~funny(X)|creative(X))=>(~rich(X)|~brave(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(~creative(X)&old(X))))&
((calm(lucy))<=>((~kind(paul)|~wise(paul))))&
(![X]:(generous(X)=>calm(X)))&
((?[X]:((patient(X)|curious(X))))=>((generous(susan)&~patient(susan))))&
(((~calm(susan)|creative(susan)))<=>((~patient(fred)|~humble(fred))))&
((?[X]:(strong(X)))=>(?[X]:(patient(X))))&
(![X]:(~wise(X)<=>(~creative(X)&tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~brave(X))))&
(((~rich(susan)<~>~old(susan)))<=>(wise(alice)))&
(![X]:(~wise(X)=>(~curious(X)|~rich(X))))&
(![X]:(~curious(X)=>(~patient(X)|generous(X))))&
(![X]:((~rich(X)|brave(X))<=>(curious(X)&patient(X))))&
(?[X]:((~rich(X)|tall(X))))&
((~funny(alice)<~>~strong(alice)))&
((funny(lucy)<~>old(lucy)))&
(~curious(mary))&
(?[X]:((tall(X)<~>~wise(X))))&
((~old(alice)|quiet(alice)))&
(curious(alice)) | strong(susan) | [] | null | 0 |
Everyone who is either brave or not kind is strong and vice versa. Everyone who is quiet or not tall is both curious and kind and vice versa. If mary is both not kind and not calm then susan is both not curious and not old. Everyone who is funny or not patient is funny or curious and vice versa. If someone is either not creative or tall then susan is not brave and vice versa. Everyone who is both not humble and strong is calm or not generous and vice versa. Everyone who is old is calm or not old and vice versa. Everyone who is both not creative and not wise is not generous or tall. If someone is both kind and wise then lucy is either not creative or not old. Everyone who is either curious or brave is both not quiet and not kind and vice versa. If fred is both calm and not happy then someone is not rich and vice versa. If alice is tall then someone is brave or humble. Everyone who is either not funny or not calm is either tall or not humble. Everyone who is either not quiet or not generous is not rich. Everyone who is both not calm and not funny is both not wise and generous and vice versa. Everyone who is both rich and not creative is not creative or not patient and vice versa. Fred is either not calm or calm. Someone is not creative. Someone is either not funny or not creative. Someone is both curious and not patient. Susan is not humble or not old. Someone is both tall and rich. | Susan is not creative. | neutral | (![X]:((brave(X)<~>~kind(X))<=>strong(X)))&
(![X]:((quiet(X)|~tall(X))<=>(curious(X)&kind(X))))&
(((~kind(mary)&~calm(mary)))=>((~curious(susan)&~old(susan))))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(![X]:((rich(X)&~creative(X))<=>(~creative(X)|~patient(X))))&
((~calm(fred)<~>calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan)))&
(?[X]:((tall(X)&rich(X)))) | ~creative(susan) | [] | null | 0 |
If someone is generous or not calm then paul is not tall and vice versa.
If someone is either not quiet or not generous then someone is both quiet and not old and vice versa.
Everyone who is either not tall or not quiet is tall and vice versa.
Everyone who is patient or tall is not happy and vice versa.
Everyone who is not tall is quiet and vice versa.
Everyone who is not generous or calm is either not patient or happy and vice versa.
Everyone who is both not brave and not tall is quiet or not creative and vice versa.
Everyone who is tall is both not funny and not generous.
If lucy is both not wise and not quiet then susan is not curious and vice versa.
If paul is not rich or curious then someone is both not calm and not curious.
Everyone who is brave or not curious is not wise or not brave.
If paul is both rich and not calm then lucy is not rich or not tall and vice versa.
If someone is both not strong and rich then john is both funny and happy.
Everyone who is both brave and not wise is not old.
Mary is tall.
Susan is not curious or calm.
Lucy is either not brave or not happy.
Someone is either kind or not old.
Someone is either not old or wise.
Someone is both not kind and calm.
Susan is both not quiet and not strong.
Susan is not old or not funny. | Susan is generous. | contradiction | ((?[X]:((generous(X)|~calm(X))))<=>(~tall(paul)))&
((?[X]:((~quiet(X)<~>~generous(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>tall(X)))&
(![X]:((patient(X)|tall(X))<=>~happy(X)))&
(![X]:(~tall(X)<=>quiet(X)))&
(![X]:((~generous(X)|calm(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~brave(X)&~tall(X))<=>(quiet(X)|~creative(X))))&
(![X]:(tall(X)=>(~funny(X)&~generous(X))))&
(((~wise(lucy)&~quiet(lucy)))<=>(~curious(susan)))&
(((~rich(paul)|curious(paul)))=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((brave(X)|~curious(X))=>(~wise(X)|~brave(X))))&
(((rich(paul)&~calm(paul)))<=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((~strong(X)&rich(X))))=>((funny(john)&happy(john))))&
(![X]:((brave(X)&~wise(X))=>~old(X)))&
(tall(mary))&
((~curious(susan)|calm(susan)))&
((~brave(lucy)<~>~happy(lucy)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((~kind(X)&calm(X))))&
((~quiet(susan)&~strong(susan)))&
((~old(susan)|~funny(susan))) | generous(susan) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 301284692959249798203930
% SZS output start Proof for 301284692959249798203930
3. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> tall(X0)) [input p2]
5. ! [X0] : (~tall(X0) <=> quiet(X0)) [input p4]
8. ! [X0] : (tall(X0) => (~generous(X0) & ~funny(X0))) [input p7]
23. generous(susan) [input hypothesis]
25. ! [X0] : ((~generous(X0) & ~funny(X0)) | ~tall(X0)) [ennf transformation 8]
41. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 3]
44. ! [X0] : ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))) [nnf transformation 5]
73. tall(X0) | ~quiet(X0) | tall(X0) [cnf transformation 41]
75. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
80. quiet(X0) | tall(X0) [cnf transformation 44]
94. ~generous(X0) | ~tall(X0) [cnf transformation 25]
125. generous(susan) [cnf transformation 23]
127. tall(X0) | ~quiet(X0) [duplicate literal removal 73]
128. ~quiet(X0) | ~tall(X0) [duplicate literal removal 75]
147. 5 <=> ! [X1] : ~generous(X1) [avatar definition]
148. ~generous(X1) <- (5) [avatar component clause 147]
181. ~quiet(X0) [subsumption resolution 127,128]
182. tall(X0) [subsumption resolution 80,181]
188. ~generous(X0) [subsumption resolution 94,182]
189. 5 [avatar split clause 188,147]
286. $false <- (5) [resolution 148,125]
287. ~5 [avatar contradiction clause 286]
288. $false [avatar sat refutation 189,287]
% SZS output end Proof for 301284692959249798203930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not curious is both generous and not strong and vice versa. If someone is not tall or patient then fred is either funny or happy. Everyone who is kind or not humble is happy or not humble. Everyone who is not wise is creative or not brave. Everyone who is strong is calm or old. Everyone who is not funny is both not brave and not patient. Everyone who is not strong or rich is both not calm and not happy. If someone is not old then someone is not creative and vice versa. If fred is quiet then someone is creative. If someone is tall or not wise then fred is both not quiet and not brave. Everyone who is both not patient and not happy is either funny or patient. If someone is not rich then someone is both not funny and not patient and vice versa. Everyone who is kind or not humble is not wise or not happy and vice versa. If someone is strong then someone is not humble or not generous and vice versa. If someone is either old or funny then someone is either old or brave and vice versa. Everyone who is rich or tall is both old and patient and vice versa. Someone is not kind or generous. Alice is humble. Fred is not rich. Someone is both creative and not old. Someone is not kind or not curious. Lucy is not happy. Someone is either tall or old. | Fred is not old. | neutral | (![X]:((humble(X)<~>~curious(X))<=>(generous(X)&~strong(X))))&
((?[X]:((~tall(X)|patient(X))))=>((funny(fred)<~>happy(fred))))&
(![X]:((kind(X)|~humble(X))=>(happy(X)|~humble(X))))&
(![X]:(~wise(X)=>(creative(X)|~brave(X))))&
(![X]:(strong(X)=>(calm(X)|old(X))))&
(![X]:(~funny(X)=>(~brave(X)&~patient(X))))&
(![X]:((~strong(X)|rich(X))=>(~calm(X)&~happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~creative(X))))&
((quiet(fred))=>(?[X]:(creative(X))))&
((?[X]:((tall(X)|~wise(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)<~>patient(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((kind(X)|~humble(X))<=>(~wise(X)|~happy(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~humble(X)|~generous(X)))))&
((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((rich(X)|tall(X))<=>(old(X)&patient(X))))&
(?[X]:((~kind(X)|generous(X))))&
(humble(alice))&
(~rich(fred))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(~happy(lucy))&
(?[X]:((tall(X)<~>old(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is happy is quiet or curious and vice versa.
Everyone who is not strong or generous is both not humble and not patient.
Everyone who is not humble is either not wise or not humble and vice versa.
Everyone who is generous or not funny is strong and vice versa.
Everyone who is either not generous or not rich is not calm or patient and vice versa.
Everyone who is either not tall or creative is either not rich or humble and vice versa.
If someone is both not generous and not creative then someone is funny.
Everyone who is creative is not wise.
Everyone who is not old is both creative and generous.
Everyone who is not curious or generous is both not tall and wise.
If john is funny or curious then someone is either brave or not tall.
Everyone who is either not happy or tall is both patient and funny and vice versa.
If someone is not quiet or not strong then susan is either not calm or kind and vice versa.
If lucy is funny then someone is both funny and not humble.
John is not rich or not creative.
Susan is either wise or curious.
Someone is brave or tall.
Alice is either not kind or kind.
Someone is either quiet or humble.
Someone is either not quiet or funny.
Paul is not tall.
Lucy is humble or not kind. | Alice is not tall. | entailment | (![X]:(happy(X)<=>(quiet(X)|curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)&~patient(X))))&
(![X]:(~humble(X)<=>(~wise(X)<~>~humble(X))))&
(![X]:((generous(X)|~funny(X))<=>strong(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~calm(X)|patient(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(~rich(X)<~>humble(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:(funny(X))))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:(~old(X)=>(creative(X)&generous(X))))&
(![X]:((~curious(X)|generous(X))=>(~tall(X)&wise(X))))&
(((funny(john)|curious(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(patient(X)&funny(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~calm(susan)<~>kind(susan))))&
((funny(lucy))=>(?[X]:((funny(X)&~humble(X)))))&
((~rich(john)|~creative(john)))&
((wise(susan)<~>curious(susan)))&
(?[X]:((brave(X)|tall(X))))&
((~kind(alice)<~>kind(alice)))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:((~quiet(X)<~>funny(X))))&
(~tall(paul))&
((humble(lucy)|~kind(lucy))) | ~tall(alice) | [
"p0",
"p1",
"p3",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5925266205218579799417311
% SZS output start Proof for 5925266205218579799417311
1. ! [X0] : (happy(X0) <=> (curious(X0) | quiet(X0))) [input p0]
2. ! [X0] : ((generous(X0) | ~strong(X0)) => (~patient(X0) & ~humble(X0))) [input p1]
4. ! [X0] : ((~funny(X0) | generous(X0)) <=> strong(X0)) [input p3]
10. ! [X0] : ((generous(X0) | ~curious(X0)) => (wise(X0) & ~tall(X0))) [input p9]
12. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (funny(X0) & patient(X0))) [input p11]
23. tall(alice) [input hypothesis]
26. ! [X0] : ((~patient(X0) & ~humble(X0)) | (~generous(X0) & strong(X0))) [ennf transformation 2]
29. ! [X0] : ((wise(X0) & ~tall(X0)) | (~generous(X0) & curious(X0))) [ennf transformation 10]
32. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ~happy(X0))) [nnf transformation 1]
33. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ~happy(X0))) [flattening 32]
35. ! [X0] : (((~funny(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (funny(X0) & ~generous(X0)))) [nnf transformation 4]
36. ! [X0] : ((~funny(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (funny(X0) & ~generous(X0)))) [flattening 35]
46. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~funny(X0) | ~patient(X0))) & ((funny(X0) & patient(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 12]
47. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ~funny(X0) | ~patient(X0)) & ((funny(X0) & patient(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 46]
66. ~curious(X0) | happy(X0) [cnf transformation 33]
69. ~patient(X0) | strong(X0) [cnf transformation 26]
77. ~funny(X0) | generous(X0) | ~strong(X0) [cnf transformation 36]
94. ~tall(X0) | curious(X0) [cnf transformation 29]
95. ~tall(X0) | ~generous(X0) [cnf transformation 29]
103. ~tall(X0) | ~happy(X0) | patient(X0) [cnf transformation 47]
105. ~tall(X0) | ~happy(X0) | funny(X0) [cnf transformation 47]
128. tall(alice) [cnf transformation 23]
248. curious(alice) [resolution 94,128]
249. ~generous(alice) [resolution 95,128]
250. happy(alice) [resolution 248,66]
288. ~happy(alice) | patient(alice) [resolution 103,128]
291. patient(alice) [subsumption resolution 288,250]
308. ~happy(alice) | funny(alice) [resolution 105,128]
312. funny(alice) [subsumption resolution 308,250]
331. strong(alice) [resolution 291,69]
337. generous(alice) | ~strong(alice) [resolution 312,77]
338. ~strong(alice) [subsumption resolution 337,249]
339. $false [subsumption resolution 338,331]
% SZS output end Proof for 5925266205218579799417311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then fred is both generous and not happy. Everyone who is either not calm or not funny is both tall and kind. Everyone who is either strong or curious is not curious or not happy and vice versa. Everyone who is both not calm and not funny is both not rich and not brave and vice versa. Everyone who is not wise or not quiet is not curious. If someone is not humble or wise then susan is not rich or quiet. Everyone who is not curious or not strong is both not patient and rich. Everyone who is both not tall and humble is either not happy or happy and vice versa. If paul is both not creative and not old then mary is not strong or not creative and vice versa. If fred is either humble or not calm then alice is either not quiet or not humble. Everyone who is either not patient or not calm is not tall or creative. If someone is not humble then lucy is both not generous and happy. If john is both happy and not humble then someone is creative. Everyone who is generous or not calm is not wise or funny and vice versa. If john is either rich or happy then someone is not brave or not tall and vice versa. If paul is not rich or generous then mary is not calm or not tall and vice versa. Someone is both creative and not tall. Fred is both not quiet and not happy. Someone is not rich or creative. Alice is either not creative or not quiet. Lucy is both creative and generous. Someone is not strong or not old. Someone is not tall. | John is humble. | entailment | ((?[X]:(~quiet(X)))=>((generous(fred)&~happy(fred))))&
(![X]:((~calm(X)<~>~funny(X))=>(tall(X)&kind(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~curious(X)|~happy(X))))&
(![X]:((~calm(X)&~funny(X))<=>(~rich(X)&~brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>~curious(X)))&
((?[X]:((~humble(X)|wise(X))))=>((~rich(susan)|quiet(susan))))&
(![X]:((~curious(X)|~strong(X))=>(~patient(X)&rich(X))))&
(![X]:((~tall(X)&humble(X))<=>(~happy(X)<~>happy(X))))&
(((~creative(paul)&~old(paul)))<=>((~strong(mary)|~creative(mary))))&
(((humble(fred)<~>~calm(fred)))=>((~quiet(alice)<~>~humble(alice))))&
(![X]:((~patient(X)<~>~calm(X))=>(~tall(X)|creative(X))))&
((?[X]:(~humble(X)))=>((~generous(lucy)&happy(lucy))))&
(((happy(john)&~humble(john)))=>(?[X]:(creative(X))))&
(![X]:((generous(X)|~calm(X))<=>(~wise(X)|funny(X))))&
(((rich(john)<~>happy(john)))<=>(?[X]:((~brave(X)|~tall(X)))))&
(((~rich(paul)|generous(paul)))<=>((~calm(mary)|~tall(mary))))&
(?[X]:((creative(X)&~tall(X))))&
((~quiet(fred)&~happy(fred)))&
(?[X]:((~rich(X)|creative(X))))&
((~creative(alice)<~>~quiet(alice)))&
((creative(lucy)&generous(lucy)))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:(~tall(X))) | humble(john) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6822578280833100342273992
% SZS output start Proof for 6822578280833100342273992
12. ? [X0] : ~humble(X0) => (happy(lucy) & ~generous(lucy)) [input p11]
21. generous(lucy) & creative(lucy) [input p20]
24. ~humble(john) [input hypothesis]
35. (happy(lucy) & ~generous(lucy)) | ! [X0] : humble(X0) [ennf transformation 12]
107. ~generous(lucy) | humble(X0) [cnf transformation 35]
132. generous(lucy) [cnf transformation 21]
135. ~humble(john) [cnf transformation 24]
169. 7 <=> ! [X0] : humble(X0) [avatar definition]
170. humble(X0) <- (7) [avatar component clause 169]
222. 17 <=> generous(lucy) [avatar definition]
225. 7 | ~17 [avatar split clause 107,222,169]
274. 17 [avatar split clause 132,222]
284. $false <- (7) [resolution 170,135]
285. ~7 [avatar contradiction clause 284]
286. $false [avatar sat refutation 225,274,285]
% SZS output end Proof for 6822578280833100342273992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both not old and calm.
If john is both not calm and calm then john is either not funny or brave and vice versa.
Everyone who is either not patient or rich is both happy and not funny and vice versa.
If mary is not tall then someone is not quiet or tall.
Everyone who is both generous and not creative is both tall and not creative and vice versa.
If someone is both not brave and curious then someone is rich or not happy and vice versa.
Everyone who is both wise and not old is creative.
If someone is both strong and quiet then john is either not tall or creative.
If someone is funny or happy then paul is not tall.
If someone is either patient or not wise then someone is wise or rich.
Everyone who is humble is funny and vice versa.
Everyone who is strong is both creative and not curious and vice versa.
Everyone who is both curious and kind is not funny.
Everyone who is patient or not quiet is both not funny and old and vice versa.
Everyone who is not calm or generous is not curious.
Everyone who is either not creative or wise is either not quiet or patient and vice versa.
Someone is either funny or generous.
Mary is generous.
Paul is not funny or not creative.
Someone is not creative.
Someone is either brave or patient.
Paul is not calm or wise.
Susan is either not brave or strong.
Someone is not old. | Mary is not curious. | entailment | (![X]:(happy(X)=>(~old(X)&calm(X))))&
(((~calm(john)&calm(john)))<=>((~funny(john)<~>brave(john))))&
(![X]:((~patient(X)<~>rich(X))<=>(happy(X)&~funny(X))))&
((~tall(mary))=>(?[X]:((~quiet(X)|tall(X)))))&
(![X]:((generous(X)&~creative(X))<=>(tall(X)&~creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:((wise(X)&~old(X))=>creative(X)))&
((?[X]:((strong(X)&quiet(X))))=>((~tall(john)<~>creative(john))))&
((?[X]:((funny(X)|happy(X))))=>(~tall(paul)))&
((?[X]:((patient(X)<~>~wise(X))))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(humble(X)<=>funny(X)))&
(![X]:(strong(X)<=>(creative(X)&~curious(X))))&
(![X]:((curious(X)&kind(X))=>~funny(X)))&
(![X]:((patient(X)|~quiet(X))<=>(~funny(X)&old(X))))&
(![X]:((~calm(X)|generous(X))=>~curious(X)))&
(![X]:((~creative(X)<~>wise(X))<=>(~quiet(X)<~>patient(X))))&
(?[X]:((funny(X)<~>generous(X))))&
(generous(mary))&
((~funny(paul)|~creative(paul)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((~calm(paul)|wise(paul)))&
((~brave(susan)<~>strong(susan)))&
(?[X]:(~old(X))) | ~curious(mary) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8158874915781989222347282
% SZS output start Proof for 8158874915781989222347282
15. ! [X0] : ((generous(X0) | ~calm(X0)) => ~curious(X0)) [input p14]
18. generous(mary) [input p17]
25. curious(mary) [input hypothesis]
36. ! [X0] : (~curious(X0) | (~generous(X0) & calm(X0))) [ennf transformation 15]
111. ~curious(X0) | ~generous(X0) [cnf transformation 36]
122. generous(mary) [cnf transformation 18]
131. curious(mary) [cnf transformation 25]
286. ~generous(mary) [resolution 111,131]
288. $false [subsumption resolution 286,122]
% SZS output end Proof for 8158874915781989222347282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not creative then someone is both not generous and not tall. Everyone who is not curious or not rich is rich and vice versa. Everyone who is either not patient or funny is both not calm and creative and vice versa. Everyone who is either old or rich is not brave. If someone is either not old or not brave then john is both generous and not strong. If alice is either strong or not kind then mary is either calm or not kind and vice versa. If susan is not strong then someone is either funny or not wise and vice versa. Everyone who is either not curious or not happy is both curious and creative and vice versa. Everyone who is not wise or happy is either kind or humble and vice versa. Everyone who is both not happy and not wise is not strong or not old. Everyone who is creative is not tall or not old. Everyone who is both not humble and not patient is either not calm or not brave and vice versa. If fred is not tall or not rich then someone is happy or creative. Everyone who is not humble or brave is not wise or not curious. If lucy is either not wise or rich then someone is either not happy or old and vice versa. Someone is not quiet or not creative. Someone is either curious or not brave. John is both not creative and brave. Someone is both not tall and generous. Paul is both not humble and generous. Someone is not generous. | Fred is not funny. | neutral | ((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((~curious(X)|~rich(X))<=>rich(X)))&
(![X]:((~patient(X)<~>funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((old(X)<~>rich(X))=>~brave(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>((generous(john)&~strong(john))))&
(((strong(alice)<~>~kind(alice)))<=>((calm(mary)<~>~kind(mary))))&
((~strong(susan))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(![X]:((~curious(X)<~>~happy(X))<=>(curious(X)&creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~happy(X)&~wise(X))=>(~strong(X)|~old(X))))&
(![X]:(creative(X)=>(~tall(X)|~old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~calm(X)<~>~brave(X))))&
(((~tall(fred)|~rich(fred)))=>(?[X]:((happy(X)|creative(X)))))&
(![X]:((~humble(X)|brave(X))=>(~wise(X)|~curious(X))))&
(((~wise(lucy)<~>rich(lucy)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(?[X]:((~quiet(X)|~creative(X))))&
(?[X]:((curious(X)<~>~brave(X))))&
((~creative(john)&brave(john)))&
(?[X]:((~tall(X)&generous(X))))&
((~humble(paul)&generous(paul)))&
(?[X]:(~generous(X))) | ~funny(fred) | [] | null | 0 |
If mary is either not humble or not rich then lucy is both not kind and wise. Everyone who is calm is creative or not generous. Everyone who is both not funny and old is either wise or not humble and vice versa. If mary is funny then someone is not happy and vice versa. Everyone who is not calm is either not wise or not brave. If john is not wise or generous then fred is not strong. If fred is not rich then fred is calm or brave and vice versa. If mary is not calm or not kind then lucy is either not strong or not funny and vice versa. Everyone who is both quiet and old is brave or generous. If paul is not calm then someone is both not generous and not tall and vice versa. Everyone who is both wise and not funny is funny or old and vice versa. If fred is old or not patient then someone is not generous or wise and vice versa. If someone is either strong or not strong then john is both not kind and not tall. Everyone who is not funny or not curious is both not rich and not brave. If fred is either generous or rich then alice is not happy and vice versa. If alice is both patient and wise then mary is either not rich or generous and vice versa. Someone is not funny or curious. Fred is creative or not curious. Someone is not funny or not kind. John is both patient and not wise. Someone is not wise. Someone is both not generous and wise. Someone is not wise or strong. | John is not wise. | entailment | (((~humble(mary)<~>~rich(mary)))=>((~kind(lucy)&wise(lucy))))&
(![X]:(calm(X)=>(creative(X)|~generous(X))))&
(![X]:((~funny(X)&old(X))<=>(wise(X)<~>~humble(X))))&
((funny(mary))<=>(?[X]:(~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)<~>~brave(X))))&
(((~wise(john)|generous(john)))=>(~strong(fred)))&
((~rich(fred))<=>((calm(fred)|brave(fred))))&
(((~calm(mary)|~kind(mary)))<=>((~strong(lucy)<~>~funny(lucy))))&
(![X]:((quiet(X)&old(X))=>(brave(X)|generous(X))))&
((~calm(paul))<=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((wise(X)&~funny(X))<=>(funny(X)|old(X))))&
(((old(fred)|~patient(fred)))<=>(?[X]:((~generous(X)|wise(X)))))&
((?[X]:((strong(X)<~>~strong(X))))=>((~kind(john)&~tall(john))))&
(![X]:((~funny(X)|~curious(X))=>(~rich(X)&~brave(X))))&
(((generous(fred)<~>rich(fred)))<=>(~happy(alice)))&
(((patient(alice)&wise(alice)))<=>((~rich(mary)<~>generous(mary))))&
(?[X]:((~funny(X)|curious(X))))&
((creative(fred)|~curious(fred)))&
(?[X]:((~funny(X)|~kind(X))))&
((patient(john)&~wise(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~wise(X)|strong(X)))) | ~wise(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9017130409918686649773953
% SZS output start Proof for 9017130409918686649773953
20. ~wise(john) & patient(john) [input p19]
24. wise(john) [input hypothesis]
125. ~wise(john) [cnf transformation 20]
130. wise(john) [cnf transformation 24]
180. 10 <=> wise(john) [avatar definition]
316. ~10 [avatar split clause 125,180]
326. 10 [avatar split clause 130,180]
327. $false [avatar sat refutation 316,326]
% SZS output end Proof for 9017130409918686649773953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is kind or creative and vice versa.
If john is not rich then someone is kind or wise.
If someone is not generous then someone is both strong and curious and vice versa.
Everyone who is tall or strong is either patient or curious.
If someone is patient then lucy is rich or not patient.
Everyone who is not patient is curious or wise and vice versa.
Everyone who is both not kind and old is both happy and not patient.
Everyone who is both tall and not generous is either not curious or rich and vice versa.
If someone is not creative then mary is not curious and vice versa.
If mary is either strong or tall then paul is rich and vice versa.
Everyone who is both humble and brave is strong and vice versa.
Everyone who is quiet or not wise is both strong and old.
Everyone who is not tall is tall or not curious.
Everyone who is not wise or not quiet is either not brave or strong and vice versa.
Everyone who is calm is not rich or not happy and vice versa.
Everyone who is quiet or not generous is not brave.
Lucy is either not humble or wise.
Mary is both not old and rich.
Someone is both funny and not patient.
Susan is either not creative or not kind.
Fred is rich or kind.
Lucy is not wise or not funny.
Paul is both not wise and strong.
Lucy is both tall and curious. | Paul is not patient. | entailment | (![X]:(wise(X)<=>(kind(X)|creative(X))))&
((~rich(john))=>(?[X]:((kind(X)|wise(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)|strong(X))=>(patient(X)<~>curious(X))))&
((?[X]:(patient(X)))=>((rich(lucy)|~patient(lucy))))&
(![X]:(~patient(X)<=>(curious(X)|wise(X))))&
(![X]:((~kind(X)&old(X))=>(happy(X)&~patient(X))))&
(![X]:((tall(X)&~generous(X))<=>(~curious(X)<~>rich(X))))&
((?[X]:(~creative(X)))<=>(~curious(mary)))&
(((strong(mary)<~>tall(mary)))<=>(rich(paul)))&
(![X]:((humble(X)&brave(X))<=>strong(X)))&
(![X]:((quiet(X)|~wise(X))=>(strong(X)&old(X))))&
(![X]:(~tall(X)=>(tall(X)|~curious(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(calm(X)<=>(~rich(X)|~happy(X))))&
(![X]:((quiet(X)|~generous(X))=>~brave(X)))&
((~humble(lucy)<~>wise(lucy)))&
((~old(mary)&rich(mary)))&
(?[X]:((funny(X)&~patient(X))))&
((~creative(susan)<~>~kind(susan)))&
((rich(fred)|kind(fred)))&
((~wise(lucy)|~funny(lucy)))&
((~wise(paul)&strong(paul)))&
((tall(lucy)&curious(lucy))) | ~patient(paul) | [
"p0",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 998136316912831463920391
% SZS output start Proof for 998136316912831463920391
1. ! [X0] : (wise(X0) <=> (creative(X0) | kind(X0))) [input p0]
6. ! [X0] : (~patient(X0) <=> (wise(X0) | curious(X0))) [input p5]
7. ! [X0] : ((old(X0) & ~kind(X0)) => (~patient(X0) & happy(X0))) [input p6]
12. ! [X0] : ((~wise(X0) | quiet(X0)) => (old(X0) & strong(X0))) [input p11]
25. patient(paul) [input hypothesis]
27. ! [X0] : ((old(X0) & ~kind(X0)) => ~patient(X0)) [pure predicate removal 7]
32. ! [X0] : (~patient(X0) | (~old(X0) | kind(X0))) [ennf transformation 27]
33. ! [X0] : (~patient(X0) | ~old(X0) | kind(X0)) [flattening 32]
34. ! [X0] : ((old(X0) & strong(X0)) | (wise(X0) & ~quiet(X0))) [ennf transformation 12]
38. ! [X0] : ((wise(X0) | (~creative(X0) & ~kind(X0))) & ((creative(X0) | kind(X0)) | ~wise(X0))) [nnf transformation 1]
39. ! [X0] : ((wise(X0) | (~creative(X0) & ~kind(X0))) & (creative(X0) | kind(X0) | ~wise(X0))) [flattening 38]
48. ! [X0] : ((~patient(X0) | (~wise(X0) & ~curious(X0))) & ((wise(X0) | curious(X0)) | patient(X0))) [nnf transformation 6]
49. ! [X0] : ((~patient(X0) | (~wise(X0) & ~curious(X0))) & (wise(X0) | curious(X0) | patient(X0))) [flattening 48]
66. ~kind(X0) | wise(X0) [cnf transformation 39]
79. ~patient(X0) | ~wise(X0) [cnf transformation 49]
80. ~old(X0) | ~patient(X0) | kind(X0) [cnf transformation 33]
99. old(X0) | wise(X0) [cnf transformation 34]
123. patient(paul) [cnf transformation 25]
157. 8 <=> ! [X0] : ~patient(X0) [avatar definition]
158. ~patient(X0) <- (8) [avatar component clause 157]
337. ~patient(X0) | kind(X0) | wise(X0) [resolution 80,99]
338. ~patient(X0) | wise(X0) [subsumption resolution 337,66]
339. ~patient(X0) [subsumption resolution 338,79]
340. 8 [avatar split clause 339,157]
341. $false <- (8) [resolution 158,123]
343. ~8 [avatar contradiction clause 341]
344. $false [avatar sat refutation 340,343]
% SZS output end Proof for 998136316912831463920391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and strong is quiet.
Everyone who is either not calm or not brave is not calm and vice versa.
Everyone who is not brave is both not strong and tall.
If someone is both not wise and not patient then susan is not strong.
Everyone who is either not creative or not wise is not rich and vice versa.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Someone is both funny and not old.
Someone is either generous or kind.
Susan is humble or strong.
Someone is kind or curious.
Someone is not tall.
John is not rich.
Someone is quiet or not humble. | Fred is creative. | entailment | (![X]:((~wise(X)&strong(X))=>quiet(X)))&
(![X]:((~calm(X)<~>~brave(X))<=>~calm(X)))&
(![X]:(~brave(X)=>(~strong(X)&tall(X))))&
((?[X]:((~wise(X)&~patient(X))))=>(~strong(susan)))&
(![X]:((~creative(X)<~>~wise(X))<=>~rich(X)))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(?[X]:((funny(X)&~old(X))))&
(?[X]:((generous(X)<~>kind(X))))&
((humble(susan)|strong(susan)))&
(?[X]:((kind(X)|curious(X))))&
(?[X]:(~tall(X)))&
(~rich(john))&
(?[X]:((quiet(X)|~humble(X)))) | creative(fred) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7992288274437712260733116
% SZS output start Proof for 7992288274437712260733116
2. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> ~calm(X0)) [input p1]
10. ! [X0] : ((~brave(X0) <~> creative(X0)) <=> (quiet(X0) | ~quiet(X0))) [input p9]
24. ~creative(fred) [input hypothesis]
38. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 2]
45. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & ((quiet(X0) | ~quiet(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [nnf transformation 10]
46. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & (quiet(X0) | ~quiet(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [flattening 45]
71. ~calm(X0) | ~calm(X0) | brave(X0) [cnf transformation 38]
73. brave(X0) | calm(X0) | calm(X0) [cnf transformation 38]
94. creative(X0) | ~brave(X0) | quiet(X0) [cnf transformation 46]
95. creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
122. ~creative(fred) [cnf transformation 24]
123. ~calm(X0) | brave(X0) [duplicate literal removal 71]
124. brave(X0) | calm(X0) [duplicate literal removal 73]
125. brave(X0) [subsumption resolution 123,124]
149. creative(X0) | ~quiet(X0) [subsumption resolution 95,125]
150. creative(X0) | quiet(X0) [subsumption resolution 94,125]
151. creative(X0) [subsumption resolution 150,149]
244. $false [subsumption resolution 122,151]
% SZS output end Proof for 7992288274437712260733116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is not calm and vice versa.
Everyone who is both creative and strong is not happy or not kind.
Everyone who is creative or strong is not generous and vice versa.
If someone is strong then someone is not quiet.
Everyone who is both patient and not patient is brave and vice versa.
Everyone who is funny is not patient or not wise.
If paul is both not creative and not wise then someone is both tall and humble and vice versa.
If mary is not kind then fred is either not strong or not curious.
Everyone who is not strong or strong is either brave or happy and vice versa.
Everyone who is generous or not strong is both not brave and patient.
If someone is either not calm or not funny then fred is both not funny and not creative and vice versa.
Everyone who is humble is not curious or humble.
If lucy is not funny or not humble then paul is both not patient and not wise.
Everyone who is either not rich or calm is not old or kind.
Everyone who is either not tall or quiet is not wise.
If lucy is either not humble or strong then someone is funny or curious and vice versa.
Alice is both not brave and not wise.
Paul is both rich and generous.
Lucy is either happy or not quiet.
Someone is both not patient and not funny.
Someone is not brave.
Mary is both not tall and not generous.
Someone is either creative or happy.
Someone is rich or wise. | Fred is not funny. | entailment | (![X]:(~happy(X)<=>~calm(X)))&
(![X]:((creative(X)&strong(X))=>(~happy(X)|~kind(X))))&
(![X]:((creative(X)|strong(X))<=>~generous(X)))&
((?[X]:(strong(X)))=>(?[X]:(~quiet(X))))&
(![X]:((patient(X)&~patient(X))<=>brave(X)))&
(![X]:(funny(X)=>(~patient(X)|~wise(X))))&
(((~creative(paul)&~wise(paul)))<=>(?[X]:((tall(X)&humble(X)))))&
((~kind(mary))=>((~strong(fred)<~>~curious(fred))))&
(![X]:((~strong(X)|strong(X))<=>(brave(X)<~>happy(X))))&
(![X]:((generous(X)|~strong(X))=>(~brave(X)&patient(X))))&
((?[X]:((~calm(X)<~>~funny(X))))<=>((~funny(fred)&~creative(fred))))&
(![X]:(humble(X)=>(~curious(X)|humble(X))))&
(((~funny(lucy)|~humble(lucy)))=>((~patient(paul)&~wise(paul))))&
(![X]:((~rich(X)<~>calm(X))=>(~old(X)|kind(X))))&
(![X]:((~tall(X)<~>quiet(X))=>~wise(X)))&
(((~humble(lucy)<~>strong(lucy)))<=>(?[X]:((funny(X)|curious(X)))))&
((~brave(alice)&~wise(alice)))&
((rich(paul)&generous(paul)))&
((happy(lucy)<~>~quiet(lucy)))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(~brave(X)))&
((~tall(mary)&~generous(mary)))&
(?[X]:((creative(X)<~>happy(X))))&
(?[X]:((rich(X)|wise(X)))) | ~funny(fred) | [
"p0",
"p4",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7807187279019465964231624
% SZS output start Proof for 7807187279019465964231624
1. ! [X0] : (~happy(X0) <=> ~calm(X0)) [input p0]
5. ! [X0] : ((~patient(X0) & patient(X0)) <=> brave(X0)) [input p4]
9. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (brave(X0) <~> happy(X0))) [input p8]
11. ? [X0] : (~calm(X0) <~> ~funny(X0)) <=> (~creative(fred) & ~funny(fred)) [input p10]
20. ? [X0] : (~funny(X0) & ~patient(X0)) [input p19]
25. funny(fred) [input hypothesis]
41. ! [X0] : ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))) [nnf transformation 1]
47. ! [X0] : (((~patient(X0) & patient(X0)) | ~brave(X0)) & (brave(X0) | (patient(X0) | ~patient(X0)))) [nnf transformation 5]
48. ! [X0] : (((~patient(X0) & patient(X0)) | ~brave(X0)) & (brave(X0) | patient(X0) | ~patient(X0))) [flattening 47]
55. ! [X0] : (((strong(X0) | ~strong(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (~strong(X0) & strong(X0)))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~strong(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (~strong(X0) & strong(X0)))) [flattening 55]
57. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (creative(fred) | funny(fred))) & ((~creative(fred) & ~funny(fred)) | ! [X0] : ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) [nnf transformation 11]
58. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X0] : ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) [flattening 57]
59. (? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X1] : ((~calm(X1) | funny(X1)) & (~funny(X1) | calm(X1)))) [rectify 58]
60. ? [X0] : ((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) => ((funny(sK2) | calm(sK2)) & (~funny(sK2) | ~calm(sK2))) [choice axiom]
61. (((funny(sK2) | calm(sK2)) & (~funny(sK2) | ~calm(sK2))) | creative(fred) | funny(fred)) & ((~creative(fred) & ~funny(fred)) | ! [X1] : ((~calm(X1) | funny(X1)) & (~funny(X1) | calm(X1)))) [skolemisation 59,60]
68. ? [X0] : (~funny(X0) & ~patient(X0)) => (~funny(sK4) & ~patient(sK4)) [choice axiom]
69. ~funny(sK4) & ~patient(sK4) [skolemisation 20,68]
76. ~happy(X0) | calm(X0) [cnf transformation 41]
83. patient(X0) | ~brave(X0) [cnf transformation 48]
84. ~brave(X0) | ~patient(X0) [cnf transformation 48]
92. happy(X0) | brave(X0) | strong(X0) [cnf transformation 56]
93. happy(X0) | brave(X0) | ~strong(X0) [cnf transformation 56]
103. ~funny(fred) | ~calm(X1) | funny(X1) [cnf transformation 61]
127. ~funny(sK4) [cnf transformation 69]
133. funny(fred) [cnf transformation 25]
142. ~brave(X0) [subsumption resolution 83,84]
180. ~strong(X0) | happy(X0) [subsumption resolution 93,142]
181. happy(X0) | strong(X0) [subsumption resolution 92,142]
182. happy(X0) [subsumption resolution 181,180]
184. 11 <=> funny(fred) [avatar definition]
202. 15 <=> ! [X1] : (~calm(X1) | funny(X1)) [avatar definition]
203. ~calm(X1) | funny(X1) <- (15) [avatar component clause 202]
209. 15 | ~11 [avatar split clause 103,184,202]
253. 11 [avatar split clause 133,184]
259. calm(X0) [resolution 76,182]
277. funny(X0) <- (15) [resolution 203,259]
278. $false <- (15) [resolution 277,127]
279. ~15 [avatar contradiction clause 278]
280. $false [avatar sat refutation 209,253,279]
% SZS output end Proof for 7807187279019465964231624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not rich is tall and vice versa.
Everyone who is both kind and not patient is either not funny or quiet and vice versa.
Everyone who is quiet is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Everyone who is both old and not calm is not rich or not funny and vice versa.
Everyone who is both rich and not wise is both curious and quiet.
If john is both curious and old then susan is rich and vice versa.
Everyone who is either patient or happy is funny or not curious and vice versa.
If someone is rich or calm then alice is rich or not old and vice versa.
Everyone who is either tall or not funny is both strong and funny and vice versa.
Someone is both brave and not strong.
Lucy is either generous or not brave.
Someone is not strong or not quiet.
Someone is rich.
Someone is either quiet or not curious.
Someone is either humble or not wise. | Alice is not funny. | contradiction | (![X]:((~strong(X)&~rich(X))<=>tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(quiet(X)<=>(happy(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(![X]:((tall(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~strong(X))))&
((generous(lucy)<~>~brave(lucy)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~wise(X)))) | ~funny(alice) | [
"p0",
"p3",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 567496579482639164194697
% SZS output start Proof for 567496579482639164194697
1. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> tall(X0)) [input p0]
4. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p3]
11. ! [X0] : ((~calm(X0) & old(X0)) <=> (~funny(X0) | ~rich(X0))) [input p10]
15. ? [X0] : (calm(X0) | rich(X0)) <=> (~old(alice) | rich(alice)) [input p14]
16. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (funny(X0) & strong(X0))) [input p15]
17. ? [X0] : (~strong(X0) & brave(X0)) [input p16]
23. ~funny(alice) [input hypothesis]
25. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 4]
29. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) | strong(X0)))) [nnf transformation 1]
30. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | rich(X0) | strong(X0))) [flattening 29]
51. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (calm(X0) | ~old(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | calm(X0) | ~old(X0))) [flattening 51]
57. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & ((~old(alice) | rich(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) [nnf transformation 15]
58. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X0] : (~calm(X0) & ~rich(X0))) [flattening 57]
59. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [rectify 58]
60. ? [X0] : (calm(X0) | rich(X0)) => (calm(sK2) | rich(sK2)) [choice axiom]
61. ((calm(sK2) | rich(sK2)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [skolemisation 59,60]
62. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 16]
63. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 62]
64. ? [X0] : (~strong(X0) & brave(X0)) => (~strong(sK3) & brave(sK3)) [choice axiom]
65. ~strong(sK3) & brave(sK3) [skolemisation 17,64]
79. ~tall(X0) | ~rich(X0) [cnf transformation 30]
92. ~brave(X0) | rich(X0) [cnf transformation 25]
118. old(X0) | rich(X0) [cnf transformation 52]
133. ~old(alice) | rich(alice) | ~rich(X1) [cnf transformation 61]
140. funny(X0) | tall(X0) | funny(X0) [cnf transformation 63]
143. brave(sK3) [cnf transformation 65]
153. ~funny(alice) [cnf transformation 23]
154. funny(X0) | tall(X0) [duplicate literal removal 140]
219. 13 <=> rich(alice) [avatar definition]
228. rich(alice) | ~rich(X1) [subsumption resolution 133,118]
230. 15 <=> ! [X1] : ~rich(X1) [avatar definition]
231. ~rich(X1) <- (15) [avatar component clause 230]
232. 15 | 13 [avatar split clause 228,219,230]
275. rich(sK3) [resolution 92,143]
280. tall(alice) [resolution 154,153]
281. ~rich(alice) [resolution 280,79]
285. ~13 [avatar split clause 281,219]
288. $false <- (15) [resolution 231,275]
291. ~15 [avatar contradiction clause 288]
294. $false [avatar sat refutation 232,285,291]
% SZS output end Proof for 567496579482639164194697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not calm is either not funny or humble.
If someone is either not funny or not quiet then someone is either tall or brave and vice versa.
Everyone who is humble is not old or not tall.
Everyone who is strong or patient is either humble or not kind and vice versa.
If mary is tall then someone is funny.
Everyone who is either humble or curious is both not old and not brave and vice versa.
Everyone who is not tall or old is kind or strong and vice versa.
Everyone who is both not tall and not wise is patient or not rich and vice versa.
Everyone who is both curious and not calm is both not brave and brave and vice versa.
If someone is either not generous or not wise then someone is either tall or brave and vice versa.
Everyone who is curious is both not strong and not funny.
If fred is not strong or happy then john is happy or not kind and vice versa.
Everyone who is funny or generous is curious or rich.
If someone is wise then mary is both kind and strong.
If fred is either not patient or happy then alice is either brave or quiet.
Everyone who is curious is funny.
Someone is old or not rich.
Mary is not humble.
Someone is either brave or patient.
Someone is tall.
Mary is not wise or strong.
Someone is either humble or brave. | John is not curious. | entailment | (![X]:((curious(X)&~calm(X))=>(~funny(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>~quiet(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(humble(X)=>(~old(X)|~tall(X))))&
(![X]:((strong(X)|patient(X))<=>(humble(X)<~>~kind(X))))&
((tall(mary))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((~tall(X)|old(X))<=>(kind(X)|strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(patient(X)|~rich(X))))&
(![X]:((curious(X)&~calm(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(curious(X)=>(~strong(X)&~funny(X))))&
(((~strong(fred)|happy(fred)))<=>((happy(john)|~kind(john))))&
(![X]:((funny(X)|generous(X))=>(curious(X)|rich(X))))&
((?[X]:(wise(X)))=>((kind(mary)&strong(mary))))&
(((~patient(fred)<~>happy(fred)))=>((brave(alice)<~>quiet(alice))))&
(![X]:(curious(X)=>funny(X)))&
(?[X]:((old(X)|~rich(X))))&
(~humble(mary))&
(?[X]:((brave(X)<~>patient(X))))&
(?[X]:(tall(X)))&
((~wise(mary)|strong(mary)))&
(?[X]:((humble(X)<~>brave(X)))) | ~curious(john) | [
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5538971301514475048691642
% SZS output start Proof for 5538971301514475048691642
11. ! [X0] : (curious(X0) => (~funny(X0) & ~strong(X0))) [input p10]
16. ! [X0] : (curious(X0) => funny(X0)) [input p15]
23. curious(john) [input hypothesis]
31. ! [X0] : ((~funny(X0) & ~strong(X0)) | ~curious(X0)) [ennf transformation 11]
36. ! [X0] : (funny(X0) | ~curious(X0)) [ennf transformation 16]
119. ~funny(X0) | ~curious(X0) [cnf transformation 31]
132. funny(X0) | ~curious(X0) [cnf transformation 36]
141. curious(john) [cnf transformation 23]
268. ~curious(X0) [subsumption resolution 132,119]
303. $false [subsumption resolution 141,268]
% SZS output end Proof for 5538971301514475048691642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or not creative then someone is not rich. Everyone who is both not wise and not rich is funny and vice versa. Everyone who is either generous or not old is both not humble and old. If mary is either not strong or not generous then paul is either generous or wise. If john is not generous or wise then someone is both not quiet and not strong and vice versa. Everyone who is both kind and not quiet is both not kind and funny. Everyone who is either old or not curious is strong. If paul is both not strong and generous then john is not strong or not wise and vice versa. Everyone who is either calm or not calm is both not tall and curious and vice versa. If paul is both kind and not quiet then someone is not rich and vice versa. If fred is either tall or not calm then someone is both old and not tall and vice versa. Everyone who is both not quiet and strong is both not curious and not brave. Everyone who is creative is both not calm and not patient and vice versa. Everyone who is generous is kind or not humble and vice versa. Everyone who is both brave and funny is patient or not wise. Everyone who is rich is either generous or calm and vice versa. Someone is both humble and strong. Someone is old or kind. Alice is strong. Mary is curious or quiet. John is either not calm or wise. Someone is happy. Someone is either not funny or not quiet. Mary is wise or not tall. | Mary is not calm. | entailment | (((~wise(mary)|~creative(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(![X]:((brave(X)&funny(X))=>(patient(X)|~wise(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((old(X)|kind(X))))&
(strong(alice))&
((curious(mary)|quiet(mary)))&
((~calm(john)<~>wise(john)))&
(?[X]:(happy(X)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((wise(mary)|~tall(mary))) | ~calm(mary) | [
"p0",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8269069304145547400360351
% SZS output start Proof for 8269069304145547400360351
1. (~creative(mary) | ~wise(mary)) => ? [X0] : ~rich(X0) [input p0]
6. ! [X0] : ((~quiet(X0) & kind(X0)) => (funny(X0) & ~kind(X0))) [input p5]
10. (~quiet(paul) & kind(paul)) <=> ? [X0] : ~rich(X0) [input p9]
13. ! [X0] : (creative(X0) <=> (~patient(X0) & ~calm(X0))) [input p12]
25. calm(mary) [input hypothesis]
26. ! [X0] : (creative(X0) => (~patient(X0) & ~calm(X0))) [unused predicate definition removal 13]
30. ! [X0] : (creative(X0) => ~calm(X0)) [pure predicate removal 26]
31. ? [X0] : ~rich(X0) | (creative(mary) & wise(mary)) [ennf transformation 1]
34. ! [X0] : ((funny(X0) & ~kind(X0)) | (quiet(X0) | ~kind(X0))) [ennf transformation 6]
35. ! [X0] : ((funny(X0) & ~kind(X0)) | quiet(X0) | ~kind(X0)) [flattening 34]
39. ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 30]
40. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
41. ~rich(sK0) | (creative(mary) & wise(mary)) [skolemisation 31,40]
56. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (quiet(paul) | ~kind(paul))) [nnf transformation 10]
57. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | quiet(paul) | ~kind(paul)) [flattening 56]
58. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | quiet(paul) | ~kind(paul)) [rectify 57]
59. ? [X1] : ~rich(X1) => ~rich(sK2) [choice axiom]
60. ((~quiet(paul) & kind(paul)) | ! [X0] : rich(X0)) & (~rich(sK2) | quiet(paul) | ~kind(paul)) [skolemisation 58,59]
77. ~rich(sK0) | creative(mary) [cnf transformation 41]
94. ~kind(X0) | quiet(X0) | ~kind(X0) [cnf transformation 35]
110. kind(paul) | rich(X0) [cnf transformation 60]
111. ~quiet(paul) | rich(X0) [cnf transformation 60]
119. ~calm(X0) | ~creative(X0) [cnf transformation 39]
137. calm(mary) [cnf transformation 25]
142. ~kind(X0) | quiet(X0) [duplicate literal removal 94]
145. 1 <=> creative(mary) [avatar definition]
149. 2 <=> rich(sK0) [avatar definition]
151. ~rich(sK0) <- (~2) [avatar component clause 149]
152. 1 | ~2 [avatar split clause 77,149,145]
218. 15 <=> ! [X0] : rich(X0) [avatar definition]
219. rich(X0) <- (15) [avatar component clause 218]
221. 16 <=> quiet(paul) [avatar definition]
223. ~quiet(paul) <- (~16) [avatar component clause 221]
224. 15 | ~16 [avatar split clause 111,221,218]
226. 17 <=> kind(paul) [avatar definition]
228. kind(paul) <- (17) [avatar component clause 226]
229. 15 | 17 [avatar split clause 110,226,218]
272. $false <- (~2, 15) [subsumption resolution 151,219]
273. 2 | ~15 [avatar contradiction clause 272]
278. ~creative(mary) [resolution 119,137]
279. ~1 [avatar split clause 278,145]
284. quiet(paul) <- (17) [resolution 142,228]
285. $false <- (~16, 17) [subsumption resolution 284,223]
286. 16 | ~17 [avatar contradiction clause 285]
287. $false [avatar sat refutation 152,224,229,273,279,286]
% SZS output end Proof for 8269069304145547400360351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny and not tall. If someone is either not happy or not funny then someone is both not curious and not old. Everyone who is not quiet or creative is funny and vice versa. Everyone who is not old is both generous and not kind and vice versa. If susan is either strong or not calm then someone is not humble or patient and vice versa. If someone is both not old and not kind then john is either not curious or not strong. If someone is not patient then someone is either rich or not patient. If someone is either not old or wise then someone is calm or creative. Everyone who is happy or not calm is either strong or not brave and vice versa. Everyone who is either wise or quiet is either not creative or wise. Everyone who is either not creative or not wise is both not kind and quiet and vice versa. If someone is wise or not rich then susan is either not curious or not happy and vice versa. Everyone who is both not strong and not rich is patient and vice versa. Everyone who is not humble is not kind or funny and vice versa. If someone is either creative or not quiet then someone is strong and vice versa. Everyone who is brave or not curious is humble or happy and vice versa. Fred is creative or not calm. Mary is both not patient and not kind. Someone is both not brave and humble. Mary is not strong. Someone is generous or not generous. Someone is both humble and not wise. John is not patient. Someone is not funny. | John is not strong. | neutral | (![X]:(~wise(X)=>(~funny(X)&~tall(X))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((~quiet(X)|creative(X))<=>funny(X)))&
(![X]:(~old(X)<=>(generous(X)&~kind(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:((~humble(X)|patient(X)))))&
((?[X]:((~old(X)&~kind(X))))=>((~curious(john)<~>~strong(john))))&
((?[X]:(~patient(X)))=>(?[X]:((rich(X)<~>~patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))=>(?[X]:((calm(X)|creative(X)))))&
(![X]:((happy(X)|~calm(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~kind(X)&quiet(X))))&
((?[X]:((wise(X)|~rich(X))))<=>((~curious(susan)<~>~happy(susan))))&
(![X]:((~strong(X)&~rich(X))<=>patient(X)))&
(![X]:(~humble(X)<=>(~kind(X)|funny(X))))&
((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(humble(X)|happy(X))))&
((creative(fred)|~calm(fred)))&
((~patient(mary)&~kind(mary)))&
(?[X]:((~brave(X)&humble(X))))&
(~strong(mary))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((humble(X)&~wise(X))))&
(~patient(john))&
(?[X]:(~funny(X))) | ~strong(john) | [] | null | 0 |
If someone is both not strong and not kind then mary is either calm or patient and vice versa. Everyone who is either not quiet or generous is either not rich or brave. If lucy is funny or not old then john is not rich or not strong and vice versa. If someone is not curious then john is both not quiet and not creative and vice versa. If fred is not kind or not creative then someone is happy. If someone is rich or not old then john is either not curious or not happy. If paul is both not brave and not strong then someone is funny or not creative and vice versa. Everyone who is not rich or not calm is both wise and not wise and vice versa. Everyone who is strong is both calm and not creative and vice versa. Everyone who is either generous or curious is either not quiet or kind. Everyone who is not curious or funny is not humble or happy. If paul is creative or humble then someone is both creative and old. If someone is happy or not creative then someone is not brave. If someone is either not funny or old then fred is either not old or not rich and vice versa. Everyone who is brave is both brave and not old. Paul is not curious or creative. John is not humble or not curious. Lucy is old or rich. John is either tall or not humble. John is not brave. Susan is not generous or happy. Paul is kind or happy. Paul is quiet or not curious. | John is not brave. | entailment | ((?[X]:((~strong(X)&~kind(X))))<=>((calm(mary)<~>patient(mary))))&
(![X]:((~quiet(X)<~>generous(X))=>(~rich(X)<~>brave(X))))&
(((funny(lucy)|~old(lucy)))<=>((~rich(john)|~strong(john))))&
((?[X]:(~curious(X)))<=>((~quiet(john)&~creative(john))))&
(((~kind(fred)|~creative(fred)))=>(?[X]:(happy(X))))&
((?[X]:((rich(X)|~old(X))))=>((~curious(john)<~>~happy(john))))&
(((~brave(paul)&~strong(paul)))<=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(wise(X)&~wise(X))))&
(![X]:(strong(X)<=>(calm(X)&~creative(X))))&
(![X]:((generous(X)<~>curious(X))=>(~quiet(X)<~>kind(X))))&
(![X]:((~curious(X)|funny(X))=>(~humble(X)|happy(X))))&
(((creative(paul)|humble(paul)))=>(?[X]:((creative(X)&old(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(?[X]:(~brave(X))))&
((?[X]:((~funny(X)<~>old(X))))<=>((~old(fred)<~>~rich(fred))))&
(![X]:(brave(X)=>(brave(X)&~old(X))))&
((~curious(paul)|creative(paul)))&
((~humble(john)|~curious(john)))&
((old(lucy)|rich(lucy)))&
((tall(john)<~>~humble(john)))&
(~brave(john))&
((~generous(susan)|happy(susan)))&
((kind(paul)|happy(paul)))&
((quiet(paul)|~curious(paul))) | ~brave(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3874532300794223096793226
% SZS output start Proof for 3874532300794223096793226
20. ~brave(john) [input p19]
24. brave(john) [input hypothesis]
133. ~brave(john) [cnf transformation 20]
137. brave(john) [cnf transformation 24]
357. $false [subsumption resolution 137,133]
% SZS output end Proof for 3874532300794223096793226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or creative is either not patient or not humble.
If lucy is both not calm and not happy then fred is not creative and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Everyone who is quiet or old is patient and vice versa.
Alice is either wise or curious.
Someone is not creative or not strong.
Susan is both not tall and not generous.
Alice is either not funny or strong.
Someone is either tall or quiet. | Fred is strong. | neutral | (![X]:((~wise(X)<~>creative(X))=>(~patient(X)<~>~humble(X))))&
(((~calm(lucy)&~happy(lucy)))<=>(~creative(fred)))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
((wise(alice)<~>curious(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
((~tall(susan)&~generous(susan)))&
((~funny(alice)<~>strong(alice)))&
(?[X]:((tall(X)<~>quiet(X)))) | strong(fred) | [] | null | 0 |
If someone is humble or not generous then alice is both funny and not calm.
If john is humble then alice is happy.
If john is not brave then mary is kind or funny and vice versa.
If lucy is both not calm and not tall then someone is strong and vice versa.
If fred is both not wise and not rich then fred is both wise and happy.
If susan is both not strong and not happy then mary is not creative.
If lucy is generous or not strong then susan is quiet or not tall and vice versa.
Everyone who is not creative or not tall is either generous or not tall and vice versa.
Everyone who is either not tall or generous is not generous or not humble and vice versa.
If someone is both strong and brave then mary is not happy.
If someone is both old and not happy then lucy is either creative or not quiet.
If someone is calm then mary is not creative or not brave and vice versa.
Everyone who is kind or patient is both curious and not tall.
If someone is both not creative and humble then someone is creative.
If someone is both curious and not tall then someone is both kind and not patient and vice versa.
Everyone who is old is both curious and brave and vice versa.
Susan is either not tall or creative.
Someone is either old or wise.
Susan is both patient and not brave.
Someone is both not old and not quiet.
Someone is not creative or not old.
Someone is both not patient and not brave.
Someone is not kind or not strong. | Susan is not old. | entailment | ((?[X]:((humble(X)|~generous(X))))=>((funny(alice)&~calm(alice))))&
((humble(john))=>(happy(alice)))&
((~brave(john))<=>((kind(mary)|funny(mary))))&
(((~calm(lucy)&~tall(lucy)))<=>(?[X]:(strong(X))))&
(((~wise(fred)&~rich(fred)))=>((wise(fred)&happy(fred))))&
(((~strong(susan)&~happy(susan)))=>(~creative(mary)))&
(((generous(lucy)|~strong(lucy)))<=>((quiet(susan)|~tall(susan))))&
(![X]:((~creative(X)|~tall(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)<~>generous(X))<=>(~generous(X)|~humble(X))))&
((?[X]:((strong(X)&brave(X))))=>(~happy(mary)))&
((?[X]:((old(X)&~happy(X))))=>((creative(lucy)<~>~quiet(lucy))))&
((?[X]:(calm(X)))<=>((~creative(mary)|~brave(mary))))&
(![X]:((kind(X)|patient(X))=>(curious(X)&~tall(X))))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(old(X)<=>(curious(X)&brave(X))))&
((~tall(susan)<~>creative(susan)))&
(?[X]:((old(X)<~>wise(X))))&
((patient(susan)&~brave(susan)))&
(?[X]:((~old(X)&~quiet(X))))&
(?[X]:((~creative(X)|~old(X))))&
(?[X]:((~patient(X)&~brave(X))))&
(?[X]:((~kind(X)|~strong(X)))) | ~old(susan) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1816594993274986798675924
% SZS output start Proof for 1816594993274986798675924
16. ! [X0] : (old(X0) <=> (brave(X0) & curious(X0))) [input p15]
19. ~brave(susan) & patient(susan) [input p18]
24. old(susan) [input hypothesis]
63. ! [X0] : ((old(X0) | (~brave(X0) | ~curious(X0))) & ((brave(X0) & curious(X0)) | ~old(X0))) [nnf transformation 16]
64. ! [X0] : ((old(X0) | ~brave(X0) | ~curious(X0)) & ((brave(X0) & curious(X0)) | ~old(X0))) [flattening 63]
121. ~old(X0) | brave(X0) [cnf transformation 64]
128. ~brave(susan) [cnf transformation 19]
135. old(susan) [cnf transformation 24]
341. brave(susan) [resolution 121,135]
343. $false [subsumption resolution 341,128]
% SZS output end Proof for 1816594993274986798675924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is creative or not happy then someone is not old and vice versa.
If someone is funny then someone is not strong and vice versa.
If someone is not quiet then alice is both not creative and not funny.
Everyone who is either not humble or quiet is both not strong and not tall and vice versa.
If alice is not calm or not rich then someone is wise and vice versa.
If someone is not happy then lucy is not quiet or wise and vice versa.
Everyone who is either patient or not strong is tall or curious.
If someone is funny or not funny then mary is either calm or not brave and vice versa.
If alice is both old and not patient then someone is not happy or not quiet and vice versa.
Everyone who is not creative or brave is patient and vice versa.
Everyone who is generous is either not curious or tall and vice versa.
Everyone who is either not rich or not humble is not creative.
Everyone who is not curious is both humble and not old.
Everyone who is either not quiet or not tall is humble or kind and vice versa.
If paul is funny then someone is not funny.
If lucy is either patient or not quiet then alice is not old.
John is both tall and not humble.
Mary is either not generous or creative.
Someone is funny or not old.
Someone is calm.
Someone is curious or kind.
Someone is patient or old.
Alice is either curious or happy.
Someone is not humble or happy. | Alice is not old. | neutral | (((creative(fred)|~happy(fred)))<=>(?[X]:(~old(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~strong(X))))&
((?[X]:(~quiet(X)))=>((~creative(alice)&~funny(alice))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~strong(X)&~tall(X))))&
(((~calm(alice)|~rich(alice)))<=>(?[X]:(wise(X))))&
((?[X]:(~happy(X)))<=>((~quiet(lucy)|wise(lucy))))&
(![X]:((patient(X)<~>~strong(X))=>(tall(X)|curious(X))))&
((?[X]:((funny(X)|~funny(X))))<=>((calm(mary)<~>~brave(mary))))&
(((old(alice)&~patient(alice)))<=>(?[X]:((~happy(X)|~quiet(X)))))&
(![X]:((~creative(X)|brave(X))<=>patient(X)))&
(![X]:(generous(X)<=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>~humble(X))=>~creative(X)))&
(![X]:(~curious(X)=>(humble(X)&~old(X))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(humble(X)|kind(X))))&
((funny(paul))=>(?[X]:(~funny(X))))&
(((patient(lucy)<~>~quiet(lucy)))=>(~old(alice)))&
((tall(john)&~humble(john)))&
((~generous(mary)<~>creative(mary)))&
(?[X]:((funny(X)|~old(X))))&
(?[X]:(calm(X)))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:((patient(X)|old(X))))&
((curious(alice)<~>happy(alice)))&
(?[X]:((~humble(X)|happy(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is wise is humble or tall and vice versa.
If someone is not wise then someone is old and vice versa.
If someone is not curious then someone is either tall or not calm.
If someone is not creative or not happy then someone is either not rich or creative.
If mary is either not kind or happy then someone is funny and vice versa.
Everyone who is both not strong and not rich is not quiet and vice versa.
Everyone who is either rich or not humble is both not brave and wise and vice versa.
Everyone who is both rich and generous is either not tall or old.
Everyone who is not rich is either old or strong.
If john is both not tall and not patient then someone is strong.
Everyone who is not creative is curious or not humble and vice versa.
Everyone who is kind or curious is not kind.
If paul is both not rich and not quiet then someone is either brave or creative and vice versa.
If lucy is both calm and not tall then someone is both wise and not curious and vice versa.
Everyone who is either brave or wise is either not calm or tall.
Everyone who is both not patient and not wise is funny or old and vice versa.
Someone is both calm and not funny.
Susan is both not happy and old.
John is not rich.
John is strong.
Paul is not generous.
Mary is calm. | John is not patient. | neutral | (![X]:(wise(X)<=>(humble(X)|tall(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(old(X))))&
((?[X]:(~curious(X)))=>(?[X]:((tall(X)<~>~calm(X)))))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:((~rich(X)<~>creative(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(?[X]:(funny(X))))&
(![X]:((~strong(X)&~rich(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((rich(X)&generous(X))=>(~tall(X)<~>old(X))))&
(![X]:(~rich(X)=>(old(X)<~>strong(X))))&
(((~tall(john)&~patient(john)))=>(?[X]:(strong(X))))&
(![X]:(~creative(X)<=>(curious(X)|~humble(X))))&
(![X]:((kind(X)|curious(X))=>~kind(X)))&
(((~rich(paul)&~quiet(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(((calm(lucy)&~tall(lucy)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((brave(X)<~>wise(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&~wise(X))<=>(funny(X)|old(X))))&
(?[X]:((calm(X)&~funny(X))))&
((~happy(susan)&old(susan)))&
(~rich(john))&
(strong(john))&
(~generous(paul))&
(calm(mary)) | ~patient(john) | [] | null | 0 |
If john is either not funny or quiet then fred is happy.
If someone is brave or not wise then susan is both tall and not rich and vice versa.
If someone is humble then lucy is either humble or quiet.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | John is patient. | contradiction | (((~funny(john)<~>quiet(john)))=>(happy(fred)))&
((?[X]:((brave(X)|~wise(X))))<=>((tall(susan)&~rich(susan))))&
((?[X]:(humble(X)))=>((humble(lucy)<~>quiet(lucy))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | patient(john) | [
"p5",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5876256388958220606205561
% SZS output start Proof for 5876256388958220606205561
6. ! [X0] : ((creative(X0) | curious(X0)) => tall(X0)) [input p5]
7. ! [X0] : (generous(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
11. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X0] : (~curious(X0) | ~tall(X0)) [input p10]
22. patient(john) [input hypothesis]
23. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X1] : (~curious(X1) | ~tall(X1)) [rectify 11]
30. ! [X0] : (tall(X0) | (~creative(X0) & ~curious(X0))) [ennf transformation 6]
31. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
46. ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))) [nnf transformation 7]
47. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 8]
48. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | calm(X0) | generous(X0))) [flattening 47]
49. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (curious(X1) & tall(X1))) & (? [X1] : (~curious(X1) | ~tall(X1)) | ! [X0] : ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 23]
50. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (curious(X1) & tall(X1))) & (? [X2] : (~curious(X2) | ~tall(X2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [rectify 49]
51. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) => ((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) [choice axiom]
52. ? [X2] : (~curious(X2) | ~tall(X2)) => (~curious(sK2) | ~tall(sK2)) [choice axiom]
53. (((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) | ! [X1] : (curious(X1) & tall(X1))) & ((~curious(sK2) | ~tall(sK2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [skolemisation 50,52,51]
79. ~curious(X0) | tall(X0) [cnf transformation 30]
81. ~generous(X0) | curious(X0) [cnf transformation 46]
87. ~calm(X0) | generous(X0) [cnf transformation 48]
90. calm(X0) | generous(X0) [cnf transformation 31]
94. ~curious(sK2) | ~tall(sK2) | ~patient(X3) | ~tall(X3) [cnf transformation 53]
124. patient(john) [cnf transformation 22]
180. generous(X0) [subsumption resolution 90,87]
195. 16 <=> ! [X1] : curious(X1) [avatar definition]
196. curious(X1) <- (16) [avatar component clause 195]
207. 19 <=> ! [X1] : tall(X1) [avatar definition]
208. tall(X1) <- (19) [avatar component clause 207]
212. ~curious(sK2) | ~patient(X3) | ~tall(X3) [subsumption resolution 94,79]
214. 20 <=> ! [X3] : (~patient(X3) | ~tall(X3)) [avatar definition]
215. ~patient(X3) | ~tall(X3) <- (20) [avatar component clause 214]
217. 21 <=> curious(sK2) [avatar definition]
219. ~curious(sK2) <- (~21) [avatar component clause 217]
220. 20 | ~21 [avatar split clause 212,217,214]
307. curious(X0) [resolution 81,180]
308. 16 [avatar split clause 307,195]
309. $false <- (16, ~21) [resolution 196,219]
310. tall(X0) <- (16) [resolution 196,79]
311. ~16 | 21 [avatar contradiction clause 309]
312. 19 | ~16 [avatar split clause 310,195,207]
335. ~tall(john) <- (20) [resolution 215,124]
336. $false <- (19, 20) [subsumption resolution 335,208]
337. ~19 | ~20 [avatar contradiction clause 336]
338. $false [avatar sat refutation 220,308,311,312,337]
% SZS output end Proof for 5876256388958220606205561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then john is creative or patient.
If lucy is either rich or curious then someone is both wise and old and vice versa.
If fred is both not kind and not humble then someone is not humble or not curious.
Everyone who is not funny is both patient and humble and vice versa.
Everyone who is not calm or not strong is either not creative or not curious and vice versa.
Everyone who is not funny is both not calm and not humble.
If john is patient or wise then someone is both not wise and patient and vice versa.
Everyone who is wise is either brave or strong and vice versa.
Everyone who is both happy and not rich is either quiet or not quiet and vice versa.
If someone is not rich then fred is not generous.
Everyone who is both not strong and not old is both not quiet and not tall and vice versa.
Everyone who is brave is either strong or curious and vice versa.
Everyone who is both strong and happy is kind.
If john is not happy then someone is both rich and kind.
Everyone who is either patient or funny is strong and vice versa.
Everyone who is either not strong or tall is creative or curious.
Paul is strong or quiet.
John is not brave or not happy.
Susan is both wise and not calm.
Mary is either curious or strong.
Paul is both not curious and generous.
Lucy is not kind or tall.
Lucy is happy. | Paul is not rich. | entailment | ((?[X]:(old(X)))=>((creative(john)|patient(john))))&
(((rich(lucy)<~>curious(lucy)))<=>(?[X]:((wise(X)&old(X)))))&
(((~kind(fred)&~humble(fred)))=>(?[X]:((~humble(X)|~curious(X)))))&
(![X]:(~funny(X)<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)|~strong(X))<=>(~creative(X)<~>~curious(X))))&
(![X]:(~funny(X)=>(~calm(X)&~humble(X))))&
(((patient(john)|wise(john)))<=>(?[X]:((~wise(X)&patient(X)))))&
(![X]:(wise(X)<=>(brave(X)<~>strong(X))))&
(![X]:((happy(X)&~rich(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:(~rich(X)))=>(~generous(fred)))&
(![X]:((~strong(X)&~old(X))<=>(~quiet(X)&~tall(X))))&
(![X]:(brave(X)<=>(strong(X)<~>curious(X))))&
(![X]:((strong(X)&happy(X))=>kind(X)))&
((~happy(john))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((patient(X)<~>funny(X))<=>strong(X)))&
(![X]:((~strong(X)<~>tall(X))=>(creative(X)|curious(X))))&
((strong(paul)|quiet(paul)))&
((~brave(john)|~happy(john)))&
((wise(susan)&~calm(susan)))&
((curious(mary)<~>strong(mary)))&
((~curious(paul)&generous(paul)))&
((~kind(lucy)|tall(lucy)))&
(happy(lucy)) | ~rich(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7166643862728537583933931
% SZS output start Proof for 7166643862728537583933931
9. ! [X0] : ((~rich(X0) & happy(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p8]
24. rich(paul) [input hypothesis]
52. ! [X0] : (((~rich(X0) & happy(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (rich(X0) | ~happy(X0)))) [nnf transformation 9]
53. ! [X0] : (((~rich(X0) & happy(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | rich(X0) | ~happy(X0))) [flattening 52]
94. ~rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 53]
95. ~rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 53]
124. rich(paul) [cnf transformation 24]
127. ~rich(X0) | ~quiet(X0) [duplicate literal removal 94]
128. ~rich(X0) | quiet(X0) [duplicate literal removal 95]
204. ~rich(X0) [subsumption resolution 127,128]
240. $false [subsumption resolution 124,204]
% SZS output end Proof for 7166643862728537583933931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and kind is generous. If someone is both happy and humble then someone is both rich and not patient and vice versa. Everyone who is either wise or kind is generous or not old and vice versa. Everyone who is calm is curious. If john is not funny or not wise then mary is either not brave or not happy and vice versa. Everyone who is either wise or strong is both creative and not wise and vice versa. Everyone who is not brave is not creative or not patient and vice versa. If someone is either not generous or brave then susan is either not humble or strong and vice versa. Everyone who is both not patient and strong is both creative and not generous and vice versa. Everyone who is rich or not humble is either not generous or not quiet and vice versa. If someone is either funny or happy then someone is either wise or old and vice versa. Everyone who is both calm and not kind is both not rich and strong. If someone is creative then mary is both calm and happy. Everyone who is brave or not quiet is both not patient and not rich. Everyone who is either patient or tall is wise or humble. Everyone who is both not quiet and not generous is creative or curious and vice versa. Mary is wise or not strong. John is both calm and not brave. Someone is not generous. Susan is curious or not kind. Someone is brave or not strong. Someone is both not happy and tall. Someone is either tall or not wise. Someone is both wise and tall. | Susan is happy. | neutral | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((wise(X)<~>kind(X))<=>(generous(X)|~old(X))))&
(![X]:(calm(X)=>curious(X)))&
(((~funny(john)|~wise(john)))<=>((~brave(mary)<~>~happy(mary))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)&strong(X))<=>(creative(X)&~generous(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((calm(X)&~kind(X))=>(~rich(X)&strong(X))))&
((?[X]:(creative(X)))=>((calm(mary)&happy(mary))))&
(![X]:((brave(X)|~quiet(X))=>(~patient(X)&~rich(X))))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)|humble(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(creative(X)|curious(X))))&
((wise(mary)|~strong(mary)))&
((calm(john)&~brave(john)))&
(?[X]:(~generous(X)))&
((curious(susan)|~kind(susan)))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:((wise(X)&tall(X)))) | happy(susan) | [] | null | 0 |
If john is both kind and not rich then fred is creative or brave and vice versa.
If someone is not wise or not creative then someone is calm and vice versa.
Everyone who is not curious is both not humble and generous and vice versa.
If someone is patient then someone is strong or humble and vice versa.
Everyone who is both not creative and not calm is either happy or not wise and vice versa.
Everyone who is both not old and happy is not curious and vice versa.
Everyone who is brave or not patient is tall and vice versa.
Everyone who is tall or old is either not kind or not wise.
Everyone who is both not old and not strong is either generous or not patient and vice versa.
Everyone who is both humble and not generous is either not quiet or patient.
Everyone who is either not rich or not strong is either patient or not patient.
Everyone who is both not strong and patient is not humble or patient and vice versa.
If fred is not curious then someone is either wise or creative.
Everyone who is either not generous or not strong is both not patient and tall and vice versa.
If paul is either creative or rich then alice is curious and vice versa.
If john is either not creative or not tall then someone is both not funny and not rich and vice versa.
Someone is both not creative and wise.
Alice is rich.
John is both not funny and not calm.
Paul is happy.
Someone is both not brave and not strong.
Lucy is both not brave and old.
Someone is either not brave or not old.
Someone is not curious or happy. | John is not creative. | neutral | (((kind(john)&~rich(john)))<=>((creative(fred)|brave(fred))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:(calm(X))))&
(![X]:(~curious(X)<=>(~humble(X)&generous(X))))&
((?[X]:(patient(X)))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~old(X)&happy(X))<=>~curious(X)))&
(![X]:((brave(X)|~patient(X))<=>tall(X)))&
(![X]:((tall(X)|old(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((~old(X)&~strong(X))<=>(generous(X)<~>~patient(X))))&
(![X]:((humble(X)&~generous(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(patient(X)<~>~patient(X))))&
(![X]:((~strong(X)&patient(X))<=>(~humble(X)|patient(X))))&
((~curious(fred))=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:((~generous(X)<~>~strong(X))<=>(~patient(X)&tall(X))))&
(((creative(paul)<~>rich(paul)))<=>(curious(alice)))&
(((~creative(john)<~>~tall(john)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(?[X]:((~creative(X)&wise(X))))&
(rich(alice))&
((~funny(john)&~calm(john)))&
(happy(paul))&
(?[X]:((~brave(X)&~strong(X))))&
((~brave(lucy)&old(lucy)))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((~curious(X)|happy(X)))) | ~creative(john) | [] | null | 0 |
If someone is both tall and not patient then john is not strong.
If mary is not humble then someone is both brave and not patient and vice versa.
Everyone who is not calm or not humble is both old and funny.
If someone is humble or wise then someone is both tall and creative.
If susan is patient or not curious then someone is not happy or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
If someone is both not happy and not tall then someone is either not generous or kind and vice versa.
If someone is both not creative and wise then john is not old.
If susan is either brave or not calm then john is both not tall and tall.
Everyone who is not tall or wise is both funny and not brave.
Everyone who is not creative or not rich is either quiet or happy and vice versa.
Alice is humble.
John is not old.
John is strong or tall.
Someone is not strong or not rich.
Someone is either patient or funny.
Someone is both not curious and calm.
Mary is either not curious or not calm. | John is not rich. | neutral | ((?[X]:((tall(X)&~patient(X))))=>(~strong(john)))&
((~humble(mary))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:((~calm(X)|~humble(X))=>(old(X)&funny(X))))&
((?[X]:((humble(X)|wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
(((patient(susan)|~curious(susan)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:((~creative(X)&wise(X))))=>(~old(john)))&
(((brave(susan)<~>~calm(susan)))=>((~tall(john)&tall(john))))&
(![X]:((~tall(X)|wise(X))=>(funny(X)&~brave(X))))&
(![X]:((~creative(X)|~rich(X))<=>(quiet(X)<~>happy(X))))&
(humble(alice))&
(~old(john))&
((strong(john)|tall(john)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:((~curious(X)&calm(X))))&
((~curious(mary)<~>~calm(mary))) | ~rich(john) | [] | null | 0 |
Everyone who is both quiet and not calm is not curious or calm and vice versa.
If someone is either humble or not kind then someone is tall and vice versa.
Everyone who is either not creative or not happy is both calm and not creative.
If mary is not strong or not curious then john is both old and not happy and vice versa.
If someone is either happy or not patient then someone is not kind or patient.
Everyone who is either not kind or not creative is both humble and not tall and vice versa.
If paul is rich then someone is either wise or creative.
Everyone who is not strong is both not rich and creative.
Everyone who is not patient is both calm and quiet.
If alice is not brave then john is both wise and not old.
Everyone who is both strong and curious is both creative and not creative.
If john is not old then someone is not rich and vice versa.
Everyone who is both quiet and curious is either patient or not funny.
If someone is both not tall and kind then someone is patient or not happy and vice versa.
Fred is either generous or not calm.
Someone is not tall.
Someone is creative. | John is not patient. | contradiction | (![X]:((quiet(X)&~calm(X))<=>(~curious(X)|calm(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:(tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(calm(X)&~creative(X))))&
(((~strong(mary)|~curious(mary)))<=>((old(john)&~happy(john))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((~kind(X)<~>~creative(X))<=>(humble(X)&~tall(X))))&
((rich(paul))=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:(~strong(X)=>(~rich(X)&creative(X))))&
(![X]:(~patient(X)=>(calm(X)&quiet(X))))&
((~brave(alice))=>((wise(john)&~old(john))))&
(![X]:((strong(X)&curious(X))=>(creative(X)&~creative(X))))&
((~old(john))<=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)&curious(X))=>(patient(X)<~>~funny(X))))&
((?[X]:((~tall(X)&kind(X))))<=>(?[X]:((patient(X)|~happy(X)))))&
((generous(fred)<~>~calm(fred)))&
(?[X]:(~tall(X)))&
(?[X]:(creative(X))) | ~patient(john) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 449299246806582331237575
% SZS output start Proof for 449299246806582331237575
1. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (calm(X0) | ~curious(X0))) [input p0]
9. ! [X0] : (~patient(X0) => (quiet(X0) & calm(X0))) [input p8]
18. ~patient(john) [input hypothesis]
27. ! [X0] : ((quiet(X0) & calm(X0)) | patient(X0)) [ennf transformation 9]
32. ! [X0] : (((~calm(X0) & quiet(X0)) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 1]
33. ! [X0] : (((~calm(X0) & quiet(X0)) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | calm(X0) | ~quiet(X0))) [flattening 32]
70. ~calm(X0) | ~calm(X0) [cnf transformation 33]
96. calm(X0) | patient(X0) [cnf transformation 27]
113. ~patient(john) [cnf transformation 18]
116. ~calm(X0) [duplicate literal removal 70]
195. patient(X0) [subsumption resolution 96,116]
224. $false [subsumption resolution 113,195]
% SZS output end Proof for 449299246806582331237575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is brave or not creative.
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 quiet or not funny.
Someone is not brave or calm.
Fred is not brave or not rich.
Paul is either happy or not tall.
Fred is both not strong and generous.
Paul is not curious or curious.
Alice is tall or strong.
Paul is either kind or tall. | Paul is not brave. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((brave(X)|~creative(X)))))&
((?[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]:((~quiet(X)|~funny(X))))&
(?[X]:((~brave(X)|calm(X))))&
((~brave(fred)|~rich(fred)))&
((happy(paul)<~>~tall(paul)))&
((~strong(fred)&generous(fred)))&
((~curious(paul)|curious(paul)))&
((tall(alice)|strong(alice)))&
((kind(paul)<~>tall(paul))) | ~brave(paul) | [] | null | 0 |
Everyone who is quiet is kind or curious and vice versa.
Everyone who is both not calm and not funny is rich.
If someone is tall or calm then mary is not calm or creative and vice versa.
Everyone who is either not creative or strong is both old and not wise and vice versa.
If someone is tall then mary is both not creative and brave and vice versa.
If alice is either not patient or kind then someone is either not brave or not happy and vice versa.
If someone is either not quiet or quiet then fred is both not patient and not funny.
Everyone who is kind or rich is quiet.
If lucy is quiet or not creative then john is wise or happy and vice versa.
If john is both not generous and not rich then someone is both not old and patient.
Everyone who is either rich or not strong is not generous.
Everyone who is not calm or rich is not brave.
If alice is both funny and happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
Lucy is both not funny and rich.
Someone is not patient or happy.
Mary is not strong or brave.
Someone is not tall or not generous.
Fred is not wise.
Susan is not wise or humble.
Susan is both rich and strong. | John is generous. | neutral | (![X]:(quiet(X)<=>(kind(X)|curious(X))))&
(![X]:((~calm(X)&~funny(X))=>rich(X)))&
((?[X]:((tall(X)|calm(X))))<=>((~calm(mary)|creative(mary))))&
(![X]:((~creative(X)<~>strong(X))<=>(old(X)&~wise(X))))&
((?[X]:(tall(X)))<=>((~creative(mary)&brave(mary))))&
(((~patient(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((~quiet(X)<~>quiet(X))))=>((~patient(fred)&~funny(fred))))&
(![X]:((kind(X)|rich(X))=>quiet(X)))&
(((quiet(lucy)|~creative(lucy)))<=>((wise(john)|happy(john))))&
(((~generous(john)&~rich(john)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((rich(X)<~>~strong(X))=>~generous(X)))&
(![X]:((~calm(X)|rich(X))=>~brave(X)))&
(((funny(alice)&happy(alice)))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
((~funny(lucy)&rich(lucy)))&
(?[X]:((~patient(X)|happy(X))))&
((~strong(mary)|brave(mary)))&
(?[X]:((~tall(X)|~generous(X))))&
(~wise(fred))&
((~wise(susan)|humble(susan)))&
((rich(susan)&strong(susan))) | generous(john) | [] | null | 0 |
If someone is not creative then fred is not funny and vice versa.
If john is either not happy or humble then john is both brave and generous and vice versa.
Everyone who is not wise is calm and vice versa.
If alice is quiet then paul is either funny or not wise and vice versa.
If someone is both not happy and not funny then fred is both not rich and not humble and vice versa.
If someone is not quiet then john is rich and vice versa.
If someone is not humble then mary is either quiet or not funny and vice versa.
Everyone who is either tall or not wise is not rich or rich.
Everyone who is not wise is happy.
Everyone who is either not happy or not kind is either wise or old and vice versa.
If someone is not creative or funny then paul is either not curious or old.
Everyone who is not kind is creative and vice versa.
Everyone who is either curious or not generous is both quiet and not happy and vice versa.
Everyone who is funny or not curious is generous or tall and vice versa.
If someone is both happy and quiet then someone is both not wise and quiet and vice versa.
If john is not brave or not quiet then john is not happy and vice versa.
Lucy is strong.
Paul is both not creative and patient.
Mary is generous or happy.
Someone is patient or brave.
Someone is either wise or not patient.
Lucy is either not kind or brave.
Fred is creative.
Paul is either patient or humble. | Fred is kind. | contradiction | ((?[X]:(~creative(X)))<=>(~funny(fred)))&
(((~happy(john)<~>humble(john)))<=>((brave(john)&generous(john))))&
(![X]:(~wise(X)<=>calm(X)))&
((quiet(alice))<=>((funny(paul)<~>~wise(paul))))&
((?[X]:((~happy(X)&~funny(X))))<=>((~rich(fred)&~humble(fred))))&
((?[X]:(~quiet(X)))<=>(rich(john)))&
((?[X]:(~humble(X)))<=>((quiet(mary)<~>~funny(mary))))&
(![X]:((tall(X)<~>~wise(X))=>(~rich(X)|rich(X))))&
(![X]:(~wise(X)=>happy(X)))&
(![X]:((~happy(X)<~>~kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:((~creative(X)|funny(X))))=>((~curious(paul)<~>old(paul))))&
(![X]:(~kind(X)<=>creative(X)))&
(![X]:((curious(X)<~>~generous(X))<=>(quiet(X)&~happy(X))))&
(![X]:((funny(X)|~curious(X))<=>(generous(X)|tall(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((~wise(X)&quiet(X)))))&
(((~brave(john)|~quiet(john)))<=>(~happy(john)))&
(strong(lucy))&
((~creative(paul)&patient(paul)))&
((generous(mary)|happy(mary)))&
(?[X]:((patient(X)|brave(X))))&
(?[X]:((wise(X)<~>~patient(X))))&
((~kind(lucy)<~>brave(lucy)))&
(creative(fred))&
((patient(paul)<~>humble(paul))) | kind(fred) | [
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4550552048035329707119359
% SZS output start Proof for 4550552048035329707119359
12. ! [X0] : (~kind(X0) <=> creative(X0)) [input p11]
23. creative(fred) [input p22]
25. kind(fred) [input hypothesis]
56. ! [X0] : ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))) [nnf transformation 12]
115. ~kind(X0) | ~creative(X0) [cnf transformation 56]
141. creative(fred) [cnf transformation 23]
144. kind(fred) [cnf transformation 25]
345. ~creative(fred) [resolution 115,144]
347. $false [subsumption resolution 345,141]
% SZS output end Proof for 4550552048035329707119359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not rich then someone is both not strong and not creative and vice versa.
Everyone who is patient or generous is both not brave and not calm and vice versa.
Everyone who is both funny and not funny is not humble or calm.
If someone is brave then mary is either curious or old and vice versa.
If mary is quiet then fred is happy.
If john is either humble or funny then mary is both brave and creative.
If alice is either funny or humble then someone is not quiet or wise.
If someone is either curious or not creative then mary is quiet.
Everyone who is not funny or not curious is both humble and funny and vice versa.
If someone is not calm then someone is both not quiet and kind and vice versa.
If susan is either not happy or humble then someone is not strong and vice versa.
Everyone who is either generous or not calm is not generous or not quiet and vice versa.
Everyone who is either not humble or generous is curious or strong and vice versa.
Everyone who is rich is not funny or not old.
Everyone who is both not quiet and humble is not happy or humble and vice versa.
Everyone who is not old is wise or not curious and vice versa.
John is either not funny or not creative.
Fred is wise or not humble.
Susan is not humble or kind.
Alice is not tall. | Fred is generous. | contradiction | ((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((patient(X)|generous(X))<=>(~brave(X)&~calm(X))))&
(![X]:((funny(X)&~funny(X))=>(~humble(X)|calm(X))))&
((?[X]:(brave(X)))<=>((curious(mary)<~>old(mary))))&
((quiet(mary))=>(happy(fred)))&
(((humble(john)<~>funny(john)))=>((brave(mary)&creative(mary))))&
(((funny(alice)<~>humble(alice)))=>(?[X]:((~quiet(X)|wise(X)))))&
((?[X]:((curious(X)<~>~creative(X))))=>(quiet(mary)))&
(![X]:((~funny(X)|~curious(X))<=>(humble(X)&funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~quiet(X)&kind(X)))))&
(((~happy(susan)<~>humble(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(curious(X)|strong(X))))&
(![X]:(rich(X)=>(~funny(X)|~old(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~happy(X)|humble(X))))&
(![X]:(~old(X)<=>(wise(X)|~curious(X))))&
((~funny(john)<~>~creative(john)))&
((wise(fred)|~humble(fred)))&
((~humble(susan)|kind(susan)))&
(~tall(alice)) | generous(fred) | [
"p1",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 140530715491687198455565
% SZS output start Proof for 140530715491687198455565
2. ! [X0] : ((generous(X0) | patient(X0)) <=> (~calm(X0) & ~brave(X0))) [input p1]
9. ! [X0] : ((~curious(X0) | ~funny(X0)) <=> (funny(X0) & humble(X0))) [input p8]
12. ! [X0] : ((generous(X0) <~> ~calm(X0)) <=> (~quiet(X0) | ~generous(X0))) [input p11]
13. ! [X0] : ((~humble(X0) <~> generous(X0)) <=> (strong(X0) | curious(X0))) [input p12]
15. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (humble(X0) | ~happy(X0))) [input p14]
21. generous(fred) [input hypothesis]
38. ! [X0] : (((generous(X0) | patient(X0)) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((generous(X0) | patient(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | (~generous(X0) & ~patient(X0)))) [flattening 38]
49. ! [X0] : (((~curious(X0) | ~funny(X0)) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | (curious(X0) & funny(X0)))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | ~funny(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | (curious(X0) & funny(X0)))) [flattening 49]
60. ! [X0] : ((((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (quiet(X0) & generous(X0))) & ((~quiet(X0) | ~generous(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))))) [nnf transformation 12]
61. ! [X0] : ((((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (quiet(X0) & generous(X0))) & (~quiet(X0) | ~generous(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))))) [flattening 60]
62. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~strong(X0) & ~curious(X0))) & ((strong(X0) | curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [nnf transformation 13]
63. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~strong(X0) & ~curious(X0))) & (strong(X0) | curious(X0) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [flattening 62]
64. ! [X0] : (((humble(X0) & ~quiet(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 15]
65. ! [X0] : (((humble(X0) & ~quiet(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | ~humble(X0) | quiet(X0))) [flattening 64]
77. ~generous(X0) | ~calm(X0) [cnf transformation 39]
94. curious(X0) | humble(X0) [cnf transformation 50]
110. calm(X0) | ~generous(X0) | quiet(X0) [cnf transformation 61]
115. ~generous(X0) | humble(X0) | ~curious(X0) [cnf transformation 63]
120. ~quiet(X0) | ~humble(X0) [cnf transformation 65]
130. generous(fred) [cnf transformation 21]
279. ~generous(X0) | quiet(X0) [subsumption resolution 110,77]
283. ~generous(X0) | humble(X0) [subsumption resolution 115,94]
292. 34 <=> humble(fred) [avatar definition]
334. quiet(fred) [resolution 279,130]
335. ~humble(fred) [resolution 334,120]
337. humble(fred) [resolution 283,130]
340. 34 [avatar split clause 337,292]
341. ~34 [avatar split clause 335,292]
342. $false [avatar sat refutation 340,341]
% SZS output end Proof for 140530715491687198455565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is rich and vice versa. Everyone who is not kind is not creative and vice versa. If alice is either not kind or quiet then someone is not strong or not brave and vice versa. Everyone who is either humble or brave is not brave and vice versa. Everyone who is either not patient or not quiet is either not humble or curious and vice versa. Everyone who is both humble and happy is either not tall or funny and vice versa. If someone is not funny then fred is either not tall or not old. If john is curious then john is not curious or calm. If someone is either quiet or kind then lucy is both not generous and not wise. Everyone who is humble is not happy or old. Everyone who is tall or old is not tall or strong and vice versa. If someone is quiet or not old then someone is both not wise and wise. If someone is both patient and not quiet then fred is calm. Everyone who is either not tall or not calm is both creative and not wise and vice versa. If someone is not creative or not generous then someone is both wise and not kind. If fred is both happy and old then john is funny and vice versa. Someone is both creative and not calm. Someone is not generous. Alice is happy or funny. Mary is not creative. Someone is not calm or strong. Alice is not old or funny. Alice is both not quiet and creative. | Alice is not creative. | contradiction | (![X]:(~wise(X)<=>rich(X)))&
(![X]:(~kind(X)<=>~creative(X)))&
(((~kind(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~generous(X)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice))) | ~creative(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3587559225784687601527960
% SZS output start Proof for 3587559225784687601527960
23. creative(alice) & ~quiet(alice) [input p22]
24. ~creative(alice) [input hypothesis]
132. creative(alice) [cnf transformation 23]
133. ~creative(alice) [cnf transformation 24]
291. $false [subsumption resolution 133,132]
% SZS output end Proof for 3587559225784687601527960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind or not curious then someone is tall.
If someone is either rich or wise then someone is patient and vice versa.
If mary is both not humble and curious then someone is both not strong and not rich and vice versa.
Everyone who is not curious or patient is generous or not creative and vice versa.
Everyone who is not kind is both not funny and not old.
Everyone who is not humble or wise is not brave or rich and vice versa.
Everyone who is either not calm or generous is both patient and not curious and vice versa.
Everyone who is both not rich and brave is not calm or generous.
Everyone who is either not patient or wise is either happy or not creative.
If fred is not curious then someone is both brave and not old and vice versa.
Everyone who is strong or not funny is both not humble and not quiet and vice versa.
Everyone who is both not kind and tall is both calm and not wise.
Everyone who is not patient or not funny is both patient and not rich and vice versa.
Everyone who is brave is creative or patient and vice versa.
If fred is tall then someone is not funny or not calm and vice versa.
Everyone who is either not strong or happy is not tall or calm.
Alice is patient.
Susan is not strong.
Someone is either tall or not brave.
Paul is either creative or not rich.
Fred is not curious or not happy.
Fred is tall or not old. | Fred is curious. | neutral | (((~kind(alice)|~curious(alice)))=>(?[X]:(tall(X))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:(patient(X))))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((~strong(X)&~rich(X)))))&
(![X]:((~curious(X)|patient(X))<=>(generous(X)|~creative(X))))&
(![X]:(~kind(X)=>(~funny(X)&~old(X))))&
(![X]:((~humble(X)|wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(patient(alice))&
(~strong(susan))&
(?[X]:((tall(X)<~>~brave(X))))&
((creative(paul)<~>~rich(paul)))&
((~curious(fred)|~happy(fred)))&
((tall(fred)|~old(fred))) | curious(fred) | [] | null | 0 |
If john is quiet or not old then someone is quiet and vice versa.
Everyone who is both happy and creative is not humble or not curious and vice versa.
Everyone who is curious or not strong is both creative and not old and vice versa.
Everyone who is wise is not creative or not calm and vice versa.
If mary is both funny and not quiet then someone is not creative or not brave and vice versa.
Everyone who is rich is both not wise and strong.
If fred is not brave then alice is strong or not quiet and vice versa.
If someone is not happy or not old then alice is both brave and tall.
Everyone who is patient or not happy is patient and vice versa.
If someone is either not tall or not strong then someone is both kind and calm.
Everyone who is both funny and kind is generous or creative.
Everyone who is both funny and not calm is either not happy or not patient.
Everyone who is not humble or calm is not strong and vice versa.
If someone is calm or curious then someone is not humble or not funny.
Everyone who is both not calm and not kind is either not humble or tall and vice versa.
If alice is quiet then someone is not curious or tall.
Alice is either not calm or creative.
Someone is either brave or not creative.
John is both not patient and not rich.
Alice is both funny and not quiet.
Someone is either not quiet or rich.
Alice is not strong or strong. | John is not rich. | entailment | (((quiet(john)|~old(john)))<=>(?[X]:(quiet(X))))&
(![X]:((happy(X)&creative(X))<=>(~humble(X)|~curious(X))))&
(![X]:((curious(X)|~strong(X))<=>(creative(X)&~old(X))))&
(![X]:(wise(X)<=>(~creative(X)|~calm(X))))&
(((funny(mary)&~quiet(mary)))<=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:(rich(X)=>(~wise(X)&strong(X))))&
((~brave(fred))<=>((strong(alice)|~quiet(alice))))&
((?[X]:((~happy(X)|~old(X))))=>((brave(alice)&tall(alice))))&
(![X]:((patient(X)|~happy(X))<=>patient(X)))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((funny(X)&kind(X))=>(generous(X)|creative(X))))&
(![X]:((funny(X)&~calm(X))=>(~happy(X)<~>~patient(X))))&
(![X]:((~humble(X)|calm(X))<=>~strong(X)))&
((?[X]:((calm(X)|curious(X))))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~calm(X)&~kind(X))<=>(~humble(X)<~>tall(X))))&
((quiet(alice))=>(?[X]:((~curious(X)|tall(X)))))&
((~calm(alice)<~>creative(alice)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(john)&~rich(john)))&
((funny(alice)&~quiet(alice)))&
(?[X]:((~quiet(X)<~>rich(X))))&
((~strong(alice)|strong(alice))) | ~rich(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1781364159252301662393177
% SZS output start Proof for 1781364159252301662393177
19. ~rich(john) & ~patient(john) [input p18]
23. rich(john) [input hypothesis]
130. ~rich(john) [cnf transformation 19]
136. rich(john) [cnf transformation 23]
265. $false [subsumption resolution 136,130]
% SZS output end Proof for 1781364159252301662393177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and calm then someone is generous. If mary is patient then lucy is either old or not brave and vice versa. If alice is not rich then paul is calm. If alice is both not calm and strong then alice is either rich or not humble. Everyone who is either kind or not kind is tall or strong. Everyone who is not kind is both not calm and creative. If someone is rich or not creative then someone is kind. If susan is not curious or patient then someone is not rich and vice versa. Everyone who is both brave and strong is wise and vice versa. If susan is funny or not brave then someone is calm or not funny. Everyone who is either not patient or not funny is either not kind or not strong and vice versa. If paul is wise or not strong then someone is patient and vice versa. If lucy is not generous then alice is wise or not curious. Everyone who is both curious and not creative is either creative or not strong and vice versa. Everyone who is both funny and not calm is either not kind or not happy and vice versa. Everyone who is either not humble or not wise is both not funny and not curious and vice versa. Someone is patient or quiet. Someone is both quiet and not happy. Someone is not humble or wise. Lucy is not calm. Someone is not patient or not happy. Someone is either not patient or not strong. Someone is both rich and tall. Alice is not humble or wise. | Alice is humble. | neutral | ((?[X]:((~old(X)&calm(X))))=>(?[X]:(generous(X))))&
((patient(mary))<=>((old(lucy)<~>~brave(lucy))))&
((~rich(alice))=>(calm(paul)))&
(((~calm(alice)&strong(alice)))=>((rich(alice)<~>~humble(alice))))&
(![X]:((kind(X)<~>~kind(X))=>(tall(X)|strong(X))))&
(![X]:(~kind(X)=>(~calm(X)&creative(X))))&
((?[X]:((rich(X)|~creative(X))))=>(?[X]:(kind(X))))&
(((~curious(susan)|patient(susan)))<=>(?[X]:(~rich(X))))&
(![X]:((brave(X)&strong(X))<=>wise(X)))&
(((funny(susan)|~brave(susan)))=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~kind(X)<~>~strong(X))))&
(((wise(paul)|~strong(paul)))<=>(?[X]:(patient(X))))&
((~generous(lucy))=>((wise(alice)|~curious(alice))))&
(![X]:((curious(X)&~creative(X))<=>(creative(X)<~>~strong(X))))&
(![X]:((funny(X)&~calm(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(~funny(X)&~curious(X))))&
(?[X]:((patient(X)|quiet(X))))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((~humble(X)|wise(X))))&
(~calm(lucy))&
(?[X]:((~patient(X)|~happy(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((rich(X)&tall(X))))&
((~humble(alice)|wise(alice))) | humble(alice) | [] | null | 0 |
Everyone who is both not old and not happy is both not funny and not quiet.
Everyone who is either brave or not happy is not quiet and vice versa.
If someone is both rich and strong then alice is either wise or funny.
Everyone who is both not kind and rich is wise or not old and vice versa.
If someone is strong or not curious then paul is not calm or not tall.
Everyone who is not brave is both happy and not old.
If mary is both not strong and old then alice is either not old or funny.
Everyone who is patient is both wise and not calm and vice versa.
Everyone who is not quiet is not generous or not old.
If john is either not strong or not happy then someone is not patient or not tall.
Everyone who is both brave and tall is humble or generous and vice versa.
Everyone who is rich is old and vice versa.
If someone is either curious or kind then someone is not quiet and vice versa.
If someone is both brave and patient then mary is not generous or not old.
Everyone who is either old or not strong is not quiet and vice versa.
If john is humble then someone is not strong and vice versa.
Someone is rich or generous.
Someone is both quiet and creative.
Someone is both creative and generous.
Someone is either not kind or old.
Someone is either patient or not quiet.
John is not brave or patient. | Alice is funny. | neutral | (![X]:((~old(X)&~happy(X))=>(~funny(X)&~quiet(X))))&
(![X]:((brave(X)<~>~happy(X))<=>~quiet(X)))&
((?[X]:((rich(X)&strong(X))))=>((wise(alice)<~>funny(alice))))&
(![X]:((~kind(X)&rich(X))<=>(wise(X)|~old(X))))&
((?[X]:((strong(X)|~curious(X))))=>((~calm(paul)|~tall(paul))))&
(![X]:(~brave(X)=>(happy(X)&~old(X))))&
(((~strong(mary)&old(mary)))=>((~old(alice)<~>funny(alice))))&
(![X]:(patient(X)<=>(wise(X)&~calm(X))))&
(![X]:(~quiet(X)=>(~generous(X)|~old(X))))&
(((~strong(john)<~>~happy(john)))=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((brave(X)&tall(X))<=>(humble(X)|generous(X))))&
(![X]:(rich(X)<=>old(X)))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((brave(X)&patient(X))))=>((~generous(mary)|~old(mary))))&
(![X]:((old(X)<~>~strong(X))<=>~quiet(X)))&
((humble(john))<=>(?[X]:(~strong(X))))&
(?[X]:((rich(X)|generous(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((~kind(X)<~>old(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~brave(john)|patient(john))) | funny(alice) | [] | null | 0 |
Everyone who is not funny is both not brave and funny. Everyone who is quiet or not old is both generous and not humble. If someone is both not kind and kind then lucy is both wise and not humble and vice versa. Everyone who is patient or not creative is old and vice versa. Everyone who is either humble or curious is both not funny and not brave. If lucy is old then someone is either not wise or not old. If alice is either not wise or not funny then someone is not strong. If alice is either humble or brave then someone is both not happy and strong and vice versa. If someone is wise or not generous then someone is calm or funny. Everyone who is either old or humble is both not happy and curious and vice versa. Everyone who is calm is not happy and vice versa. If someone is either funny or strong then someone is not strong or patient. Everyone who is either rich or kind is kind or not happy. Everyone who is creative or tall is either not tall or not generous and vice versa. Everyone who is both rich and not creative is not funny or not creative and vice versa. If someone is either patient or not quiet then someone is either not strong or creative and vice versa. Fred is either not strong or not kind. Lucy is not curious. John is not creative or humble. Someone is both not wise and old. Alice is both brave and not patient. Someone is creative. Someone is not calm or happy. Alice is calm. | Lucy is tall. | contradiction | (![X]:(~funny(X)=>(~brave(X)&funny(X))))&
(![X]:((quiet(X)|~old(X))=>(generous(X)&~humble(X))))&
((?[X]:((~kind(X)&kind(X))))<=>((wise(lucy)&~humble(lucy))))&
(![X]:((patient(X)|~creative(X))<=>old(X)))&
(![X]:((humble(X)<~>curious(X))=>(~funny(X)&~brave(X))))&
((old(lucy))=>(?[X]:((~wise(X)<~>~old(X)))))&
(((~wise(alice)<~>~funny(alice)))=>(?[X]:(~strong(X))))&
(((humble(alice)<~>brave(alice)))<=>(?[X]:((~happy(X)&strong(X)))))&
((?[X]:((wise(X)|~generous(X))))=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((old(X)<~>humble(X))<=>(~happy(X)&curious(X))))&
(![X]:(calm(X)<=>~happy(X)))&
((?[X]:((funny(X)<~>strong(X))))=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:((rich(X)<~>kind(X))=>(kind(X)|~happy(X))))&
(![X]:((creative(X)|tall(X))<=>(~tall(X)<~>~generous(X))))&
(![X]:((rich(X)&~creative(X))<=>(~funny(X)|~creative(X))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>creative(X)))))&
((~strong(fred)<~>~kind(fred)))&
(~curious(lucy))&
((~creative(john)|humble(john)))&
(?[X]:((~wise(X)&old(X))))&
((brave(alice)&~patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)|happy(X))))&
(calm(alice)) | tall(lucy) | [
"p0",
"p1",
"p4",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2406431812656326629165418
% SZS output start Proof for 2406431812656326629165418
1. ! [X0] : (~funny(X0) => (funny(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((~old(X0) | quiet(X0)) => (~humble(X0) & generous(X0))) [input p1]
5. ! [X0] : ((humble(X0) <~> curious(X0)) => (~brave(X0) & ~funny(X0))) [input p4]
10. ! [X0] : ((old(X0) <~> humble(X0)) <=> (curious(X0) & ~happy(X0))) [input p9]
14. ! [X0] : ((tall(X0) | creative(X0)) <=> (~tall(X0) <~> ~generous(X0))) [input p13]
18. ~curious(lucy) [input p17]
25. tall(lucy) [input hypothesis]
29. ! [X0] : ((funny(X0) & ~brave(X0)) | funny(X0)) [ennf transformation 1]
30. ! [X0] : ((~humble(X0) & generous(X0)) | (old(X0) & ~quiet(X0))) [ennf transformation 2]
31. ! [X0] : ((~brave(X0) & ~funny(X0)) | (humble(X0) <=> curious(X0))) [ennf transformation 5]
45. ! [X0] : ((~brave(X0) & ~funny(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0)))) [nnf transformation 31]
59. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 10]
60. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [flattening 59]
67. ! [X0] : (((tall(X0) | creative(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~tall(X0) & ~creative(X0)))) [nnf transformation 14]
68. ! [X0] : ((tall(X0) | creative(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~tall(X0) & ~creative(X0)))) [flattening 67]
84. funny(X0) | funny(X0) [cnf transformation 29]
86. generous(X0) | old(X0) [cnf transformation 30]
96. ~funny(X0) | curious(X0) | ~humble(X0) [cnf transformation 45]
114. curious(X0) | humble(X0) | ~old(X0) [cnf transformation 60]
125. ~generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 68]
145. ~curious(lucy) [cnf transformation 18]
154. tall(lucy) [cnf transformation 25]
155. ~tall(X0) | ~generous(X0) [duplicate literal removal 125]
158. funny(X0) [duplicate literal removal 84]
174. ~humble(X0) | curious(X0) [subsumption resolution 96,158]
176. 4 <=> old(lucy) [avatar definition]
177. old(lucy) <- (4) [avatar component clause 176]
225. ~old(X0) | curious(X0) [subsumption resolution 114,174]
303. ~generous(lucy) [resolution 155,154]
304. old(lucy) [resolution 303,86]
307. 4 [avatar split clause 304,176]
311. curious(lucy) <- (4) [resolution 225,177]
316. $false <- (4) [subsumption resolution 311,145]
317. ~4 [avatar contradiction clause 316]
318. $false [avatar sat refutation 307,317]
% SZS output end Proof for 2406431812656326629165418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient is generous.
If someone is strong then someone is both curious and not old and vice versa.
If paul is not tall or creative then susan is not old or not rich and vice versa.
If someone is both not funny and brave then someone is not kind.
Everyone who is not strong is not curious.
If someone is both rich and not humble then someone is both not funny and strong and vice versa.
Everyone who is not humble is tall and vice versa.
If someone is both not old and calm then someone is both strong and not happy.
If someone is not humble or not patient then fred is either not brave or not curious.
If lucy is both not funny and not tall then someone is kind or not tall and vice versa.
If lucy is not creative then fred is tall or not brave and vice versa.
If someone is both not generous and calm then someone is curious and vice versa.
If someone is funny then someone is both calm and not curious and vice versa.
Everyone who is both curious and not curious is not curious or not rich and vice versa.
Everyone who is either curious or not curious is either patient or brave and vice versa.
If someone is both not tall and humble then john is not funny and vice versa.
Lucy is either not patient or rich.
Someone is not brave.
Someone is both not brave and happy.
Someone is generous or creative.
Lucy is both generous and not quiet.
Paul is not funny.
John is creative or not wise.
Mary is either not curious or rich. | Susan is funny. | contradiction | (![X]:(~patient(X)=>generous(X)))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)&~old(X)))))&
(((~tall(paul)|creative(paul)))<=>((~old(susan)|~rich(susan))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:(~kind(X))))&
(![X]:(~strong(X)=>~curious(X)))&
((?[X]:((rich(X)&~humble(X))))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:(~humble(X)<=>tall(X)))&
((?[X]:((~old(X)&calm(X))))=>(?[X]:((strong(X)&~happy(X)))))&
((?[X]:((~humble(X)|~patient(X))))=>((~brave(fred)<~>~curious(fred))))&
(((~funny(lucy)&~tall(lucy)))<=>(?[X]:((kind(X)|~tall(X)))))&
((~creative(lucy))<=>((tall(fred)|~brave(fred))))&
((?[X]:((~generous(X)&calm(X))))<=>(?[X]:(curious(X))))&
((?[X]:(funny(X)))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((curious(X)&~curious(X))<=>(~curious(X)|~rich(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(patient(X)<~>brave(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(~funny(john)))&
((~patient(lucy)<~>rich(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((generous(X)|creative(X))))&
((generous(lucy)&~quiet(lucy)))&
(~funny(paul))&
((creative(john)|~wise(john)))&
((~curious(mary)<~>rich(mary))) | funny(susan) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6858158970765320178897230
% SZS output start Proof for 6858158970765320178897230
13. ? [X0] : funny(X0) <=> ? [X0] : (~curious(X0) & calm(X0)) [input p12]
14. ! [X0] : ((~curious(X0) & curious(X0)) <=> (~rich(X0) | ~curious(X0))) [input p13]
25. funny(susan) [input hypothesis]
31. ? [X0] : funny(X0) <=> ? [X1] : (~curious(X1) & calm(X1)) [rectify 13]
71. (? [X0] : funny(X0) | ! [X1] : (curious(X1) | ~calm(X1))) & (? [X1] : (~curious(X1) & calm(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 31]
72. (? [X0] : funny(X0) | ! [X1] : (curious(X1) | ~calm(X1))) & (? [X2] : (~curious(X2) & calm(X2)) | ! [X3] : ~funny(X3)) [rectify 71]
73. ? [X0] : funny(X0) => funny(sK9) [choice axiom]
74. ? [X2] : (~curious(X2) & calm(X2)) => (~curious(sK10) & calm(sK10)) [choice axiom]
75. (funny(sK9) | ! [X1] : (curious(X1) | ~calm(X1))) & ((~curious(sK10) & calm(sK10)) | ! [X3] : ~funny(X3)) [skolemisation 72,74,73]
76. ! [X0] : (((~curious(X0) & curious(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 14]
77. ! [X0] : (((~curious(X0) & curious(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | curious(X0) | ~curious(X0))) [flattening 76]
125. ~curious(sK10) | ~funny(X3) [cnf transformation 75]
128. curious(X0) | curious(X0) [cnf transformation 77]
153. funny(susan) [cnf transformation 25]
159. curious(X0) [duplicate literal removal 128]
334. 40 <=> ! [X3] : ~funny(X3) [avatar definition]
335. ~funny(X3) <- (40) [avatar component clause 334]
337. 41 <=> curious(sK10) [avatar definition]
339. ~curious(sK10) <- (~41) [avatar component clause 337]
340. 40 | ~41 [avatar split clause 125,337,334]
391. $false <- (40) [resolution 335,153]
392. ~40 [avatar contradiction clause 391]
393. $false <- (~41) [subsumption resolution 339,159]
394. 41 [avatar contradiction clause 393]
395. $false [avatar sat refutation 340,392,394]
% SZS output end Proof for 6858158970765320178897230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not creative is kind and vice versa. Everyone who is not humble is either not patient or not happy and vice versa. If fred is both brave and curious then susan is not funny and vice versa. If john is both not creative and humble then susan is either wise or calm and vice versa. If someone is kind then someone is wise or patient. Everyone who is both not humble and rich is not patient or humble and vice versa. Everyone who is calm or rich is not patient or not happy. Everyone who is both not brave and strong is happy or humble. Everyone who is patient is not brave or not humble and vice versa. Everyone who is both not happy and not tall is not humble. Everyone who is not kind or not creative is both not strong and generous and vice versa. Everyone who is both calm and patient is either tall or not funny and vice versa. Everyone who is both not creative and kind is either not strong or rich. If mary is either brave or tall then john is quiet. Everyone who is not kind is both not brave and old. If alice is creative or brave then someone is either not rich or calm and vice versa. Someone is generous. Mary is both not tall and not funny. John is not brave or not wise. Fred is not quiet. Mary is kind or not happy. Someone is both not kind and not calm. Someone is both not strong and not tall. | Fred is generous. | entailment | (![X]:((~patient(X)&~creative(X))<=>kind(X)))&
(![X]:(~humble(X)<=>(~patient(X)<~>~happy(X))))&
(((brave(fred)&curious(fred)))<=>(~funny(susan)))&
(((~creative(john)&humble(john)))<=>((wise(susan)<~>calm(susan))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~humble(X)&rich(X))<=>(~patient(X)|humble(X))))&
(![X]:((calm(X)|rich(X))=>(~patient(X)|~happy(X))))&
(![X]:((~brave(X)&strong(X))=>(happy(X)|humble(X))))&
(![X]:(patient(X)<=>(~brave(X)|~humble(X))))&
(![X]:((~happy(X)&~tall(X))=>~humble(X)))&
(![X]:((~kind(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((calm(X)&patient(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((~creative(X)&kind(X))=>(~strong(X)<~>rich(X))))&
(((brave(mary)<~>tall(mary)))=>(quiet(john)))&
(![X]:(~kind(X)=>(~brave(X)&old(X))))&
(((creative(alice)|brave(alice)))<=>(?[X]:((~rich(X)<~>calm(X)))))&
(?[X]:(generous(X)))&
((~tall(mary)&~funny(mary)))&
((~brave(john)|~wise(john)))&
(~quiet(fred))&
((kind(mary)|~happy(mary)))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~strong(X)&~tall(X)))) | generous(fred) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8043489246238423575519343
% SZS output start Proof for 8043489246238423575519343
1. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> kind(X0)) [input p0]
6. ! [X0] : ((rich(X0) & ~humble(X0)) <=> (humble(X0) | ~patient(X0))) [input p5]
9. ! [X0] : (patient(X0) <=> (~humble(X0) | ~brave(X0))) [input p8]
11. ! [X0] : ((~creative(X0) | ~kind(X0)) <=> (generous(X0) & ~strong(X0))) [input p10]
24. ~generous(fred) [input hypothesis]
38. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~kind(X0)) & (kind(X0) | (creative(X0) | patient(X0)))) [nnf transformation 1]
39. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~kind(X0)) & (kind(X0) | creative(X0) | patient(X0))) [flattening 38]
48. ! [X0] : (((rich(X0) & ~humble(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~rich(X0) | humble(X0)))) [nnf transformation 6]
49. ! [X0] : (((rich(X0) & ~humble(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~rich(X0) | humble(X0))) [flattening 48]
50. ! [X0] : ((patient(X0) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | ~patient(X0))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~patient(X0))) [flattening 50]
52. ! [X0] : (((~creative(X0) | ~kind(X0)) | (~generous(X0) | strong(X0))) & ((generous(X0) & ~strong(X0)) | (creative(X0) & kind(X0)))) [nnf transformation 11]
53. ! [X0] : ((~creative(X0) | ~kind(X0) | ~generous(X0) | strong(X0)) & ((generous(X0) & ~strong(X0)) | (creative(X0) & kind(X0)))) [flattening 52]
70. ~kind(X0) | ~patient(X0) [cnf transformation 39]
88. ~humble(X0) | ~humble(X0) [cnf transformation 49]
96. patient(X0) | humble(X0) [cnf transformation 51]
100. generous(X0) | kind(X0) [cnf transformation 53]
130. ~generous(fred) [cnf transformation 24]
132. ~humble(X0) [duplicate literal removal 88]
184. patient(X0) [subsumption resolution 96,132]
250. kind(fred) [resolution 100,130]
254. ~patient(fred) [resolution 250,70]
255. $false [subsumption resolution 254,184]
% SZS output end Proof for 8043489246238423575519343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and funny then john is not kind or not curious. If someone is both quiet and old then someone is both strong and not strong. Everyone who is not kind or patient is both not quiet and creative. If john is not strong then someone is either rich or not humble and vice versa. If someone is either creative or kind then mary is both patient and not old. Everyone who is wise is kind and vice versa. Everyone who is either not quiet or not calm is not strong or not calm and vice versa. Everyone who is creative is not quiet or kind and vice versa. If someone is kind then someone is tall. If alice is either not creative or patient then someone is either creative or not happy. If john is both quiet and not tall then someone is both not strong and not tall. If alice is both not calm and calm then someone is either tall or happy. Everyone who is both not funny and not calm is either happy or not funny and vice versa. Everyone who is either not creative or happy is not happy or old and vice versa. Everyone who is both wise and humble is not old and vice versa. Everyone who is either wise or not quiet is not quiet. Someone is not patient or not quiet. Susan is either patient or humble. Fred is strong or rich. Mary is either not funny or curious. | Fred is not kind. | contradiction | ((?[X]:((~patient(X)&funny(X))))=>((~kind(john)|~curious(john))))&
((?[X]:((quiet(X)&old(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~kind(X)|patient(X))=>(~quiet(X)&creative(X))))&
((~strong(john))<=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:((creative(X)<~>kind(X))))=>((patient(mary)&~old(mary))))&
(![X]:(wise(X)<=>kind(X)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)|~calm(X))))&
(![X]:(creative(X)<=>(~quiet(X)|kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(tall(X))))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((creative(X)<~>~happy(X)))))&
(((quiet(john)&~tall(john)))=>(?[X]:((~strong(X)&~tall(X)))))&
(((~calm(alice)&calm(alice)))=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~happy(X)|old(X))))&
(![X]:((wise(X)&humble(X))<=>~old(X)))&
(![X]:((wise(X)<~>~quiet(X))=>~quiet(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
((patient(susan)<~>humble(susan)))&
((strong(fred)|rich(fred)))&
((~funny(mary)<~>curious(mary))) | ~kind(fred) | [
"p1",
"p2",
"p4",
"p7",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6916644255925104893300348
% SZS output start Proof for 6916644255925104893300348
2. ? [X0] : (old(X0) & quiet(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p1]
3. ! [X0] : ((patient(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p2]
5. ? [X0] : (creative(X0) <~> kind(X0)) => (~old(mary) & patient(mary)) [input p4]
8. ! [X0] : (creative(X0) <=> (kind(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (old(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((humble(X0) & wise(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => ~quiet(X0)) [input p15]
21. ~kind(fred) [input hypothesis]
22. ? [X0] : (old(X0) & quiet(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 2]
26. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (~old(X0) | ~quiet(X0)) [ennf transformation 22]
27. ! [X0] : ((creative(X0) & ~quiet(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 3]
28. (~old(mary) & patient(mary)) | ! [X0] : (creative(X0) <=> kind(X0)) [ennf transformation 5]
35. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 16]
36. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [rectify 26]
37. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK0) & strong(sK0)) [choice axiom]
38. (~strong(sK0) & strong(sK0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [skolemisation 36,37]
43. (~old(mary) & patient(mary)) | ! [X0] : ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))) [nnf transformation 28]
47. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 8]
48. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
62. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 14]
63. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 62]
64. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 15]
65. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | ~humble(X0) | ~wise(X0))) [flattening 64]
66. ! [X0] : (~quiet(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 35]
72. strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
73. ~strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
76. creative(X0) | kind(X0) [cnf transformation 27]
84. ~old(mary) | kind(X0) | ~creative(X0) [cnf transformation 43]
95. creative(X0) | quiet(X0) [cnf transformation 48]
113. old(X0) | ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 63]
114. happy(X0) | ~creative(X0) | happy(X0) [cnf transformation 63]
119. wise(X0) | old(X0) [cnf transformation 65]
121. ~quiet(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 66]
129. ~kind(fred) [cnf transformation 21]
130. ~wise(X0) | ~quiet(X0) [duplicate literal removal 121]
131. old(X0) | ~happy(X0) | ~creative(X0) [duplicate literal removal 113]
132. ~creative(X0) | happy(X0) [duplicate literal removal 114]
150. 4 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
151. ~old(X1) | ~quiet(X1) <- (4) [avatar component clause 150]
153. 5 <=> strong(sK0) [avatar definition]
156. 4 | ~5 [avatar split clause 73,153,150]
157. 4 | 5 [avatar split clause 72,153,150]
185. 12 <=> old(mary) [avatar definition]
187. ~old(mary) <- (~12) [avatar component clause 185]
189. ~old(mary) | kind(X0) [subsumption resolution 84,76]
191. 13 <=> ! [X0] : kind(X0) [avatar definition]
192. kind(X0) <- (13) [avatar component clause 191]
193. 13 | ~12 [avatar split clause 189,185,191]
256. ~creative(X0) | old(X0) [subsumption resolution 131,132]
296. $false <- (13) [resolution 192,129]
298. ~13 [avatar contradiction clause 296]
301. ~quiet(X0) | old(X0) [resolution 130,119]
302. ~quiet(X0) <- (4) [subsumption resolution 301,151]
316. old(X0) | quiet(X0) [resolution 256,95]
319. old(X0) <- (4) [subsumption resolution 316,302]
320. $false <- (4, ~12) [resolution 319,187]
322. ~4 | 12 [avatar contradiction clause 320]
323. $false [avatar sat refutation 156,157,193,298,322]
% SZS output end Proof for 6916644255925104893300348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not calm. Everyone who is either not creative or not wise is both patient and creative. If someone is either humble or generous then lucy is both not kind and generous and vice versa. Everyone who is not brave is not curious and vice versa. Everyone who is both not generous and humble is both kind and generous and vice versa. If someone is funny then paul is not old and vice versa. Everyone who is both not tall and wise is either not humble or not kind. If someone is either generous or not tall then someone is not rich or not curious and vice versa. Everyone who is both rich and not brave is either calm or humble and vice versa. Everyone who is either old or not curious is either brave or not happy. If someone is either not funny or strong then alice is both old and not curious. If paul is both brave and kind then mary is patient. If someone is both quiet and not strong then someone is not kind or not strong. If someone is either not humble or not curious then fred is not old or not quiet. If john is either not calm or brave then paul is both rich and not creative. Everyone who is either curious or not old is not curious or not kind and vice versa. Paul is not tall or not curious. Someone is either tall or happy. Alice is both tall and happy. Susan is not calm or happy. Someone is happy or brave. Fred is both tall and curious. Lucy is not brave or not old. Fred is both not wise and not patient. | Fred is not brave. | contradiction | (![X]:(creative(X)=>~calm(X)))&
(![X]:((~creative(X)<~>~wise(X))=>(patient(X)&creative(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>((~kind(lucy)&generous(lucy))))&
(![X]:(~brave(X)<=>~curious(X)))&
(![X]:((~generous(X)&humble(X))<=>(kind(X)&generous(X))))&
((?[X]:(funny(X)))<=>(~old(paul)))&
(![X]:((~tall(X)&wise(X))=>(~humble(X)<~>~kind(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((rich(X)&~brave(X))<=>(calm(X)<~>humble(X))))&
(![X]:((old(X)<~>~curious(X))=>(brave(X)<~>~happy(X))))&
((?[X]:((~funny(X)<~>strong(X))))=>((old(alice)&~curious(alice))))&
(((brave(paul)&kind(paul)))=>(patient(mary)))&
((?[X]:((quiet(X)&~strong(X))))=>(?[X]:((~kind(X)|~strong(X)))))&
((?[X]:((~humble(X)<~>~curious(X))))=>((~old(fred)|~quiet(fred))))&
(((~calm(john)<~>brave(john)))=>((rich(paul)&~creative(paul))))&
(![X]:((curious(X)<~>~old(X))<=>(~curious(X)|~kind(X))))&
((~tall(paul)|~curious(paul)))&
(?[X]:((tall(X)<~>happy(X))))&
((tall(alice)&happy(alice)))&
((~calm(susan)|happy(susan)))&
(?[X]:((happy(X)|brave(X))))&
((tall(fred)&curious(fred)))&
((~brave(lucy)|~old(lucy)))&
((~wise(fred)&~patient(fred))) | ~brave(fred) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2769205307242748754766623
% SZS output start Proof for 2769205307242748754766623
4. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p3]
22. curious(fred) & tall(fred) [input p21]
25. ~brave(fred) [input hypothesis]
45. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 4]
81. ~curious(X0) | brave(X0) [cnf transformation 45]
130. curious(fred) [cnf transformation 22]
134. ~brave(fred) [cnf transformation 25]
316. brave(fred) [resolution 81,130]
317. $false [subsumption resolution 316,134]
% SZS output end Proof for 2769205307242748754766623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or old is strong or curious. Everyone who is either patient or not rich is both wise and rich. If someone is not generous or not quiet then someone is both not quiet and patient and vice versa. Everyone who is not funny is either not tall or not happy and vice versa. Everyone who is both happy and not wise is either not patient or not calm and vice versa. If someone is funny then fred is brave. Everyone who is not rich or not quiet is not wise and vice versa. If someone is not creative then someone is both wise and creative. If someone is not tall then someone is not rich. Everyone who is not generous or not rich is happy or humble and vice versa. If paul is not funny then someone is old. Everyone who is curious or humble is not old and vice versa. Everyone who is either generous or not curious is not creative. If susan is either creative or not funny then someone is either not funny or not brave. Everyone who is not wise or not rich is patient. Everyone who is both creative and not curious is strong or not brave. Someone is not tall. Someone is calm. Alice is either kind or not quiet. Someone is either creative or not tall. Lucy is either tall or brave. John is both rich and generous. Mary is calm or patient. | Mary is funny. | neutral | (![X]:((calm(X)|old(X))=>(strong(X)|curious(X))))&
(![X]:((patient(X)<~>~rich(X))=>(wise(X)&rich(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(~funny(X)<=>(~tall(X)<~>~happy(X))))&
(![X]:((happy(X)&~wise(X))<=>(~patient(X)<~>~calm(X))))&
((?[X]:(funny(X)))=>(brave(fred)))&
(![X]:((~rich(X)|~quiet(X))<=>~wise(X)))&
((?[X]:(~creative(X)))=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:(~rich(X))))&
(![X]:((~generous(X)|~rich(X))<=>(happy(X)|humble(X))))&
((~funny(paul))=>(?[X]:(old(X))))&
(![X]:((curious(X)|humble(X))<=>~old(X)))&
(![X]:((generous(X)<~>~curious(X))=>~creative(X)))&
(((creative(susan)<~>~funny(susan)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~wise(X)|~rich(X))=>patient(X)))&
(![X]:((creative(X)&~curious(X))=>(strong(X)|~brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:(calm(X)))&
((kind(alice)<~>~quiet(alice)))&
(?[X]:((creative(X)<~>~tall(X))))&
((tall(lucy)<~>brave(lucy)))&
((rich(john)&generous(john)))&
((calm(mary)|patient(mary))) | funny(mary) | [] | null | 0 |
If someone is either calm or not strong then someone is either not rich or happy.
Everyone who is both not brave and not humble is either not brave or not quiet.
If someone is either not curious or funny then john is either not brave or creative and vice versa.
Everyone who is strong or not happy is quiet or not calm.
Everyone who is not kind or not old is not creative or not curious.
If someone is either quiet or tall then someone is not curious and vice versa.
Everyone who is not brave or not rich is not happy.
If someone is strong or creative then john is both patient and not brave.
If paul is not strong or not brave then someone is both not wise and not generous and vice versa.
Everyone who is either strong or not wise is either not old or tall and vice versa.
If someone is funny or creative then fred is not tall.
Everyone who is both not tall and not happy is kind.
If fred is both curious and quiet then someone is not tall or wise.
Everyone who is not strong or not rich is both kind and not happy and vice versa.
Everyone who is wise is either not curious or humble.
If mary is tall or not humble then someone is quiet or strong and vice versa.
Alice is either not tall or not brave.
John is both not funny and calm.
John is either not funny or not old.
Someone is both not strong and humble.
Someone is calm.
Alice is either not calm or rich.
Someone is both not quiet and not strong. | Fred is rich. | neutral | ((?[X]:((calm(X)<~>~strong(X))))=>(?[X]:((~rich(X)<~>happy(X)))))&
(![X]:((~brave(X)&~humble(X))=>(~brave(X)<~>~quiet(X))))&
((?[X]:((~curious(X)<~>funny(X))))<=>((~brave(john)<~>creative(john))))&
(![X]:((strong(X)|~happy(X))=>(quiet(X)|~calm(X))))&
(![X]:((~kind(X)|~old(X))=>(~creative(X)|~curious(X))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~brave(X)|~rich(X))=>~happy(X)))&
((?[X]:((strong(X)|creative(X))))=>((patient(john)&~brave(john))))&
(((~strong(paul)|~brave(paul)))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((strong(X)<~>~wise(X))<=>(~old(X)<~>tall(X))))&
((?[X]:((funny(X)|creative(X))))=>(~tall(fred)))&
(![X]:((~tall(X)&~happy(X))=>kind(X)))&
(((curious(fred)&quiet(fred)))=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((~strong(X)|~rich(X))<=>(kind(X)&~happy(X))))&
(![X]:(wise(X)=>(~curious(X)<~>humble(X))))&
(((tall(mary)|~humble(mary)))<=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(alice)<~>~brave(alice)))&
((~funny(john)&calm(john)))&
((~funny(john)<~>~old(john)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:(calm(X)))&
((~calm(alice)<~>rich(alice)))&
(?[X]:((~quiet(X)&~strong(X)))) | rich(fred) | [] | null | 0 |
Everyone who is calm is not old and vice versa.
If john is both not kind and creative then john is both strong and humble and vice versa.
If susan is both old and kind then someone is generous or wise and vice versa.
If john is calm then someone is both strong and not happy and vice versa.
Everyone who is both quiet and not humble is not calm or not funny and vice versa.
Everyone who is not tall or humble is quiet.
Everyone who is both not strong and not old is both not curious and kind and vice versa.
Everyone who is quiet is not strong and vice versa.
Everyone who is either calm or patient is both funny and quiet.
Everyone who is calm is not brave and vice versa.
Everyone who is either not brave or patient is generous or not funny and vice versa.
Everyone who is not generous is both curious and not brave.
If someone is either rich or not funny then alice is either not brave or not kind and vice versa.
If someone is not quiet or humble then fred is not kind or funny and vice versa.
Someone is either generous or strong.
Someone is generous or quiet.
Someone is happy.
Someone is either not kind or quiet.
Alice is happy or generous.
Someone is both not old and funny. | Susan is calm. | contradiction | (![X]:(calm(X)<=>~old(X)))&
(((~kind(john)&creative(john)))<=>((strong(john)&humble(john))))&
(((old(susan)&kind(susan)))<=>(?[X]:((generous(X)|wise(X)))))&
((calm(john))<=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((quiet(X)&~humble(X))<=>(~calm(X)|~funny(X))))&
(![X]:((~tall(X)|humble(X))=>quiet(X)))&
(![X]:((~strong(X)&~old(X))<=>(~curious(X)&kind(X))))&
(![X]:(quiet(X)<=>~strong(X)))&
(![X]:((calm(X)<~>patient(X))=>(funny(X)&quiet(X))))&
(![X]:(calm(X)<=>~brave(X)))&
(![X]:((~brave(X)<~>patient(X))<=>(generous(X)|~funny(X))))&
(![X]:(~generous(X)=>(curious(X)&~brave(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((~quiet(X)|humble(X))))<=>((~kind(fred)|funny(fred))))&
(?[X]:((generous(X)<~>strong(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:((~kind(X)<~>quiet(X))))&
((happy(alice)|generous(alice)))&
(?[X]:((~old(X)&funny(X)))) | calm(susan) | [
"p0",
"p2",
"p6",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5787575010950893443246596
% SZS output start Proof for 5787575010950893443246596
1. ! [X0] : (calm(X0) <=> ~old(X0)) [input p0]
3. (kind(susan) & old(susan)) <=> ? [X0] : (wise(X0) | generous(X0)) [input p2]
7. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (kind(X0) & ~curious(X0))) [input p6]
8. ! [X0] : (quiet(X0) <=> ~strong(X0)) [input p7]
10. ! [X0] : (calm(X0) <=> ~brave(X0)) [input p9]
12. ! [X0] : (~generous(X0) => (~brave(X0) & curious(X0))) [input p11]
16. ? [X0] : (quiet(X0) | generous(X0)) [input p15]
21. calm(susan) [input hypothesis]
25. ! [X0] : ((~brave(X0) & curious(X0)) | generous(X0)) [ennf transformation 12]
26. ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))) [nnf transformation 1]
29. ((kind(susan) & old(susan)) | ! [X0] : (~wise(X0) & ~generous(X0))) & (? [X0] : (wise(X0) | generous(X0)) | (~kind(susan) | ~old(susan))) [nnf transformation 3]
30. ((kind(susan) & old(susan)) | ! [X0] : (~wise(X0) & ~generous(X0))) & (? [X0] : (wise(X0) | generous(X0)) | ~kind(susan) | ~old(susan)) [flattening 29]
31. ((kind(susan) & old(susan)) | ! [X0] : (~wise(X0) & ~generous(X0))) & (? [X1] : (wise(X1) | generous(X1)) | ~kind(susan) | ~old(susan)) [rectify 30]
32. ? [X1] : (wise(X1) | generous(X1)) => (wise(sK0) | generous(sK0)) [choice axiom]
33. ((kind(susan) & old(susan)) | ! [X0] : (~wise(X0) & ~generous(X0))) & ((wise(sK0) | generous(sK0)) | ~kind(susan) | ~old(susan)) [skolemisation 31,32]
40. ! [X0] : (((~old(X0) & ~strong(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (old(X0) | strong(X0)))) [nnf transformation 7]
41. ! [X0] : (((~old(X0) & ~strong(X0)) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | old(X0) | strong(X0))) [flattening 40]
42. ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0))) [nnf transformation 8]
44. ! [X0] : ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))) [nnf transformation 10]
59. ? [X0] : (quiet(X0) | generous(X0)) => (quiet(sK5) | generous(sK5)) [choice axiom]
60. quiet(sK5) | generous(sK5) [skolemisation 16,59]
68. ~old(X0) | ~calm(X0) [cnf transformation 26]
75. old(susan) | ~generous(X0) [cnf transformation 33]
88. ~curious(X0) | old(X0) | strong(X0) [cnf transformation 41]
92. ~quiet(X0) | ~strong(X0) [cnf transformation 42]
99. brave(X0) | calm(X0) [cnf transformation 44]
106. curious(X0) | generous(X0) [cnf transformation 25]
107. ~brave(X0) | generous(X0) [cnf transformation 25]
122. quiet(sK5) | generous(sK5) [cnf transformation 60]
129. calm(susan) [cnf transformation 21]
159. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
160. ~generous(X0) <- (7) [avatar component clause 159]
163. 8 <=> old(susan) [avatar definition]
165. old(susan) <- (8) [avatar component clause 163]
167. 7 | 8 [avatar split clause 75,163,159]
263. 29 <=> generous(sK5) [avatar definition]
265. generous(sK5) <- (29) [avatar component clause 263]
267. 30 <=> quiet(sK5) [avatar definition]
269. quiet(sK5) <- (30) [avatar component clause 267]
270. 29 | 30 [avatar split clause 122,267,263]
292. ~calm(susan) <- (8) [resolution 68,165]
293. $false <- (8) [subsumption resolution 292,129]
294. ~8 [avatar contradiction clause 293]
295. $false <- (7, 29) [resolution 160,265]
298. ~7 | ~29 [avatar contradiction clause 295]
305. ~strong(sK5) <- (30) [resolution 92,269]
313. generous(X0) | calm(X0) [resolution 107,99]
314. calm(X0) <- (7) [subsumption resolution 313,160]
323. old(X0) | strong(X0) | generous(X0) [resolution 88,106]
324. strong(X0) | old(X0) <- (7) [subsumption resolution 323,160]
337. 36 <=> old(sK5) [avatar definition]
339. old(sK5) <- (36) [avatar component clause 337]
410. old(sK5) <- (7, 30) [resolution 324,305]
416. 36 | ~7 | ~30 [avatar split clause 410,267,159,337]
418. ~calm(sK5) <- (36) [resolution 339,68]
419. $false <- (7, 36) [subsumption resolution 418,314]
420. ~7 | ~36 [avatar contradiction clause 419]
421. $false [avatar sat refutation 167,270,294,298,416,420]
% SZS output end Proof for 5787575010950893443246596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is either not brave or not creative.
If someone is both happy and rich then someone is kind or funny.
Everyone who is both patient and not wise is generous.
Everyone who is both not quiet and not strong is quiet.
Everyone who is both not kind and brave is not quiet or not kind and vice versa.
If mary is either patient or not creative then someone is funny.
If someone is both curious and not rich then lucy is quiet or happy.
If lucy is both tall and not generous then alice is either brave or kind.
If someone is curious or not humble then alice is not tall or not kind and vice versa.
Everyone who is both not wise and quiet is both rich and patient.
Everyone who is either curious or not creative is both not funny and curious.
Everyone who is either wise or not funny is not tall or not happy and vice versa.
Everyone who is both not old and wise is old or not calm and vice versa.
Everyone who is either wise or not curious is both patient and not quiet.
Everyone who is not calm or calm is both tall and not calm.
If lucy is either quiet or not kind then someone is either happy or curious.
Someone is tall or not patient.
Fred is both generous and strong.
Someone is either quiet or calm.
Someone is either kind or not funny.
Lucy is quiet. | Lucy is not wise. | contradiction | (![X]:(humble(X)=>(~brave(X)<~>~creative(X))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((patient(X)&~wise(X))=>generous(X)))&
(![X]:((~quiet(X)&~strong(X))=>quiet(X)))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)|~kind(X))))&
(((patient(mary)<~>~creative(mary)))=>(?[X]:(funny(X))))&
((?[X]:((curious(X)&~rich(X))))=>((quiet(lucy)|happy(lucy))))&
(((tall(lucy)&~generous(lucy)))=>((brave(alice)<~>kind(alice))))&
((?[X]:((curious(X)|~humble(X))))<=>((~tall(alice)|~kind(alice))))&
(![X]:((~wise(X)&quiet(X))=>(rich(X)&patient(X))))&
(![X]:((curious(X)<~>~creative(X))=>(~funny(X)&curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~old(X)&wise(X))<=>(old(X)|~calm(X))))&
(![X]:((wise(X)<~>~curious(X))=>(patient(X)&~quiet(X))))&
(![X]:((~calm(X)|calm(X))=>(tall(X)&~calm(X))))&
(((quiet(lucy)<~>~kind(lucy)))=>(?[X]:((happy(X)<~>curious(X)))))&
(?[X]:((tall(X)|~patient(X))))&
((generous(fred)&strong(fred)))&
(?[X]:((quiet(X)<~>calm(X))))&
(?[X]:((kind(X)<~>~funny(X))))&
(quiet(lucy)) | ~wise(lucy) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8240659026824961329402569
% SZS output start Proof for 8240659026824961329402569
13. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~calm(X0) | old(X0))) [input p12]
15. ! [X0] : ((calm(X0) | ~calm(X0)) => (~calm(X0) & tall(X0))) [input p14]
22. ~wise(lucy) [input hypothesis]
38. ! [X0] : ((~calm(X0) & tall(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 15]
57. ! [X0] : (((wise(X0) & ~old(X0)) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 13]
58. ! [X0] : (((wise(X0) & ~old(X0)) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | ~wise(X0) | old(X0))) [flattening 57]
102. calm(X0) | wise(X0) [cnf transformation 58]
110. ~calm(X0) | ~calm(X0) [cnf transformation 38]
121. ~wise(lucy) [cnf transformation 22]
122. ~calm(X0) [duplicate literal removal 110]
229. wise(X0) [resolution 102,122]
230. $false [resolution 229,121]
% SZS output end Proof for 8240659026824961329402569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not humble is both calm and not kind.
Everyone who is not calm is curious and vice versa.
If mary is patient then someone is either not old or not generous.
If paul is brave then someone is either not generous or kind.
If susan is both old and not quiet then someone is either patient or curious and vice versa.
Everyone who is not humble is not patient.
If mary is not funny or patient then mary is not rich or not creative.
Everyone who is wise or not wise is both rich and curious.
Everyone who is not humble is both rich and not happy and vice versa.
Everyone who is both not old and not calm is either not tall or not curious and vice versa.
Everyone who is both not quiet and not kind is both rich and kind.
Everyone who is not strong is both humble and not patient and vice versa.
If susan is either not rich or not humble then someone is quiet and vice versa.
If paul is not generous or patient then someone is either kind or old.
Everyone who is wise is brave or not kind.
Fred is not old or not kind.
Susan is either not patient or humble.
Lucy is not humble or generous.
Someone is both rich and generous.
Someone is not old or strong.
Fred is not tall. | Mary is tall. | contradiction | (![X]:((old(X)|~humble(X))=>(calm(X)&~kind(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((patient(mary))=>(?[X]:((~old(X)<~>~generous(X)))))&
((brave(paul))=>(?[X]:((~generous(X)<~>kind(X)))))&
(((old(susan)&~quiet(susan)))<=>(?[X]:((patient(X)<~>curious(X)))))&
(![X]:(~humble(X)=>~patient(X)))&
(((~funny(mary)|patient(mary)))=>((~rich(mary)|~creative(mary))))&
(![X]:((wise(X)|~wise(X))=>(rich(X)&curious(X))))&
(![X]:(~humble(X)<=>(rich(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((~quiet(X)&~kind(X))=>(rich(X)&kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~patient(X))))&
(((~rich(susan)<~>~humble(susan)))<=>(?[X]:(quiet(X))))&
(((~generous(paul)|patient(paul)))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:(wise(X)=>(brave(X)|~kind(X))))&
((~old(fred)|~kind(fred)))&
((~patient(susan)<~>humble(susan)))&
((~humble(lucy)|generous(lucy)))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((~old(X)|strong(X))))&
(~tall(fred)) | tall(mary) | [
"p0",
"p1",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7728889751885664218311516
% SZS output start Proof for 7728889751885664218311516
1. ! [X0] : ((~humble(X0) | old(X0)) => (~kind(X0) & calm(X0))) [input p0]
2. ! [X0] : (~calm(X0) <=> curious(X0)) [input p1]
8. ! [X0] : ((~wise(X0) | wise(X0)) => (curious(X0) & rich(X0))) [input p7]
10. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> ~curious(X0))) [input p9]
22. tall(mary) [input hypothesis]
25. ! [X0] : ((~kind(X0) & calm(X0)) | (humble(X0) & ~old(X0))) [ennf transformation 1]
29. ! [X0] : ((curious(X0) & rich(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0))) [nnf transformation 2]
51. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) & (((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 10]
52. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) & (((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 51]
65. ~old(X0) | calm(X0) [cnf transformation 25]
70. ~curious(X0) | ~calm(X0) [cnf transformation 37]
84. curious(X0) | ~wise(X0) [cnf transformation 29]
85. wise(X0) | curious(X0) [cnf transformation 29]
89. ~curious(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 52]
115. tall(mary) [cnf transformation 22]
173. curious(X0) [subsumption resolution 84,85]
177. ~tall(X0) | calm(X0) | old(X0) [subsumption resolution 89,173]
178. ~tall(X0) | calm(X0) [subsumption resolution 177,65]
245. ~calm(X1) [resolution 70,173]
267. calm(mary) [resolution 178,115]
268. $false [subsumption resolution 267,245]
% SZS output end Proof for 7728889751885664218311516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Alice is not old. | contradiction | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | ~old(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 142616828076384265061896
% SZS output start Proof for 142616828076384265061896
2. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p1]
3. ! [X0] : ((tall(X0) <~> ~rich(X0)) => (~wise(X0) & patient(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
9. ? [X0] : ~old(X0) <=> (~old(fred) & quiet(fred)) [input p8]
10. ! [X0] : (happy(X0) => (~wise(X0) <~> ~old(X0))) [input p9]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
13. ? [X0] : patient(X0) <=> (~rich(lucy) & wise(lucy)) [input p12]
16. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~quiet(X0) <~> tall(X0))) [input p15]
24. ~old(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 2]
26. ! [X0] : (~rich(X0) => (~happy(X0) & ~generous(X0))) [pure predicate removal 5]
28. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 25]
29. ! [X0] : ((~wise(X0) & patient(X0)) | (tall(X0) <=> ~rich(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~wise(X0) <~> ~old(X0)) | ~happy(X0)) [ennf transformation 10]
32. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
35. ! [X0] : ((~quiet(X0) <~> tall(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 16]
37. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 28]
38. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
39. patient(sK0) | ! [X1] : ~generous(X1) [skolemisation 37,38]
40. ! [X0] : ((~wise(X0) & patient(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 29]
45. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 45]
51. (? [X0] : ~old(X0) | (old(fred) | ~quiet(fred))) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [nnf transformation 9]
52. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [flattening 51]
53. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [rectify 52]
54. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
55. (~old(sK2) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [skolemisation 53,54]
56. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~happy(X0)) [nnf transformation 31]
58. (? [X0] : patient(X0) | (rich(lucy) | ~wise(lucy))) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [nnf transformation 13]
59. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [flattening 58]
60. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [rectify 59]
61. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
62. (patient(sK3) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [skolemisation 60,61]
68. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 35]
81. patient(sK0) | ~generous(X1) [cnf transformation 39]
82. ~tall(X0) | ~rich(X0) | patient(X0) [cnf transformation 40]
90. ~generous(X0) | rich(X0) [cnf transformation 30]
91. ~happy(X0) | rich(X0) [cnf transformation 30]
92. ~kind(X0) | happy(X0) [cnf transformation 46]
104. quiet(fred) | old(X1) [cnf transformation 55]
105. ~old(fred) | old(X1) [cnf transformation 55]
108. ~happy(X0) | wise(X0) | old(X0) [cnf transformation 56]
109. kind(X0) | generous(X0) [cnf transformation 32]
110. kind(X0) | wise(X0) [cnf transformation 32]
116. ~rich(lucy) | ~patient(X1) [cnf transformation 62]
124. ~quiet(X0) | tall(X0) | ~wise(X0) | generous(X0) [cnf transformation 68]
137. ~old(alice) [cnf transformation 24]
141. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
142. ~generous(X1) <- (1) [avatar component clause 141]
144. 2 <=> patient(sK0) [avatar definition]
146. patient(sK0) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 81,144,141]
192. 12 <=> quiet(fred) [avatar definition]
193. quiet(fred) <- (12) [avatar component clause 192]
196. 13 <=> old(fred) [avatar definition]
205. 15 <=> ! [X1] : old(X1) [avatar definition]
206. old(X1) <- (15) [avatar component clause 205]
207. 15 | ~13 [avatar split clause 105,196,205]
208. 15 | 12 [avatar split clause 104,192,205]
213. 17 <=> tall(fred) [avatar definition]
214. ~tall(fred) <- (~17) [avatar component clause 213]
215. tall(fred) <- (17) [avatar component clause 213]
232. 21 <=> rich(lucy) [avatar definition]
233. ~rich(lucy) <- (~21) [avatar component clause 232]
241. 23 <=> ! [X1] : ~patient(X1) [avatar definition]
242. ~patient(X1) <- (23) [avatar component clause 241]
243. 23 | ~21 [avatar split clause 116,232,241]
293. happy(X0) | generous(X0) [resolution 109,92]
294. happy(X0) | wise(X0) [resolution 110,92]
301. generous(X0) | rich(X0) [resolution 293,91]
302. rich(X0) [subsumption resolution 301,90]
303. ~rich(fred) | patient(fred) <- (17) [resolution 82,215]
305. patient(fred) <- (17) [subsumption resolution 303,302]
308. $false <- (~21) [resolution 302,233]
309. 21 [avatar contradiction clause 308]
310. $false <- (2, 23) [resolution 242,146]
312. $false <- (17, 23) [resolution 242,305]
313. ~17 | ~23 [avatar contradiction clause 312]
315. ~2 | ~23 [avatar contradiction clause 310]
371. wise(X0) | old(X0) | wise(X0) [resolution 108,294]
378. wise(X0) | old(X0) [duplicate literal removal 371]
390. tall(fred) | ~wise(fred) | generous(fred) <- (12) [resolution 124,193]
402. ~wise(fred) | generous(fred) <- (12, ~17) [subsumption resolution 390,214]
403. ~wise(fred) <- (1, 12, ~17) [subsumption resolution 402,142]
409. old(fred) <- (1, 12, ~17) [resolution 403,378]
412. 13 | ~1 | ~12 | 17 [avatar split clause 409,213,192,141,196]
414. $false <- (15) [resolution 206,137]
421. ~15 [avatar contradiction clause 414]
422. $false [avatar sat refutation 147,207,208,243,309,313,315,412,421]
% SZS output end Proof for 142616828076384265061896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is strong then someone is not patient or not strong and vice versa. If someone is either calm or wise then someone is kind and vice versa. If lucy is both old and not quiet then someone is both strong and curious. Everyone who is both brave and funny is both old and quiet. If someone is both tall and patient then someone is brave or not calm and vice versa. If someone is either funny or old then paul is both calm and old and vice versa. If paul is either generous or not kind then john is not kind and vice versa. Everyone who is either rich or strong is not creative. Everyone who is both not brave and not generous is either not generous or calm. Everyone who is kind or not humble is both not happy and patient and vice versa. Everyone who is not calm or rich is not rich or not humble. Everyone who is not rich or not old is happy. Everyone who is happy or not humble is not old or not tall. Everyone who is both not curious and not brave is either rich or not quiet. If susan is both brave and not curious then someone is either curious or happy and vice versa. Everyone who is calm or happy is generous. Someone is generous. Fred is both not patient and not curious. Someone is not humble or not strong. John is not old. Someone is tall or not brave. Fred is both not old and creative. Alice is funny. Paul is rich. | John is rich. | contradiction | ((strong(susan))<=>(?[X]:((~patient(X)|~strong(X)))))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:(kind(X))))&
(((old(lucy)&~quiet(lucy)))=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((brave(X)&funny(X))=>(old(X)&quiet(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((brave(X)|~calm(X)))))&
((?[X]:((funny(X)<~>old(X))))<=>((calm(paul)&old(paul))))&
(((generous(paul)<~>~kind(paul)))<=>(~kind(john)))&
(![X]:((rich(X)<~>strong(X))=>~creative(X)))&
(![X]:((~brave(X)&~generous(X))=>(~generous(X)<~>calm(X))))&
(![X]:((kind(X)|~humble(X))<=>(~happy(X)&patient(X))))&
(![X]:((~calm(X)|rich(X))=>(~rich(X)|~humble(X))))&
(![X]:((~rich(X)|~old(X))=>happy(X)))&
(![X]:((happy(X)|~humble(X))=>(~old(X)|~tall(X))))&
(![X]:((~curious(X)&~brave(X))=>(rich(X)<~>~quiet(X))))&
(((brave(susan)&~curious(susan)))<=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:((calm(X)|happy(X))=>generous(X)))&
(?[X]:(generous(X)))&
((~patient(fred)&~curious(fred)))&
(?[X]:((~humble(X)|~strong(X))))&
(~old(john))&
(?[X]:((tall(X)|~brave(X))))&
((~old(fred)&creative(fred)))&
(funny(alice))&
(rich(paul)) | rich(john) | [
"p9",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7491074974771658428161091
% SZS output start Proof for 7491074974771658428161091
10. ! [X0] : ((~humble(X0) | kind(X0)) <=> (patient(X0) & ~happy(X0))) [input p9]
11. ! [X0] : ((rich(X0) | ~calm(X0)) => (~humble(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((~old(X0) | ~rich(X0)) => happy(X0)) [input p11]
20. ~old(john) [input p19]
25. rich(john) [input hypothesis]
35. ! [X0] : ((~humble(X0) | ~rich(X0)) | (~rich(X0) & calm(X0))) [ennf transformation 11]
36. ! [X0] : (~humble(X0) | ~rich(X0) | (~rich(X0) & calm(X0))) [flattening 35]
37. ! [X0] : (happy(X0) | (old(X0) & rich(X0))) [ennf transformation 12]
67. ! [X0] : (((~humble(X0) | kind(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (humble(X0) & ~kind(X0)))) [nnf transformation 10]
68. ! [X0] : ((~humble(X0) | kind(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | (humble(X0) & ~kind(X0)))) [flattening 67]
112. ~happy(X0) | humble(X0) [cnf transformation 68]
117. ~humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 36]
119. happy(X0) | old(X0) [cnf transformation 37]
136. ~old(john) [cnf transformation 20]
142. rich(john) [cnf transformation 25]
143. ~humble(X0) | ~rich(X0) [duplicate literal removal 117]
336. humble(X0) | old(X0) [resolution 119,112]
375. ~rich(X0) | old(X0) [resolution 336,143]
525. old(john) [resolution 375,142]
527. $false [subsumption resolution 525,136]
% SZS output end Proof for 7491074974771658428161091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not quiet or old and vice versa.
Everyone who is not patient is both not patient and tall.
If john is both not rich and happy then someone is both funny and not funny.
If susan is either happy or not generous then mary is not tall.
If someone is both not quiet and not rich then someone is tall and vice versa.
If someone is not creative or not kind then someone is funny.
Everyone who is happy is not funny or not old.
Everyone who is kind is both not curious and not happy.
Everyone who is not rich is both not quiet and not creative and vice versa.
Everyone who is happy or generous is not happy or patient.
Everyone who is either not calm or not quiet is patient or not patient and vice versa.
Everyone who is not creative is brave or strong.
Everyone who is either not kind or calm is both not quiet and not calm.
Everyone who is curious is both not happy and tall and vice versa.
Everyone who is not funny is generous or not generous and vice versa.
If someone is either happy or creative then alice is not brave and vice versa.
Someone is not old.
Someone is both not tall and not strong.
Someone is not curious or not happy.
Lucy is either not patient or not humble. | Mary is tall. | contradiction | (![X]:(~rich(X)<=>(~quiet(X)<~>old(X))))&
(![X]:(~patient(X)=>(~patient(X)&tall(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((funny(X)&~funny(X)))))&
(((happy(susan)<~>~generous(susan)))=>(~tall(mary)))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:(tall(X))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(funny(X))))&
(![X]:(happy(X)=>(~funny(X)|~old(X))))&
(![X]:(kind(X)=>(~curious(X)&~happy(X))))&
(![X]:(~rich(X)<=>(~quiet(X)&~creative(X))))&
(![X]:((happy(X)|generous(X))=>(~happy(X)|patient(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(patient(X)|~patient(X))))&
(![X]:(~creative(X)=>(brave(X)|strong(X))))&
(![X]:((~kind(X)<~>calm(X))=>(~quiet(X)&~calm(X))))&
(![X]:(curious(X)<=>(~happy(X)&tall(X))))&
(![X]:(~funny(X)<=>(generous(X)|~generous(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(~brave(alice)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)&~strong(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~patient(lucy)<~>~humble(lucy))) | tall(mary) | [
"p4",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4486611406848547088850201
% SZS output start Proof for 4486611406848547088850201
5. ? [X0] : (~rich(X0) & ~quiet(X0)) <=> ? [X0] : tall(X0) [input p4]
6. ? [X0] : (~kind(X0) | ~creative(X0)) => ? [X0] : funny(X0) [input p5]
9. ! [X0] : (~rich(X0) <=> (~creative(X0) & ~quiet(X0))) [input p8]
15. ! [X0] : (~funny(X0) <=> (~generous(X0) | generous(X0))) [input p14]
21. tall(mary) [input hypothesis]
22. ? [X0] : (~rich(X0) & ~quiet(X0)) <=> ? [X1] : tall(X1) [rectify 5]
23. ? [X0] : (~kind(X0) | ~creative(X0)) => ? [X1] : funny(X1) [rectify 6]
29. ? [X1] : funny(X1) | ! [X0] : (kind(X0) & creative(X0)) [ennf transformation 23]
44. (? [X0] : (~rich(X0) & ~quiet(X0)) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : (rich(X0) | quiet(X0))) [nnf transformation 22]
45. (? [X0] : (~rich(X0) & ~quiet(X0)) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : (rich(X3) | quiet(X3))) [rectify 44]
46. ? [X0] : (~rich(X0) & ~quiet(X0)) => (~rich(sK1) & ~quiet(sK1)) [choice axiom]
47. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
48. ((~rich(sK1) & ~quiet(sK1)) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : (rich(X3) | quiet(X3))) [skolemisation 45,47,46]
49. ? [X0] : funny(X0) | ! [X1] : (kind(X1) & creative(X1)) [rectify 29]
50. ? [X0] : funny(X0) => funny(sK3) [choice axiom]
51. funny(sK3) | ! [X1] : (kind(X1) & creative(X1)) [skolemisation 49,50]
52. ! [X0] : ((~rich(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | rich(X0))) [nnf transformation 9]
53. ! [X0] : ((~rich(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | rich(X0))) [flattening 52]
57. ! [X0] : ((~funny(X0) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | funny(X0))) [nnf transformation 15]
58. ! [X0] : ((~funny(X0) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | funny(X0))) [flattening 57]
82. ~rich(sK1) | ~tall(X1) [cnf transformation 48]
83. funny(sK3) | creative(X1) [cnf transformation 51]
89. ~creative(X0) | rich(X0) [cnf transformation 53]
106. ~funny(X0) | ~generous(X0) [cnf transformation 58]
107. ~funny(X0) | generous(X0) [cnf transformation 58]
118. tall(mary) [cnf transformation 21]
144. 6 <=> tall(mary) [avatar definition]
145. tall(mary) <- (6) [avatar component clause 144]
150. 7 <=> ! [X1] : ~tall(X1) [avatar definition]
151. ~tall(X1) <- (7) [avatar component clause 150]
153. 8 <=> rich(sK1) [avatar definition]
155. ~rich(sK1) <- (~8) [avatar component clause 153]
156. 7 | ~8 [avatar split clause 82,153,150]
174. 13 <=> funny(sK3) [avatar definition]
176. funny(sK3) <- (13) [avatar component clause 174]
179. 14 <=> ! [X1] : creative(X1) [avatar definition]
180. creative(X1) <- (14) [avatar component clause 179]
181. 14 | 13 [avatar split clause 83,174,179]
185. ~funny(X0) [subsumption resolution 106,107]
227. 6 [avatar split clause 118,144]
228. $false <- (13) [subsumption resolution 176,185]
229. ~13 [avatar contradiction clause 228]
233. $false <- (6, 7) [resolution 151,145]
234. ~6 | ~7 [avatar contradiction clause 233]
239. rich(X0) <- (14) [resolution 89,180]
240. $false <- (~8, 14) [resolution 239,155]
241. 8 | ~14 [avatar contradiction clause 240]
242. $false [avatar sat refutation 156,181,227,229,234,241]
% SZS output end Proof for 4486611406848547088850201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not tall or curious and vice versa.
If someone is quiet then someone is generous.
Everyone who is not happy or patient is either kind or old and vice versa.
Everyone who is both funny and not strong is both happy and not kind and vice versa.
If fred is not old or curious then alice is either not wise or not creative.
If someone is not generous or not funny then fred is both patient and not patient and vice versa.
Everyone who is either humble or not humble is either not humble or not curious.
If someone is old or not happy then someone is patient or humble and vice versa.
If someone is either not strong or funny then someone is not quiet.
Everyone who is generous or wise is either not humble or kind and vice versa.
Everyone who is either not wise or funny is strong and vice versa.
Everyone who is calm or not old is either patient or not humble.
Everyone who is either creative or not kind is not wise.
Everyone who is not wise is both not old and brave.
If lucy is either not strong or quiet then someone is not happy or patient and vice versa.
If john is not brave then someone is not tall or kind and vice versa.
Someone is not funny or tall.
Someone is either generous or not calm.
Someone is both old and rich.
Paul is either humble or not kind.
Susan is either not generous or not creative.
Susan is not rich.
Someone is either old or generous. | John is not brave. | entailment | (![X]:(~generous(X)<=>(~tall(X)|curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)|patient(X))<=>(kind(X)<~>old(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)&~kind(X))))&
(((~old(fred)|curious(fred)))=>((~wise(alice)<~>~creative(alice))))&
((?[X]:((~generous(X)|~funny(X))))<=>((patient(fred)&~patient(fred))))&
(![X]:((humble(X)<~>~humble(X))=>(~humble(X)<~>~curious(X))))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:((patient(X)|humble(X)))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|wise(X))<=>(~humble(X)<~>kind(X))))&
(![X]:((~wise(X)<~>funny(X))<=>strong(X)))&
(![X]:((calm(X)|~old(X))=>(patient(X)<~>~humble(X))))&
(![X]:((creative(X)<~>~kind(X))=>~wise(X)))&
(![X]:(~wise(X)=>(~old(X)&brave(X))))&
(((~strong(lucy)<~>quiet(lucy)))<=>(?[X]:((~happy(X)|patient(X)))))&
((~brave(john))<=>(?[X]:((~tall(X)|kind(X)))))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((old(X)&rich(X))))&
((humble(paul)<~>~kind(paul)))&
((~generous(susan)<~>~creative(susan)))&
(~rich(susan))&
(?[X]:((old(X)<~>generous(X)))) | ~brave(john) | [
"p0",
"p5",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5037517523344005822480002
% SZS output start Proof for 5037517523344005822480002
1. ! [X0] : (~generous(X0) <=> (curious(X0) | ~tall(X0))) [input p0]
6. ? [X0] : (~funny(X0) | ~generous(X0)) <=> (~patient(fred) & patient(fred)) [input p5]
7. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (~humble(X0) <~> ~curious(X0))) [input p6]
16. ~brave(john) <=> ? [X0] : (kind(X0) | ~tall(X0)) [input p15]
20. humble(paul) <~> ~kind(paul) [input p19]
24. brave(john) [input hypothesis]
30. ! [X0] : ((~humble(X0) <~> ~curious(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 7]
35. ! [X0] : ((~generous(X0) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | generous(X0))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | generous(X0))) [flattening 35]
45. (? [X0] : (~funny(X0) | ~generous(X0)) | (patient(fred) | ~patient(fred))) & ((~patient(fred) & patient(fred)) | ! [X0] : (funny(X0) & generous(X0))) [nnf transformation 6]
46. (? [X0] : (~funny(X0) | ~generous(X0)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X0] : (funny(X0) & generous(X0))) [flattening 45]
47. (? [X0] : (~funny(X0) | ~generous(X0)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X1] : (funny(X1) & generous(X1))) [rectify 46]
48. ? [X0] : (~funny(X0) | ~generous(X0)) => (~funny(sK1) | ~generous(sK1)) [choice axiom]
49. ((~funny(sK1) | ~generous(sK1)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X1] : (funny(X1) & generous(X1))) [skolemisation 47,48]
50. ! [X0] : (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 30]
69. (~brave(john) | ! [X0] : (~kind(X0) & tall(X0))) & (? [X0] : (kind(X0) | ~tall(X0)) | brave(john)) [nnf transformation 16]
70. (~brave(john) | ! [X0] : (~kind(X0) & tall(X0))) & (? [X1] : (kind(X1) | ~tall(X1)) | brave(john)) [rectify 69]
71. ? [X1] : (kind(X1) | ~tall(X1)) => (kind(sK6) | ~tall(sK6)) [choice axiom]
72. (~brave(john) | ! [X0] : (~kind(X0) & tall(X0))) & ((kind(sK6) | ~tall(sK6)) | brave(john)) [skolemisation 70,71]
80. (kind(paul) | ~humble(paul)) & (~kind(paul) | humble(paul)) [nnf transformation 20]
87. ~curious(X0) | ~generous(X0) [cnf transformation 36]
103. patient(fred) | generous(X1) [cnf transformation 49]
105. ~patient(fred) | generous(X1) [cnf transformation 49]
111. curious(X0) | humble(X0) | humble(X0) | humble(X0) [cnf transformation 50]
144. ~brave(john) | ~kind(X0) [cnf transformation 72]
151. kind(paul) | ~humble(paul) [cnf transformation 80]
157. brave(john) [cnf transformation 24]
161. humble(X0) | curious(X0) [duplicate literal removal 111]
194. 8 <=> patient(fred) [avatar definition]
199. 9 <=> ! [X1] : generous(X1) [avatar definition]
200. generous(X1) <- (9) [avatar component clause 199]
201. 9 | ~8 [avatar split clause 105,194,199]
203. 9 | 8 [avatar split clause 103,194,199]
271. 25 <=> ! [X0] : ~kind(X0) [avatar definition]
272. ~kind(X0) <- (25) [avatar component clause 271]
274. 26 <=> brave(john) [avatar definition]
277. 25 | ~26 [avatar split clause 144,274,271]
311. 34 <=> humble(paul) [avatar definition]
313. ~humble(paul) <- (~34) [avatar component clause 311]
315. 35 <=> kind(paul) [avatar definition]
317. kind(paul) <- (35) [avatar component clause 315]
318. ~34 | 35 [avatar split clause 151,315,311]
340. 26 [avatar split clause 157,274]
350. curious(paul) <- (~34) [resolution 161,313]
353. ~generous(paul) <- (~34) [resolution 350,87]
354. $false <- (9, ~34) [subsumption resolution 353,200]
355. ~9 | 34 [avatar contradiction clause 354]
356. $false <- (25, 35) [subsumption resolution 317,272]
357. ~25 | ~35 [avatar contradiction clause 356]
358. $false [avatar sat refutation 201,203,277,318,340,355,357]
% SZS output end Proof for 5037517523344005822480002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or creative is either quiet or creative.
Everyone who is generous is not happy and vice versa.
Everyone who is both tall and not generous is creative.
If someone is not creative or rich then someone is both generous and tall.
If someone is either not generous or not humble then someone is wise.
If someone is either patient or creative then someone is old or calm.
Everyone who is either wise or not funny is happy and vice versa.
If someone is either not funny or not brave then someone is both happy and quiet.
Everyone who is either not tall or not generous is not curious or creative and vice versa.
If someone is either wise or not calm then lucy is not humble and vice versa.
If someone is either creative or strong then someone is both not wise and wise.
Everyone who is both not generous and not strong is not creative.
If mary is either creative or not patient then someone is both not rich and rich.
Everyone who is both not tall and not curious is either happy or not calm and vice versa.
Everyone who is both not creative and patient is not generous and vice versa.
Everyone who is both patient and not rich is both not strong and not rich.
Someone is not strong or not old.
Someone is both humble and patient.
Alice is both wise and tall.
Mary is not humble.
Mary is not quiet.
Someone is both kind and funny.
Someone is wise.
Someone is old or quiet. | Lucy is humble. | contradiction | (![X]:((humble(X)<~>creative(X))=>(quiet(X)<~>creative(X))))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((tall(X)&~generous(X))=>creative(X)))&
((?[X]:((~creative(X)|rich(X))))=>(?[X]:((generous(X)&tall(X)))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((old(X)|calm(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>happy(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~curious(X)|creative(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(~humble(lucy)))&
((?[X]:((creative(X)<~>strong(X))))=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((~generous(X)&~strong(X))=>~creative(X)))&
(((creative(mary)<~>~patient(mary)))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((~tall(X)&~curious(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~creative(X)&patient(X))<=>~generous(X)))&
(![X]:((patient(X)&~rich(X))=>(~strong(X)&~rich(X))))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((humble(X)&patient(X))))&
((wise(alice)&tall(alice)))&
(~humble(mary))&
(~quiet(mary))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:(wise(X)))&
(?[X]:((old(X)|quiet(X)))) | humble(lucy) | [
"p1",
"p2",
"p9",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 335084139409588822775106
% SZS output start Proof for 335084139409588822775106
2. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p1]
3. ! [X0] : ((~generous(X0) & tall(X0)) => creative(X0)) [input p2]
10. ? [X0] : (wise(X0) <~> ~calm(X0)) <=> ~humble(lucy) [input p9]
14. ! [X0] : ((~curious(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~generous(X0)) [input p14]
19. tall(alice) & wise(alice) [input p18]
25. humble(lucy) [input hypothesis]
33. ! [X0] : (creative(X0) | (generous(X0) | ~tall(X0))) [ennf transformation 3]
34. ! [X0] : (creative(X0) | generous(X0) | ~tall(X0)) [flattening 33]
46. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 2]
65. (? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | humble(lucy)) & (~humble(lucy) | ! [X0] : ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) [nnf transformation 10]
66. (? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((wise(X1) | calm(X1)) & (~calm(X1) | ~wise(X1)))) [rectify 65]
67. ? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) => ((calm(sK4) | ~wise(sK4)) & (~calm(sK4) | wise(sK4))) [choice axiom]
68. (((calm(sK4) | ~wise(sK4)) & (~calm(sK4) | wise(sK4))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((wise(X1) | calm(X1)) & (~calm(X1) | ~wise(X1)))) [skolemisation 66,67]
76. ! [X0] : (((~curious(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (curious(X0) | tall(X0)))) [nnf transformation 14]
77. ! [X0] : (((~curious(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | curious(X0) | tall(X0))) [flattening 76]
78. ! [X0] : (((patient(X0) & ~creative(X0)) | generous(X0)) & (~generous(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 15]
79. ! [X0] : (((patient(X0) & ~creative(X0)) | generous(X0)) & (~generous(X0) | ~patient(X0) | creative(X0))) [flattening 78]
94. ~happy(X0) | ~generous(X0) [cnf transformation 46]
96. ~tall(X0) | generous(X0) | creative(X0) [cnf transformation 34]
119. ~humble(lucy) | ~calm(X1) | ~wise(X1) [cnf transformation 68]
135. ~tall(X0) | happy(X0) | calm(X0) [cnf transformation 77]
139. ~creative(X0) | generous(X0) [cnf transformation 79]
146. wise(alice) [cnf transformation 19]
147. tall(alice) [cnf transformation 19]
153. humble(lucy) [cnf transformation 25]
221. 16 <=> humble(lucy) [avatar definition]
239. 20 <=> ! [X1] : (~calm(X1) | ~wise(X1)) [avatar definition]
240. ~calm(X1) | ~wise(X1) <- (20) [avatar component clause 239]
241. 20 | ~16 [avatar split clause 119,221,239]
290. 16 [avatar split clause 153,221]
296. generous(alice) | creative(alice) [resolution 96,147]
298. generous(alice) [subsumption resolution 296,139]
321. 33 <=> happy(alice) [avatar definition]
322. happy(alice) <- (33) [avatar component clause 321]
323. ~happy(alice) <- (~33) [avatar component clause 321]
370. happy(alice) | calm(alice) [resolution 135,147]
372. calm(alice) <- (~33) [subsumption resolution 370,323]
402. ~wise(alice) <- (20, ~33) [resolution 372,240]
403. $false <- (20, ~33) [subsumption resolution 402,146]
404. ~20 | 33 [avatar contradiction clause 403]
413. ~generous(alice) <- (33) [resolution 322,94]
414. $false <- (33) [subsumption resolution 413,298]
415. ~33 [avatar contradiction clause 414]
416. $false [avatar sat refutation 241,290,404,415]
% SZS output end Proof for 335084139409588822775106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then paul is calm or not wise and vice versa. If someone is not generous or not wise then susan is both not kind and not old. If alice is either generous or patient then someone is not creative or not humble. Everyone who is both brave and not humble is patient or not kind and vice versa. Everyone who is either not old or not brave is rich or curious. If someone is not brave or kind then mary is both tall and creative. If paul is either not tall or not generous then someone is either quiet or not quiet and vice versa. Everyone who is calm is either quiet or not generous and vice versa. If someone is not quiet or not humble then fred is either creative or not happy. Everyone who is either not kind or quiet is both not humble and not happy. If susan is either not old or patient then john is both not old and not patient and vice versa. Everyone who is both not creative and not calm is funny or generous and vice versa. Everyone who is either humble or kind is not quiet. Everyone who is tall or kind is strong. If someone is either generous or humble then someone is not rich. If someone is either old or not funny then someone is kind. Someone is not quiet or creative. Lucy is either quiet or tall. Mary is both funny and not happy. Lucy is either humble or rich. Lucy is tall or not generous. Fred is old. Someone is not funny. | John is not brave. | contradiction | ((?[X]:(~generous(X)))<=>((calm(paul)|~wise(paul))))&
((?[X]:((~generous(X)|~wise(X))))=>((~kind(susan)&~old(susan))))&
(((generous(alice)<~>patient(alice)))=>(?[X]:((~creative(X)|~humble(X)))))&
(![X]:((brave(X)&~humble(X))<=>(patient(X)|~kind(X))))&
(![X]:((~old(X)<~>~brave(X))=>(rich(X)|curious(X))))&
((?[X]:((~brave(X)|kind(X))))=>((tall(mary)&creative(mary))))&
(((~tall(paul)<~>~generous(paul)))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(calm(X)<=>(quiet(X)<~>~generous(X))))&
((?[X]:((~quiet(X)|~humble(X))))=>((creative(fred)<~>~happy(fred))))&
(![X]:((~kind(X)<~>quiet(X))=>(~humble(X)&~happy(X))))&
(((~old(susan)<~>patient(susan)))<=>((~old(john)&~patient(john))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|generous(X))))&
(![X]:((humble(X)<~>kind(X))=>~quiet(X)))&
(![X]:((tall(X)|kind(X))=>strong(X)))&
((?[X]:((generous(X)<~>humble(X))))=>(?[X]:(~rich(X))))&
((?[X]:((old(X)<~>~funny(X))))=>(?[X]:(kind(X))))&
(?[X]:((~quiet(X)|creative(X))))&
((quiet(lucy)<~>tall(lucy)))&
((funny(mary)&~happy(mary)))&
((humble(lucy)<~>rich(lucy)))&
((tall(lucy)|~generous(lucy)))&
(old(fred))&
(?[X]:(~funny(X))) | ~brave(john) | [
"p5",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3141089603173837496906115
% SZS output start Proof for 3141089603173837496906115
6. ? [X0] : (kind(X0) | ~brave(X0)) => (creative(mary) & tall(mary)) [input p5]
12. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (generous(X0) | funny(X0))) [input p11]
19. ~happy(mary) & funny(mary) [input p18]
24. ~brave(john) [input hypothesis]
31. (creative(mary) & tall(mary)) | ! [X0] : (~kind(X0) & brave(X0)) [ennf transformation 6]
56. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 12]
57. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | calm(X0) | creative(X0))) [flattening 56]
89. creative(mary) | brave(X0) [cnf transformation 31]
118. ~funny(X0) | ~creative(X0) [cnf transformation 57]
131. funny(mary) [cnf transformation 19]
138. ~brave(john) [cnf transformation 24]
198. 13 <=> creative(mary) [avatar definition]
200. creative(mary) <- (13) [avatar component clause 198]
203. 14 <=> ! [X0] : brave(X0) [avatar definition]
204. brave(X0) <- (14) [avatar component clause 203]
205. 14 | 13 [avatar split clause 89,198,203]
323. $false <- (14) [resolution 204,138]
324. ~14 [avatar contradiction clause 323]
330. ~creative(mary) [resolution 118,131]
331. $false <- (13) [subsumption resolution 330,200]
332. ~13 [avatar contradiction clause 331]
333. $false [avatar sat refutation 205,324,332]
% SZS output end Proof for 3141089603173837496906115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not strong then someone is wise. Everyone who is not humble is not strong. Everyone who is either funny or kind is both not brave and tall. Everyone who is patient is either not funny or not tall and vice versa. Everyone who is patient is both not kind and humble and vice versa. Everyone who is tall or not rich is strong. If someone is not patient then someone is either creative or not generous. Everyone who is not generous is not wise. Everyone who is both not rich and tall is not generous. Everyone who is either not funny or rich is patient. Everyone who is both kind and not generous is either not calm or rich and vice versa. Everyone who is not generous is patient and vice versa. Everyone who is creative is either rich or not quiet and vice versa. If someone is kind or not happy then someone is both not generous and not humble and vice versa. Everyone who is either generous or strong is both not wise and not brave and vice versa. Everyone who is both curious and not wise is not generous and vice versa. Someone is quiet or generous. Someone is not happy or not quiet. Alice is humble or funny. Someone is not wise or quiet. | Alice is tall. | entailment | ((?[X]:((creative(X)|~strong(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((funny(X)<~>kind(X))=>(~brave(X)&tall(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
((humble(alice)|funny(alice)))&
(?[X]:((~wise(X)|quiet(X)))) | tall(alice) | [
"p2",
"p3",
"p4",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8903610657940769833754339
% SZS output start Proof for 8903610657940769833754339
3. ! [X0] : ((funny(X0) <~> kind(X0)) => (tall(X0) & ~brave(X0))) [input p2]
4. ! [X0] : (patient(X0) <=> (~funny(X0) <~> ~tall(X0))) [input p3]
5. ! [X0] : (patient(X0) <=> (humble(X0) & ~kind(X0))) [input p4]
12. ! [X0] : (~generous(X0) <=> patient(X0)) [input p11]
14. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X0] : (~humble(X0) & ~generous(X0)) [input p13]
19. funny(alice) | humble(alice) [input p18]
21. ~tall(alice) [input hypothesis]
24. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X1] : (~humble(X1) & ~generous(X1)) [rectify 14]
27. ! [X0] : ((tall(X0) & ~brave(X0)) | (funny(X0) <=> kind(X0))) [ennf transformation 3]
37. ! [X0] : ((tall(X0) & ~brave(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) [nnf transformation 27]
38. ! [X0] : ((patient(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ~patient(X0))) [nnf transformation 4]
39. ! [X0] : ((patient(X0) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [nnf transformation 5]
40. ! [X0] : ((patient(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [flattening 39]
48. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 12]
50. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X1] : (~humble(X1) & ~generous(X1)) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 24]
51. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X2] : (~humble(X2) & ~generous(X2)) | ! [X3] : (happy(X3) & ~kind(X3))) [rectify 50]
52. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK2) | kind(sK2)) [choice axiom]
53. ? [X2] : (~humble(X2) & ~generous(X2)) => (~humble(sK3) & ~generous(sK3)) [choice axiom]
54. ((~happy(sK2) | kind(sK2)) | ! [X1] : (humble(X1) | generous(X1))) & ((~humble(sK3) & ~generous(sK3)) | ! [X3] : (happy(X3) & ~kind(X3))) [skolemisation 51,53,52]
70. ~funny(X0) | kind(X0) | tall(X0) [cnf transformation 37]
73. ~patient(X0) | funny(X0) | tall(X0) [cnf transformation 38]
77. ~patient(X0) | humble(X0) [cnf transformation 40]
78. ~humble(X0) | patient(X0) | kind(X0) [cnf transformation 40]
93. generous(X0) | patient(X0) [cnf transformation 48]
99. ~generous(sK3) | ~kind(X3) [cnf transformation 54]
101. ~humble(sK3) | ~kind(X3) [cnf transformation 54]
115. funny(alice) | humble(alice) [cnf transformation 19]
117. ~tall(alice) [cnf transformation 21]
159. 11 <=> humble(sK3) [avatar definition]
164. 12 <=> ! [X3] : ~kind(X3) [avatar definition]
165. ~kind(X3) <- (12) [avatar component clause 164]
166. 12 | ~11 [avatar split clause 101,159,164]
168. 13 <=> generous(sK3) [avatar definition]
170. ~generous(sK3) <- (~13) [avatar component clause 168]
172. 12 | ~13 [avatar split clause 99,168,164]
194. 18 <=> humble(alice) [avatar definition]
196. humble(alice) <- (18) [avatar component clause 194]
198. 19 <=> funny(alice) [avatar definition]
200. funny(alice) <- (19) [avatar component clause 198]
201. 18 | 19 [avatar split clause 115,198,194]
213. patient(sK3) <- (~13) [resolution 93,170]
218. humble(sK3) <- (~13) [resolution 213,77]
222. 11 | 13 [avatar split clause 218,168,159]
273. patient(alice) | kind(alice) <- (18) [resolution 78,196]
277. patient(alice) <- (12, 18) [subsumption resolution 273,165]
298. funny(alice) | tall(alice) <- (12, 18) [resolution 277,73]
302. funny(alice) <- (12, 18) [subsumption resolution 298,117]
303. 19 | ~12 | ~18 [avatar split clause 302,194,164,198]
305. kind(alice) | tall(alice) <- (19) [resolution 200,70]
306. tall(alice) <- (12, 19) [subsumption resolution 305,165]
307. $false <- (12, 19) [subsumption resolution 306,117]
308. ~12 | ~19 [avatar contradiction clause 307]
309. $false [avatar sat refutation 166,172,201,222,303,308]
% SZS output end Proof for 8903610657940769833754339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and strong is either not wise or not calm.
Everyone who is not calm is wise and vice versa.
Everyone who is either wise or not generous is both not tall and not creative.
If fred is happy then fred is not old.
If lucy is either curious or not calm then someone is funny or not calm.
If someone is both not calm and not creative then lucy is not happy or humble.
Everyone who is not brave or strong is both not calm and not old and vice versa.
Everyone who is old is both not old and not quiet and vice versa.
If someone is both calm and rich then lucy is tall or not funny.
Everyone who is both not rich and not old is either not kind or not creative and vice versa.
If paul is either curious or not strong then someone is strong or not funny and vice versa.
If someone is creative or not tall then someone is generous.
If someone is either kind or tall then someone is humble and vice versa.
Everyone who is not brave or not old is not patient and vice versa.
Everyone who is kind or generous is either not happy or tall.
Everyone who is either not generous or strong is not rich or generous and vice versa.
Paul is creative.
Someone is either quiet or creative.
Paul is not strong or kind.
Paul is not tall.
Someone is wise.
Susan is not humble.
Someone is not rich.
John is calm or tall. | Paul is wise. | entailment | (![X]:((brave(X)&strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:(~calm(X)<=>wise(X)))&
(![X]:((wise(X)<~>~generous(X))=>(~tall(X)&~creative(X))))&
((happy(fred))=>(~old(fred)))&
(((curious(lucy)<~>~calm(lucy)))=>(?[X]:((funny(X)|~calm(X)))))&
((?[X]:((~calm(X)&~creative(X))))=>((~happy(lucy)|humble(lucy))))&
(![X]:((~brave(X)|strong(X))<=>(~calm(X)&~old(X))))&
(![X]:(old(X)<=>(~old(X)&~quiet(X))))&
((?[X]:((calm(X)&rich(X))))=>((tall(lucy)|~funny(lucy))))&
(![X]:((~rich(X)&~old(X))<=>(~kind(X)<~>~creative(X))))&
(((curious(paul)<~>~strong(paul)))<=>(?[X]:((strong(X)|~funny(X)))))&
((?[X]:((creative(X)|~tall(X))))=>(?[X]:(generous(X))))&
((?[X]:((kind(X)<~>tall(X))))<=>(?[X]:(humble(X))))&
(![X]:((~brave(X)|~old(X))<=>~patient(X)))&
(![X]:((kind(X)|generous(X))=>(~happy(X)<~>tall(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(~rich(X)|generous(X))))&
(creative(paul))&
(?[X]:((quiet(X)<~>creative(X))))&
((~strong(paul)|kind(paul)))&
(~tall(paul))&
(?[X]:(wise(X)))&
(~humble(susan))&
(?[X]:(~rich(X)))&
((calm(john)|tall(john))) | wise(paul) | [
"p1",
"p2",
"p6",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7654618528009317593195465
% SZS output start Proof for 7654618528009317593195465
2. ! [X0] : (~calm(X0) <=> wise(X0)) [input p1]
3. ! [X0] : ((wise(X0) <~> ~generous(X0)) => (~creative(X0) & ~tall(X0))) [input p2]
7. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (~old(X0) & ~calm(X0))) [input p6]
16. ! [X0] : ((~generous(X0) <~> strong(X0)) <=> (generous(X0) | ~rich(X0))) [input p15]
17. creative(paul) [input p16]
25. ~wise(paul) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~tall(X0)) | (wise(X0) <=> ~generous(X0))) [ennf transformation 3]
40. ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))) [nnf transformation 2]
41. ! [X0] : ((~creative(X0) & ~tall(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0)))) [nnf transformation 30]
45. ! [X0] : (((strong(X0) | ~brave(X0)) | (old(X0) | calm(X0))) & ((~old(X0) & ~calm(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 7]
46. ! [X0] : ((strong(X0) | ~brave(X0) | old(X0) | calm(X0)) & ((~old(X0) & ~calm(X0)) | (~strong(X0) & brave(X0)))) [flattening 45]
64. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~generous(X0) & rich(X0))) & ((generous(X0) | ~rich(X0)) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [nnf transformation 16]
65. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~generous(X0) & rich(X0))) & (generous(X0) | ~rich(X0) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [flattening 64]
75. calm(X0) | wise(X0) [cnf transformation 40]
80. ~creative(X0) | wise(X0) | generous(X0) [cnf transformation 41]
86. ~calm(X0) | ~strong(X0) [cnf transformation 46]
119. strong(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 65]
122. creative(paul) [cnf transformation 17]
131. ~wise(paul) [cnf transformation 25]
133. ~generous(X0) | strong(X0) [duplicate literal removal 119]
197. 15 <=> strong(paul) [avatar definition]
199. strong(paul) <- (15) [avatar component clause 197]
287. ~strong(X0) | wise(X0) [resolution 86,75]
295. wise(paul) | generous(paul) [resolution 80,122]
296. generous(paul) [subsumption resolution 295,131]
297. strong(paul) [resolution 296,133]
300. 15 [avatar split clause 297,197]
301. wise(paul) <- (15) [resolution 199,287]
302. $false <- (15) [subsumption resolution 301,131]
303. ~15 [avatar contradiction clause 302]
304. $false [avatar sat refutation 300,303]
% SZS output end Proof for 7654618528009317593195465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
If someone is not creative or not tall then susan is not brave and vice versa.
Everyone who is creative or kind is both patient and not creative and vice versa.
Everyone who is brave is not funny or not wise and vice versa.
Everyone who is either not rich or curious is not patient or generous and vice versa.
Everyone who is either not funny or curious is both not rich and strong.
Someone is quiet or old.
Paul is either brave or calm.
Paul is kind or humble.
Someone is not strong.
Someone is both calm and rich.
Mary is not rich.
Someone is both strong and quiet. | Paul is not wise. | contradiction | (((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))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>(~brave(susan)))&
(![X]:((creative(X)|kind(X))<=>(patient(X)&~creative(X))))&
(![X]:(brave(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~patient(X)|generous(X))))&
(![X]:((~funny(X)<~>curious(X))=>(~rich(X)&strong(X))))&
(?[X]:((quiet(X)|old(X))))&
((brave(paul)<~>calm(paul)))&
((kind(paul)|humble(paul)))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)&rich(X))))&
(~rich(mary))&
(?[X]:((strong(X)&quiet(X)))) | ~wise(paul) | [
"p8",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 514775168397122336590771
% SZS output start Proof for 514775168397122336590771
9. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p8]
13. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) & patient(X0))) [input p12]
14. ! [X0] : (brave(X0) <=> (~wise(X0) | ~funny(X0))) [input p13]
18. brave(paul) <~> calm(paul) [input p17]
24. ~wise(paul) [input hypothesis]
32. ! [X0] : ((generous(X0) & creative(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 9]
61. ! [X0] : (((kind(X0) | creative(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 13]
62. ! [X0] : ((kind(X0) | creative(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 61]
63. ! [X0] : ((brave(X0) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | ~brave(X0))) [nnf transformation 14]
64. ! [X0] : ((brave(X0) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~brave(X0))) [flattening 63]
70. (~calm(paul) | ~brave(paul)) & (calm(paul) | brave(paul)) [nnf transformation 18]
111. creative(X0) | calm(X0) [cnf transformation 32]
131. ~creative(X0) | ~creative(X0) [cnf transformation 62]
136. wise(X0) | brave(X0) [cnf transformation 64]
149. ~calm(paul) | ~brave(paul) [cnf transformation 70]
157. ~wise(paul) [cnf transformation 24]
158. ~creative(X0) [duplicate literal removal 131]
291. 29 <=> brave(paul) [avatar definition]
293. ~brave(paul) <- (~29) [avatar component clause 291]
295. 30 <=> calm(paul) [avatar definition]
297. ~calm(paul) <- (~30) [avatar component clause 295]
298. ~29 | ~30 [avatar split clause 149,295,291]
306. calm(X0) [resolution 111,158]
307. $false <- (~30) [resolution 306,297]
308. 30 [avatar contradiction clause 307]
317. brave(paul) [resolution 136,157]
319. $false <- (~29) [subsumption resolution 317,293]
320. 29 [avatar contradiction clause 319]
321. $false [avatar sat refutation 298,308,320]
% SZS output end Proof for 514775168397122336590771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and curious is not old or not rich.
If someone is both funny and not tall then someone is not creative.
If lucy is old or brave then paul is strong and vice versa.
Everyone who is not quiet is either not tall or tall.
Everyone who is not quiet or wise is patient or generous.
If someone is calm then paul is not happy or patient.
If someone is both wise and quiet then someone is both not brave and not kind.
Everyone who is tall is either not quiet or tall.
Everyone who is either not curious or not kind is happy or not tall.
Everyone who is both rich and tall is both not funny and patient.
If lucy is funny or not wise then someone is both strong and wise.
Everyone who is both quiet and not patient is both wise and brave and vice versa.
Everyone who is either not kind or not funny is either not strong or not creative.
If paul is both old and not calm then susan is humble.
Everyone who is either funny or not brave is not curious and vice versa.
If someone is both not generous and not wise then someone is either not humble or humble and vice versa.
Paul is either not calm or not quiet.
Someone is both old and quiet.
Fred is both rich and creative.
Someone is not patient or tall.
Susan is rich.
Someone is not generous or not funny.
Paul is both kind and not brave.
Someone is not quiet or not tall. | Fred is humble. | neutral | (![X]:((wise(X)&curious(X))=>(~old(X)|~rich(X))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:(~creative(X))))&
(((old(lucy)|brave(lucy)))<=>(strong(paul)))&
(![X]:(~quiet(X)=>(~tall(X)<~>tall(X))))&
(![X]:((~quiet(X)|wise(X))=>(patient(X)|generous(X))))&
((?[X]:(calm(X)))=>((~happy(paul)|patient(paul))))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:(tall(X)=>(~quiet(X)<~>tall(X))))&
(![X]:((~curious(X)<~>~kind(X))=>(happy(X)|~tall(X))))&
(![X]:((rich(X)&tall(X))=>(~funny(X)&patient(X))))&
(((funny(lucy)|~wise(lucy)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(wise(X)&brave(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~strong(X)<~>~creative(X))))&
(((old(paul)&~calm(paul)))=>(humble(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
((~calm(paul)<~>~quiet(paul)))&
(?[X]:((old(X)&quiet(X))))&
((rich(fred)&creative(fred)))&
(?[X]:((~patient(X)|tall(X))))&
(rich(susan))&
(?[X]:((~generous(X)|~funny(X))))&
((kind(paul)&~brave(paul)))&
(?[X]:((~quiet(X)|~tall(X)))) | humble(fred) | [] | null | 0 |
If someone is either patient or humble then someone is not wise or not brave and vice versa.
Everyone who is not old is both funny and not happy.
Everyone who is either brave or humble is patient and vice versa.
If john is both brave and quiet then fred is both not creative and kind and vice versa.
Everyone who is not kind is either strong or quiet.
If john is both kind and patient then paul is both not brave and not strong.
Everyone who is not quiet is both old and not patient and vice versa.
If someone is both not creative and not calm then lucy is funny or not kind.
Everyone who is not rich is both not funny and tall and vice versa.
Everyone who is both curious and not wise is not happy and vice versa.
Everyone who is both not calm and funny is both curious and wise and vice versa.
Everyone who is either not strong or quiet is both not brave and not old and vice versa.
If lucy is either not patient or not tall then someone is brave or not kind.
Everyone who is not rich is not tall or generous.
Everyone who is either not generous or not curious is not curious or rich and vice versa.
Everyone who is either kind or not brave is either not wise or not generous and vice versa.
Susan is either generous or old.
Fred is both humble and happy.
Someone is both not calm and not strong.
John is either not kind or kind.
Someone is not rich.
Someone is not generous or not calm.
Someone is not kind or funny.
Susan is either rich or not rich. | Susan is generous. | contradiction | ((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~old(X)=>(funny(X)&~happy(X))))&
(![X]:((brave(X)<~>humble(X))<=>patient(X)))&
(((brave(john)&quiet(john)))<=>((~creative(fred)&kind(fred))))&
(![X]:(~kind(X)=>(strong(X)<~>quiet(X))))&
(((kind(john)&patient(john)))=>((~brave(paul)&~strong(paul))))&
(![X]:(~quiet(X)<=>(old(X)&~patient(X))))&
((?[X]:((~creative(X)&~calm(X))))=>((funny(lucy)|~kind(lucy))))&
(![X]:(~rich(X)<=>(~funny(X)&tall(X))))&
(![X]:((curious(X)&~wise(X))<=>~happy(X)))&
(![X]:((~calm(X)&funny(X))<=>(curious(X)&wise(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~brave(X)&~old(X))))&
(((~patient(lucy)<~>~tall(lucy)))=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:(~rich(X)=>(~tall(X)|generous(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~curious(X)|rich(X))))&
(![X]:((kind(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((generous(susan)<~>old(susan)))&
((humble(fred)&happy(fred)))&
(?[X]:((~calm(X)&~strong(X))))&
((~kind(john)<~>kind(john)))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((~kind(X)|funny(X))))&
((rich(susan)<~>~rich(susan))) | generous(susan) | [
"p1",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7464367888757714498653924
% SZS output start Proof for 7464367888757714498653924
2. ! [X0] : (~old(X0) => (~happy(X0) & funny(X0))) [input p1]
9. ! [X0] : (~rich(X0) <=> (tall(X0) & ~funny(X0))) [input p8]
10. ! [X0] : ((~wise(X0) & curious(X0)) <=> ~happy(X0)) [input p9]
15. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> (rich(X0) | ~curious(X0))) [input p14]
17. generous(susan) <~> old(susan) [input p16]
25. generous(susan) [input hypothesis]
27. ! [X0] : ((~happy(X0) & funny(X0)) | old(X0)) [ennf transformation 2]
47. ! [X0] : ((~rich(X0) | (~tall(X0) | funny(X0))) & ((tall(X0) & ~funny(X0)) | rich(X0))) [nnf transformation 9]
48. ! [X0] : ((~rich(X0) | ~tall(X0) | funny(X0)) & ((tall(X0) & ~funny(X0)) | rich(X0))) [flattening 47]
49. ! [X0] : (((~wise(X0) & curious(X0)) | happy(X0)) & (~happy(X0) | (wise(X0) | ~curious(X0)))) [nnf transformation 10]
50. ! [X0] : (((~wise(X0) & curious(X0)) | happy(X0)) & (~happy(X0) | wise(X0) | ~curious(X0))) [flattening 49]
58. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 15]
59. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [flattening 58]
61. (~old(susan) | ~generous(susan)) & (old(susan) | generous(susan)) [nnf transformation 17]
78. funny(X0) | old(X0) [cnf transformation 27]
79. ~happy(X0) | old(X0) [cnf transformation 27]
96. ~funny(X0) | rich(X0) [cnf transformation 48]
100. curious(X0) | happy(X0) [cnf transformation 50]
118. ~generous(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 59]
130. ~old(susan) | ~generous(susan) [cnf transformation 61]
142. generous(susan) [cnf transformation 25]
252. 24 <=> generous(susan) [avatar definition]
253. generous(susan) <- (24) [avatar component clause 252]
256. 25 <=> old(susan) [avatar definition]
258. ~old(susan) <- (~25) [avatar component clause 256]
259. ~24 | ~25 [avatar split clause 130,256,252]
279. 24 [avatar split clause 142,252]
282. rich(X0) | old(X0) [resolution 96,78]
328. ~curious(susan) | ~rich(susan) <- (24) [resolution 118,253]
332. 34 <=> rich(susan) [avatar definition]
334. ~rich(susan) <- (~34) [avatar component clause 332]
336. 35 <=> curious(susan) [avatar definition]
338. ~curious(susan) <- (~35) [avatar component clause 336]
339. ~34 | ~35 | ~24 [avatar split clause 328,252,336,332]
346. old(susan) <- (~34) [resolution 334,282]
347. $false <- (~25, ~34) [subsumption resolution 346,258]
348. 25 | 34 [avatar contradiction clause 347]
370. happy(susan) <- (~35) [resolution 338,100]
426. old(susan) <- (~35) [resolution 370,79]
427. $false <- (~25, ~35) [subsumption resolution 426,258]
428. 25 | 35 [avatar contradiction clause 427]
429. $false [avatar sat refutation 259,279,339,348,428]
% SZS output end Proof for 7464367888757714498653924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not patient is not old and vice versa.
If someone is humble then someone is both humble and not humble.
Everyone who is either patient or not old is either not rich or not kind and vice versa.
Everyone who is both patient and not strong is old and vice versa.
Everyone who is old or not tall is either not calm or quiet and vice versa.
Everyone who is rich is tall or curious and vice versa.
If fred is either not wise or not strong then someone is either not funny or strong.
If someone is happy then susan is not quiet and vice versa.
Everyone who is funny or humble is either not calm or not rich and vice versa.
If john is rich then someone is both not rich and not strong.
If someone is not rich or not patient then someone is both not kind and not old.
Everyone who is quiet or not happy is either strong or quiet and vice versa.
If john is happy or creative then someone is quiet and vice versa.
Everyone who is both not quiet and patient is either brave or not humble.
If someone is kind then someone is not happy.
John is both not happy and old.
Mary is either funny or not old.
John is either not kind or not generous.
John is not humble or not patient.
Fred is both wise and not happy.
Alice is both not wise and curious. | John is brave. | contradiction | (![X]:((brave(X)<~>~patient(X))<=>~old(X)))&
((?[X]:(humble(X)))=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((patient(X)<~>~old(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:((patient(X)&~strong(X))<=>old(X)))&
(![X]:((old(X)|~tall(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|curious(X))))&
(((~wise(fred)<~>~strong(fred)))=>(?[X]:((~funny(X)<~>strong(X)))))&
((?[X]:(happy(X)))<=>(~quiet(susan)))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)<~>~rich(X))))&
((rich(john))=>(?[X]:((~rich(X)&~strong(X)))))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)<~>quiet(X))))&
(((happy(john)|creative(john)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&patient(X))=>(brave(X)<~>~humble(X))))&
((?[X]:(kind(X)))=>(?[X]:(~happy(X))))&
((~happy(john)&old(john)))&
((funny(mary)<~>~old(mary)))&
((~kind(john)<~>~generous(john)))&
((~humble(john)|~patient(john)))&
((wise(fred)&~happy(fred)))&
((~wise(alice)&curious(alice))) | brave(john) | [
"p0",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4077915260226624200315768
% SZS output start Proof for 4077915260226624200315768
1. ! [X0] : ((brave(X0) <~> ~patient(X0)) <=> ~old(X0)) [input p0]
4. ! [X0] : ((~strong(X0) & patient(X0)) <=> old(X0)) [input p3]
16. old(john) & ~happy(john) [input p15]
22. brave(john) [input hypothesis]
33. ! [X0] : ((((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | old(X0)) & (~old(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0))))) [nnf transformation 1]
38. ! [X0] : (((~strong(X0) & patient(X0)) | ~old(X0)) & (old(X0) | (strong(X0) | ~patient(X0)))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) & patient(X0)) | ~old(X0)) & (old(X0) | strong(X0) | ~patient(X0))) [flattening 38]
71. ~old(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 33]
86. ~old(X0) | patient(X0) [cnf transformation 39]
128. old(john) [cnf transformation 16]
138. brave(john) [cnf transformation 22]
267. 28 <=> patient(john) [avatar definition]
268. patient(john) <- (28) [avatar component clause 267]
272. patient(john) [resolution 86,128]
273. 28 [avatar split clause 272,267]
275. ~patient(john) | ~brave(john) [resolution 71,128]
276. ~brave(john) <- (28) [subsumption resolution 275,268]
277. $false <- (28) [subsumption resolution 276,138]
278. ~28 [avatar contradiction clause 277]
279. $false [avatar sat refutation 273,278]
% SZS output end Proof for 4077915260226624200315768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not strong or not humble then someone is patient or happy.
Everyone who is both brave and creative is not humble and vice versa.
Everyone who is not funny is funny or calm and vice versa.
Everyone who is not funny is creative or rich and vice versa.
If someone is both curious and wise then mary is either happy or strong and vice versa.
If paul is calm or wise then someone is not funny and vice versa.
Everyone who is either not patient or wise is both not old and kind.
Everyone who is both not funny and not creative is happy and vice versa.
If alice is either happy or not wise then someone is both not creative and quiet and vice versa.
Everyone who is both not patient and happy is either not calm or creative and vice versa.
If someone is not kind then someone is tall and vice versa.
Everyone who is both creative and not happy is either generous or patient and vice versa.
Everyone who is either not curious or funny is either generous or not quiet and vice versa.
If john is either not happy or happy then susan is either not happy or generous and vice versa.
If someone is creative or curious then paul is not strong or not happy.
Everyone who is not kind is both patient and not quiet.
Fred is not strong or not patient.
Fred is either not brave or not kind.
Someone is not wise.
Fred is either not patient or quiet.
Susan is both not strong and humble.
Someone is either not brave or not generous.
Mary is kind. | Fred is not quiet. | contradiction | (((~strong(lucy)|~humble(lucy)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((brave(X)&creative(X))<=>~humble(X)))&
(![X]:(~funny(X)<=>(funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(creative(X)|rich(X))))&
((?[X]:((curious(X)&wise(X))))<=>((happy(mary)<~>strong(mary))))&
(((calm(paul)|wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)<~>wise(X))=>(~old(X)&kind(X))))&
(![X]:((~funny(X)&~creative(X))<=>happy(X)))&
(((happy(alice)<~>~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~happy(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(generous(X)<~>~quiet(X))))&
(((~happy(john)<~>happy(john)))<=>((~happy(susan)<~>generous(susan))))&
((?[X]:((creative(X)|curious(X))))=>((~strong(paul)|~happy(paul))))&
(![X]:(~kind(X)=>(patient(X)&~quiet(X))))&
((~strong(fred)|~patient(fred)))&
((~brave(fred)<~>~kind(fred)))&
(?[X]:(~wise(X)))&
((~patient(fred)<~>quiet(fred)))&
((~strong(susan)&humble(susan)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(kind(mary)) | ~quiet(fred) | [
"p2",
"p7",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7767106979001797499109734
% SZS output start Proof for 7767106979001797499109734
3. ! [X0] : (~funny(X0) <=> (calm(X0) | funny(X0))) [input p2]
8. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> happy(X0)) [input p7]
10. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~calm(X0) <~> creative(X0))) [input p9]
20. ~patient(fred) <~> quiet(fred) [input p19]
24. ~quiet(fred) [input hypothesis]
37. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | funny(X0))) [nnf transformation 3]
38. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | funny(X0))) [flattening 37]
51. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | funny(X0)))) [nnf transformation 8]
52. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | funny(X0))) [flattening 51]
57. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~happy(X0) | patient(X0)))) [nnf transformation 10]
58. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~happy(X0) | patient(X0))) [flattening 57]
71. (~quiet(fred) | patient(fred)) & (quiet(fred) | ~patient(fred)) [nnf transformation 20]
78. calm(X0) | funny(X0) | funny(X0) [cnf transformation 38]
79. ~funny(X0) | ~funny(X0) [cnf transformation 38]
95. happy(X0) | creative(X0) | funny(X0) [cnf transformation 52]
97. ~creative(X0) | ~happy(X0) [cnf transformation 52]
104. creative(X0) | ~calm(X0) | ~happy(X0) | patient(X0) [cnf transformation 58]
109. happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 58]
142. quiet(fred) | ~patient(fred) [cnf transformation 71]
149. ~quiet(fred) [cnf transformation 24]
154. calm(X0) | funny(X0) [duplicate literal removal 78]
155. ~funny(X0) [duplicate literal removal 79]
174. calm(X0) [subsumption resolution 154,155]
201. creative(X0) | happy(X0) [subsumption resolution 95,155]
227. happy(X0) | ~creative(X0) [subsumption resolution 109,174]
228. ~creative(X0) [subsumption resolution 227,97]
229. ~calm(X0) | ~happy(X0) | patient(X0) [subsumption resolution 104,228]
230. ~happy(X0) | patient(X0) [subsumption resolution 229,174]
285. 26 <=> patient(fred) [avatar definition]
287. ~patient(fred) <- (~26) [avatar component clause 285]
300. 29 <=> quiet(fred) [avatar definition]
304. ~26 | 29 [avatar split clause 142,300,285]
315. ~29 [avatar split clause 149,300]
325. happy(X1) [resolution 201,228]
334. patient(X1) [resolution 325,230]
347. $false <- (~26) [resolution 334,287]
349. 26 [avatar contradiction clause 347]
350. $false [avatar sat refutation 304,315,349]
% SZS output end Proof for 7767106979001797499109734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not humble then someone is either not creative or not generous and vice versa.
If someone is brave or not wise then someone is both generous and calm.
Everyone who is both strong and not strong is generous and vice versa.
Everyone who is not wise or humble is rich or not strong.
Everyone who is not tall or old is either funny or tall.
Everyone who is brave or creative is not quiet or not rich and vice versa.
If someone is not funny then paul is either not generous or not humble.
If someone is both funny and not strong then someone is not strong.
Everyone who is both kind and old is patient or tall and vice versa.
Everyone who is both old and funny is not brave or not quiet.
Everyone who is both not rich and not wise is either curious or not patient.
If mary is both strong and not creative then someone is either rich or not wise and vice versa.
If someone is strong or calm then someone is generous or not humble.
If someone is either not tall or not rich then lucy is either tall or strong.
Everyone who is creative or not quiet is either rich or not funny.
Paul is either rich or kind.
Someone is not calm or not brave.
Alice is either not humble or not brave. | Alice is kind. | neutral | (((old(alice)&~humble(alice)))<=>(?[X]:((~creative(X)<~>~generous(X)))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((generous(X)&calm(X)))))&
(![X]:((strong(X)&~strong(X))<=>generous(X)))&
(![X]:((~wise(X)|humble(X))=>(rich(X)|~strong(X))))&
(![X]:((~tall(X)|old(X))=>(funny(X)<~>tall(X))))&
(![X]:((brave(X)|creative(X))<=>(~quiet(X)|~rich(X))))&
((?[X]:(~funny(X)))=>((~generous(paul)<~>~humble(paul))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)&old(X))<=>(patient(X)|tall(X))))&
(![X]:((old(X)&funny(X))=>(~brave(X)|~quiet(X))))&
(![X]:((~rich(X)&~wise(X))=>(curious(X)<~>~patient(X))))&
(((strong(mary)&~creative(mary)))<=>(?[X]:((rich(X)<~>~wise(X)))))&
((?[X]:((strong(X)|calm(X))))=>(?[X]:((generous(X)|~humble(X)))))&
((?[X]:((~tall(X)<~>~rich(X))))=>((tall(lucy)<~>strong(lucy))))&
(![X]:((creative(X)|~quiet(X))=>(rich(X)<~>~funny(X))))&
((rich(paul)<~>kind(paul)))&
(?[X]:((~calm(X)|~brave(X))))&
((~humble(alice)<~>~brave(alice))) | kind(alice) | [] | null | 0 |
Everyone who is not creative or not rich is not rich or tall.
Everyone who is rich or patient is quiet.
Everyone who is not wise or quiet is not old.
Everyone who is not strong or curious is calm.
If susan is both not patient and calm then paul is both not rich and kind.
Everyone who is either not quiet or not generous is quiet.
Everyone who is both kind and not calm is not kind or not humble.
If alice is either not brave or not rich then someone is not kind.
Everyone who is either not creative or calm is not curious or not strong and vice versa.
If mary is wise or rich then someone is humble.
Everyone who is not humble is not rich or rich.
Everyone who is not generous is calm or patient.
If someone is not strong then someone is both kind and old and vice versa.
Everyone who is either tall or not wise is both not quiet and not tall.
Everyone who is either patient or humble is not brave and vice versa.
If paul is kind or not tall then john is either not tall or not old and vice versa.
Paul is either kind or tall.
Someone is either not humble or kind.
John is not strong.
John is not quiet.
Someone is both tall and funny.
Someone is not wise.
Someone is either strong or funny.
Someone is both quiet and not curious. | Paul is tall. | neutral | (![X]:((~creative(X)|~rich(X))=>(~rich(X)|tall(X))))&
(![X]:((rich(X)|patient(X))=>quiet(X)))&
(![X]:((~wise(X)|quiet(X))=>~old(X)))&
(![X]:((~strong(X)|curious(X))=>calm(X)))&
(((~patient(susan)&calm(susan)))=>((~rich(paul)&kind(paul))))&
(![X]:((~quiet(X)<~>~generous(X))=>quiet(X)))&
(![X]:((kind(X)&~calm(X))=>(~kind(X)|~humble(X))))&
(((~brave(alice)<~>~rich(alice)))=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~curious(X)|~strong(X))))&
(((wise(mary)|rich(mary)))=>(?[X]:(humble(X))))&
(![X]:(~humble(X)=>(~rich(X)|rich(X))))&
(![X]:(~generous(X)=>(calm(X)|patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((tall(X)<~>~wise(X))=>(~quiet(X)&~tall(X))))&
(![X]:((patient(X)<~>humble(X))<=>~brave(X)))&
(((kind(paul)|~tall(paul)))<=>((~tall(john)<~>~old(john))))&
((kind(paul)<~>tall(paul)))&
(?[X]:((~humble(X)<~>kind(X))))&
(~strong(john))&
(~quiet(john))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~wise(X)))&
(?[X]:((strong(X)<~>funny(X))))&
(?[X]:((quiet(X)&~curious(X)))) | tall(paul) | [] | null | 0 |
Everyone who is not creative is humble and vice versa. If someone is not brave then someone is not old or not quiet. Everyone who is not patient is either not strong or not quiet. Everyone who is not creative is both not creative and not tall and vice versa. If alice is not curious then fred is not calm and vice versa. Everyone who is either rich or not humble is funny and vice versa. Everyone who is either creative or not kind is brave or happy. If someone is not tall or not generous then someone is either quiet or happy. Everyone who is patient is either quiet or not wise and vice versa. If someone is not kind then someone is not humble. If john is rich then someone is either not calm or old. Everyone who is either funny or wise is kind or not calm. Everyone who is not creative or not calm is both not kind and tall and vice versa. If mary is both wise and not kind then someone is both humble and not happy. Everyone who is not patient is brave. Everyone who is either not creative or not tall is rich. Paul is generous. Someone is either calm or old. Lucy is not kind. Someone is either not creative or not happy. Mary is both creative and quiet. Paul is wise or happy. | Mary is tall. | neutral | (![X]:(~creative(X)<=>humble(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(~patient(X)=>(~strong(X)<~>~quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)&~tall(X))))&
((~curious(alice))<=>(~calm(fred)))&
(![X]:((rich(X)<~>~humble(X))<=>funny(X)))&
(![X]:((creative(X)<~>~kind(X))=>(brave(X)|happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:(patient(X)<=>(quiet(X)<~>~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~humble(X))))&
((rich(john))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:((funny(X)<~>wise(X))=>(kind(X)|~calm(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&tall(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((~creative(X)<~>~tall(X))=>rich(X)))&
(generous(paul))&
(?[X]:((calm(X)<~>old(X))))&
(~kind(lucy))&
(?[X]:((~creative(X)<~>~happy(X))))&
((creative(mary)&quiet(mary)))&
((wise(paul)|happy(paul))) | tall(mary) | [] | null | 0 |
If paul is both not strong and strong then someone is both not old and not quiet and vice versa. Everyone who is strong or generous is both old and strong and vice versa. If someone is not creative or not quiet then someone is both humble and not quiet. Everyone who is both not humble and curious is both not calm and generous. If john is either patient or not calm then someone is either not patient or old and vice versa. Everyone who is either not patient or not happy is quiet. Everyone who is old is not old. Everyone who is both quiet and not happy is brave and vice versa. Everyone who is both not tall and not rich is either wise or not generous. If mary is both generous and not happy then susan is tall or curious. Everyone who is rich is both not strong and not patient. If fred is either not kind or generous then mary is not quiet. If someone is either curious or strong then lucy is both not funny and not tall. If alice is either brave or not generous then fred is both not brave and rich and vice versa. Everyone who is either not wise or not brave is not strong or calm. Everyone who is both not funny and not strong is both not creative and brave. Someone is both happy and not humble. Susan is patient. Susan is either not kind or funny. Lucy is both kind and brave. Paul is calm. Someone is either generous or rich. Paul is either not strong or kind. | Alice is curious. | contradiction | (((~strong(paul)&strong(paul)))<=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((strong(X)|generous(X))<=>(old(X)&strong(X))))&
((?[X]:((~creative(X)|~quiet(X))))=>(?[X]:((humble(X)&~quiet(X)))))&
(![X]:((~humble(X)&curious(X))=>(~calm(X)&generous(X))))&
(((patient(john)<~>~calm(john)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:((~patient(X)<~>~happy(X))=>quiet(X)))&
(![X]:(old(X)=>~old(X)))&
(![X]:((quiet(X)&~happy(X))<=>brave(X)))&
(![X]:((~tall(X)&~rich(X))=>(wise(X)<~>~generous(X))))&
(((generous(mary)&~happy(mary)))=>((tall(susan)|curious(susan))))&
(![X]:(rich(X)=>(~strong(X)&~patient(X))))&
(((~kind(fred)<~>generous(fred)))=>(~quiet(mary)))&
((?[X]:((curious(X)<~>strong(X))))=>((~funny(lucy)&~tall(lucy))))&
(((brave(alice)<~>~generous(alice)))<=>((~brave(fred)&rich(fred))))&
(![X]:((~wise(X)<~>~brave(X))=>(~strong(X)|calm(X))))&
(![X]:((~funny(X)&~strong(X))=>(~creative(X)&brave(X))))&
(?[X]:((happy(X)&~humble(X))))&
(patient(susan))&
((~kind(susan)<~>funny(susan)))&
((kind(lucy)&brave(lucy)))&
(calm(paul))&
(?[X]:((generous(X)<~>rich(X))))&
((~strong(paul)<~>kind(paul))) | curious(alice) | [
"p0",
"p1",
"p2",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8755170452957376832941631
% SZS output start Proof for 8755170452957376832941631
1. (strong(paul) & ~strong(paul)) <=> ? [X0] : (~quiet(X0) & ~old(X0)) [input p0]
2. ! [X0] : ((generous(X0) | strong(X0)) <=> (strong(X0) & old(X0))) [input p1]
3. ? [X0] : (~quiet(X0) | ~creative(X0)) => ? [X0] : (~quiet(X0) & humble(X0)) [input p2]
7. ! [X0] : (old(X0) => ~old(X0)) [input p6]
13. ? [X0] : (curious(X0) <~> strong(X0)) => (~tall(lucy) & ~funny(lucy)) [input p12]
16. ! [X0] : ((~strong(X0) & ~funny(X0)) => (brave(X0) & ~creative(X0))) [input p15]
24. curious(alice) [input hypothesis]
25. ? [X0] : (~quiet(X0) | ~creative(X0)) => ? [X1] : (~quiet(X1) & humble(X1)) [rectify 3]
26. ? [X1] : (~quiet(X1) & humble(X1)) | ! [X0] : (quiet(X0) & creative(X0)) [ennf transformation 25]
30. ! [X0] : (~old(X0) | ~old(X0)) [ennf transformation 7]
37. (~tall(lucy) & ~funny(lucy)) | ! [X0] : (curious(X0) <=> strong(X0)) [ennf transformation 13]
40. ! [X0] : ((brave(X0) & ~creative(X0)) | (strong(X0) | funny(X0))) [ennf transformation 16]
41. ! [X0] : ((brave(X0) & ~creative(X0)) | strong(X0) | funny(X0)) [flattening 40]
42. ((strong(paul) & ~strong(paul)) | ! [X0] : (quiet(X0) | old(X0))) & (? [X0] : (~quiet(X0) & ~old(X0)) | (~strong(paul) | strong(paul))) [nnf transformation 1]
43. ((strong(paul) & ~strong(paul)) | ! [X0] : (quiet(X0) | old(X0))) & (? [X0] : (~quiet(X0) & ~old(X0)) | ~strong(paul) | strong(paul)) [flattening 42]
44. ((strong(paul) & ~strong(paul)) | ! [X0] : (quiet(X0) | old(X0))) & (? [X1] : (~quiet(X1) & ~old(X1)) | ~strong(paul) | strong(paul)) [rectify 43]
45. ? [X1] : (~quiet(X1) & ~old(X1)) => (~quiet(sK0) & ~old(sK0)) [choice axiom]
46. ((strong(paul) & ~strong(paul)) | ! [X0] : (quiet(X0) | old(X0))) & ((~quiet(sK0) & ~old(sK0)) | ~strong(paul) | strong(paul)) [skolemisation 44,45]
47. ! [X0] : (((generous(X0) | strong(X0)) | (~strong(X0) | ~old(X0))) & ((strong(X0) & old(X0)) | (~generous(X0) & ~strong(X0)))) [nnf transformation 2]
48. ! [X0] : ((generous(X0) | strong(X0) | ~strong(X0) | ~old(X0)) & ((strong(X0) & old(X0)) | (~generous(X0) & ~strong(X0)))) [flattening 47]
49. ? [X0] : (~quiet(X0) & humble(X0)) | ! [X1] : (quiet(X1) & creative(X1)) [rectify 26]
50. ? [X0] : (~quiet(X0) & humble(X0)) => (~quiet(sK1) & humble(sK1)) [choice axiom]
51. (~quiet(sK1) & humble(sK1)) | ! [X1] : (quiet(X1) & creative(X1)) [skolemisation 49,50]
61. (~tall(lucy) & ~funny(lucy)) | ! [X0] : ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))) [nnf transformation 37]
75. strong(paul) | quiet(X0) | old(X0) [cnf transformation 46]
76. ~strong(X0) | old(X0) [cnf transformation 48]
83. ~quiet(sK1) | creative(X1) [cnf transformation 51]
97. ~old(X0) | ~old(X0) [cnf transformation 30]
108. ~funny(lucy) | strong(X0) | ~curious(X0) [cnf transformation 61]
120. ~creative(X0) | strong(X0) | funny(X0) [cnf transformation 41]
134. curious(alice) [cnf transformation 24]
135. ~old(X0) [duplicate literal removal 97]
137. 1 <=> ! [X0] : (quiet(X0) | old(X0)) [avatar definition]
138. quiet(X0) | old(X0) <- (1) [avatar component clause 137]
140. 2 <=> strong(paul) [avatar definition]
142. strong(paul) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 75,140,137]
146. 3 <=> ! [X1] : quiet(X1) [avatar definition]
147. quiet(X1) <- (3) [avatar component clause 146]
149. 4 <=> quiet(sK1) [avatar definition]
151. ~quiet(sK1) <- (~4) [avatar component clause 149]
154. 5 <=> ! [X1] : creative(X1) [avatar definition]
155. creative(X1) <- (5) [avatar component clause 154]
156. 5 | ~4 [avatar split clause 83,149,154]
233. 22 <=> ! [X0] : (strong(X0) | ~curious(X0)) [avatar definition]
234. ~curious(X0) | strong(X0) <- (22) [avatar component clause 233]
237. 23 <=> funny(lucy) [avatar definition]
239. ~funny(lucy) <- (~23) [avatar component clause 237]
241. 22 | ~23 [avatar split clause 108,237,233]
292. quiet(X0) <- (1) [subsumption resolution 138,135]
293. 3 | ~1 [avatar split clause 292,137,146]
294. $false <- (3, ~4) [resolution 151,147]
295. ~3 | 4 [avatar contradiction clause 294]
296. old(paul) <- (2) [resolution 76,142]
297. $false <- (2) [subsumption resolution 296,135]
298. ~2 [avatar contradiction clause 297]
328. funny(X0) | strong(X0) <- (5) [resolution 120,155]
342. strong(lucy) <- (5, ~23) [resolution 328,239]
343. old(lucy) <- (5, ~23) [resolution 342,76]
344. $false <- (5, ~23) [subsumption resolution 343,135]
345. ~5 | 23 [avatar contradiction clause 344]
346. strong(alice) <- (22) [resolution 234,134]
348. old(alice) <- (22) [resolution 346,76]
349. $false <- (22) [subsumption resolution 348,135]
350. ~22 [avatar contradiction clause 349]
351. $false [avatar sat refutation 143,156,241,293,295,298,345,350]
% SZS output end Proof for 8755170452957376832941631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not happy and rich then someone is either not quiet or kind and vice versa.
Everyone who is calm or humble is not strong or patient.
Everyone who is either patient or not humble is not patient or not quiet.
Everyone who is either not curious or not brave is rich or not tall and vice versa.
If mary is both not creative and not humble then someone is rich.
Everyone who is both kind and quiet is tall or rich and vice versa.
If someone is both rich and calm then someone is either humble or brave and vice versa.
Everyone who is either not tall or not quiet is either not generous or not humble and vice versa.
Everyone who is both old and not strong is both not happy and not wise and vice versa.
If someone is either not brave or creative then lucy is not strong or not tall.
Everyone who is humble is patient.
Everyone who is both not wise and generous is both not generous and quiet and vice versa.
If paul is generous then someone is not strong.
If alice is not happy or not humble then someone is not happy or funny and vice versa.
If mary is strong then susan is both calm and not generous and vice versa.
Everyone who is both funny and not wise is not creative or generous and vice versa.
Someone is not brave or happy.
Alice is funny.
Someone is both not funny and patient.
Paul is both not generous and funny.
Someone is either not patient or not old. | Paul is not curious. | contradiction | (((~happy(mary)&rich(mary)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)|patient(X))))&
(![X]:((patient(X)<~>~humble(X))=>(~patient(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(rich(X)|~tall(X))))&
(((~creative(mary)&~humble(mary)))=>(?[X]:(rich(X))))&
(![X]:((kind(X)&quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((old(X)&~strong(X))<=>(~happy(X)&~wise(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>((~strong(lucy)|~tall(lucy))))&
(![X]:(humble(X)=>patient(X)))&
(![X]:((~wise(X)&generous(X))<=>(~generous(X)&quiet(X))))&
((generous(paul))=>(?[X]:(~strong(X))))&
(((~happy(alice)|~humble(alice)))<=>(?[X]:((~happy(X)|funny(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(?[X]:((~brave(X)|happy(X))))&
(funny(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~generous(paul)&funny(paul)))&
(?[X]:((~patient(X)<~>~old(X)))) | ~curious(paul) | [
"p3",
"p5",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2162179738007030803370585
% SZS output start Proof for 2162179738007030803370585
4. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (~tall(X0) | rich(X0))) [input p3]
6. ! [X0] : ((quiet(X0) & kind(X0)) <=> (rich(X0) | tall(X0))) [input p5]
7. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X0] : (humble(X0) <~> brave(X0)) [input p6]
8. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> (~generous(X0) <~> ~humble(X0))) [input p7]
12. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (quiet(X0) & ~generous(X0))) [input p11]
16. ! [X0] : ((~wise(X0) & funny(X0)) <=> (generous(X0) | ~creative(X0))) [input p15]
22. ~curious(paul) [input hypothesis]
23. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X1] : (humble(X1) <~> brave(X1)) [rectify 7]
40. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 4]
41. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 40]
44. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ~quiet(X0) | ~kind(X0))) [flattening 44]
46. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (? [X1] : ((~brave(X1) | ~humble(X1)) & (brave(X1) | humble(X1))) | ! [X0] : (~calm(X0) | ~rich(X0))) [nnf transformation 23]
47. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (? [X2] : ((~brave(X2) | ~humble(X2)) & (brave(X2) | humble(X2))) | ! [X3] : (~calm(X3) | ~rich(X3))) [rectify 46]
48. ? [X0] : (calm(X0) & rich(X0)) => (calm(sK2) & rich(sK2)) [choice axiom]
49. ? [X2] : ((~brave(X2) | ~humble(X2)) & (brave(X2) | humble(X2))) => ((~brave(sK3) | ~humble(sK3)) & (brave(sK3) | humble(sK3))) [choice axiom]
50. ((calm(sK2) & rich(sK2)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) & (((~brave(sK3) | ~humble(sK3)) & (brave(sK3) | humble(sK3))) | ! [X3] : (~calm(X3) | ~rich(X3))) [skolemisation 47,49,48]
51. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 8]
55. ! [X0] : (((generous(X0) & ~wise(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 12]
56. ! [X0] : (((generous(X0) & ~wise(X0)) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | ~generous(X0) | wise(X0))) [flattening 55]
66. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 16]
67. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | wise(X0) | ~funny(X0))) [flattening 66]
90. tall(X0) | curious(X0) | brave(X0) [cnf transformation 41]
95. ~tall(X0) | quiet(X0) [cnf transformation 45]
96. ~rich(X0) | quiet(X0) [cnf transformation 45]
100. rich(sK2) | humble(X1) | ~brave(X1) [cnf transformation 50]
109. quiet(X0) | tall(X0) | ~humble(X0) | generous(X0) [cnf transformation 51]
118. ~generous(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
121. generous(X0) | ~quiet(X0) | generous(X0) [cnf transformation 56]
134. ~wise(X0) | ~generous(X0) [cnf transformation 67]
143. ~curious(paul) [cnf transformation 22]
144. ~generous(X0) | wise(X0) [duplicate literal removal 118]
145. ~quiet(X0) | generous(X0) [duplicate literal removal 121]
189. 10 <=> ! [X1] : (humble(X1) | ~brave(X1)) [avatar definition]
190. ~brave(X1) | humble(X1) <- (10) [avatar component clause 189]
201. 13 <=> rich(sK2) [avatar definition]
203. rich(sK2) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 100,201,189]
220. ~humble(X0) | quiet(X0) | generous(X0) [subsumption resolution 109,95]
289. ~generous(X0) [subsumption resolution 134,144]
325. brave(X0) | curious(X0) | quiet(X0) [resolution 90,95]
416. quiet(sK2) <- (13) [resolution 203,96]
436. generous(sK2) <- (13) [resolution 416,145]
447. $false <- (13) [subsumption resolution 436,289]
448. ~13 [avatar contradiction clause 447]
474. curious(X0) | humble(X0) | quiet(X0) <- (10) [resolution 190,325]
537. humble(paul) | quiet(paul) <- (10) [resolution 474,143]
539. 61 <=> quiet(paul) [avatar definition]
540. ~quiet(paul) <- (~61) [avatar component clause 539]
541. quiet(paul) <- (61) [avatar component clause 539]
543. 62 <=> humble(paul) [avatar definition]
545. humble(paul) <- (62) [avatar component clause 543]
546. 61 | 62 | ~10 [avatar split clause 537,189,543,539]
554. generous(paul) <- (61) [resolution 541,145]
555. $false <- (61) [subsumption resolution 554,289]
556. ~61 [avatar contradiction clause 555]
559. quiet(paul) | generous(paul) <- (62) [resolution 545,220]
562. generous(paul) <- (~61, 62) [subsumption resolution 559,540]
563. $false <- (~61, 62) [subsumption resolution 562,289]
564. 61 | ~62 [avatar contradiction clause 563]
565. $false [avatar sat refutation 204,448,546,556,564]
% SZS output end Proof for 2162179738007030803370585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or rich is either brave or not happy and vice versa.
Everyone who is not patient or brave is not happy or not calm and vice versa.
If someone is not generous or not rich then mary is wise.
Everyone who is not humble or curious is generous and vice versa.
Everyone who is both funny and patient is not rich or not old.
If someone is both quiet and not generous then someone is kind or not calm.
Everyone who is either not brave or old is not curious and vice versa.
If someone is both not strong and not kind then someone is either not calm or strong and vice versa.
If alice is either tall or not patient then susan is both not brave and not old.
If someone is not calm or not old then susan is old.
Everyone who is both happy and generous is either brave or not curious and vice versa.
If paul is wise or not generous then someone is both calm and tall and vice versa.
If fred is quiet or calm then someone is funny or wise and vice versa.
Everyone who is curious or not happy is either humble or happy.
Everyone who is strong is not wise and vice versa.
If paul is brave then someone is rich and vice versa.
Someone is both not strong and rich.
Someone is curious or not tall.
Someone is not brave or not funny.
Someone is both brave and creative.
Lucy is both wise and not curious.
Paul is either not strong or not patient.
Mary is either old or calm.
Susan is not old or not quiet. | Mary is old. | entailment | (![X]:((patient(X)|rich(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~patient(X)|brave(X))<=>(~happy(X)|~calm(X))))&
((?[X]:((~generous(X)|~rich(X))))=>(wise(mary)))&
(![X]:((~humble(X)|curious(X))<=>generous(X)))&
(![X]:((funny(X)&patient(X))=>(~rich(X)|~old(X))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:((~brave(X)<~>old(X))<=>~curious(X)))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~calm(X)<~>strong(X)))))&
(((tall(alice)<~>~patient(alice)))=>((~brave(susan)&~old(susan))))&
((?[X]:((~calm(X)|~old(X))))=>(old(susan)))&
(![X]:((happy(X)&generous(X))<=>(brave(X)<~>~curious(X))))&
(((wise(paul)|~generous(paul)))<=>(?[X]:((calm(X)&tall(X)))))&
(((quiet(fred)|calm(fred)))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:((curious(X)|~happy(X))=>(humble(X)<~>happy(X))))&
(![X]:(strong(X)<=>~wise(X)))&
((brave(paul))<=>(?[X]:(rich(X))))&
(?[X]:((~strong(X)&rich(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~brave(X)|~funny(X))))&
(?[X]:((brave(X)&creative(X))))&
((wise(lucy)&~curious(lucy)))&
((~strong(paul)<~>~patient(paul)))&
((old(mary)<~>calm(mary)))&
((~old(susan)|~quiet(susan))) | old(mary) | [
"p0",
"p1",
"p6",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7003838505180344595311353
% SZS output start Proof for 7003838505180344595311353
1. ! [X0] : ((rich(X0) | patient(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((brave(X0) | ~patient(X0)) <=> (~calm(X0) | ~happy(X0))) [input p1]
7. ! [X0] : ((~brave(X0) <~> old(X0)) <=> ~curious(X0)) [input p6]
11. ! [X0] : ((generous(X0) & happy(X0)) <=> (brave(X0) <~> ~curious(X0))) [input p10]
23. old(mary) <~> calm(mary) [input p22]
25. ~old(mary) [input hypothesis]
36. ! [X0] : (((rich(X0) | patient(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~rich(X0) & ~patient(X0)))) [nnf transformation 1]
37. ! [X0] : ((rich(X0) | patient(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~rich(X0) & ~patient(X0)))) [flattening 36]
38. ! [X0] : (((brave(X0) | ~patient(X0)) | (calm(X0) & happy(X0))) & ((~calm(X0) | ~happy(X0)) | (~brave(X0) & patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~patient(X0) | (calm(X0) & happy(X0))) & (~calm(X0) | ~happy(X0) | (~brave(X0) & patient(X0)))) [flattening 38]
45. ! [X0] : ((((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | curious(X0)) & (~curious(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0))))) [nnf transformation 7]
52. ! [X0] : (((generous(X0) & happy(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | (~generous(X0) | ~happy(X0)))) [nnf transformation 11]
53. ! [X0] : (((generous(X0) & happy(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | ~generous(X0) | ~happy(X0))) [flattening 52]
79. (~calm(mary) | ~old(mary)) & (calm(mary) | old(mary)) [nnf transformation 23]
80. ~happy(X0) | brave(X0) | ~patient(X0) [cnf transformation 37]
86. ~calm(X0) | ~happy(X0) | patient(X0) [cnf transformation 39]
87. ~calm(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 39]
88. brave(X0) | ~patient(X0) | happy(X0) [cnf transformation 39]
97. ~curious(X0) | old(X0) | brave(X0) [cnf transformation 45]
99. ~brave(X0) | old(X0) | curious(X0) [cnf transformation 45]
115. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 53]
116. curious(X0) | brave(X0) | happy(X0) [cnf transformation 53]
145. calm(mary) | old(mary) [cnf transformation 79]
148. ~old(mary) [cnf transformation 25]
150. ~patient(X0) | brave(X0) [subsumption resolution 88,80]
328. 40 <=> old(mary) [avatar definition]
330. ~old(mary) <- (~40) [avatar component clause 328]
332. 41 <=> calm(mary) [avatar definition]
333. calm(mary) <- (41) [avatar component clause 332]
336. 40 | 41 [avatar split clause 145,332,328]
342. ~40 [avatar split clause 148,328]
386. ~happy(mary) | patient(mary) <- (41) [resolution 86,333]
397. 50 <=> patient(mary) [avatar definition]
399. patient(mary) <- (50) [avatar component clause 397]
401. 51 <=> happy(mary) [avatar definition]
403. ~happy(mary) <- (~51) [avatar component clause 401]
404. 50 | ~51 | ~41 [avatar split clause 386,332,401,397]
406. ~happy(mary) | ~brave(mary) <- (41) [resolution 87,333]
491. brave(X1) | happy(X1) | old(X1) | brave(X1) [resolution 116,97]
494. old(X1) | happy(X1) | brave(X1) [duplicate literal removal 491]
549. 68 <=> brave(mary) [avatar definition]
551. brave(mary) <- (68) [avatar component clause 549]
608. happy(mary) | brave(mary) <- (~40) [resolution 494,330]
616. 68 | 51 | 40 [avatar split clause 608,328,401,549]
617. ~68 | ~51 | ~41 [avatar split clause 406,332,401,549]
619. brave(mary) <- (50) [resolution 399,150]
622. 68 | ~50 [avatar split clause 619,397,549]
624. old(mary) | curious(mary) <- (68) [resolution 551,99]
627. curious(mary) <- (~40, 68) [subsumption resolution 624,330]
642. happy(mary) | ~brave(mary) <- (~40, 68) [resolution 627,115]
645. ~brave(mary) <- (~40, ~51, 68) [subsumption resolution 642,403]
646. $false <- (~40, ~51, 68) [subsumption resolution 645,551]
647. 40 | 51 | ~68 [avatar contradiction clause 646]
648. $false [avatar sat refutation 336,342,404,616,617,622,647]
% SZS output end Proof for 7003838505180344595311353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is happy then john is either tall or not tall and vice versa.
If john is either generous or not kind then john is not strong or humble and vice versa.
Everyone who is tall is not curious or patient.
Everyone who is either quiet or not creative is not kind or happy and vice versa.
Everyone who is not rich or patient is both not strong and happy.
Everyone who is both calm and kind is not wise or calm and vice versa.
If paul is both not tall and quiet then mary is not funny and vice versa.
Everyone who is brave is both quiet and old.
Everyone who is calm or wise is both strong and not tall and vice versa.
Everyone who is not wise is not old or not humble and vice versa.
If mary is either curious or humble then someone is both not rich and quiet and vice versa.
If someone is both strong and not calm then john is either wise or rich.
Everyone who is either not quiet or brave is either happy or not kind.
Everyone who is humble or not funny is not strong.
Everyone who is not old or not calm is both not creative and old.
Someone is either wise or not quiet.
Someone is both not patient and not creative.
Susan is curious or not wise.
Someone is kind or not patient. | Paul is kind. | entailment | ((happy(susan))<=>((tall(john)<~>~tall(john))))&
(((generous(john)<~>~kind(john)))<=>((~strong(john)|humble(john))))&
(![X]:(tall(X)=>(~curious(X)|patient(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~kind(X)|happy(X))))&
(![X]:((~rich(X)|patient(X))=>(~strong(X)&happy(X))))&
(![X]:((calm(X)&kind(X))<=>(~wise(X)|calm(X))))&
(((~tall(paul)&quiet(paul)))<=>(~funny(mary)))&
(![X]:(brave(X)=>(quiet(X)&old(X))))&
(![X]:((calm(X)|wise(X))<=>(strong(X)&~tall(X))))&
(![X]:(~wise(X)<=>(~old(X)|~humble(X))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~rich(X)&quiet(X)))))&
((?[X]:((strong(X)&~calm(X))))=>((wise(john)<~>rich(john))))&
(![X]:((~quiet(X)<~>brave(X))=>(happy(X)<~>~kind(X))))&
(![X]:((humble(X)|~funny(X))=>~strong(X)))&
(![X]:((~old(X)|~calm(X))=>(~creative(X)&old(X))))&
(?[X]:((wise(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~creative(X))))&
((curious(susan)|~wise(susan)))&
(?[X]:((kind(X)|~patient(X)))) | kind(paul) | [
"p5",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6041655011129676048640263
% SZS output start Proof for 6041655011129676048640263
6. ! [X0] : ((kind(X0) & calm(X0)) <=> (calm(X0) | ~wise(X0))) [input p5]
9. ! [X0] : ((wise(X0) | calm(X0)) <=> (~tall(X0) & strong(X0))) [input p8]
10. ! [X0] : (~wise(X0) <=> (~humble(X0) | ~old(X0))) [input p9]
14. ! [X0] : ((~funny(X0) | humble(X0)) => ~strong(X0)) [input p13]
20. ~kind(paul) [input hypothesis]
27. ! [X0] : (~strong(X0) | (funny(X0) & ~humble(X0))) [ennf transformation 14]
34. ! [X0] : (((kind(X0) & calm(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~kind(X0) | ~calm(X0)))) [nnf transformation 6]
35. ! [X0] : (((kind(X0) & calm(X0)) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | ~kind(X0) | ~calm(X0))) [flattening 34]
38. ! [X0] : (((wise(X0) | calm(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~wise(X0) & ~calm(X0)))) [nnf transformation 9]
39. ! [X0] : ((wise(X0) | calm(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | (~wise(X0) & ~calm(X0)))) [flattening 38]
40. ! [X0] : ((~wise(X0) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | wise(X0))) [nnf transformation 10]
41. ! [X0] : ((~wise(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | wise(X0))) [flattening 40]
77. wise(X0) | calm(X0) [cnf transformation 35]
79. wise(X0) | kind(X0) [cnf transformation 35]
86. ~calm(X0) | strong(X0) [cnf transformation 39]
87. ~wise(X0) | strong(X0) [cnf transformation 39]
93. ~wise(X0) | humble(X0) [cnf transformation 41]
106. ~humble(X0) | ~strong(X0) [cnf transformation 27]
118. ~kind(paul) [cnf transformation 20]
249. strong(X1) | calm(X1) [resolution 87,77]
269. strong(X1) [subsumption resolution 249,86]
280. humble(X0) | kind(X0) [resolution 93,79]
297. kind(X0) | ~strong(X0) [resolution 280,106]
299. kind(X0) [subsumption resolution 297,269]
301. $false [resolution 299,118]
% SZS output end Proof for 6041655011129676048640263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind or not creative then fred is either not kind or not generous and vice versa.
Everyone who is not old is patient.
Everyone who is both generous and patient is strong or not quiet and vice versa.
If someone is both humble and patient then someone is both not patient and not brave and vice versa.
If john is both tall and rich then someone is creative.
If susan is not humble then someone is both not humble and not wise.
Everyone who is strong or generous is not happy.
Everyone who is not patient or not old is either not rich or not creative and vice versa.
If alice is strong then mary is brave.
If someone is humble then fred is both not old and not generous and vice versa.
Everyone who is either not quiet or tall is either not curious or kind.
Everyone who is either not humble or wise is funny and vice versa.
Everyone who is not wise or not rich is both not quiet and old and vice versa.
If mary is either not happy or not rich then someone is either funny or not happy.
Everyone who is quiet is both old and not humble.
Everyone who is both creative and funny is brave or calm and vice versa.
Someone is old or kind.
Fred is either not creative or not kind.
Someone is not strong.
Fred is not brave.
Someone is either rich or not tall.
Mary is not creative. | Fred is not generous. | neutral | (((kind(paul)|~creative(paul)))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((generous(X)&patient(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((tall(john)&rich(john)))=>(?[X]:(creative(X))))&
((~humble(susan))=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((strong(X)|generous(X))=>~happy(X)))&
(![X]:((~patient(X)|~old(X))<=>(~rich(X)<~>~creative(X))))&
((strong(alice))=>(brave(mary)))&
((?[X]:(humble(X)))<=>((~old(fred)&~generous(fred))))&
(![X]:((~quiet(X)<~>tall(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>funny(X)))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(?[X]:((old(X)|kind(X))))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:(~strong(X)))&
(~brave(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(~creative(mary)) | ~generous(fred) | [] | null | 0 |
Everyone who is both generous and strong is not funny or rich and vice versa. If someone is both funny and brave then alice is both rich and curious and vice versa. If lucy is both calm and not strong then someone is either calm or creative and vice versa. Everyone who is both not kind and not rich is either creative or kind and vice versa. Everyone who is both not quiet and not happy is generous and vice versa. If someone is not patient then john is brave. If someone is either brave or not old then someone is not curious or not brave and vice versa. Everyone who is not curious is both not kind and not humble. Everyone who is either happy or calm is humble. If lucy is both humble and not brave then someone is strong or not generous and vice versa. Everyone who is not brave is not calm and vice versa. If someone is not generous or not old then mary is either not wise or not quiet. If someone is either not humble or not strong then john is either brave or wise and vice versa. If susan is both strong and not kind then fred is funny. If someone is either not creative or generous then someone is either old or not wise. Everyone who is both kind and calm is both not happy and brave and vice versa. Someone is both not rich and humble. Someone is not creative or rich. Alice is both curious and not brave. Someone is quiet or old. John is happy. Paul is both not funny and not humble. Someone is either not quiet or old. | Alice is not quiet. | entailment | (![X]:((generous(X)&strong(X))<=>(~funny(X)|rich(X))))&
((?[X]:((funny(X)&brave(X))))<=>((rich(alice)&curious(alice))))&
(((calm(lucy)&~strong(lucy)))<=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(creative(X)<~>kind(X))))&
(![X]:((~quiet(X)&~happy(X))<=>generous(X)))&
((?[X]:(~patient(X)))=>(brave(john)))&
((?[X]:((brave(X)<~>~old(X))))<=>(?[X]:((~curious(X)|~brave(X)))))&
(![X]:(~curious(X)=>(~kind(X)&~humble(X))))&
(![X]:((happy(X)<~>calm(X))=>humble(X)))&
(((humble(lucy)&~brave(lucy)))<=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:(~brave(X)<=>~calm(X)))&
((?[X]:((~generous(X)|~old(X))))=>((~wise(mary)<~>~quiet(mary))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>((brave(john)<~>wise(john))))&
(((strong(susan)&~kind(susan)))=>(funny(fred)))&
((?[X]:((~creative(X)<~>generous(X))))=>(?[X]:((old(X)<~>~wise(X)))))&
(![X]:((kind(X)&calm(X))<=>(~happy(X)&brave(X))))&
(?[X]:((~rich(X)&humble(X))))&
(?[X]:((~creative(X)|rich(X))))&
((curious(alice)&~brave(alice)))&
(?[X]:((quiet(X)|old(X))))&
(happy(john))&
((~funny(paul)&~humble(paul)))&
(?[X]:((~quiet(X)<~>old(X)))) | ~quiet(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p9",
"p10",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2857311068889982437627175
% SZS output start Proof for 2857311068889982437627175
1. ! [X0] : ((strong(X0) & generous(X0)) <=> (rich(X0) | ~funny(X0))) [input p0]
2. ? [X0] : (brave(X0) & funny(X0)) <=> (curious(alice) & rich(alice)) [input p1]
3. (~strong(lucy) & calm(lucy)) <=> ? [X0] : (calm(X0) <~> creative(X0)) [input p2]
4. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (creative(X0) <~> kind(X0))) [input p3]
5. ! [X0] : ((~happy(X0) & ~quiet(X0)) <=> generous(X0)) [input p4]
10. (~brave(lucy) & humble(lucy)) <=> ? [X0] : (~generous(X0) | strong(X0)) [input p9]
11. ! [X0] : (~brave(X0) <=> ~calm(X0)) [input p10]
21. happy(john) [input p20]
22. ~humble(paul) & ~funny(paul) [input p21]
24. quiet(alice) [input hypothesis]
34. ! [X0] : (((strong(X0) & generous(X0)) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 1]
35. ! [X0] : (((strong(X0) & generous(X0)) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ~strong(X0) | ~generous(X0))) [flattening 34]
36. (? [X0] : (brave(X0) & funny(X0)) | (~curious(alice) | ~rich(alice))) & ((curious(alice) & rich(alice)) | ! [X0] : (~brave(X0) | ~funny(X0))) [nnf transformation 2]
37. (? [X0] : (brave(X0) & funny(X0)) | ~curious(alice) | ~rich(alice)) & ((curious(alice) & rich(alice)) | ! [X0] : (~brave(X0) | ~funny(X0))) [flattening 36]
38. (? [X0] : (brave(X0) & funny(X0)) | ~curious(alice) | ~rich(alice)) & ((curious(alice) & rich(alice)) | ! [X1] : (~brave(X1) | ~funny(X1))) [rectify 37]
39. ? [X0] : (brave(X0) & funny(X0)) => (brave(sK0) & funny(sK0)) [choice axiom]
40. ((brave(sK0) & funny(sK0)) | ~curious(alice) | ~rich(alice)) & ((curious(alice) & rich(alice)) | ! [X1] : (~brave(X1) | ~funny(X1))) [skolemisation 38,39]
41. ((~strong(lucy) & calm(lucy)) | ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (? [X0] : ((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (strong(lucy) | ~calm(lucy))) [nnf transformation 3]
42. ((~strong(lucy) & calm(lucy)) | ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (? [X0] : ((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | strong(lucy) | ~calm(lucy)) [flattening 41]
43. ((~strong(lucy) & calm(lucy)) | ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (? [X1] : ((~creative(X1) | ~calm(X1)) & (creative(X1) | calm(X1))) | strong(lucy) | ~calm(lucy)) [rectify 42]
44. ? [X1] : ((~creative(X1) | ~calm(X1)) & (creative(X1) | calm(X1))) => ((~creative(sK1) | ~calm(sK1)) & (creative(sK1) | calm(sK1))) [choice axiom]
45. ((~strong(lucy) & calm(lucy)) | ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(sK1) | ~calm(sK1)) & (creative(sK1) | calm(sK1))) | strong(lucy) | ~calm(lucy)) [skolemisation 43,44]
46. ! [X0] : (((~rich(X0) & ~kind(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (rich(X0) | kind(X0)))) [nnf transformation 4]
47. ! [X0] : (((~rich(X0) & ~kind(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | rich(X0) | kind(X0))) [flattening 46]
48. ! [X0] : (((~happy(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (happy(X0) | quiet(X0)))) [nnf transformation 5]
49. ! [X0] : (((~happy(X0) & ~quiet(X0)) | ~generous(X0)) & (generous(X0) | happy(X0) | quiet(X0))) [flattening 48]
56. ((~brave(lucy) & humble(lucy)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X0] : (~generous(X0) | strong(X0)) | (brave(lucy) | ~humble(lucy))) [nnf transformation 10]
57. ((~brave(lucy) & humble(lucy)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X0] : (~generous(X0) | strong(X0)) | brave(lucy) | ~humble(lucy)) [flattening 56]
58. ((~brave(lucy) & humble(lucy)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X1] : (~generous(X1) | strong(X1)) | brave(lucy) | ~humble(lucy)) [rectify 57]
59. ? [X1] : (~generous(X1) | strong(X1)) => (~generous(sK4) | strong(sK4)) [choice axiom]
60. ((~brave(lucy) & humble(lucy)) | ! [X0] : (generous(X0) & ~strong(X0))) & ((~generous(sK4) | strong(sK4)) | brave(lucy) | ~humble(lucy)) [skolemisation 58,59]
61. ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))) [nnf transformation 11]
83. funny(X0) | generous(X0) [cnf transformation 35]
84. ~rich(X0) | generous(X0) [cnf transformation 35]
85. funny(X0) | strong(X0) [cnf transformation 35]
87. rich(alice) | ~brave(X1) | ~funny(X1) [cnf transformation 40]
94. calm(lucy) | calm(X0) | ~creative(X0) [cnf transformation 45]
97. kind(X0) | creative(X0) | rich(X0) | kind(X0) [cnf transformation 47]
100. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 47]
104. ~quiet(X0) | ~generous(X0) [cnf transformation 49]
105. ~happy(X0) | ~generous(X0) [cnf transformation 49]
119. ~brave(lucy) | ~strong(X0) [cnf transformation 60]
121. ~calm(X0) | brave(X0) [cnf transformation 61]
150. happy(john) [cnf transformation 21]
151. ~funny(paul) [cnf transformation 22]
155. quiet(alice) [cnf transformation 24]
156. kind(X0) | creative(X0) | rich(X0) [duplicate literal removal 97]
157. ~kind(X0) | creative(X0) [duplicate literal removal 100]
159. 1 <=> rich(alice) [avatar definition]
160. rich(alice) <- (1) [avatar component clause 159]
177. 5 <=> ! [X1] : (~brave(X1) | ~funny(X1)) [avatar definition]
178. ~brave(X1) | ~funny(X1) <- (5) [avatar component clause 177]
180. 5 | 1 [avatar split clause 87,159,177]
182. 6 <=> ! [X0] : (calm(X0) | ~creative(X0)) [avatar definition]
183. ~creative(X0) | calm(X0) <- (6) [avatar component clause 182]
194. 9 <=> calm(lucy) [avatar definition]
196. calm(lucy) <- (9) [avatar component clause 194]
197. 6 | 9 [avatar split clause 94,194,182]
209. creative(X0) | rich(X0) [subsumption resolution 156,157]
248. 21 <=> brave(lucy) [avatar definition]
250. ~brave(lucy) <- (~21) [avatar component clause 248]
253. 22 <=> ! [X0] : ~strong(X0) [avatar definition]
254. ~strong(X0) <- (22) [avatar component clause 253]
255. 22 | ~21 [avatar split clause 119,248,253]
291. 30 <=> brave(john) [avatar definition]
293. brave(john) <- (30) [avatar component clause 291]
378. strong(paul) [resolution 85,151]
379. $false <- (22) [subsumption resolution 378,254]
380. ~22 [avatar contradiction clause 379]
384. ~generous(alice) [resolution 104,155]
386. ~generous(john) [resolution 105,150]
394. calm(X0) | rich(X0) <- (6) [resolution 209,183]
417. 49 <=> calm(john) [avatar definition]
418. ~calm(john) <- (~49) [avatar component clause 417]
419. calm(john) <- (49) [avatar component clause 417]
455. rich(john) <- (6, ~49) [resolution 394,418]
465. brave(lucy) <- (9) [resolution 196,121]
466. $false <- (9, ~21) [subsumption resolution 465,250]
467. ~9 | 21 [avatar contradiction clause 466]
486. generous(john) <- (6, ~49) [resolution 455,84]
487. $false <- (6, ~49) [subsumption resolution 486,386]
488. ~6 | 49 [avatar contradiction clause 487]
491. brave(john) <- (49) [resolution 419,121]
494. 30 | ~49 [avatar split clause 491,417,291]
496. ~funny(john) <- (5, 30) [resolution 293,178]
515. generous(john) <- (5, 30) [resolution 496,83]
516. $false <- (5, 30) [subsumption resolution 515,386]
517. ~5 | ~30 [avatar contradiction clause 516]
528. generous(alice) <- (1) [resolution 160,84]
529. $false <- (1) [subsumption resolution 528,384]
530. ~1 [avatar contradiction clause 529]
531. $false [avatar sat refutation 180,197,255,380,467,488,494,517,530]
% SZS output end Proof for 2857311068889982437627175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both not rich and rich and vice versa.
If someone is kind then fred is both quiet and not humble and vice versa.
Everyone who is not wise is patient or not patient and vice versa.
If someone is strong then someone is both not funny and not old.
Everyone who is not rich is either not funny or not creative and vice versa.
Everyone who is not calm is both quiet and generous.
Everyone who is not funny is curious or kind.
If someone is either not curious or not wise then someone is not quiet or not patient.
Everyone who is not humble or not funny is either happy or kind and vice versa.
Everyone who is not generous or patient is both not old and generous.
Everyone who is not tall or not calm is not curious and vice versa.
Everyone who is either not funny or not tall is either funny or not happy.
Everyone who is either funny or not quiet is either not funny or tall.
Everyone who is both not wise and not brave is either funny or not old and vice versa.
Everyone who is rich is both not generous and not strong and vice versa.
Someone is both happy and not calm.
Mary is old or curious.
Paul is not tall or patient.
John is either humble or old.
Someone is not calm.
Someone is both strong and quiet.
Someone is brave. | Fred is not quiet. | contradiction | (![X]:(~patient(X)<=>(~rich(X)&rich(X))))&
((?[X]:(kind(X)))<=>((quiet(fred)&~humble(fred))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~funny(X)&~old(X)))))&
(![X]:(~rich(X)<=>(~funny(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(quiet(X)&generous(X))))&
(![X]:(~funny(X)=>(curious(X)|kind(X))))&
((?[X]:((~curious(X)<~>~wise(X))))=>(?[X]:((~quiet(X)|~patient(X)))))&
(![X]:((~humble(X)|~funny(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~generous(X)|patient(X))=>(~old(X)&generous(X))))&
(![X]:((~tall(X)|~calm(X))<=>~curious(X)))&
(![X]:((~funny(X)<~>~tall(X))=>(funny(X)<~>~happy(X))))&
(![X]:((funny(X)<~>~quiet(X))=>(~funny(X)<~>tall(X))))&
(![X]:((~wise(X)&~brave(X))<=>(funny(X)<~>~old(X))))&
(![X]:(rich(X)<=>(~generous(X)&~strong(X))))&
(?[X]:((happy(X)&~calm(X))))&
((old(mary)|curious(mary)))&
((~tall(paul)|patient(paul)))&
((humble(john)<~>old(john)))&
(?[X]:(~calm(X)))&
(?[X]:((strong(X)&quiet(X))))&
(?[X]:(brave(X))) | ~quiet(fred) | [
"p1",
"p3",
"p6",
"p8",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3705252689099560290967845
% SZS output start Proof for 3705252689099560290967845
2. ? [X0] : kind(X0) <=> (~humble(fred) & quiet(fred)) [input p1]
4. ? [X0] : strong(X0) => ? [X0] : (~old(X0) & ~funny(X0)) [input p3]
7. ! [X0] : (~funny(X0) => (kind(X0) | curious(X0))) [input p6]
9. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (happy(X0) <~> kind(X0))) [input p8]
11. ! [X0] : ((~calm(X0) | ~tall(X0)) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((~funny(X0) <~> ~tall(X0)) => (funny(X0) <~> ~happy(X0))) [input p11]
21. ? [X0] : (quiet(X0) & strong(X0)) [input p20]
23. ~quiet(fred) [input hypothesis]
24. ? [X0] : strong(X0) => ? [X1] : (~old(X1) & ~funny(X1)) [rectify 4]
26. ? [X1] : (~old(X1) & ~funny(X1)) | ! [X0] : ~strong(X0) [ennf transformation 24]
28. ! [X0] : ((kind(X0) | curious(X0)) | funny(X0)) [ennf transformation 7]
29. ! [X0] : (kind(X0) | curious(X0) | funny(X0)) [flattening 28]
32. ! [X0] : ((funny(X0) <~> ~happy(X0)) | (~funny(X0) <=> ~tall(X0))) [ennf transformation 12]
36. (? [X0] : kind(X0) | (humble(fred) | ~quiet(fred))) & ((~humble(fred) & quiet(fred)) | ! [X0] : ~kind(X0)) [nnf transformation 2]
37. (? [X0] : kind(X0) | humble(fred) | ~quiet(fred)) & ((~humble(fred) & quiet(fred)) | ! [X0] : ~kind(X0)) [flattening 36]
38. (? [X0] : kind(X0) | humble(fred) | ~quiet(fred)) & ((~humble(fred) & quiet(fred)) | ! [X1] : ~kind(X1)) [rectify 37]
39. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
40. (kind(sK0) | humble(fred) | ~quiet(fred)) & ((~humble(fred) & quiet(fred)) | ! [X1] : ~kind(X1)) [skolemisation 38,39]
43. ? [X0] : (~old(X0) & ~funny(X0)) | ! [X1] : ~strong(X1) [rectify 26]
44. ? [X0] : (~old(X0) & ~funny(X0)) => (~old(sK1) & ~funny(sK1)) [choice axiom]
45. (~old(sK1) & ~funny(sK1)) | ! [X1] : ~strong(X1) [skolemisation 43,44]
51. ! [X0] : (((~funny(X0) | ~humble(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) & (((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (funny(X0) & humble(X0)))) [nnf transformation 9]
52. ! [X0] : ((~funny(X0) | ~humble(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) & (((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (funny(X0) & humble(X0)))) [flattening 51]
53. ! [X0] : (((~calm(X0) | ~tall(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) & tall(X0)))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | ~tall(X0) | curious(X0)) & (~curious(X0) | (calm(X0) & tall(X0)))) [flattening 53]
55. ! [X0] : (((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) [nnf transformation 32]
66. ? [X0] : (quiet(X0) & strong(X0)) => (quiet(sK5) & strong(sK5)) [choice axiom]
67. quiet(sK5) & strong(sK5) [skolemisation 21,66]
73. quiet(fred) | ~kind(X1) [cnf transformation 40]
79. ~funny(sK1) | ~strong(X1) [cnf transformation 45]
87. curious(X0) | kind(X0) | funny(X0) [cnf transformation 29]
91. happy(X0) | kind(X0) | funny(X0) [cnf transformation 52]
100. ~curious(X0) | tall(X0) [cnf transformation 54]
103. ~happy(X0) | funny(X0) | ~tall(X0) | funny(X0) [cnf transformation 55]
127. strong(sK5) [cnf transformation 67]
130. ~quiet(fred) [cnf transformation 23]
133. ~tall(X0) | funny(X0) | ~happy(X0) [duplicate literal removal 103]
138. 1 <=> quiet(fred) [avatar definition]
151. 4 <=> ! [X1] : ~kind(X1) [avatar definition]
152. ~kind(X1) <- (4) [avatar component clause 151]
154. 4 | 1 [avatar split clause 73,138,151]
157. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
158. ~strong(X1) <- (5) [avatar component clause 157]
165. 7 <=> funny(sK1) [avatar definition]
167. ~funny(sK1) <- (~7) [avatar component clause 165]
168. 5 | ~7 [avatar split clause 79,165,157]
187. ~1 [avatar split clause 130,138]
202. kind(X1) | funny(X1) | tall(X1) [resolution 87,100]
204. tall(X1) | funny(X1) <- (4) [subsumption resolution 202,152]
292. funny(X0) | funny(X0) | ~happy(X0) <- (4) [resolution 204,133]
296. ~happy(X0) | funny(X0) <- (4) [duplicate literal removal 292]
311. funny(X0) | kind(X0) | funny(X0) <- (4) [resolution 296,91]
313. funny(X0) | kind(X0) <- (4) [duplicate literal removal 311]
314. funny(X0) <- (4) [subsumption resolution 313,152]
323. $false <- (4, ~7) [resolution 314,167]
329. ~4 | 7 [avatar contradiction clause 323]
330. $false <- (5) [resolution 158,127]
331. ~5 [avatar contradiction clause 330]
332. $false [avatar sat refutation 154,168,187,329,331]
% SZS output end Proof for 3705252689099560290967845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then mary is not kind or not brave. Everyone who is both old and not quiet is either not funny or not generous. If someone is not brave or not kind then paul is not wise and vice versa. Everyone who is either not wise or not tall is not kind or kind. Everyone who is both creative and not kind is either not kind or patient and vice versa. Everyone who is both curious and not tall is brave and vice versa. Everyone who is either curious or not curious is both kind and wise and vice versa. Everyone who is not strong is not rich and vice versa. If someone is not generous then someone is not generous or calm and vice versa. If john is either not brave or creative then someone is not wise. Everyone who is both not brave and not curious is not happy or tall. Everyone who is not quiet is kind. Everyone who is not rich is not brave or generous. Everyone who is happy or not rich is not quiet and vice versa. Everyone who is both curious and not humble is either not humble or old and vice versa. Someone is both not calm and not rich. Lucy is not calm or not kind. Someone is both humble and not strong. Mary is wise. Mary is not happy or not rich. Someone is both not tall and happy. | Mary is not tall. | entailment | ((?[X]:(creative(X)))=>((~kind(mary)|~brave(mary))))&
(![X]:((old(X)&~quiet(X))=>(~funny(X)<~>~generous(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~wise(paul)))&
(![X]:((~wise(X)<~>~tall(X))=>(~kind(X)|kind(X))))&
(![X]:((creative(X)&~kind(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((curious(X)&~tall(X))<=>brave(X)))&
(![X]:((curious(X)<~>~curious(X))<=>(kind(X)&wise(X))))&
(![X]:(~strong(X)<=>~rich(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)|calm(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(~wise(X))))&
(![X]:((~brave(X)&~curious(X))=>(~happy(X)|tall(X))))&
(![X]:(~quiet(X)=>kind(X)))&
(![X]:(~rich(X)=>(~brave(X)|generous(X))))&
(![X]:((happy(X)|~rich(X))<=>~quiet(X)))&
(![X]:((curious(X)&~humble(X))<=>(~humble(X)<~>old(X))))&
(?[X]:((~calm(X)&~rich(X))))&
((~calm(lucy)|~kind(lucy)))&
(?[X]:((humble(X)&~strong(X))))&
(wise(mary))&
((~happy(mary)|~rich(mary)))&
(?[X]:((~tall(X)&happy(X)))) | ~tall(mary) | [
"p2",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3659822614495446801291932
% SZS output start Proof for 3659822614495446801291932
3. ? [X0] : (~kind(X0) | ~brave(X0)) <=> ~wise(paul) [input p2]
6. ! [X0] : ((~tall(X0) & curious(X0)) <=> brave(X0)) [input p5]
7. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (wise(X0) & kind(X0))) [input p6]
22. tall(mary) [input hypothesis]
41. (? [X0] : (~kind(X0) | ~brave(X0)) | wise(paul)) & (~wise(paul) | ! [X0] : (kind(X0) & brave(X0))) [nnf transformation 3]
42. (? [X0] : (~kind(X0) | ~brave(X0)) | wise(paul)) & (~wise(paul) | ! [X1] : (kind(X1) & brave(X1))) [rectify 41]
43. ? [X0] : (~kind(X0) | ~brave(X0)) => (~kind(sK0) | ~brave(sK0)) [choice axiom]
44. ((~kind(sK0) | ~brave(sK0)) | wise(paul)) & (~wise(paul) | ! [X1] : (kind(X1) & brave(X1))) [skolemisation 42,43]
48. ! [X0] : (((~tall(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | (tall(X0) | ~curious(X0)))) [nnf transformation 6]
49. ! [X0] : (((~tall(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | tall(X0) | ~curious(X0))) [flattening 48]
50. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 7]
51. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 50]
71. ~wise(paul) | brave(X1) [cnf transformation 44]
84. ~tall(X0) | ~brave(X0) [cnf transformation 49]
87. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 51]
88. wise(X0) | curious(X0) | curious(X0) [cnf transformation 51]
117. tall(mary) [cnf transformation 22]
122. wise(X0) | ~curious(X0) [duplicate literal removal 87]
123. wise(X0) | curious(X0) [duplicate literal removal 88]
139. 4 <=> wise(paul) [avatar definition]
140. ~wise(paul) <- (~4) [avatar component clause 139]
156. 8 <=> ! [X1] : brave(X1) [avatar definition]
157. brave(X1) <- (8) [avatar component clause 156]
158. 8 | ~4 [avatar split clause 71,139,156]
160. wise(X0) [subsumption resolution 122,123]
216. $false <- (~4) [subsumption resolution 140,160]
217. 4 [avatar contradiction clause 216]
229. ~brave(mary) [resolution 84,117]
230. $false <- (8) [subsumption resolution 229,157]
231. ~8 [avatar contradiction clause 230]
232. $false [avatar sat refutation 158,217,231]
% SZS output end Proof for 3659822614495446801291932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then fred is either not curious or not happy and vice versa.
If someone is not quiet then someone is both generous and not quiet and vice versa.
Everyone who is not tall or tall is either patient or not happy.
Everyone who is either curious or happy is both brave and not brave and vice versa.
If mary is not creative then mary is either brave or tall and vice versa.
Everyone who is not creative is generous.
If someone is brave or creative then paul is not generous.
If someone is both calm and not brave then mary is both wise and curious.
Everyone who is either calm or curious is either generous or not funny and vice versa.
Everyone who is kind is both not brave and not funny and vice versa.
If susan is both tall and not curious then susan is both not rich and not funny and vice versa.
Everyone who is humble or patient is happy or patient and vice versa.
Everyone who is both not calm and not strong is either rich or not wise.
If john is not tall or not curious then someone is not strong or strong.
Everyone who is both not brave and creative is both not patient and quiet.
Someone is either not rich or humble.
Someone is either not creative or patient.
Mary is funny.
Someone is either old or not quiet.
Someone is generous or not happy.
Someone is generous.
Mary is tall. | Mary is brave. | neutral | ((?[X]:(~patient(X)))<=>((~curious(fred)<~>~happy(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((?[X]:((brave(X)|creative(X))))=>(~generous(paul)))&
((?[X]:((calm(X)&~brave(X))))=>((wise(mary)&curious(mary))))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)<~>~funny(X))))&
(![X]:(kind(X)<=>(~brave(X)&~funny(X))))&
(((tall(susan)&~curious(susan)))<=>((~rich(susan)&~funny(susan))))&
(![X]:((humble(X)|patient(X))<=>(happy(X)|patient(X))))&
(![X]:((~calm(X)&~strong(X))=>(rich(X)<~>~wise(X))))&
(((~tall(john)|~curious(john)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((~brave(X)&creative(X))=>(~patient(X)&quiet(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(funny(mary))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:(generous(X)))&
(tall(mary)) | brave(mary) | [] | null | 0 |
If alice is either not strong or not rich then paul is strong. If john is wise then fred is calm or strong. Everyone who is curious or not kind is quiet. If someone is quiet or calm then fred is both not curious and quiet and vice versa. If someone is not curious then someone is not funny or not brave. If someone is not brave or calm then someone is either generous or not calm. Everyone who is quiet or humble is both not happy and patient and vice versa. If alice is either not kind or not brave then someone is either not funny or not humble. If someone is tall then lucy is either not old or not strong. If someone is both creative and not kind then someone is both tall and funny. Everyone who is not old or not wise is rich and vice versa. Everyone who is rich is both not tall and wise. Everyone who is either not patient or patient is both strong and not curious and vice versa. If someone is calm or humble then someone is both wise and calm. If someone is not creative or not strong then lucy is both kind and brave. Everyone who is kind is both not kind and not strong. Fred is both wise and calm. Someone is not calm. Someone is wise or calm. John is not calm. | John is not funny. | neutral | (((~strong(alice)<~>~rich(alice)))=>(strong(paul)))&
((wise(john))=>((calm(fred)|strong(fred))))&
(![X]:((curious(X)|~kind(X))=>quiet(X)))&
((?[X]:((quiet(X)|calm(X))))<=>((~curious(fred)&quiet(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|~brave(X)))))&
((?[X]:((~brave(X)|calm(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((quiet(X)|humble(X))<=>(~happy(X)&patient(X))))&
(((~kind(alice)<~>~brave(alice)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:(tall(X)))=>((~old(lucy)<~>~strong(lucy))))&
((?[X]:((creative(X)&~kind(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~old(X)|~wise(X))<=>rich(X)))&
(![X]:(rich(X)=>(~tall(X)&wise(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:((~creative(X)|~strong(X))))=>((kind(lucy)&brave(lucy))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
((wise(fred)&calm(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)|calm(X))))&
(~calm(john)) | ~funny(john) | [] | null | 0 |
Subsets and Splits