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 susan is either calm or patient then paul is both kind and old. Everyone who is both not tall and not patient is rich. If someone is humble then susan is both kind and quiet and vice versa. If mary is rich or not rich then alice is quiet. Everyone who is rich or wise is humble and vice versa. Everyone who is either patient or strong is both generous and not creative and vice versa. Everyone who is wise or not calm is either rich or not humble and vice versa. Everyone who is either quiet or not creative is not rich or not quiet and vice versa. Everyone who is either brave or curious is either not quiet or rich. If lucy is not humble then someone is not tall and vice versa. If mary is brave or funny then someone is not old or not brave and vice versa. If alice is both strong and tall then john is quiet or tall. Everyone who is not humble or kind is either not rich or not strong. If someone is both rich and strong then mary is either not old or not humble. Everyone who is kind is both not tall and not old and vice versa. If alice is either happy or not generous then someone is not strong and vice versa. Someone is either not quiet or not humble. Mary is either tall or not wise. Mary is old or not creative. Lucy is curious. Susan is old or generous. Someone is not creative or old. | Paul is brave. | neutral | (((calm(susan)<~>patient(susan)))=>((kind(paul)&old(paul))))&
(![X]:((~tall(X)&~patient(X))=>rich(X)))&
((?[X]:(humble(X)))<=>((kind(susan)&quiet(susan))))&
(((rich(mary)|~rich(mary)))=>(quiet(alice)))&
(![X]:((rich(X)|wise(X))<=>humble(X)))&
(![X]:((patient(X)<~>strong(X))<=>(generous(X)&~creative(X))))&
(![X]:((wise(X)|~calm(X))<=>(rich(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~rich(X)|~quiet(X))))&
(![X]:((brave(X)<~>curious(X))=>(~quiet(X)<~>rich(X))))&
((~humble(lucy))<=>(?[X]:(~tall(X))))&
(((brave(mary)|funny(mary)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((strong(alice)&tall(alice)))=>((quiet(john)|tall(john))))&
(![X]:((~humble(X)|kind(X))=>(~rich(X)<~>~strong(X))))&
((?[X]:((rich(X)&strong(X))))=>((~old(mary)<~>~humble(mary))))&
(![X]:(kind(X)<=>(~tall(X)&~old(X))))&
(((happy(alice)<~>~generous(alice)))<=>(?[X]:(~strong(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((tall(mary)<~>~wise(mary)))&
((old(mary)|~creative(mary)))&
(curious(lucy))&
((old(susan)|generous(susan)))&
(?[X]:((~creative(X)|old(X)))) | brave(paul) | [] | null | 0 |
Everyone who is not creative or calm is both not calm and not patient and vice versa. If someone is both not calm and not humble then someone is not humble or curious and vice versa. Everyone who is not patient is creative or humble and vice versa. If paul is tall or not generous then someone is funny or quiet. Everyone who is not funny or not brave is creative and vice versa. If john is both not generous and humble then susan is either calm or brave and vice versa. If someone is either tall or brave then someone is not funny. If someone is both kind and not patient then someone is both old and not tall. If lucy is both not tall and old then someone is both humble and not quiet. Everyone who is both not happy and not wise is either creative or patient. If paul is quiet then alice is either not kind or wise and vice versa. If lucy is old then someone is not happy. If alice is both not wise and creative then someone is not happy and vice versa. If someone is generous or happy then someone is strong or not funny. Someone is either old or not tall. Someone is not funny or happy. Alice is old or not quiet. Someone is funny or patient. | Susan is tall. | entailment | (![X]:((~creative(X)|calm(X))<=>(~calm(X)&~patient(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:(~patient(X)<=>(creative(X)|humble(X))))&
(((tall(paul)|~generous(paul)))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((~funny(X)|~brave(X))<=>creative(X)))&
(((~generous(john)&humble(john)))<=>((calm(susan)<~>brave(susan))))&
((?[X]:((tall(X)<~>brave(X))))=>(?[X]:(~funny(X))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((old(X)&~tall(X)))))&
(((~tall(lucy)&old(lucy)))=>(?[X]:((humble(X)&~quiet(X)))))&
(![X]:((~happy(X)&~wise(X))=>(creative(X)<~>patient(X))))&
((quiet(paul))<=>((~kind(alice)<~>wise(alice))))&
((old(lucy))=>(?[X]:(~happy(X))))&
(((~wise(alice)&creative(alice)))<=>(?[X]:(~happy(X))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:((strong(X)|~funny(X)))))&
(?[X]:((old(X)<~>~tall(X))))&
(?[X]:((~funny(X)|happy(X))))&
((old(alice)|~quiet(alice)))&
(?[X]:((funny(X)|patient(X)))) | tall(susan) | [
"p0",
"p2",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8696047949315101171879033
% SZS output start Proof for 8696047949315101171879033
1. ! [X0] : ((calm(X0) | ~creative(X0)) <=> (~patient(X0) & ~calm(X0))) [input p0]
3. ! [X0] : (~patient(X0) <=> (humble(X0) | creative(X0))) [input p2]
5. ! [X0] : ((~brave(X0) | ~funny(X0)) <=> creative(X0)) [input p4]
7. ? [X0] : (tall(X0) <~> brave(X0)) => ? [X0] : ~funny(X0) [input p6]
19. ~tall(susan) [input hypothesis]
21. ? [X0] : (tall(X0) <~> brave(X0)) => ? [X1] : ~funny(X1) [rectify 7]
26. ? [X1] : ~funny(X1) | ! [X0] : (tall(X0) <=> brave(X0)) [ennf transformation 21]
33. ! [X0] : (((calm(X0) | ~creative(X0)) | (patient(X0) | calm(X0))) & ((~patient(X0) & ~calm(X0)) | (~calm(X0) & creative(X0)))) [nnf transformation 1]
34. ! [X0] : ((calm(X0) | ~creative(X0) | patient(X0) | calm(X0)) & ((~patient(X0) & ~calm(X0)) | (~calm(X0) & creative(X0)))) [flattening 33]
40. ! [X0] : ((~patient(X0) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | patient(X0))) [nnf transformation 3]
41. ! [X0] : ((~patient(X0) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | patient(X0))) [flattening 40]
44. ! [X0] : (((~brave(X0) | ~funny(X0)) | ~creative(X0)) & (creative(X0) | (brave(X0) & funny(X0)))) [nnf transformation 5]
45. ! [X0] : ((~brave(X0) | ~funny(X0) | ~creative(X0)) & (creative(X0) | (brave(X0) & funny(X0)))) [flattening 44]
48. ? [X1] : ~funny(X1) | ! [X0] : ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))) [nnf transformation 26]
49. ? [X0] : ~funny(X0) | ! [X1] : ((tall(X1) | ~brave(X1)) & (brave(X1) | ~tall(X1))) [rectify 48]
50. ? [X0] : ~funny(X0) => ~funny(sK3) [choice axiom]
51. ~funny(sK3) | ! [X1] : ((tall(X1) | ~brave(X1)) & (brave(X1) | ~tall(X1))) [skolemisation 49,50]
74. ~calm(X0) | ~calm(X0) [cnf transformation 34]
75. ~patient(X0) | creative(X0) [cnf transformation 34]
77. calm(X0) | ~creative(X0) | patient(X0) | calm(X0) [cnf transformation 34]
84. ~patient(X0) | ~creative(X0) [cnf transformation 41]
88. funny(X0) | creative(X0) [cnf transformation 45]
89. brave(X0) | creative(X0) [cnf transformation 45]
98. ~funny(sK3) | tall(X1) | ~brave(X1) [cnf transformation 51]
118. ~tall(susan) [cnf transformation 19]
119. ~calm(X0) [duplicate literal removal 74]
120. ~creative(X0) | calm(X0) | patient(X0) [duplicate literal removal 77]
143. ~patient(X0) [subsumption resolution 84,75]
165. 10 <=> brave(susan) [avatar definition]
166. brave(susan) <- (10) [avatar component clause 165]
167. ~brave(susan) <- (~10) [avatar component clause 165]
182. 13 <=> ! [X1] : (tall(X1) | ~brave(X1)) [avatar definition]
183. ~brave(X1) | tall(X1) <- (13) [avatar component clause 182]
185. 14 <=> funny(sK3) [avatar definition]
187. ~funny(sK3) <- (~14) [avatar component clause 185]
188. 13 | ~14 [avatar split clause 98,185,182]
291. creative(sK3) <- (~14) [resolution 88,187]
293. creative(susan) <- (~10) [resolution 89,167]
299. calm(sK3) | patient(sK3) <- (~14) [resolution 120,291]
301. calm(susan) | patient(susan) <- (~10) [resolution 120,293]
302. patient(sK3) <- (~14) [subsumption resolution 299,119]
303. $false <- (~14) [subsumption resolution 302,143]
304. 14 [avatar contradiction clause 303]
308. patient(susan) <- (~10) [subsumption resolution 301,119]
309. $false <- (~10) [subsumption resolution 308,143]
310. 10 [avatar contradiction clause 309]
323. tall(susan) <- (10, 13) [resolution 183,166]
324. $false <- (10, 13) [subsumption resolution 323,118]
325. ~10 | ~13 [avatar contradiction clause 324]
326. $false [avatar sat refutation 188,304,310,325]
% SZS output end Proof for 8696047949315101171879033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and calm then someone is both not funny and tall. If someone is funny or not patient then susan is brave or rich. If someone is wise or brave then someone is either not brave or generous. If mary is not wise or not brave then someone is humble and vice versa. If someone is humble then someone is not creative or rich and vice versa. Everyone who is either not old or rich is either happy or not funny and vice versa. Everyone who is either funny or not rich is generous or quiet. Everyone who is funny is both old and not humble and vice versa. If lucy is both not generous and strong then someone is not curious or not humble and vice versa. If lucy is not generous then fred is not creative and vice versa. If john is either not rich or not kind then susan is calm or humble and vice versa. Everyone who is both humble and wise is both old and not curious and vice versa. Everyone who is both not quiet and brave is rich. Everyone who is both calm and not tall is not strong and vice versa. If lucy is either generous or not generous then susan is either brave or not creative. Everyone who is both not generous and old is not old. Mary is old. Mary is kind or not humble. Mary is not wise or not humble. Lucy is not humble. Lucy is calm or not generous. Susan is either wise or patient. Paul is patient. Paul is not generous. | Mary is not generous. | contradiction | ((?[X]:((brave(X)&calm(X))))=>(?[X]:((~funny(X)&tall(X)))))&
((?[X]:((funny(X)|~patient(X))))=>((brave(susan)|rich(susan))))&
((?[X]:((wise(X)|brave(X))))=>(?[X]:((~brave(X)<~>generous(X)))))&
(((~wise(mary)|~brave(mary)))<=>(?[X]:(humble(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((funny(X)<~>~rich(X))=>(generous(X)|quiet(X))))&
(![X]:(funny(X)<=>(old(X)&~humble(X))))&
(((~generous(lucy)&strong(lucy)))<=>(?[X]:((~curious(X)|~humble(X)))))&
((~generous(lucy))<=>(~creative(fred)))&
(((~rich(john)<~>~kind(john)))<=>((calm(susan)|humble(susan))))&
(![X]:((humble(X)&wise(X))<=>(old(X)&~curious(X))))&
(![X]:((~quiet(X)&brave(X))=>rich(X)))&
(![X]:((calm(X)&~tall(X))<=>~strong(X)))&
(((generous(lucy)<~>~generous(lucy)))=>((brave(susan)<~>~creative(susan))))&
(![X]:((~generous(X)&old(X))=>~old(X)))&
(old(mary))&
((kind(mary)|~humble(mary)))&
((~wise(mary)|~humble(mary)))&
(~humble(lucy))&
((calm(lucy)|~generous(lucy)))&
((wise(susan)<~>patient(susan)))&
(patient(paul))&
(~generous(paul)) | ~generous(mary) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4594000282788125458471942
% SZS output start Proof for 4594000282788125458471942
16. ! [X0] : ((old(X0) & ~generous(X0)) => ~old(X0)) [input p15]
17. old(mary) [input p16]
25. ~generous(mary) [input hypothesis]
36. ! [X0] : (~old(X0) | (~old(X0) | generous(X0))) [ennf transformation 16]
37. ! [X0] : (~old(X0) | ~old(X0) | generous(X0)) [flattening 36]
121. ~old(X0) | ~old(X0) | generous(X0) [cnf transformation 37]
122. old(mary) [cnf transformation 17]
131. ~generous(mary) [cnf transformation 25]
132. ~old(X0) | generous(X0) [duplicate literal removal 121]
316. generous(mary) [resolution 132,122]
317. $false [subsumption resolution 316,131]
% SZS output end Proof for 4594000282788125458471942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or old then john is either not creative or not funny and vice versa.
If john is either not tall or generous then someone is either tall or happy and vice versa.
Everyone who is either not brave or curious is creative or not creative.
Everyone who is both humble and not happy is not creative and vice versa.
If someone is curious then john is either strong or not brave and vice versa.
If someone is not creative or brave then someone is wise or generous.
If someone is not funny then susan is tall or not wise and vice versa.
Everyone who is either strong or not curious is both not brave and patient and vice versa.
If someone is calm or kind then susan is quiet or calm and vice versa.
Everyone who is both patient and not creative is curious or old and vice versa.
Everyone who is wise is either not tall or strong and vice versa.
If lucy is brave then someone is creative or not strong.
Everyone who is not happy or not rich is either not old or tall.
If alice is not patient then someone is not old or happy and vice versa.
Everyone who is either not quiet or not generous is not generous or patient and vice versa.
If john is funny then someone is patient or calm.
Alice is either not creative or not happy.
Fred is not humble or funny.
Someone is either wise or rich.
Alice is not generous.
Mary is tall.
Someone is either old or not wise.
Someone is either curious or not wise.
Lucy is creative or quiet. | Susan is creative. | neutral | ((?[X]:((~calm(X)|old(X))))<=>((~creative(john)<~>~funny(john))))&
(((~tall(john)<~>generous(john)))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(creative(X)|~creative(X))))&
(![X]:((humble(X)&~happy(X))<=>~creative(X)))&
((?[X]:(curious(X)))<=>((strong(john)<~>~brave(john))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:(~funny(X)))<=>((tall(susan)|~wise(susan))))&
(![X]:((strong(X)<~>~curious(X))<=>(~brave(X)&patient(X))))&
((?[X]:((calm(X)|kind(X))))<=>((quiet(susan)|calm(susan))))&
(![X]:((patient(X)&~creative(X))<=>(curious(X)|old(X))))&
(![X]:(wise(X)<=>(~tall(X)<~>strong(X))))&
((brave(lucy))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((~happy(X)|~rich(X))=>(~old(X)<~>tall(X))))&
((~patient(alice))<=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~generous(X)|patient(X))))&
((funny(john))=>(?[X]:((patient(X)|calm(X)))))&
((~creative(alice)<~>~happy(alice)))&
((~humble(fred)|funny(fred)))&
(?[X]:((wise(X)<~>rich(X))))&
(~generous(alice))&
(tall(mary))&
(?[X]:((old(X)<~>~wise(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
((creative(lucy)|quiet(lucy))) | creative(susan) | [] | null | 0 |
Everyone who is either not happy or creative is old and vice versa.
Everyone who is old is both not rich and creative and vice versa.
If someone is not humble or not wise then someone is both not curious and patient and vice versa.
If paul is both not wise and not funny then paul is wise or brave.
Everyone who is not rich or patient is creative or not calm and vice versa.
Everyone who is not rich is both humble and patient.
If paul is both generous and not generous then someone is not rich or kind and vice versa.
Everyone who is either not strong or not calm is patient.
Everyone who is either strong or brave is either not creative or humble.
If mary is rich then alice is not patient or not happy and vice versa.
Everyone who is both creative and not kind is not creative.
If paul is funny or not wise then paul is both not funny and not kind and vice versa.
Everyone who is both old and curious is not humble or kind and vice versa.
If someone is not calm or not rich then john is both not calm and not quiet.
If mary is strong or not happy then fred is either not generous or not wise.
If someone is either curious or not rich then someone is either not funny or not patient and vice versa.
Someone is tall.
Someone is calm.
Someone is not calm or not brave.
John is strong.
Someone is not strong or not wise.
Someone is not calm.
Lucy is either happy or tall.
Someone is not generous. | Mary is kind. | contradiction | (![X]:((~happy(X)<~>creative(X))<=>old(X)))&
(![X]:(old(X)<=>(~rich(X)&creative(X))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(((~wise(paul)&~funny(paul)))=>((wise(paul)|brave(paul))))&
(![X]:((~rich(X)|patient(X))<=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)=>(humble(X)&patient(X))))&
(((generous(paul)&~generous(paul)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))=>patient(X)))&
(![X]:((strong(X)<~>brave(X))=>(~creative(X)<~>humble(X))))&
((rich(mary))<=>((~patient(alice)|~happy(alice))))&
(![X]:((creative(X)&~kind(X))=>~creative(X)))&
(((funny(paul)|~wise(paul)))<=>((~funny(paul)&~kind(paul))))&
(![X]:((old(X)&curious(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((~calm(john)&~quiet(john))))&
(((strong(mary)|~happy(mary)))=>((~generous(fred)<~>~wise(fred))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(?[X]:(tall(X)))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)|~brave(X))))&
(strong(john))&
(?[X]:((~strong(X)|~wise(X))))&
(?[X]:(~calm(X)))&
((happy(lucy)<~>tall(lucy)))&
(?[X]:(~generous(X))) | kind(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2988525403814911448111701
% SZS output start Proof for 2988525403814911448111701
7. (~generous(paul) & generous(paul)) <=> ? [X0] : (kind(X0) | ~rich(X0)) [input p6]
25. kind(mary) [input hypothesis]
48. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | (generous(paul) | ~generous(paul))) [nnf transformation 7]
49. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | generous(paul) | ~generous(paul)) [flattening 48]
50. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X1] : (kind(X1) | ~rich(X1)) | generous(paul) | ~generous(paul)) [rectify 49]
51. ? [X1] : (kind(X1) | ~rich(X1)) => (kind(sK2) | ~rich(sK2)) [choice axiom]
52. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & ((kind(sK2) | ~rich(sK2)) | generous(paul) | ~generous(paul)) [skolemisation 50,51]
101. generous(paul) | ~kind(X0) [cnf transformation 52]
103. ~generous(paul) | ~kind(X0) [cnf transformation 52]
147. kind(mary) [cnf transformation 25]
196. 11 <=> ! [X0] : ~kind(X0) [avatar definition]
197. ~kind(X0) <- (11) [avatar component clause 196]
199. 12 <=> generous(paul) [avatar definition]
202. 11 | ~12 [avatar split clause 103,199,196]
207. 11 | 12 [avatar split clause 101,199,196]
332. $false <- (11) [resolution 197,147]
333. ~11 [avatar contradiction clause 332]
334. $false [avatar sat refutation 202,207,333]
% SZS output end Proof for 2988525403814911448111701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not strong is both not humble and not strong.
Everyone who is either not wise or not generous is not rich.
Everyone who is patient is not calm or humble.
Everyone who is both not brave and creative is both funny and humble.
If someone is both not humble and creative then someone is not quiet or patient.
Everyone who is calm is both happy and tall.
Everyone who is either wise or kind is quiet and vice versa.
Everyone who is both not old and rich is either quiet or calm.
Everyone who is either calm or happy is humble or wise and vice versa.
Everyone who is either not generous or not calm is not brave or not funny and vice versa.
Everyone who is happy or not curious is not happy and vice versa.
If paul is not tall then john is tall and vice versa.
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Everyone who is either not tall or not funny is not tall and vice versa.
If someone is kind then someone is quiet.
Lucy is either old or not creative.
Someone is humble or not kind.
Someone is generous or patient.
Someone is brave.
Someone is patient or not humble. | Lucy is not humble. | entailment | (![X]:((happy(X)&~strong(X))=>(~humble(X)&~strong(X))))&
(![X]:((~wise(X)<~>~generous(X))=>~rich(X)))&
(![X]:(patient(X)=>(~calm(X)|humble(X))))&
(![X]:((~brave(X)&creative(X))=>(funny(X)&humble(X))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:(calm(X)=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>kind(X))<=>quiet(X)))&
(![X]:((~old(X)&rich(X))=>(quiet(X)<~>calm(X))))&
(![X]:((calm(X)<~>happy(X))<=>(humble(X)|wise(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~brave(X)|~funny(X))))&
(![X]:((happy(X)|~curious(X))<=>~happy(X)))&
((~tall(paul))<=>(tall(john)))&
(((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
((old(lucy)<~>~creative(lucy)))&
(?[X]:((humble(X)|~kind(X))))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((patient(X)|~humble(X)))) | ~humble(lucy) | [
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3503115170025248726926239
% SZS output start Proof for 3503115170025248726926239
6. ! [X0] : (calm(X0) => (tall(X0) & happy(X0))) [input p5]
9. ! [X0] : ((calm(X0) <~> happy(X0)) <=> (wise(X0) | humble(X0))) [input p8]
11. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~happy(X0)) [input p10]
22. humble(lucy) [input hypothesis]
34. ! [X0] : ((tall(X0) & happy(X0)) | ~calm(X0)) [ennf transformation 6]
40. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [nnf transformation 9]
41. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [flattening 40]
44. ! [X0] : (((~curious(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 11]
45. ! [X0] : ((~curious(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [flattening 44]
73. ~calm(X0) | happy(X0) [cnf transformation 34]
81. happy(X0) | calm(X0) | ~humble(X0) [cnf transformation 41]
83. ~happy(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 41]
91. ~happy(X0) | ~happy(X0) [cnf transformation 45]
114. humble(lucy) [cnf transformation 22]
117. ~happy(X0) [duplicate literal removal 91]
132. ~calm(X0) | ~humble(X0) [subsumption resolution 83,73]
134. ~humble(X0) | happy(X0) [subsumption resolution 81,132]
212. happy(lucy) [resolution 134,114]
213. $false [subsumption resolution 212,117]
% SZS output end Proof for 3503115170025248726926239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not curious is not strong and vice versa.
If someone is not curious or funny then paul is not rich and vice versa.
Everyone who is both not quiet and not strong is both not generous and old and vice versa.
If someone is happy then alice is both patient and brave.
If lucy is happy then paul is not rich or not curious and vice versa.
Everyone who is either not kind or not wise is not humble or calm and vice versa.
If john is patient then someone is quiet.
Everyone who is either not patient or not quiet is either funny or humble.
If someone is either not old or not quiet then susan is either humble or not wise.
Everyone who is either happy or brave is either humble or not creative.
Everyone who is not kind or not curious is creative.
If someone is either patient or humble then john is happy or not generous and vice versa.
If paul is not quiet or old then someone is either generous or not happy and vice versa.
Everyone who is not patient is humble or not old and vice versa.
Everyone who is not old is generous or wise and vice versa.
If someone is curious or not old then paul is not funny or kind and vice versa.
Someone is either strong or not curious.
Someone is not old.
Someone is kind or not old.
Someone is either not old or wise.
Mary is not generous.
Someone is either tall or not happy. | John is generous. | neutral | (![X]:((~happy(X)&~curious(X))<=>~strong(X)))&
((?[X]:((~curious(X)|funny(X))))<=>(~rich(paul)))&
(![X]:((~quiet(X)&~strong(X))<=>(~generous(X)&old(X))))&
((?[X]:(happy(X)))=>((patient(alice)&brave(alice))))&
((happy(lucy))<=>((~rich(paul)|~curious(paul))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~humble(X)|calm(X))))&
((patient(john))=>(?[X]:(quiet(X))))&
(![X]:((~patient(X)<~>~quiet(X))=>(funny(X)<~>humble(X))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((humble(susan)<~>~wise(susan))))&
(![X]:((happy(X)<~>brave(X))=>(humble(X)<~>~creative(X))))&
(![X]:((~kind(X)|~curious(X))=>creative(X)))&
((?[X]:((patient(X)<~>humble(X))))<=>((happy(john)|~generous(john))))&
(((~quiet(paul)|old(paul)))<=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(~patient(X)<=>(humble(X)|~old(X))))&
(![X]:(~old(X)<=>(generous(X)|wise(X))))&
((?[X]:((curious(X)|~old(X))))<=>((~funny(paul)|kind(paul))))&
(?[X]:((strong(X)<~>~curious(X))))&
(?[X]:(~old(X)))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(~generous(mary))&
(?[X]:((tall(X)<~>~happy(X)))) | generous(john) | [] | null | 0 |
If someone is both quiet and not wise then someone is either not kind or not curious and vice versa.
Everyone who is both wise and kind is wise.
Everyone who is funny is both not tall and not brave.
Everyone who is not humble or creative is tall or not tall.
If someone is both brave and not creative then fred is quiet and vice versa.
Everyone who is not generous or humble is either strong or not strong and vice versa.
Everyone who is creative or rich is not quiet or old.
Everyone who is tall is curious or patient and vice versa.
Everyone who is both not kind and calm is both not quiet and not kind and vice versa.
If someone is not happy then someone is not funny and vice versa.
Everyone who is both happy and not quiet is either humble or not curious.
If someone is not patient then someone is not calm or not happy.
Everyone who is both not strong and kind is both not tall and happy and vice versa.
If fred is both creative and kind then paul is either kind or quiet.
Everyone who is both not happy and brave is not creative or not kind.
If paul is both not wise and not kind then someone is not brave or humble.
Someone is wise or happy.
Fred is not brave or generous.
Someone is either curious or quiet.
Someone is either not happy or kind.
Susan is both humble and brave.
Paul is not curious.
Someone is both not wise and not rich.
John is either not tall or humble. | Fred is wise. | neutral | ((?[X]:((quiet(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((wise(X)&kind(X))=>wise(X)))&
(![X]:(funny(X)=>(~tall(X)&~brave(X))))&
(![X]:((~humble(X)|creative(X))=>(tall(X)|~tall(X))))&
((?[X]:((brave(X)&~creative(X))))<=>(quiet(fred)))&
(![X]:((~generous(X)|humble(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((creative(X)|rich(X))=>(~quiet(X)|old(X))))&
(![X]:(tall(X)<=>(curious(X)|patient(X))))&
(![X]:((~kind(X)&calm(X))<=>(~quiet(X)&~kind(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~funny(X))))&
(![X]:((happy(X)&~quiet(X))=>(humble(X)<~>~curious(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~strong(X)&kind(X))<=>(~tall(X)&happy(X))))&
(((creative(fred)&kind(fred)))=>((kind(paul)<~>quiet(paul))))&
(![X]:((~happy(X)&brave(X))=>(~creative(X)|~kind(X))))&
(((~wise(paul)&~kind(paul)))=>(?[X]:((~brave(X)|humble(X)))))&
(?[X]:((wise(X)|happy(X))))&
((~brave(fred)|generous(fred)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((humble(susan)&brave(susan)))&
(~curious(paul))&
(?[X]:((~wise(X)&~rich(X))))&
((~tall(john)<~>humble(john))) | wise(fred) | [] | null | 0 |
Everyone who is both not kind and humble is creative.
If someone is both not funny and old then someone is either not strong or calm and vice versa.
If mary is both old and patient then someone is either not generous or creative.
If mary is tall or funny then someone is either not tall or not brave.
If fred is kind then someone is both tall and curious.
If paul is both quiet and not generous then john is not happy or not kind and vice versa.
Everyone who is both old and brave is humble or not kind.
Everyone who is old or not brave is not tall.
Everyone who is both happy and curious is both kind and happy.
If susan is patient or not calm then paul is not tall or not creative and vice versa.
If alice is both not calm and not brave then someone is both not kind and curious.
Everyone who is both brave and quiet is not strong and vice versa.
Everyone who is either not calm or not brave is wise or happy.
Everyone who is calm or not funny is humble.
Everyone who is humble or not humble is both not curious and not old and vice versa.
Everyone who is rich or not funny is funny.
John is both tall and quiet.
Paul is not kind or funny.
Susan is tall.
Someone is wise or not strong.
Someone is either curious or not creative.
Lucy is not calm.
Someone is either not patient or not tall.
John is either humble or kind. | Lucy is not funny. | contradiction | (![X]:((~kind(X)&humble(X))=>creative(X)))&
((?[X]:((~funny(X)&old(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(((old(mary)&patient(mary)))=>(?[X]:((~generous(X)<~>creative(X)))))&
(((tall(mary)|funny(mary)))=>(?[X]:((~tall(X)<~>~brave(X)))))&
((kind(fred))=>(?[X]:((tall(X)&curious(X)))))&
(((quiet(paul)&~generous(paul)))<=>((~happy(john)|~kind(john))))&
(![X]:((old(X)&brave(X))=>(humble(X)|~kind(X))))&
(![X]:((old(X)|~brave(X))=>~tall(X)))&
(![X]:((happy(X)&curious(X))=>(kind(X)&happy(X))))&
(((patient(susan)|~calm(susan)))<=>((~tall(paul)|~creative(paul))))&
(((~calm(alice)&~brave(alice)))=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((brave(X)&quiet(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(wise(X)|happy(X))))&
(![X]:((calm(X)|~funny(X))=>humble(X)))&
(![X]:((humble(X)|~humble(X))<=>(~curious(X)&~old(X))))&
(![X]:((rich(X)|~funny(X))=>funny(X)))&
((tall(john)&quiet(john)))&
((~kind(paul)|funny(paul)))&
(tall(susan))&
(?[X]:((wise(X)|~strong(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(~calm(lucy))&
(?[X]:((~patient(X)<~>~tall(X))))&
((humble(john)<~>kind(john))) | ~funny(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6485153812527781871357885
% SZS output start Proof for 6485153812527781871357885
16. ! [X0] : ((~funny(X0) | rich(X0)) => funny(X0)) [input p15]
25. ~funny(lucy) [input hypothesis]
27. ! [X0] : (~funny(X0) => funny(X0)) [pure predicate removal 16]
44. ! [X0] : (funny(X0) | funny(X0)) [ennf transformation 27]
116. funny(X0) | funny(X0) [cnf transformation 44]
128. ~funny(lucy) [cnf transformation 25]
129. funny(X0) [duplicate literal removal 116]
291. $false [subsumption resolution 128,129]
% SZS output end Proof for 6485153812527781871357885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or patient is either funny or not curious and vice versa.
Everyone who is either tall or not calm is both not curious and not humble.
If paul is either not patient or patient then mary is not patient and vice versa.
If fred is not creative or not strong then someone is either brave or not curious and vice versa.
If lucy is both patient and not kind then someone is either kind or not funny.
If fred is both not calm and creative then mary is brave or wise.
If someone is either not funny or not kind then someone is not humble and vice versa.
Everyone who is not humble is not quiet or not strong and vice versa.
If someone is patient or humble then john is either quiet or patient and vice versa.
If alice is old or not brave then lucy is both not quiet and not brave and vice versa.
Everyone who is both rich and creative is both not generous and strong and vice versa.
Everyone who is creative is both not happy and not creative and vice versa.
Everyone who is not brave or not happy is old.
Everyone who is either wise or curious is either quiet or not old and vice versa.
If alice is both curious and not patient then susan is both not generous and patient.
Someone is both not wise and not creative.
Mary is either not curious or not quiet.
John is curious or not old.
Someone is not wise.
Susan is tall or not happy.
Alice is patient.
Someone is not generous or curious.
Someone is both not patient and generous. | Mary is not funny. | entailment | (![X]:((~curious(X)<~>patient(X))<=>(funny(X)<~>~curious(X))))&
(![X]:((tall(X)<~>~calm(X))=>(~curious(X)&~humble(X))))&
(((~patient(paul)<~>patient(paul)))<=>(~patient(mary)))&
(((~creative(fred)|~strong(fred)))<=>(?[X]:((brave(X)<~>~curious(X)))))&
(((patient(lucy)&~kind(lucy)))=>(?[X]:((kind(X)<~>~funny(X)))))&
(((~calm(fred)&creative(fred)))=>((brave(mary)|wise(mary))))&
((?[X]:((~funny(X)<~>~kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~strong(X))))&
((?[X]:((patient(X)|humble(X))))<=>((quiet(john)<~>patient(john))))&
(((old(alice)|~brave(alice)))<=>((~quiet(lucy)&~brave(lucy))))&
(![X]:((rich(X)&creative(X))<=>(~generous(X)&strong(X))))&
(![X]:(creative(X)<=>(~happy(X)&~creative(X))))&
(![X]:((~brave(X)|~happy(X))=>old(X)))&
(![X]:((wise(X)<~>curious(X))<=>(quiet(X)<~>~old(X))))&
(((curious(alice)&~patient(alice)))=>((~generous(susan)&patient(susan))))&
(?[X]:((~wise(X)&~creative(X))))&
((~curious(mary)<~>~quiet(mary)))&
((curious(john)|~old(john)))&
(?[X]:(~wise(X)))&
((tall(susan)|~happy(susan)))&
(patient(alice))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((~patient(X)&generous(X)))) | ~funny(mary) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8732027954638704497816966
% SZS output start Proof for 8732027954638704497816966
1. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> (funny(X0) <~> ~curious(X0))) [input p0]
3. (~patient(paul) <~> patient(paul)) <=> ~patient(mary) [input p2]
24. funny(mary) [input hypothesis]
34. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 1]
36. (((~patient(paul) | patient(paul)) & (patient(paul) | ~patient(paul))) | patient(mary)) & (~patient(mary) | ((~patient(paul) | ~patient(paul)) & (patient(paul) | patient(paul)))) [nnf transformation 3]
74. curious(X0) | ~funny(X0) | patient(X0) | curious(X0) [cnf transformation 34]
76. patient(X0) | ~curious(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 34]
84. ~patient(mary) | patient(paul) | patient(paul) [cnf transformation 36]
85. ~patient(mary) | ~patient(paul) | ~patient(paul) [cnf transformation 36]
145. funny(mary) [cnf transformation 24]
148. ~patient(mary) | patient(paul) [duplicate literal removal 84]
149. ~patient(mary) | ~patient(paul) [duplicate literal removal 85]
151. curious(X0) | ~funny(X0) | patient(X0) [duplicate literal removal 74]
152. patient(X0) | ~curious(X0) | ~funny(X0) [duplicate literal removal 76]
154. ~funny(X0) | patient(X0) [subsumption resolution 151,152]
157. 1 <=> patient(paul) [avatar definition]
161. 2 <=> patient(mary) [avatar definition]
163. ~patient(mary) <- (~2) [avatar component clause 161]
164. ~1 | ~2 [avatar split clause 149,161,157]
165. 1 | ~2 [avatar split clause 148,161,157]
362. patient(mary) [resolution 154,145]
364. $false <- (~2) [subsumption resolution 362,163]
365. 2 [avatar contradiction clause 364]
366. $false [avatar sat refutation 164,165,365]
% SZS output end Proof for 8732027954638704497816966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not kind then someone is either curious or not wise and vice versa.
If paul is both not curious and not funny then susan is both quiet and not generous and vice versa.
Everyone who is both not kind and not creative is both not curious and brave.
Everyone who is both humble and generous is either rich or kind.
Everyone who is both not funny and not patient is either quiet or not brave.
If lucy is both not wise and brave then mary is both not happy and not creative and vice versa.
If susan is not kind or not rich then fred is not calm or happy.
If someone is calm then john is both quiet and not creative.
Everyone who is either not generous or kind is generous or strong.
If paul is quiet then someone is either not rich or wise.
Everyone who is both brave and not humble is either not generous or tall and vice versa.
Everyone who is both not patient and curious is strong or not quiet and vice versa.
If someone is both funny and patient then someone is generous.
Everyone who is either patient or not patient is either not humble or funny and vice versa.
Everyone who is not humble is either not humble or not rich and vice versa.
If john is not old then fred is not strong or not quiet.
Lucy is either curious or patient.
Susan is funny.
Someone is either strong or not patient.
Someone is funny or not strong.
Someone is not patient.
Someone is either patient or not creative.
John is not funny. | Paul is not curious. | neutral | (((patient(susan)|~kind(susan)))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~curious(paul)&~funny(paul)))<=>((quiet(susan)&~generous(susan))))&
(![X]:((~kind(X)&~creative(X))=>(~curious(X)&brave(X))))&
(![X]:((humble(X)&generous(X))=>(rich(X)<~>kind(X))))&
(![X]:((~funny(X)&~patient(X))=>(quiet(X)<~>~brave(X))))&
(((~wise(lucy)&brave(lucy)))<=>((~happy(mary)&~creative(mary))))&
(((~kind(susan)|~rich(susan)))=>((~calm(fred)|happy(fred))))&
((?[X]:(calm(X)))=>((quiet(john)&~creative(john))))&
(![X]:((~generous(X)<~>kind(X))=>(generous(X)|strong(X))))&
((quiet(paul))=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((brave(X)&~humble(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~patient(X)&curious(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((funny(X)&patient(X))))=>(?[X]:(generous(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~humble(X)<~>funny(X))))&
(![X]:(~humble(X)<=>(~humble(X)<~>~rich(X))))&
((~old(john))=>((~strong(fred)|~quiet(fred))))&
((curious(lucy)<~>patient(lucy)))&
(funny(susan))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~funny(john)) | ~curious(paul) | [] | null | 0 |
Everyone who is not old is both kind and curious and vice versa. If someone is quiet then mary is not tall and vice versa. Everyone who is both not brave and not rich is not kind or not happy and vice versa. Everyone who is not rich is both quiet and brave and vice versa. If lucy is both calm and not tall then fred is calm or not curious. If john is quiet then john is not creative or not patient and vice versa. If alice is old then lucy is both wise and kind and vice versa. Everyone who is either happy or humble is either not strong or not kind and vice versa. Everyone who is generous is either patient or not happy. If alice is patient then fred is either not strong or wise and vice versa. Everyone who is either not brave or not patient is funny. If mary is calm or not calm then susan is either rich or not happy. Everyone who is not funny or creative is happy. If john is curious or humble then someone is not patient or patient. If paul is old or not humble then susan is curious. Everyone who is quiet is brave. Paul is both calm and not wise. John is not funny or not calm. John is both not patient and not old. Someone is wise or humble. Someone is either not tall or brave. Someone is not funny or not generous. Paul is kind. | Mary is calm. | neutral | (![X]:(~old(X)<=>(kind(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(~tall(mary)))&
(![X]:((~brave(X)&~rich(X))<=>(~kind(X)|~happy(X))))&
(![X]:(~rich(X)<=>(quiet(X)&brave(X))))&
(((calm(lucy)&~tall(lucy)))=>((calm(fred)|~curious(fred))))&
((quiet(john))<=>((~creative(john)|~patient(john))))&
((old(alice))<=>((wise(lucy)&kind(lucy))))&
(![X]:((happy(X)<~>humble(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(generous(X)=>(patient(X)<~>~happy(X))))&
((patient(alice))<=>((~strong(fred)<~>wise(fred))))&
(![X]:((~brave(X)<~>~patient(X))=>funny(X)))&
(((calm(mary)|~calm(mary)))=>((rich(susan)<~>~happy(susan))))&
(![X]:((~funny(X)|creative(X))=>happy(X)))&
(((curious(john)|humble(john)))=>(?[X]:((~patient(X)|patient(X)))))&
(((old(paul)|~humble(paul)))=>(curious(susan)))&
(![X]:(quiet(X)=>brave(X)))&
((calm(paul)&~wise(paul)))&
((~funny(john)|~calm(john)))&
((~patient(john)&~old(john)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~tall(X)<~>brave(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(kind(paul)) | calm(mary) | [] | null | 0 |
Everyone who is both not happy and not kind is happy and vice versa.
If lucy is not calm or not curious then susan is kind and vice versa.
Everyone who is both not generous and creative is rich or quiet and vice versa.
If paul is both patient and not wise then someone is either quiet or not happy and vice versa.
If someone is not humble then alice is not creative or not rich and vice versa.
Everyone who is both old and not kind is quiet or not humble.
If alice is not wise then mary is generous.
Everyone who is either not funny or not rich is either not generous or brave.
Everyone who is either not happy or not curious is either not kind or funny and vice versa.
Everyone who is old is strong or not old and vice versa.
Everyone who is kind is either not tall or not happy.
If alice is either patient or not quiet then lucy is both happy and not strong and vice versa.
Everyone who is not wise is not funny or not kind and vice versa.
Everyone who is both funny and not generous is kind and vice versa.
If someone is wise or rich then susan is curious and vice versa.
If john is both funny and not happy then someone is calm.
Lucy is not rich.
Someone is either curious or rich. | Paul is not humble. | neutral | (![X]:((~happy(X)&~kind(X))<=>happy(X)))&
(((~calm(lucy)|~curious(lucy)))<=>(kind(susan)))&
(![X]:((~generous(X)&creative(X))<=>(rich(X)|quiet(X))))&
(((patient(paul)&~wise(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:(~humble(X)))<=>((~creative(alice)|~rich(alice))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|~humble(X))))&
((~wise(alice))=>(generous(mary)))&
(![X]:((~funny(X)<~>~rich(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(old(X)<=>(strong(X)|~old(X))))&
(![X]:(kind(X)=>(~tall(X)<~>~happy(X))))&
(((patient(alice)<~>~quiet(alice)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:(~wise(X)<=>(~funny(X)|~kind(X))))&
(![X]:((funny(X)&~generous(X))<=>kind(X)))&
((?[X]:((wise(X)|rich(X))))<=>(curious(susan)))&
(((funny(john)&~happy(john)))=>(?[X]:(calm(X))))&
(~rich(lucy))&
(?[X]:((curious(X)<~>rich(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is not patient or not brave is either creative or funny and vice versa.
If alice is creative then susan is not strong or not wise and vice versa.
If someone is both brave and strong then fred is both kind and not curious and vice versa.
Everyone who is not happy is happy or kind.
Everyone who is not rich is brave or not happy and vice versa.
If someone is both not brave and not generous then mary is not old or patient and vice versa.
Everyone who is both not rich and not humble is either brave or not creative and vice versa.
If someone is not creative then alice is patient or kind.
Everyone who is either brave or tall is both not brave and not patient.
Everyone who is not humble is either creative or not kind.
Everyone who is not wise or not patient is both wise and not patient and vice versa.
Everyone who is not brave is both kind and old and vice versa.
If fred is not generous then someone is both not creative and funny.
If lucy is not wise or humble then john is not humble.
Everyone who is quiet or not generous is both funny and not quiet.
If mary is strong or not quiet then john is either not old or not calm.
Alice is both not patient and wise.
Someone is not rich or not happy.
Someone is kind.
Paul is creative.
Someone is not calm.
Someone is either wise or not curious.
Someone is not old or creative. | Alice is kind. | entailment | (![X]:((~patient(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((creative(alice))<=>((~strong(susan)|~wise(susan))))&
((?[X]:((brave(X)&strong(X))))<=>((kind(fred)&~curious(fred))))&
(![X]:(~happy(X)=>(happy(X)|kind(X))))&
(![X]:(~rich(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~brave(X)&~generous(X))))<=>((~old(mary)|patient(mary))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)<~>~creative(X))))&
((?[X]:(~creative(X)))=>((patient(alice)|kind(alice))))&
(![X]:((brave(X)<~>tall(X))=>(~brave(X)&~patient(X))))&
(![X]:(~humble(X)=>(creative(X)<~>~kind(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&~patient(X))))&
(![X]:(~brave(X)<=>(kind(X)&old(X))))&
((~generous(fred))=>(?[X]:((~creative(X)&funny(X)))))&
(((~wise(lucy)|humble(lucy)))=>(~humble(john)))&
(![X]:((quiet(X)|~generous(X))=>(funny(X)&~quiet(X))))&
(((strong(mary)|~quiet(mary)))=>((~old(john)<~>~calm(john))))&
((~patient(alice)&wise(alice)))&
(?[X]:((~rich(X)|~happy(X))))&
(?[X]:(kind(X)))&
(creative(paul))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((~old(X)|creative(X)))) | kind(alice) | [
"p6",
"p7",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4987572000838747040217458
% SZS output start Proof for 4987572000838747040217458
7. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (brave(X0) <~> ~creative(X0))) [input p6]
8. ? [X0] : ~creative(X0) => (kind(alice) | patient(alice)) [input p7]
10. ! [X0] : (~humble(X0) => (creative(X0) <~> ~kind(X0))) [input p9]
12. ! [X0] : (~brave(X0) <=> (old(X0) & kind(X0))) [input p11]
17. wise(alice) & ~patient(alice) [input p16]
24. ~kind(alice) [input hypothesis]
27. (kind(alice) | patient(alice)) | ! [X0] : creative(X0) [ennf transformation 8]
28. kind(alice) | patient(alice) | ! [X0] : creative(X0) [flattening 27]
30. ! [X0] : ((creative(X0) <~> ~kind(X0)) | humble(X0)) [ennf transformation 10]
51. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (humble(X0) | rich(X0)))) [nnf transformation 7]
52. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | humble(X0) | rich(X0))) [flattening 51]
54. ! [X0] : (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | humble(X0)) [nnf transformation 30]
57. ! [X0] : ((~brave(X0) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | brave(X0))) [nnf transformation 12]
58. ! [X0] : ((~brave(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | brave(X0))) [flattening 57]
99. ~humble(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 52]
101. kind(alice) | patient(alice) | creative(X0) [cnf transformation 28]
107. ~creative(X0) | kind(X0) | humble(X0) [cnf transformation 54]
113. kind(X0) | brave(X0) [cnf transformation 58]
128. ~patient(alice) [cnf transformation 17]
137. ~kind(alice) [cnf transformation 24]
208. 14 <=> ! [X0] : creative(X0) [avatar definition]
209. creative(X0) <- (14) [avatar component clause 208]
211. 15 <=> patient(alice) [avatar definition]
215. 16 <=> kind(alice) [avatar definition]
216. ~kind(alice) <- (~16) [avatar component clause 215]
218. 14 | 15 | 16 [avatar split clause 101,215,211,208]
261. ~15 [avatar split clause 128,211]
273. ~16 [avatar split clause 137,215]
313. humble(X0) | kind(X0) <- (14) [resolution 107,209]
377. kind(X1) | ~creative(X1) | ~brave(X1) <- (14) [resolution 313,99]
380. kind(X1) | ~brave(X1) <- (14) [subsumption resolution 377,209]
381. kind(X1) <- (14) [subsumption resolution 380,113]
427. $false <- (14, ~16) [resolution 381,216]
429. ~14 | 16 [avatar contradiction clause 427]
430. $false [avatar sat refutation 218,261,273,429]
% SZS output end Proof for 4987572000838747040217458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is creative or funny and vice versa.
If someone is either curious or not generous then john is patient or curious and vice versa.
Everyone who is not happy or not wise is both tall and not happy.
Everyone who is either tall or patient is not old and vice versa.
If fred is wise then fred is wise or rich.
Everyone who is both not wise and patient is either not funny or not tall and vice versa.
If someone is not generous then someone is both patient and not tall and vice versa.
Everyone who is both not patient and happy is not generous.
Everyone who is both patient and not tall is tall.
If paul is both tall and calm then someone is quiet and vice versa.
If susan is either not happy or tall then someone is curious and vice versa.
Everyone who is brave is both not brave and not humble.
Everyone who is both not generous and old is both not old and not quiet.
If someone is either old or wise then fred is quiet or kind and vice versa.
Everyone who is kind or not quiet is not happy or creative and vice versa.
John is either humble or not humble.
Paul is creative.
Fred is both not kind and not brave.
Paul is not generous or calm.
Someone is both quiet and not happy. | Susan is wise. | entailment | (![X]:(patient(X)<=>(creative(X)|funny(X))))&
((?[X]:((curious(X)<~>~generous(X))))<=>((patient(john)|curious(john))))&
(![X]:((~happy(X)|~wise(X))=>(tall(X)&~happy(X))))&
(![X]:((tall(X)<~>patient(X))<=>~old(X)))&
((wise(fred))=>((wise(fred)|rich(fred))))&
(![X]:((~wise(X)&patient(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:((~patient(X)&happy(X))=>~generous(X)))&
(![X]:((patient(X)&~tall(X))=>tall(X)))&
(((tall(paul)&calm(paul)))<=>(?[X]:(quiet(X))))&
(((~happy(susan)<~>tall(susan)))<=>(?[X]:(curious(X))))&
(![X]:(brave(X)=>(~brave(X)&~humble(X))))&
(![X]:((~generous(X)&old(X))=>(~old(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))<=>((quiet(fred)|kind(fred))))&
(![X]:((kind(X)|~quiet(X))<=>(~happy(X)|creative(X))))&
((humble(john)<~>~humble(john)))&
(creative(paul))&
((~kind(fred)&~brave(fred)))&
((~generous(paul)|calm(paul)))&
(?[X]:((quiet(X)&~happy(X)))) | wise(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3012491464462063718236142
% SZS output start Proof for 3012491464462063718236142
1. ! [X0] : (patient(X0) <=> (funny(X0) | creative(X0))) [input p0]
2. ? [X0] : (curious(X0) <~> ~generous(X0)) <=> (curious(john) | patient(john)) [input p1]
3. ! [X0] : ((~wise(X0) | ~happy(X0)) => (~happy(X0) & tall(X0))) [input p2]
6. ! [X0] : ((patient(X0) & ~wise(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p5]
7. ? [X0] : ~generous(X0) <=> ? [X0] : (~tall(X0) & patient(X0)) [input p6]
8. ! [X0] : ((happy(X0) & ~patient(X0)) => ~generous(X0)) [input p7]
9. ! [X0] : ((~tall(X0) & patient(X0)) => tall(X0)) [input p8]
11. (~happy(susan) <~> tall(susan)) <=> ? [X0] : curious(X0) [input p10]
21. ~wise(susan) [input hypothesis]
22. ? [X0] : ~generous(X0) <=> ? [X1] : (~tall(X1) & patient(X1)) [rectify 7]
26. ! [X0] : ((~happy(X0) & tall(X0)) | (wise(X0) & happy(X0))) [ennf transformation 3]
27. ! [X0] : (~generous(X0) | (~happy(X0) | patient(X0))) [ennf transformation 8]
28. ! [X0] : (~generous(X0) | ~happy(X0) | patient(X0)) [flattening 27]
29. ! [X0] : (tall(X0) | (tall(X0) | ~patient(X0))) [ennf transformation 9]
30. ! [X0] : (tall(X0) | tall(X0) | ~patient(X0)) [flattening 29]
33. ! [X0] : ((patient(X0) | (~funny(X0) & ~creative(X0))) & ((funny(X0) | creative(X0)) | ~patient(X0))) [nnf transformation 1]
34. ! [X0] : ((patient(X0) | (~funny(X0) & ~creative(X0))) & (funny(X0) | creative(X0) | ~patient(X0))) [flattening 33]
35. (? [X0] : ((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~curious(john) & ~patient(john))) & ((curious(john) | patient(john)) | ! [X0] : ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 2]
36. (? [X0] : ((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~curious(john) & ~patient(john))) & (curious(john) | patient(john) | ! [X0] : ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [flattening 35]
37. (? [X0] : ((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~curious(john) & ~patient(john))) & (curious(john) | patient(john) | ! [X1] : ((curious(X1) | generous(X1)) & (~generous(X1) | ~curious(X1)))) [rectify 36]
38. ? [X0] : ((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) => ((generous(sK0) | ~curious(sK0)) & (~generous(sK0) | curious(sK0))) [choice axiom]
39. (((generous(sK0) | ~curious(sK0)) & (~generous(sK0) | curious(sK0))) | (~curious(john) & ~patient(john))) & (curious(john) | patient(john) | ! [X1] : ((curious(X1) | generous(X1)) & (~generous(X1) | ~curious(X1)))) [skolemisation 37,38]
41. ! [X0] : (((patient(X0) & ~wise(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (~patient(X0) | wise(X0)))) [nnf transformation 6]
42. ! [X0] : (((patient(X0) & ~wise(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ~patient(X0) | wise(X0))) [flattening 41]
43. (? [X0] : ~generous(X0) | ! [X1] : (tall(X1) | ~patient(X1))) & (? [X1] : (~tall(X1) & patient(X1)) | ! [X0] : generous(X0)) [nnf transformation 22]
44. (? [X0] : ~generous(X0) | ! [X1] : (tall(X1) | ~patient(X1))) & (? [X2] : (~tall(X2) & patient(X2)) | ! [X3] : generous(X3)) [rectify 43]
45. ? [X0] : ~generous(X0) => ~generous(sK1) [choice axiom]
46. ? [X2] : (~tall(X2) & patient(X2)) => (~tall(sK2) & patient(sK2)) [choice axiom]
47. (~generous(sK1) | ! [X1] : (tall(X1) | ~patient(X1))) & ((~tall(sK2) & patient(sK2)) | ! [X3] : generous(X3)) [skolemisation 44,46,45]
53. (((~tall(susan) | happy(susan)) & (tall(susan) | ~happy(susan))) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ((~happy(susan) | ~tall(susan)) & (tall(susan) | happy(susan)))) [nnf transformation 11]
54. (((~tall(susan) | happy(susan)) & (tall(susan) | ~happy(susan))) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ((~happy(susan) | ~tall(susan)) & (tall(susan) | happy(susan)))) [rectify 53]
55. ? [X1] : curious(X1) => curious(sK4) [choice axiom]
56. (((~tall(susan) | happy(susan)) & (tall(susan) | ~happy(susan))) | ! [X0] : ~curious(X0)) & (curious(sK4) | ((~happy(susan) | ~tall(susan)) & (tall(susan) | happy(susan)))) [skolemisation 54,55]
69. ~funny(X0) | patient(X0) [cnf transformation 34]
72. ~generous(sK0) | curious(sK0) | ~patient(john) [cnf transformation 39]
76. tall(X0) | happy(X0) [cnf transformation 26]
79. ~happy(X0) | wise(X0) [cnf transformation 26]
88. patient(X0) | ~tall(X0) | funny(X0) [cnf transformation 42]
90. patient(sK2) | generous(X3) [cnf transformation 47]
91. ~tall(sK2) | generous(X3) [cnf transformation 47]
93. ~happy(X0) | ~generous(X0) | patient(X0) [cnf transformation 28]
94. tall(X0) | tall(X0) | ~patient(X0) [cnf transformation 30]
101. ~tall(susan) | happy(susan) | ~curious(X0) [cnf transformation 56]
121. ~wise(susan) [cnf transformation 21]
123. tall(X0) | ~patient(X0) [duplicate literal removal 94]
129. 2 <=> curious(sK0) [avatar definition]
130. curious(sK0) <- (2) [avatar component clause 129]
133. 3 <=> generous(sK0) [avatar definition]
134. ~generous(sK0) <- (~3) [avatar component clause 133]
138. 4 <=> patient(john) [avatar definition]
140. ~patient(john) <- (~4) [avatar component clause 138]
143. ~4 | 2 | ~3 [avatar split clause 72,133,129,138]
152. ~tall(X0) | patient(X0) [subsumption resolution 88,69]
157. 7 <=> ! [X1] : (tall(X1) | ~patient(X1)) [avatar definition]
158. ~patient(X1) | tall(X1) <- (7) [avatar component clause 157]
165. 9 <=> ! [X3] : generous(X3) [avatar definition]
166. generous(X3) <- (9) [avatar component clause 165]
168. 10 <=> tall(sK2) [avatar definition]
171. 9 | ~10 [avatar split clause 91,168,165]
173. 11 <=> patient(sK2) [avatar definition]
175. patient(sK2) <- (11) [avatar component clause 173]
176. 9 | 11 [avatar split clause 90,173,165]
177. 7 [avatar split clause 123,157]
196. happy(susan) | ~curious(X0) [subsumption resolution 101,76]
198. 16 <=> ! [X0] : ~curious(X0) [avatar definition]
199. ~curious(X0) <- (16) [avatar component clause 198]
201. 17 <=> happy(susan) [avatar definition]
203. happy(susan) <- (17) [avatar component clause 201]
204. 16 | 17 [avatar split clause 196,201,198]
250. $false <- (~3, 9) [subsumption resolution 134,166]
251. 3 | ~9 [avatar contradiction clause 250]
265. happy(X1) | patient(X1) [resolution 152,76]
267. tall(sK2) <- (7, 11) [resolution 158,175]
271. 10 | ~7 | ~11 [avatar split clause 267,173,157,168]
272. $false <- (2, 16) [subsumption resolution 130,199]
273. ~2 | ~16 [avatar contradiction clause 272]
397. patient(X1) | ~generous(X1) | patient(X1) [resolution 265,93]
402. patient(X1) | ~generous(X1) [duplicate literal removal 397]
404. patient(X1) <- (9) [subsumption resolution 402,166]
413. $false <- (~4, 9) [resolution 404,140]
414. 4 | ~9 [avatar contradiction clause 413]
419. wise(susan) <- (17) [resolution 203,79]
420. $false <- (17) [subsumption resolution 419,121]
421. ~17 [avatar contradiction clause 420]
422. $false [avatar sat refutation 143,171,176,177,204,251,271,273,414,421]
% SZS output end Proof for 3012491464462063718236142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or rich is either calm or humble and vice versa.
If someone is either not brave or not rich then someone is either brave or not wise and vice versa.
Everyone who is either old or not wise is either not quiet or brave.
If someone is not brave then mary is old or humble.
Everyone who is either calm or wise is humble or not brave and vice versa.
If mary is not patient or kind then mary is patient or creative.
If susan is not humble then someone is both generous and not wise and vice versa.
Everyone who is not rich is both humble and not calm.
If someone is not funny or tall then someone is either strong or happy and vice versa.
If someone is either not wise or not curious then paul is tall or not brave and vice versa.
Everyone who is either not happy or strong is humble and vice versa.
If alice is not calm then fred is both not tall and generous and vice versa.
Everyone who is both brave and funny is calm.
Everyone who is both curious and not curious is not strong and vice versa.
Everyone who is either wise or funny is not happy.
If lucy is tall or not tall then someone is not wise or patient and vice versa.
Susan is funny or not patient.
Someone is either strong or funny.
John is either not funny or patient.
Someone is both happy and not wise.
Susan is either not rich or rich.
Susan is either funny or humble.
Someone is not rich. | Susan is not happy. | entailment | (![X]:((patient(X)<~>rich(X))<=>(calm(X)<~>humble(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((old(X)<~>~wise(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:(~brave(X)))=>((old(mary)|humble(mary))))&
(![X]:((calm(X)<~>wise(X))<=>(humble(X)|~brave(X))))&
(((~patient(mary)|kind(mary)))=>((patient(mary)|creative(mary))))&
((~humble(susan))<=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:(~rich(X)=>(humble(X)&~calm(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((strong(X)<~>happy(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((tall(paul)|~brave(paul))))&
(![X]:((~happy(X)<~>strong(X))<=>humble(X)))&
((~calm(alice))<=>((~tall(fred)&generous(fred))))&
(![X]:((brave(X)&funny(X))=>calm(X)))&
(![X]:((curious(X)&~curious(X))<=>~strong(X)))&
(![X]:((wise(X)<~>funny(X))=>~happy(X)))&
(((tall(lucy)|~tall(lucy)))<=>(?[X]:((~wise(X)|patient(X)))))&
((funny(susan)|~patient(susan)))&
(?[X]:((strong(X)<~>funny(X))))&
((~funny(john)<~>patient(john)))&
(?[X]:((happy(X)&~wise(X))))&
((~rich(susan)<~>rich(susan)))&
((funny(susan)<~>humble(susan)))&
(?[X]:(~rich(X))) | ~happy(susan) | [
"p0",
"p4",
"p7",
"p10",
"p13",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6942410472052809075307518
% SZS output start Proof for 6942410472052809075307518
1. ! [X0] : ((patient(X0) <~> rich(X0)) <=> (calm(X0) <~> humble(X0))) [input p0]
5. ! [X0] : ((calm(X0) <~> wise(X0)) <=> (~brave(X0) | humble(X0))) [input p4]
8. ! [X0] : (~rich(X0) => (~calm(X0) & humble(X0))) [input p7]
11. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> humble(X0)) [input p10]
14. ! [X0] : ((~curious(X0) & curious(X0)) <=> ~strong(X0)) [input p13]
15. ! [X0] : ((wise(X0) <~> funny(X0)) => ~happy(X0)) [input p14]
17. ~patient(susan) | funny(susan) [input p16]
22. funny(susan) <~> humble(susan) [input p21]
24. happy(susan) [input hypothesis]
31. ! [X0] : ((~calm(X0) & humble(X0)) | rich(X0)) [ennf transformation 8]
34. ! [X0] : (~happy(X0) | (wise(X0) <=> funny(X0))) [ennf transformation 15]
35. ! [X0] : ((((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0))))) [nnf transformation 1]
42. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | (brave(X0) & ~humble(X0))) & ((~brave(X0) | humble(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | (brave(X0) & ~humble(X0))) & (~brave(X0) | humble(X0) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [flattening 42]
58. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | ~humble(X0)) & (humble(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 11]
61. ! [X0] : (((~curious(X0) & curious(X0)) | strong(X0)) & (~strong(X0) | (curious(X0) | ~curious(X0)))) [nnf transformation 14]
62. ! [X0] : (((~curious(X0) & curious(X0)) | strong(X0)) & (~strong(X0) | curious(X0) | ~curious(X0))) [flattening 61]
63. ! [X0] : (~happy(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) [nnf transformation 34]
76. (~humble(susan) | ~funny(susan)) & (humble(susan) | funny(susan)) [nnf transformation 22]
82. ~humble(X0) | ~calm(X0) | patient(X0) | ~rich(X0) [cnf transformation 35]
102. ~humble(X0) | calm(X0) | wise(X0) [cnf transformation 43]
110. ~calm(X0) | rich(X0) [cnf transformation 31]
124. ~happy(X0) | humble(X0) | ~strong(X0) [cnf transformation 58]
132. curious(X0) | strong(X0) [cnf transformation 62]
133. ~curious(X0) | strong(X0) [cnf transformation 62]
134. ~happy(X0) | funny(X0) | ~wise(X0) [cnf transformation 63]
140. ~patient(susan) | funny(susan) [cnf transformation 17]
150. ~humble(susan) | ~funny(susan) [cnf transformation 76]
152. happy(susan) [cnf transformation 24]
205. 13 <=> humble(susan) [avatar definition]
206. humble(susan) <- (13) [avatar component clause 205]
296. strong(X0) [subsumption resolution 132,133]
312. 36 <=> funny(susan) [avatar definition]
313. ~funny(susan) <- (~36) [avatar component clause 312]
316. 37 <=> patient(susan) [avatar definition]
318. ~patient(susan) <- (~37) [avatar component clause 316]
319. 36 | ~37 [avatar split clause 140,316,312]
331. ~36 | ~13 [avatar split clause 150,205,312]
341. 40 <=> wise(susan) [avatar definition]
345. 41 <=> calm(susan) [avatar definition]
347. calm(susan) <- (41) [avatar component clause 345]
384. calm(susan) | wise(susan) <- (13) [resolution 206,102]
434. humble(susan) | ~strong(susan) [resolution 124,152]
462. funny(susan) | ~wise(susan) [resolution 134,152]
464. ~wise(susan) <- (~36) [subsumption resolution 462,313]
467. ~40 | 36 [avatar split clause 464,312,341]
468. 40 | 41 | ~13 [avatar split clause 384,205,345,341]
474. rich(susan) <- (41) [resolution 347,110]
485. ~calm(susan) | patient(susan) | ~rich(susan) <- (13) [resolution 82,206]
487. patient(susan) | ~rich(susan) <- (13, 41) [subsumption resolution 485,347]
488. ~rich(susan) <- (13, ~37, 41) [subsumption resolution 487,318]
489. $false <- (13, ~37, 41) [subsumption resolution 488,474]
490. ~13 | 37 | ~41 [avatar contradiction clause 489]
501. humble(susan) [subsumption resolution 434,296]
502. 13 [avatar split clause 501,205]
510. $false [avatar sat refutation 319,331,467,468,490,502]
% SZS output end Proof for 6942410472052809075307518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or curious is old and vice versa.
If alice is not calm or generous then paul is both calm and generous and vice versa.
If alice is not patient or not humble then someone is not old.
If alice is not patient then mary is both not rich and brave.
Everyone who is tall is both generous and strong and vice versa.
If fred is either strong or patient then someone is both creative and old and vice versa.
If paul is old then someone is not kind or calm and vice versa.
Everyone who is both happy and not old is both quiet and creative.
If susan is quiet or not kind then paul is either quiet or curious and vice versa.
If alice is not brave or wise then alice is both patient and not happy and vice versa.
If paul is either not old or generous then fred is either not old or not strong.
If someone is both old and not funny then fred is kind.
If someone is both generous and funny then fred is not wise and vice versa.
Everyone who is humble or strong is either not kind or not generous and vice versa.
If someone is not rich or humble then someone is calm or not curious and vice versa.
Everyone who is either tall or not rich is either creative or old.
Susan is strong.
Lucy is wise or not wise.
Someone is either not brave or not old.
Someone is quiet or patient.
Lucy is tall.
Lucy is either strong or brave.
John is both not patient and not strong. | Paul is tall. | neutral | (![X]:((~patient(X)<~>curious(X))<=>old(X)))&
(((~calm(alice)|generous(alice)))<=>((calm(paul)&generous(paul))))&
(((~patient(alice)|~humble(alice)))=>(?[X]:(~old(X))))&
((~patient(alice))=>((~rich(mary)&brave(mary))))&
(![X]:(tall(X)<=>(generous(X)&strong(X))))&
(((strong(fred)<~>patient(fred)))<=>(?[X]:((creative(X)&old(X)))))&
((old(paul))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((happy(X)&~old(X))=>(quiet(X)&creative(X))))&
(((quiet(susan)|~kind(susan)))<=>((quiet(paul)<~>curious(paul))))&
(((~brave(alice)|wise(alice)))<=>((patient(alice)&~happy(alice))))&
(((~old(paul)<~>generous(paul)))=>((~old(fred)<~>~strong(fred))))&
((?[X]:((old(X)&~funny(X))))=>(kind(fred)))&
((?[X]:((generous(X)&funny(X))))<=>(~wise(fred)))&
(![X]:((humble(X)|strong(X))<=>(~kind(X)<~>~generous(X))))&
((?[X]:((~rich(X)|humble(X))))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((tall(X)<~>~rich(X))=>(creative(X)<~>old(X))))&
(strong(susan))&
((wise(lucy)|~wise(lucy)))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((quiet(X)|patient(X))))&
(tall(lucy))&
((strong(lucy)<~>brave(lucy)))&
((~patient(john)&~strong(john))) | tall(paul) | [] | null | 0 |
If someone is not rich or not strong then someone is both not funny and old.
If someone is both not strong and not brave then john is not wise or not kind.
Everyone who is old or rich is either not humble or not patient and vice versa.
Everyone who is not humble is either generous or not kind.
If someone is not creative or humble then fred is not wise and vice versa.
Everyone who is both rich and humble is not old or tall.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Everyone who is either quiet or not creative is either rich or old and vice versa.
If someone is either not quiet or quiet then fred is not tall or tall and vice versa.
If someone is humble or not funny then someone is not patient or quiet.
Everyone who is brave or curious is not brave.
Everyone who is curious or not old is either wise or not curious and vice versa.
Everyone who is wise or not funny is both brave and not curious.
Everyone who is either not strong or funny is either not wise or not funny and vice versa.
Someone is not generous.
Someone is either quiet or kind.
Paul is happy or not curious.
Fred is humble or not calm.
Paul is both funny and not old.
Someone is strong. | Lucy is funny. | entailment | ((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>((~wise(john)|~kind(john))))&
(![X]:((old(X)|rich(X))<=>(~humble(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~creative(X)|humble(X))))<=>(~wise(fred)))&
(![X]:((rich(X)&humble(X))=>(~old(X)|tall(X))))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~tall(fred)|tall(fred))))&
((?[X]:((humble(X)|~funny(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((brave(X)|curious(X))=>~brave(X)))&
(![X]:((curious(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>kind(X))))&
((happy(paul)|~curious(paul)))&
((humble(fred)|~calm(fred)))&
((funny(paul)&~old(paul)))&
(?[X]:(strong(X))) | funny(lucy) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2141841541809552710676794
% SZS output start Proof for 2141841541809552710676794
13. ! [X0] : ((curious(X0) | brave(X0)) => ~brave(X0)) [input p12]
15. ! [X0] : ((~funny(X0) | wise(X0)) => (~curious(X0) & brave(X0))) [input p14]
23. ~funny(lucy) [input hypothesis]
35. ! [X0] : (~brave(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 13]
36. ! [X0] : ((~curious(X0) & brave(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 15]
116. ~brave(X0) | ~brave(X0) [cnf transformation 35]
125. brave(X0) | funny(X0) [cnf transformation 36]
143. ~funny(lucy) [cnf transformation 23]
150. ~brave(X0) [duplicate literal removal 116]
226. 16 <=> ! [X1] : funny(X1) [avatar definition]
227. funny(X1) <- (16) [avatar component clause 226]
239. funny(X0) [subsumption resolution 125,150]
240. 16 [avatar split clause 239,226]
256. $false <- (16) [resolution 227,143]
257. ~16 [avatar contradiction clause 256]
258. $false [avatar sat refutation 240,257]
% SZS output end Proof for 2141841541809552710676794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Everyone who is either not brave or patient is either not rich or curious.
Someone is both calm and wise.
Lucy is rich or not tall.
Mary is wise or happy.
Someone is curious or old. | Mary is funny. | contradiction | (![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((rich(lucy)|~tall(lucy)))&
((wise(mary)|happy(mary)))&
(?[X]:((curious(X)|old(X)))) | funny(mary) | [
"p5",
"p6",
"p8",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7233981399793839293657019
% SZS output start Proof for 7233981399793839293657019
6. ! [X0] : (funny(X0) <=> (tall(X0) <~> rich(X0))) [input p5]
7. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p6]
9. ? [X0] : tall(X0) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p8]
12. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p11]
13. ! [X0] : ((quiet(X0) <~> ~patient(X0)) <=> (~calm(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~brave(X0) <~> patient(X0)) => (~rich(X0) <~> curious(X0))) [input p14]
20. funny(mary) [input hypothesis]
23. ? [X0] : tall(X0) <=> ? [X1] : (generous(X1) & ~quiet(X1)) [rectify 9]
25. ! [X0] : (funny(X0) => (tall(X0) <~> rich(X0))) [unused predicate definition removal 6]
31. ! [X0] : ((tall(X0) <~> rich(X0)) | ~funny(X0)) [ennf transformation 25]
34. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 14]
35. ! [X0] : ((~rich(X0) <~> curious(X0)) | (~brave(X0) <=> patient(X0))) [ennf transformation 15]
41. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | ~funny(X0)) [nnf transformation 31]
42. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 7]
43. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 42]
46. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X1] : (generous(X1) & ~quiet(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 23]
47. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X2] : (generous(X2) & ~quiet(X2)) | ! [X3] : ~tall(X3)) [rectify 46]
48. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
49. ? [X2] : (generous(X2) & ~quiet(X2)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
50. (tall(sK1) | ! [X1] : (~generous(X1) | quiet(X1))) & ((generous(sK2) & ~quiet(sK2)) | ! [X3] : ~tall(X3)) [skolemisation 47,49,48]
57. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 12]
58. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 57]
59. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [nnf transformation 13]
60. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [flattening 59]
61. ! [X0] : (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) [nnf transformation 35]
73. ~funny(X0) | tall(X0) | rich(X0) [cnf transformation 41]
77. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 43]
82. ~quiet(sK2) | ~tall(X3) [cnf transformation 50]
83. generous(sK2) | ~tall(X3) [cnf transformation 50]
92. happy(X0) | curious(X0) [cnf transformation 58]
93. ~curious(X0) | happy(X0) [cnf transformation 58]
94. ~brave(X0) | curious(X0) [cnf transformation 58]
95. ~curious(X0) | ~brave(X0) [cnf transformation 58]
98. ~generous(X0) | quiet(X0) | patient(X0) [cnf transformation 60]
103. ~patient(X0) | ~happy(X0) [cnf transformation 34]
107. curious(X0) | ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 61]
116. funny(mary) [cnf transformation 20]
126. 3 <=> ! [X3] : ~tall(X3) [avatar definition]
127. ~tall(X3) <- (3) [avatar component clause 126]
129. 4 <=> generous(sK2) [avatar definition]
131. generous(sK2) <- (4) [avatar component clause 129]
132. 3 | 4 [avatar split clause 83,129,126]
134. 5 <=> quiet(sK2) [avatar definition]
136. ~quiet(sK2) <- (~5) [avatar component clause 134]
137. 3 | ~5 [avatar split clause 82,134,126]
152. ~brave(X0) [subsumption resolution 94,95]
153. happy(X0) [subsumption resolution 92,93]
155. ~patient(X0) [subsumption resolution 103,153]
156. curious(X0) | ~rich(X0) | brave(X0) [subsumption resolution 107,155]
157. ~rich(X0) | curious(X0) [subsumption resolution 156,152]
169. tall(mary) | rich(mary) [resolution 73,116]
171. 11 <=> rich(mary) [avatar definition]
173. rich(mary) <- (11) [avatar component clause 171]
175. 12 <=> tall(mary) [avatar definition]
177. tall(mary) <- (12) [avatar component clause 175]
178. 11 | 12 [avatar split clause 169,175,171]
179. curious(mary) <- (11) [resolution 173,157]
183. brave(mary) | patient(mary) <- (11) [resolution 179,77]
186. patient(mary) <- (11) [subsumption resolution 183,152]
187. $false <- (11) [subsumption resolution 186,155]
188. ~11 [avatar contradiction clause 187]
202. quiet(sK2) | patient(sK2) <- (4) [resolution 98,131]
203. patient(sK2) <- (4, ~5) [subsumption resolution 202,136]
204. $false <- (4, ~5) [subsumption resolution 203,155]
205. ~4 | 5 [avatar contradiction clause 204]
207. $false <- (3, 12) [resolution 127,177]
208. ~3 | ~12 [avatar contradiction clause 207]
210. $false [avatar sat refutation 132,137,178,188,205,208]
% SZS output end Proof for 7233981399793839293657019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or quiet then paul is either not happy or rich and vice versa. If paul is either not curious or quiet then someone is either happy or not wise and vice versa. Everyone who is old or quiet is tall and vice versa. If fred is calm or not tall then someone is not happy. If someone is both happy and not tall then someone is either calm or not wise. Everyone who is creative is not old or patient and vice versa. Everyone who is both not tall and happy is not old and vice versa. If someone is kind then someone is either curious or not curious. If someone is calm or not creative then mary is creative or not funny. Everyone who is not kind is not old or patient and vice versa. If john is either not humble or funny then mary is curious or calm. Everyone who is either not brave or not wise is both curious and wise and vice versa. Everyone who is both not patient and quiet is not brave. If someone is both patient and not creative then someone is generous. If john is brave then john is both rich and wise and vice versa. Everyone who is both kind and calm is calm and vice versa. John is tall or quiet. Alice is quiet or old. Someone is not generous. John is both not patient and not funny. Someone is not quiet. Alice is either brave or quiet. Fred is both funny and not quiet. Someone is either not generous or humble. | Mary is happy. | neutral | ((?[X]:((~curious(X)|quiet(X))))<=>((~happy(paul)<~>rich(paul))))&
(((~curious(paul)<~>quiet(paul)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((old(X)|quiet(X))<=>tall(X)))&
(((calm(fred)|~tall(fred)))=>(?[X]:(~happy(X))))&
((?[X]:((happy(X)&~tall(X))))=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:(creative(X)<=>(~old(X)|patient(X))))&
(![X]:((~tall(X)&happy(X))<=>~old(X)))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((calm(X)|~creative(X))))=>((creative(mary)|~funny(mary))))&
(![X]:(~kind(X)<=>(~old(X)|patient(X))))&
(((~humble(john)<~>funny(john)))=>((curious(mary)|calm(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(curious(X)&wise(X))))&
(![X]:((~patient(X)&quiet(X))=>~brave(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(generous(X))))&
((brave(john))<=>((rich(john)&wise(john))))&
(![X]:((kind(X)&calm(X))<=>calm(X)))&
((tall(john)|quiet(john)))&
((quiet(alice)|old(alice)))&
(?[X]:(~generous(X)))&
((~patient(john)&~funny(john)))&
(?[X]:(~quiet(X)))&
((brave(alice)<~>quiet(alice)))&
((funny(fred)&~quiet(fred)))&
(?[X]:((~generous(X)<~>humble(X)))) | happy(mary) | [] | null | 0 |
If someone is both brave and happy then someone is both not brave and calm.
If someone is happy then someone is both not happy and not generous and vice versa.
Everyone who is both tall and not happy is either rich or not old.
Everyone who is both calm and not quiet is either not brave or curious.
Everyone who is creative or kind is creative and vice versa.
Everyone who is either not funny or not humble is both not happy and curious and vice versa.
If susan is both not wise and not kind then someone is either not generous or not old.
Everyone who is either creative or not quiet is not old and vice versa.
If someone is both not curious and brave then paul is either not calm or rich.
If mary is curious then someone is both not rich and old and vice versa.
Everyone who is both not creative and tall is both humble and not rich.
If someone is both not calm and generous then someone is patient or not generous.
Everyone who is brave is both not patient and not generous and vice versa.
If someone is rich or not kind then lucy is tall or not curious and vice versa.
Everyone who is not tall or not old is curious.
If someone is generous or quiet then someone is not curious or not funny.
Susan is both not happy and brave.
John is either kind or not old.
Someone is both not creative and curious.
Someone is not humble or wise.
John is both not funny and not curious.
Someone is not rich or not curious.
Someone is not kind or rich. | John is old. | entailment | ((?[X]:((brave(X)&happy(X))))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:((tall(X)&~happy(X))=>(rich(X)<~>~old(X))))&
(![X]:((calm(X)&~quiet(X))=>(~brave(X)<~>curious(X))))&
(![X]:((creative(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~humble(X))<=>(~happy(X)&curious(X))))&
(((~wise(susan)&~kind(susan)))=>(?[X]:((~generous(X)<~>~old(X)))))&
(![X]:((creative(X)<~>~quiet(X))<=>~old(X)))&
((?[X]:((~curious(X)&brave(X))))=>((~calm(paul)<~>rich(paul))))&
((curious(mary))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((~creative(X)&tall(X))=>(humble(X)&~rich(X))))&
((?[X]:((~calm(X)&generous(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:(brave(X)<=>(~patient(X)&~generous(X))))&
((?[X]:((rich(X)|~kind(X))))<=>((tall(lucy)|~curious(lucy))))&
(![X]:((~tall(X)|~old(X))=>curious(X)))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~curious(X)|~funny(X)))))&
((~happy(susan)&brave(susan)))&
((kind(john)<~>~old(john)))&
(?[X]:((~creative(X)&curious(X))))&
(?[X]:((~humble(X)|wise(X))))&
((~funny(john)&~curious(john)))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((~kind(X)|rich(X)))) | old(john) | [
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5110436527742991255277117
% SZS output start Proof for 5110436527742991255277117
15. ! [X0] : ((~old(X0) | ~tall(X0)) => curious(X0)) [input p14]
21. ~curious(john) & ~funny(john) [input p20]
24. ~old(john) [input hypothesis]
40. ! [X0] : (curious(X0) | (old(X0) & tall(X0))) [ennf transformation 15]
120. curious(X0) | old(X0) [cnf transformation 40]
130. ~curious(john) [cnf transformation 21]
133. ~old(john) [cnf transformation 24]
258. 30 <=> old(john) [avatar definition]
259. ~old(john) <- (~30) [avatar component clause 258]
281. ~30 [avatar split clause 133,258]
289. old(john) [resolution 120,130]
291. $false <- (~30) [subsumption resolution 289,259]
292. 30 [avatar contradiction clause 291]
293. $false [avatar sat refutation 281,292]
% SZS output end Proof for 5110436527742991255277117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and not quiet is rich and vice versa. Everyone who is either not brave or tall is both brave and not tall. Everyone who is funny is old or not curious and vice versa. If lucy is both not old and old then someone is not brave or not funny. Everyone who is both brave and not kind is quiet and vice versa. Everyone who is strong or humble is either not calm or strong and vice versa. If lucy is either brave or not patient then someone is both funny and wise. If lucy is funny then alice is wise. Everyone who is generous is not wise or not patient and vice versa. If someone is strong or calm then paul is either not brave or generous. Everyone who is old is either quiet or patient. Everyone who is not patient is tall and vice versa. If lucy is not calm then someone is both happy and not happy. If someone is not kind then fred is both creative and not humble and vice versa. Everyone who is either not brave or humble is both not tall and happy. If paul is not calm then john is both curious and not strong. Lucy is generous or not wise. Someone is happy. Paul is rich or not happy. Mary is not brave. Someone is quiet. Someone is both curious and not wise. | Fred is not funny. | neutral | (![X]:((kind(X)&~quiet(X))<=>rich(X)))&
(![X]:((~brave(X)<~>tall(X))=>(brave(X)&~tall(X))))&
(![X]:(funny(X)<=>(old(X)|~curious(X))))&
(((~old(lucy)&old(lucy)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((strong(X)|humble(X))<=>(~calm(X)<~>strong(X))))&
(((brave(lucy)<~>~patient(lucy)))=>(?[X]:((funny(X)&wise(X)))))&
((funny(lucy))=>(wise(alice)))&
(![X]:(generous(X)<=>(~wise(X)|~patient(X))))&
((?[X]:((strong(X)|calm(X))))=>((~brave(paul)<~>generous(paul))))&
(![X]:(old(X)=>(quiet(X)<~>patient(X))))&
(![X]:(~patient(X)<=>tall(X)))&
((~calm(lucy))=>(?[X]:((happy(X)&~happy(X)))))&
((?[X]:(~kind(X)))<=>((creative(fred)&~humble(fred))))&
(![X]:((~brave(X)<~>humble(X))=>(~tall(X)&happy(X))))&
((~calm(paul))=>((curious(john)&~strong(john))))&
((generous(lucy)|~wise(lucy)))&
(?[X]:(happy(X)))&
((rich(paul)|~happy(paul)))&
(~brave(mary))&
(?[X]:(quiet(X)))&
(?[X]:((curious(X)&~wise(X)))) | ~funny(fred) | [] | null | 0 |
If someone is not brave then someone is either not kind or curious and vice versa.
If someone is both creative and not old then someone is creative or not calm and vice versa.
Everyone who is not old or curious is not quiet and vice versa.
Everyone who is either humble or not humble is not calm.
If someone is not creative or wise then someone is either not calm or not wise.
If someone is either funny or brave then someone is not generous and vice versa.
Everyone who is both generous and not calm is not quiet or creative.
If someone is both quiet and strong then mary is calm or rich.
Everyone who is either brave or strong is kind or not brave.
If alice is both not quiet and not creative then fred is either not tall or not patient and vice versa.
Everyone who is creative is both not generous and not strong and vice versa.
If mary is old then mary is generous or not brave and vice versa.
If john is funny then mary is both not rich and not happy and vice versa.
Everyone who is both not wise and old is not rich and vice versa.
If fred is either not quiet or brave then susan is old or not generous and vice versa.
If john is either not happy or generous then mary is old or not tall and vice versa.
Paul is either not calm or tall.
Someone is not calm.
Someone is either wise or not funny.
Someone is funny or tall.
Someone is generous.
Susan is both not rich and not tall.
Someone is both not old and not happy.
Mary is calm or not old. | John is funny. | contradiction | ((?[X]:(~brave(X)))<=>(?[X]:((~kind(X)<~>curious(X)))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~old(X)|curious(X))<=>~quiet(X)))&
(![X]:((humble(X)<~>~humble(X))=>~calm(X)))&
((?[X]:((~creative(X)|wise(X))))=>(?[X]:((~calm(X)<~>~wise(X)))))&
((?[X]:((funny(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)&~calm(X))=>(~quiet(X)|creative(X))))&
((?[X]:((quiet(X)&strong(X))))=>((calm(mary)|rich(mary))))&
(![X]:((brave(X)<~>strong(X))=>(kind(X)|~brave(X))))&
(((~quiet(alice)&~creative(alice)))<=>((~tall(fred)<~>~patient(fred))))&
(![X]:(creative(X)<=>(~generous(X)&~strong(X))))&
((old(mary))<=>((generous(mary)|~brave(mary))))&
((funny(john))<=>((~rich(mary)&~happy(mary))))&
(![X]:((~wise(X)&old(X))<=>~rich(X)))&
(((~quiet(fred)<~>brave(fred)))<=>((old(susan)|~generous(susan))))&
(((~happy(john)<~>generous(john)))<=>((old(mary)|~tall(mary))))&
((~calm(paul)<~>tall(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:(generous(X)))&
((~rich(susan)&~tall(susan)))&
(?[X]:((~old(X)&~happy(X))))&
((calm(mary)|~old(mary))) | funny(john) | [
"p3",
"p12",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5300630974657405017871361
% SZS output start Proof for 5300630974657405017871361
4. ! [X0] : ((humble(X0) <~> ~humble(X0)) => ~calm(X0)) [input p3]
13. funny(john) <=> (~happy(mary) & ~rich(mary)) [input p12]
14. ! [X0] : ((old(X0) & ~wise(X0)) <=> ~rich(X0)) [input p13]
24. ~old(mary) | calm(mary) [input p23]
25. funny(john) [input hypothesis]
30. ! [X0] : (~calm(X0) | (humble(X0) <=> ~humble(X0))) [ennf transformation 4]
50. ! [X0] : (~calm(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 30]
67. (funny(john) | (happy(mary) | rich(mary))) & ((~happy(mary) & ~rich(mary)) | ~funny(john)) [nnf transformation 13]
68. (funny(john) | happy(mary) | rich(mary)) & ((~happy(mary) & ~rich(mary)) | ~funny(john)) [flattening 67]
69. ! [X0] : (((old(X0) & ~wise(X0)) | rich(X0)) & (~rich(X0) | (~old(X0) | wise(X0)))) [nnf transformation 14]
70. ! [X0] : (((old(X0) & ~wise(X0)) | rich(X0)) & (~rich(X0) | ~old(X0) | wise(X0))) [flattening 69]
99. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 50]
100. ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 50]
125. ~rich(mary) | ~funny(john) [cnf transformation 68]
130. rich(X0) | old(X0) [cnf transformation 70]
154. ~old(mary) | calm(mary) [cnf transformation 24]
155. funny(john) [cnf transformation 25]
157. ~calm(X0) | ~humble(X0) [duplicate literal removal 99]
158. ~calm(X0) | humble(X0) [duplicate literal removal 100]
214. ~calm(X0) [subsumption resolution 157,158]
260. 24 <=> rich(mary) [avatar definition]
261. ~rich(mary) <- (~24) [avatar component clause 260]
291. 30 <=> old(mary) [avatar definition]
292. ~old(mary) <- (~30) [avatar component clause 291]
306. 33 <=> funny(john) [avatar definition]
311. ~33 | ~24 [avatar split clause 125,260,306]
372. ~old(mary) [subsumption resolution 154,214]
373. ~30 [avatar split clause 372,291]
374. 33 [avatar split clause 155,306]
384. old(mary) <- (~24) [resolution 130,261]
386. $false <- (~24, ~30) [subsumption resolution 384,292]
387. 24 | 30 [avatar contradiction clause 386]
388. $false [avatar sat refutation 311,373,374,387]
% SZS output end Proof for 5300630974657405017871361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not strong is not funny or strong and vice versa. Everyone who is both not old and wise is strong. Everyone who is both tall and humble is either not curious or not brave and vice versa. Everyone who is not happy or tall is not humble or not wise and vice versa. Everyone who is both not tall and not calm is old and vice versa. If paul is either not curious or not humble then john is not brave or quiet. Everyone who is both not rich and not kind is both funny and kind and vice versa. Everyone who is generous is either not strong or happy and vice versa. Everyone who is patient is both curious and funny. Everyone who is both not calm and old is quiet and vice versa. Everyone who is either not funny or wise is humble and vice versa. If someone is not funny then someone is funny or old and vice versa. If fred is either not humble or patient then someone is not brave or humble and vice versa. If someone is both happy and not humble then lucy is not wise or not rich and vice versa. If someone is either quiet or not patient then alice is not tall and vice versa. Everyone who is not calm is brave or not rich and vice versa. Lucy is not calm or not patient. Someone is either calm or patient. Alice is either old or wise. Lucy is both funny and rich. John is both wise and not funny. Mary is either old or not old. Paul is not kind or wise. Fred is not curious or generous. | Fred is humble. | contradiction | (![X]:((old(X)&~strong(X))<=>(~funny(X)|strong(X))))&
(![X]:((~old(X)&wise(X))=>strong(X)))&
(![X]:((tall(X)&humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((~happy(X)|tall(X))<=>(~humble(X)|~wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>old(X)))&
(((~curious(paul)<~>~humble(paul)))=>((~brave(john)|quiet(john))))&
(![X]:((~rich(X)&~kind(X))<=>(funny(X)&kind(X))))&
(![X]:(generous(X)<=>(~strong(X)<~>happy(X))))&
(![X]:(patient(X)=>(curious(X)&funny(X))))&
(![X]:((~calm(X)&old(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>wise(X))<=>humble(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)|old(X)))))&
(((~humble(fred)<~>patient(fred)))<=>(?[X]:((~brave(X)|humble(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>((~wise(lucy)|~rich(lucy))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(~tall(alice)))&
(![X]:(~calm(X)<=>(brave(X)|~rich(X))))&
((~calm(lucy)|~patient(lucy)))&
(?[X]:((calm(X)<~>patient(X))))&
((old(alice)<~>wise(alice)))&
((funny(lucy)&rich(lucy)))&
((wise(john)&~funny(john)))&
((old(mary)<~>~old(mary)))&
((~kind(paul)|wise(paul)))&
((~curious(fred)|generous(fred))) | humble(fred) | [
"p0",
"p3",
"p7",
"p8",
"p10",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4719591297373630121647564
% SZS output start Proof for 4719591297373630121647564
1. ! [X0] : ((~strong(X0) & old(X0)) <=> (strong(X0) | ~funny(X0))) [input p0]
4. ! [X0] : ((tall(X0) | ~happy(X0)) <=> (~wise(X0) | ~humble(X0))) [input p3]
8. ! [X0] : (generous(X0) <=> (~strong(X0) <~> happy(X0))) [input p7]
9. ! [X0] : (patient(X0) => (funny(X0) & curious(X0))) [input p8]
11. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> humble(X0)) [input p10]
13. (~humble(fred) <~> patient(fred)) <=> ? [X0] : (humble(X0) | ~brave(X0)) [input p12]
24. generous(fred) | ~curious(fred) [input p23]
25. humble(fred) [input hypothesis]
27. ! [X0] : (generous(X0) => (~strong(X0) <~> happy(X0))) [unused predicate definition removal 8]
32. ! [X0] : ((~strong(X0) <~> happy(X0)) | ~generous(X0)) [ennf transformation 27]
33. ! [X0] : ((funny(X0) & curious(X0)) | ~patient(X0)) [ennf transformation 9]
34. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 1]
35. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | strong(X0) | ~old(X0))) [flattening 34]
38. ! [X0] : (((tall(X0) | ~happy(X0)) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | (~tall(X0) & happy(X0)))) [nnf transformation 4]
39. ! [X0] : ((tall(X0) | ~happy(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | (~tall(X0) & happy(X0)))) [flattening 38]
45. ! [X0] : (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ~generous(X0)) [nnf transformation 32]
48. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ~humble(X0)) & (humble(X0) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 11]
54. (((~patient(fred) | humble(fred)) & (patient(fred) | ~humble(fred))) | ! [X0] : (~humble(X0) & brave(X0))) & (? [X0] : (humble(X0) | ~brave(X0)) | ((~humble(fred) | ~patient(fred)) & (patient(fred) | humble(fred)))) [nnf transformation 13]
55. (((~patient(fred) | humble(fred)) & (patient(fred) | ~humble(fred))) | ! [X0] : (~humble(X0) & brave(X0))) & (? [X1] : (humble(X1) | ~brave(X1)) | ((~humble(fred) | ~patient(fred)) & (patient(fred) | humble(fred)))) [rectify 54]
56. ? [X1] : (humble(X1) | ~brave(X1)) => (humble(sK2) | ~brave(sK2)) [choice axiom]
57. (((~patient(fred) | humble(fred)) & (patient(fred) | ~humble(fred))) | ! [X0] : (~humble(X0) & brave(X0))) & ((humble(sK2) | ~brave(sK2)) | ((~humble(fred) | ~patient(fred)) & (patient(fred) | humble(fred)))) [skolemisation 55,56]
78. ~strong(X0) | ~strong(X0) [cnf transformation 35]
86. ~humble(X0) | ~wise(X0) | happy(X0) [cnf transformation 39]
100. ~happy(X0) | strong(X0) | ~generous(X0) [cnf transformation 45]
101. ~patient(X0) | curious(X0) [cnf transformation 33]
102. ~patient(X0) | funny(X0) [cnf transformation 33]
108. ~humble(X0) | ~funny(X0) | wise(X0) [cnf transformation 48]
116. patient(fred) | ~humble(fred) | ~humble(X0) [cnf transformation 57]
143. generous(fred) | ~curious(fred) [cnf transformation 24]
144. humble(fred) [cnf transformation 25]
148. ~strong(X0) [duplicate literal removal 78]
169. ~generous(X0) | ~happy(X0) [subsumption resolution 100,148]
184. 8 <=> ! [X0] : ~humble(X0) [avatar definition]
185. ~humble(X0) <- (8) [avatar component clause 184]
187. 9 <=> humble(fred) [avatar definition]
189. humble(fred) <- (9) [avatar component clause 187]
191. 10 <=> patient(fred) [avatar definition]
192. patient(fred) <- (10) [avatar component clause 191]
199. 8 | ~9 | 10 [avatar split clause 116,191,187,184]
289. 30 <=> curious(fred) [avatar definition]
291. ~curious(fred) <- (~30) [avatar component clause 289]
293. 31 <=> generous(fred) [avatar definition]
295. generous(fred) <- (31) [avatar component clause 293]
296. ~30 | 31 [avatar split clause 143,293,289]
297. 9 [avatar split clause 144,187]
301. curious(fred) <- (10) [resolution 101,192]
302. $false <- (10, ~30) [subsumption resolution 301,291]
303. ~10 | 30 [avatar contradiction clause 302]
304. $false <- (8, 9) [resolution 185,189]
305. ~8 | ~9 [avatar contradiction clause 304]
311. funny(fred) <- (10) [resolution 102,192]
320. ~happy(fred) <- (31) [resolution 169,295]
342. ~wise(fred) | happy(fred) <- (9) [resolution 86,189]
343. ~wise(fred) <- (9, 31) [subsumption resolution 342,320]
390. ~funny(fred) | wise(fred) <- (9) [resolution 108,189]
393. wise(fred) <- (9, 10) [subsumption resolution 390,311]
394. $false <- (9, 10, 31) [subsumption resolution 393,343]
395. ~9 | ~10 | ~31 [avatar contradiction clause 394]
396. $false [avatar sat refutation 199,296,297,303,305,395]
% SZS output end Proof for 4719591297373630121647564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either not humble or not strong. Everyone who is creative or wise is both not generous and not curious and vice versa. Everyone who is both not rich and funny is wise or curious. If someone is either funny or creative then someone is either not kind or rich and vice versa. If mary is either brave or not creative then alice is both not tall and tall. If someone is both not strong and not humble then alice is tall. If someone is both old and not kind then someone is either not creative or not rich. Everyone who is both not calm and not wise is both funny and not quiet. If mary is both not calm and happy then someone is creative or not old. Everyone who is not rich or not quiet is not curious. Everyone who is calm is funny and vice versa. If someone is either not generous or not brave then mary is patient or not generous. Everyone who is either curious or patient is both not rich and not humble. If lucy is not generous or generous then someone is either quiet or not rich and vice versa. If someone is either not tall or old then fred is not funny or strong. If alice is both not funny and not quiet then someone is both old and quiet and vice versa. Paul is not funny. Lucy is not funny. Someone is not creative. Someone is both not rich and strong. Someone is old or not strong. Lucy is either tall or curious. Someone is happy. Alice is not funny or not old. | Lucy is tall. | entailment | (![X]:(old(X)=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)|wise(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~rich(X)&funny(X))=>(wise(X)|curious(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((brave(mary)<~>~creative(mary)))=>((~tall(alice)&tall(alice))))&
((?[X]:((~strong(X)&~humble(X))))=>(tall(alice)))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~calm(X)&~wise(X))=>(funny(X)&~quiet(X))))&
(((~calm(mary)&happy(mary)))=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~rich(X)|~quiet(X))=>~curious(X)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((~generous(X)<~>~brave(X))))=>((patient(mary)|~generous(mary))))&
(![X]:((curious(X)<~>patient(X))=>(~rich(X)&~humble(X))))&
(((~generous(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>((~funny(fred)|strong(fred))))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:((old(X)&quiet(X)))))&
(~funny(paul))&
(~funny(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((old(X)|~strong(X))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(happy(X)))&
((~funny(alice)|~old(alice))) | tall(lucy) | [
"p1",
"p7",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1841698109414864738947995
% SZS output start Proof for 1841698109414864738947995
2. ! [X0] : ((wise(X0) | creative(X0)) <=> (~curious(X0) & ~generous(X0))) [input p1]
8. ! [X0] : ((~wise(X0) & ~calm(X0)) => (~quiet(X0) & funny(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> funny(X0)) [input p10]
18. ~funny(lucy) [input p17]
22. tall(lucy) <~> curious(lucy) [input p21]
25. ~tall(lucy) [input hypothesis]
28. ! [X0] : (calm(X0) => funny(X0)) [unused predicate definition removal 11]
35. ! [X0] : ((~quiet(X0) & funny(X0)) | (wise(X0) | calm(X0))) [ennf transformation 8]
36. ! [X0] : ((~quiet(X0) & funny(X0)) | wise(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (funny(X0) | ~calm(X0)) [ennf transformation 28]
47. ! [X0] : (((wise(X0) | creative(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 2]
48. ! [X0] : ((wise(X0) | creative(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [flattening 47]
80. (~curious(lucy) | ~tall(lucy)) & (curious(lucy) | tall(lucy)) [nnf transformation 22]
88. ~curious(X0) | ~wise(X0) [cnf transformation 48]
106. calm(X0) | wise(X0) | funny(X0) [cnf transformation 36]
111. ~calm(X0) | funny(X0) [cnf transformation 40]
131. ~funny(lucy) [cnf transformation 18]
136. curious(lucy) | tall(lucy) [cnf transformation 80]
140. ~tall(lucy) [cnf transformation 25]
309. 38 <=> tall(lucy) [avatar definition]
313. 39 <=> curious(lucy) [avatar definition]
314. curious(lucy) <- (39) [avatar component clause 313]
317. 38 | 39 [avatar split clause 136,313,309]
323. ~38 [avatar split clause 140,309]
325. ~wise(lucy) <- (39) [resolution 88,314]
342. wise(X0) | funny(X0) | funny(X0) [resolution 106,111]
343. funny(X0) | wise(X0) [duplicate literal removal 342]
345. wise(lucy) [resolution 343,131]
348. $false <- (39) [subsumption resolution 345,325]
349. ~39 [avatar contradiction clause 348]
350. $false [avatar sat refutation 317,323,349]
% SZS output end Proof for 1841698109414864738947995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not quiet then someone is either not creative or humble and vice versa. Everyone who is both not curious and not tall is either not curious or not happy. If someone is wise or not happy then lucy is either not generous or strong and vice versa. If john is not brave or not curious then alice is both funny and not humble. Everyone who is either tall or rich is either tall or not wise. Everyone who is patient or kind is wise and vice versa. Everyone who is not rich is either generous or not happy. If lucy is not strong or not kind then someone is not patient and vice versa. Everyone who is calm is both not patient and not funny and vice versa. Everyone who is both not old and generous is not brave and vice versa. Everyone who is both quiet and not rich is either not funny or brave and vice versa. If susan is either not brave or quiet then paul is funny. If someone is rich or creative then fred is both not happy and happy and vice versa. Everyone who is either humble or curious is not curious or happy. If susan is calm or humble then john is not curious or not tall and vice versa. Everyone who is both not tall and wise is funny or old. Mary is either not patient or happy. Alice is calm. Lucy is not tall or not calm. Someone is calm or funny. Someone is not humble or not calm. Someone is not calm or humble. Someone is not funny or humble. | Lucy is tall. | neutral | ((?[X]:((humble(X)&~quiet(X))))<=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((~curious(X)&~tall(X))=>(~curious(X)<~>~happy(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((~generous(lucy)<~>strong(lucy))))&
(((~brave(john)|~curious(john)))=>((funny(alice)&~humble(alice))))&
(![X]:((tall(X)<~>rich(X))=>(tall(X)<~>~wise(X))))&
(![X]:((patient(X)|kind(X))<=>wise(X)))&
(![X]:(~rich(X)=>(generous(X)<~>~happy(X))))&
(((~strong(lucy)|~kind(lucy)))<=>(?[X]:(~patient(X))))&
(![X]:(calm(X)<=>(~patient(X)&~funny(X))))&
(![X]:((~old(X)&generous(X))<=>~brave(X)))&
(![X]:((quiet(X)&~rich(X))<=>(~funny(X)<~>brave(X))))&
(((~brave(susan)<~>quiet(susan)))=>(funny(paul)))&
((?[X]:((rich(X)|creative(X))))<=>((~happy(fred)&happy(fred))))&
(![X]:((humble(X)<~>curious(X))=>(~curious(X)|happy(X))))&
(((calm(susan)|humble(susan)))<=>((~curious(john)|~tall(john))))&
(![X]:((~tall(X)&wise(X))=>(funny(X)|old(X))))&
((~patient(mary)<~>happy(mary)))&
(calm(alice))&
((~tall(lucy)|~calm(lucy)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((~calm(X)|humble(X))))&
(?[X]:((~funny(X)|humble(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is not wise is kind.
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
If fred is curious or not kind then lucy is both old and quiet.
Everyone who is strong or not happy is not rich or not quiet.
Everyone who is calm is not strong.
Everyone who is brave is either happy or old and vice versa.
Everyone who is generous is kind and vice versa.
Someone is either not rich or humble.
Lucy is quiet.
Paul is kind or not creative.
Mary is either quiet or not funny.
Someone is not funny.
Mary is quiet.
Someone is either not humble or not patient. | Paul is not happy. | entailment | (![X]:(~wise(X)=>kind(X)))&
(((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
(((curious(fred)|~kind(fred)))=>((old(lucy)&quiet(lucy))))&
(![X]:((strong(X)|~happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:(brave(X)<=>(happy(X)<~>old(X))))&
(![X]:(generous(X)<=>kind(X)))&
(?[X]:((~rich(X)<~>humble(X))))&
(quiet(lucy))&
((kind(paul)|~creative(paul)))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:(~funny(X)))&
(quiet(mary))&
(?[X]:((~humble(X)<~>~patient(X)))) | ~happy(paul) | [
"p0",
"p4",
"p6",
"p7",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8106856763594842066434657
% SZS output start Proof for 8106856763594842066434657
1. ! [X0] : (~wise(X0) => kind(X0)) [input p0]
5. ! [X0] : ((~calm(X0) | ~quiet(X0)) => (~wise(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (~old(X0) & ~kind(X0))) [input p6]
8. ! [X0] : (strong(X0) <=> (~generous(X0) | ~creative(X0))) [input p7]
14. ! [X0] : (calm(X0) => ~strong(X0)) [input p13]
15. ! [X0] : (brave(X0) <=> (happy(X0) <~> old(X0))) [input p14]
19. ~creative(paul) | kind(paul) [input p18]
24. happy(paul) [input hypothesis]
26. ! [X0] : (kind(X0) | wise(X0)) [ennf transformation 1]
30. ! [X0] : ((~wise(X0) & ~creative(X0)) | (calm(X0) & quiet(X0))) [ennf transformation 5]
36. ! [X0] : (~strong(X0) | ~calm(X0)) [ennf transformation 14]
41. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 7]
42. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 41]
43. ! [X0] : ((strong(X0) | (generous(X0) & creative(X0))) & ((~generous(X0) | ~creative(X0)) | ~strong(X0))) [nnf transformation 8]
44. ! [X0] : ((strong(X0) | (generous(X0) & creative(X0))) & (~generous(X0) | ~creative(X0) | ~strong(X0))) [flattening 43]
51. ! [X0] : ((brave(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ~brave(X0))) [nnf transformation 15]
62. kind(X0) | wise(X0) [cnf transformation 26]
78. ~wise(X0) | calm(X0) [cnf transformation 30]
86. ~brave(X0) | ~kind(X0) | old(X0) [cnf transformation 42]
87. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 42]
92. creative(X0) | strong(X0) [cnf transformation 44]
112. ~calm(X0) | ~strong(X0) [cnf transformation 36]
114. ~old(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 51]
115. brave(X0) | old(X0) | ~happy(X0) [cnf transformation 51]
122. ~creative(paul) | kind(paul) [cnf transformation 19]
129. happy(paul) [cnf transformation 24]
130. ~old(X0) | brave(X0) [duplicate literal removal 87]
222. ~happy(X0) | brave(X0) [subsumption resolution 115,130]
223. ~happy(X0) | ~old(X0) [subsumption resolution 114,130]
236. 21 <=> kind(paul) [avatar definition]
237. ~kind(paul) <- (~21) [avatar component clause 236]
240. 22 <=> creative(paul) [avatar definition]
242. ~creative(paul) <- (~22) [avatar component clause 240]
243. 21 | ~22 [avatar split clause 122,240,236]
265. strong(paul) <- (~22) [resolution 92,242]
272. brave(paul) [resolution 222,129]
274. ~old(paul) [resolution 223,129]
279. ~kind(paul) | old(paul) [resolution 86,272]
281. ~kind(paul) [subsumption resolution 279,274]
282. ~21 [avatar split clause 281,236]
301. wise(paul) <- (~21) [resolution 237,62]
302. calm(paul) <- (~21) [resolution 301,78]
306. ~strong(paul) <- (~21) [resolution 302,112]
307. $false <- (~21, ~22) [subsumption resolution 306,265]
308. 21 | 22 [avatar contradiction clause 307]
309. $false [avatar sat refutation 243,282,308]
% SZS output end Proof for 8106856763594842066434657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not brave is both happy and not humble and vice versa.
Everyone who is old is not rich and vice versa.
Everyone who is either not curious or strong is either funny or not kind.
If alice is patient then paul is either not kind or not humble.
If someone is either rich or not funny then susan is not happy and vice versa.
If someone is brave then john is humble or brave.
If mary is both not old and not rich then john is either not wise or not brave and vice versa.
If mary is either happy or tall then someone is either not quiet or not old and vice versa.
Everyone who is both happy and generous is not generous.
Everyone who is either quiet or funny is both not funny and humble and vice versa.
Everyone who is not happy or not brave is not generous or happy.
If someone is both not kind and not creative then someone is either not creative or kind.
Everyone who is not brave is either humble or not strong.
If someone is not tall then lucy is not tall or quiet.
If someone is curious then someone is humble.
Everyone who is either old or not old is both not rich and not quiet and vice versa.
John is both wise and not strong.
Someone is happy or old.
Someone is both not tall and strong. | Lucy is not kind. | neutral | (![X]:((~rich(X)&~brave(X))<=>(happy(X)&~humble(X))))&
(![X]:(old(X)<=>~rich(X)))&
(![X]:((~curious(X)<~>strong(X))=>(funny(X)<~>~kind(X))))&
((patient(alice))=>((~kind(paul)<~>~humble(paul))))&
((?[X]:((rich(X)<~>~funny(X))))<=>(~happy(susan)))&
((?[X]:(brave(X)))=>((humble(john)|brave(john))))&
(((~old(mary)&~rich(mary)))<=>((~wise(john)<~>~brave(john))))&
(((happy(mary)<~>tall(mary)))<=>(?[X]:((~quiet(X)<~>~old(X)))))&
(![X]:((happy(X)&generous(X))=>~generous(X)))&
(![X]:((quiet(X)<~>funny(X))<=>(~funny(X)&humble(X))))&
(![X]:((~happy(X)|~brave(X))=>(~generous(X)|happy(X))))&
((?[X]:((~kind(X)&~creative(X))))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:(~brave(X)=>(humble(X)<~>~strong(X))))&
((?[X]:(~tall(X)))=>((~tall(lucy)|quiet(lucy))))&
((?[X]:(curious(X)))=>(?[X]:(humble(X))))&
(![X]:((old(X)<~>~old(X))<=>(~rich(X)&~quiet(X))))&
((wise(john)&~strong(john)))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((~tall(X)&strong(X)))) | ~kind(lucy) | [] | null | 0 |
Everyone who is either humble or strong is either not kind or old.
Everyone who is not happy is not old and vice versa.
Everyone who is rich is both old and patient and vice versa.
Everyone who is not patient or patient is not calm or not rich and vice versa.
If lucy is either not wise or quiet then someone is both generous and curious.
If mary is both funny and not funny then lucy is funny and vice versa.
Everyone who is funny is not brave or not happy.
If john is creative or not tall then someone is either quiet or not generous and vice versa.
If someone is creative or not kind then someone is patient or generous and vice versa.
Everyone who is either not calm or happy is both calm and wise and vice versa.
Everyone who is not happy is either not curious or not kind and vice versa.
Everyone who is calm is not calm or wise and vice versa.
If alice is brave or curious then someone is both creative and tall.
If someone is either old or wise then john is humble and vice versa.
Everyone who is both kind and not quiet is old or not patient and vice versa.
If someone is either tall or wise then someone is either not strong or not quiet.
Mary is brave or funny.
Someone is either not strong or not brave.
Susan is not brave or not kind.
Someone is not patient or strong.
Someone is both funny and not creative.
John is either not strong or creative.
Mary is not curious or funny. | John is not humble. | entailment | (![X]:((humble(X)<~>strong(X))=>(~kind(X)<~>old(X))))&
(![X]:(~happy(X)<=>~old(X)))&
(![X]:(rich(X)<=>(old(X)&patient(X))))&
(![X]:((~patient(X)|patient(X))<=>(~calm(X)|~rich(X))))&
(((~wise(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&curious(X)))))&
(((funny(mary)&~funny(mary)))<=>(funny(lucy)))&
(![X]:(funny(X)=>(~brave(X)|~happy(X))))&
(((creative(john)|~tall(john)))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(calm(X)&wise(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>~kind(X))))&
(![X]:(calm(X)<=>(~calm(X)|wise(X))))&
(((brave(alice)|curious(alice)))=>(?[X]:((creative(X)&tall(X)))))&
((?[X]:((old(X)<~>wise(X))))<=>(humble(john)))&
(![X]:((kind(X)&~quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((brave(mary)|funny(mary)))&
(?[X]:((~strong(X)<~>~brave(X))))&
((~brave(susan)|~kind(susan)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((funny(X)&~creative(X))))&
((~strong(john)<~>creative(john)))&
((~curious(mary)|funny(mary))) | ~humble(john) | [
"p1",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1137135826912193869514626
% SZS output start Proof for 1137135826912193869514626
2. ! [X0] : (~happy(X0) <=> ~old(X0)) [input p1]
10. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> (wise(X0) & calm(X0))) [input p9]
12. ! [X0] : (calm(X0) <=> (wise(X0) | ~calm(X0))) [input p11]
14. ? [X0] : (old(X0) <~> wise(X0)) <=> humble(john) [input p13]
24. humble(john) [input hypothesis]
34. ! [X0] : ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))) [nnf transformation 2]
54. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~wise(X0) | ~calm(X0))) & ((wise(X0) & calm(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~wise(X0) | ~calm(X0)) & ((wise(X0) & calm(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [flattening 54]
57. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & ((wise(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 12]
58. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & (wise(X0) | ~calm(X0) | ~calm(X0))) [flattening 57]
61. (? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | ~humble(john)) & (humble(john) | ! [X0] : ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) [nnf transformation 14]
62. (? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | ~humble(john)) & (humble(john) | ! [X1] : ((old(X1) | ~wise(X1)) & (wise(X1) | ~old(X1)))) [rectify 61]
63. ? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) => ((~wise(sK5) | ~old(sK5)) & (wise(sK5) | old(sK5))) [choice axiom]
64. (((~wise(sK5) | ~old(sK5)) & (wise(sK5) | old(sK5))) | ~humble(john)) & (humble(john) | ! [X1] : ((old(X1) | ~wise(X1)) & (wise(X1) | ~old(X1)))) [skolemisation 62,63]
84. ~happy(X0) | old(X0) [cnf transformation 34]
114. happy(X0) | ~calm(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 55]
120. wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 58]
121. calm(X0) | calm(X0) [cnf transformation 58]
130. ~wise(sK5) | ~old(sK5) | ~humble(john) [cnf transformation 64]
150. humble(john) [cnf transformation 24]
151. wise(X0) | ~calm(X0) [duplicate literal removal 120]
152. calm(X0) [duplicate literal removal 121]
154. ~wise(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 114]
246. wise(X0) [subsumption resolution 151,152]
267. ~old(sK5) | ~humble(john) [subsumption resolution 130,246]
269. 25 <=> humble(john) [avatar definition]
273. 26 <=> old(sK5) [avatar definition]
275. ~old(sK5) <- (~26) [avatar component clause 273]
276. ~25 | ~26 [avatar split clause 267,273,269]
279. 27 <=> ! [X1] : old(X1) [avatar definition]
280. old(X1) <- (27) [avatar component clause 279]
341. 25 [avatar split clause 150,269]
383. ~calm(X1) | happy(X1) [resolution 154,246]
385. happy(X1) [subsumption resolution 383,152]
397. old(X1) [resolution 385,84]
400. 27 [avatar split clause 397,279]
406. $false <- (~26, 27) [resolution 280,275]
407. 26 | ~27 [avatar contradiction clause 406]
411. $false [avatar sat refutation 276,341,400,407]
% SZS output end Proof for 1137135826912193869514626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not rich then someone is both not humble and not strong. Everyone who is either not tall or not quiet is tall and vice versa. If paul is not tall or old then someone is not curious. If mary is both not creative and generous then alice is curious or happy. Everyone who is wise or not curious is either not old or not patient. Everyone who is not rich or strong is old or not strong and vice versa. If someone is strong or wise then someone is quiet. Everyone who is either tall or brave is either patient or curious and vice versa. If someone is rich or not quiet then paul is not patient and vice versa. Everyone who is not rich is not humble and vice versa. If john is not calm then susan is rich or funny. Everyone who is brave or humble is not humble or not curious. If susan is both funny and not calm then someone is both kind and not happy. If susan is not humble then someone is curious and vice versa. Everyone who is patient is not calm and vice versa. Everyone who is both not old and not wise is either not generous or not strong. Someone is not happy. Mary is either tall or not kind. Someone is either old or not calm. Paul is both generous and not humble. Someone is either generous or old. | Mary is old. | neutral | ((~rich(fred))=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>tall(X)))&
(((~tall(paul)|old(paul)))=>(?[X]:(~curious(X))))&
(((~creative(mary)&generous(mary)))=>((curious(alice)|happy(alice))))&
(![X]:((wise(X)|~curious(X))=>(~old(X)<~>~patient(X))))&
(![X]:((~rich(X)|strong(X))<=>(old(X)|~strong(X))))&
((?[X]:((strong(X)|wise(X))))=>(?[X]:(quiet(X))))&
(![X]:((tall(X)<~>brave(X))<=>(patient(X)<~>curious(X))))&
((?[X]:((rich(X)|~quiet(X))))<=>(~patient(paul)))&
(![X]:(~rich(X)<=>~humble(X)))&
((~calm(john))=>((rich(susan)|funny(susan))))&
(![X]:((brave(X)|humble(X))=>(~humble(X)|~curious(X))))&
(((funny(susan)&~calm(susan)))=>(?[X]:((kind(X)&~happy(X)))))&
((~humble(susan))<=>(?[X]:(curious(X))))&
(![X]:(patient(X)<=>~calm(X)))&
(![X]:((~old(X)&~wise(X))=>(~generous(X)<~>~strong(X))))&
(?[X]:(~happy(X)))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((old(X)<~>~calm(X))))&
((generous(paul)&~humble(paul)))&
(?[X]:((generous(X)<~>old(X)))) | old(mary) | [] | null | 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa.
If someone is both not generous and calm then mary is quiet or happy.
If someone is either not rich or not funny then someone is not humble.
Everyone who is old or not quiet is humble and vice versa.
If someone is both not strong and wise then someone is wise and vice versa.
If paul is either humble or not tall then mary is not creative.
Everyone who is either creative or not humble is generous and vice versa.
If someone is brave or not old then someone is both wise and not wise and vice versa.
Everyone who is not kind is happy or funny.
Everyone who is both funny and old is both not curious and not calm and vice versa.
If someone is rich or funny then john is creative or not calm.
Everyone who is not old is not happy and vice versa.
Everyone who is quiet is both not humble and wise and vice versa.
Everyone who is either old or not wise is both not curious and not generous and vice versa.
Everyone who is either not kind or tall is not wise and vice versa.
Fred is either wise or happy.
Lucy is generous.
John is not humble or not brave.
Paul is wise or funny.
Someone is old or quiet. | Mary is wise. | contradiction | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((~generous(X)&calm(X))))=>((quiet(mary)|happy(mary))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:(~humble(X))))&
(![X]:((old(X)|~quiet(X))<=>humble(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(wise(X))))&
(((humble(paul)<~>~tall(paul)))=>(~creative(mary)))&
(![X]:((creative(X)<~>~humble(X))<=>generous(X)))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
((wise(fred)<~>happy(fred)))&
(generous(lucy))&
((~humble(john)|~brave(john)))&
((wise(paul)|funny(paul)))&
(?[X]:((old(X)|quiet(X)))) | wise(mary) | [
"p0",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5093936774434434720825774
% SZS output start Proof for 5093936774434434720825774
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
8. ? [X0] : (~old(X0) | brave(X0)) <=> ? [X0] : (~wise(X0) & wise(X0)) [input p7]
12. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p11]
14. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (~generous(X0) & ~curious(X0))) [input p13]
21. wise(mary) [input hypothesis]
24. ? [X0] : (~old(X0) | brave(X0)) <=> ? [X1] : (~wise(X1) & wise(X1)) [rectify 8]
33. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((funny(X0) | ~funny(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [flattening 33]
48. (? [X0] : (~old(X0) | brave(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (old(X0) & ~brave(X0))) [nnf transformation 24]
49. (? [X0] : (~old(X0) | brave(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X2] : (~wise(X2) & wise(X2)) | ! [X3] : (old(X3) & ~brave(X3))) [rectify 48]
50. ? [X0] : (~old(X0) | brave(X0)) => (~old(sK3) | brave(sK3)) [choice axiom]
51. ? [X2] : (~wise(X2) & wise(X2)) => (~wise(sK4) & wise(sK4)) [choice axiom]
52. ((~old(sK3) | brave(sK3)) | ! [X1] : (wise(X1) | ~wise(X1))) & ((~wise(sK4) & wise(sK4)) | ! [X3] : (old(X3) & ~brave(X3))) [skolemisation 49,51,50]
55. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 12]
58. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 14]
59. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [flattening 58]
64. generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 34]
65. ~happy(X0) | generous(X0) | ~funny(X0) [cnf transformation 34]
86. wise(sK4) | old(X3) [cnf transformation 52]
88. ~wise(sK4) | old(X3) [cnf transformation 52]
98. ~old(X0) | happy(X0) [cnf transformation 55]
104. ~wise(X0) | ~generous(X0) | ~old(X0) [cnf transformation 59]
118. wise(mary) [cnf transformation 21]
120. ~happy(X0) | generous(X0) [subsumption resolution 64,65]
181. 15 <=> ! [X3] : old(X3) [avatar definition]
182. old(X3) <- (15) [avatar component clause 181]
184. 16 <=> wise(sK4) [avatar definition]
187. 15 | ~16 [avatar split clause 88,184,181]
192. 15 | 16 [avatar split clause 86,184,181]
253. happy(X0) <- (15) [resolution 98,182]
261. generous(X0) <- (15) [resolution 120,253]
298. ~generous(mary) | ~old(mary) [resolution 104,118]
302. ~old(mary) <- (15) [subsumption resolution 298,261]
303. $false <- (15) [subsumption resolution 302,182]
304. ~15 [avatar contradiction clause 303]
314. $false [avatar sat refutation 187,192,304]
% SZS output end Proof for 5093936774434434720825774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and old then lucy is either not tall or calm. If john is either humble or not old then someone is both not curious and not generous. Everyone who is rich is either strong or not strong. Everyone who is either not calm or quiet is either not calm or humble and vice versa. Everyone who is not tall or not generous is both not patient and tall. Everyone who is curious or not tall is either not tall or kind and vice versa. Everyone who is both not strong and not calm is not funny or funny and vice versa. Everyone who is calm or not funny is not creative or not tall. Everyone who is not old is either brave or curious. Everyone who is happy is not patient. Everyone who is not tall is either not creative or curious and vice versa. If john is either not creative or not brave then paul is either tall or funny. Everyone who is curious is not old. If someone is either not happy or brave then alice is funny or tall. Everyone who is not old or calm is both strong and not funny. Everyone who is either happy or not curious is both generous and not old. Someone is brave or not humble. Someone is funny or not brave. Someone is happy. Someone is both quiet and funny. Someone is funny. Lucy is rich or old. | Alice is not old. | contradiction | ((?[X]:((calm(X)&old(X))))=>((~tall(lucy)<~>calm(lucy))))&
(((humble(john)<~>~old(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:(rich(X)=>(strong(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~generous(X))=>(~patient(X)&tall(X))))&
(![X]:((curious(X)|~tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
(![X]:((calm(X)|~funny(X))=>(~creative(X)|~tall(X))))&
(![X]:(~old(X)=>(brave(X)<~>curious(X))))&
(![X]:(happy(X)=>~patient(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>curious(X))))&
(((~creative(john)<~>~brave(john)))=>((tall(paul)<~>funny(paul))))&
(![X]:(curious(X)=>~old(X)))&
((?[X]:((~happy(X)<~>brave(X))))=>((funny(alice)|tall(alice))))&
(![X]:((~old(X)|calm(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)<~>~curious(X))=>(generous(X)&~old(X))))&
(?[X]:((brave(X)|~humble(X))))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(funny(X)))&
((rich(lucy)|old(lucy))) | ~old(alice) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1442587805406339805211868
% SZS output start Proof for 1442587805406339805211868
7. ! [X0] : ((~calm(X0) & ~strong(X0)) <=> (funny(X0) | ~funny(X0))) [input p6]
15. ! [X0] : ((calm(X0) | ~old(X0)) => (~funny(X0) & strong(X0))) [input p14]
23. ~old(alice) [input hypothesis]
37. ! [X0] : ((~funny(X0) & strong(X0)) | (~calm(X0) & old(X0))) [ennf transformation 15]
47. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (calm(X0) | strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | calm(X0) | strong(X0))) [flattening 47]
89. ~strong(X0) | funny(X0) [cnf transformation 48]
90. ~strong(X0) | ~funny(X0) [cnf transformation 48]
108. strong(X0) | old(X0) [cnf transformation 37]
123. ~old(alice) [cnf transformation 23]
169. ~strong(X0) [subsumption resolution 89,90]
189. old(X0) [subsumption resolution 108,169]
209. $false [subsumption resolution 123,189]
% SZS output end Proof for 1442587805406339805211868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or generous is old and vice versa.
If someone is both not creative and brave then alice is both not old and not strong and vice versa.
If lucy is either strong or not funny then fred is kind or patient and vice versa.
If alice is both tall and not calm then someone is both happy and not quiet.
Everyone who is not tall is both wise and tall.
Everyone who is not generous is not wise or tall and vice versa.
Everyone who is either not calm or not wise is happy or calm.
Everyone who is old is not generous and vice versa.
Everyone who is quiet or old is either rich or not brave and vice versa.
Everyone who is not calm or patient is either not funny or not humble and vice versa.
Everyone who is either not rich or not quiet is wise or patient and vice versa.
Everyone who is curious is not wise and vice versa.
Everyone who is both generous and patient is not quiet or not strong.
Everyone who is calm or happy is either not tall or not happy and vice versa.
Everyone who is not old is either not brave or kind.
Everyone who is both not curious and strong is not quiet or patient and vice versa.
Alice is not rich or creative.
Someone is curious or kind.
Someone is either curious or not creative.
Someone is old.
Mary is happy or patient.
Lucy is not wise or strong. | Lucy is not kind. | neutral | (![X]:((tall(X)<~>generous(X))<=>old(X)))&
((?[X]:((~creative(X)&brave(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
(((tall(alice)&~calm(alice)))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:(~tall(X)=>(wise(X)&tall(X))))&
(![X]:(~generous(X)<=>(~wise(X)|tall(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(happy(X)|calm(X))))&
(![X]:(old(X)<=>~generous(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~calm(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((generous(X)&patient(X))=>(~quiet(X)|~strong(X))))&
(![X]:((calm(X)|happy(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:(~old(X)=>(~brave(X)<~>kind(X))))&
(![X]:((~curious(X)&strong(X))<=>(~quiet(X)|patient(X))))&
((~rich(alice)|creative(alice)))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:(old(X)))&
((happy(mary)|patient(mary)))&
((~wise(lucy)|strong(lucy))) | ~kind(lucy) | [] | null | 0 |
If someone is tall then someone is either not funny or creative and vice versa.
Everyone who is both not humble and wise is either not curious or not old.
If someone is not happy then someone is not patient or not generous and vice versa.
Everyone who is both not calm and strong is not patient and vice versa.
If mary is patient or not humble then mary is both not generous and calm.
Everyone who is generous is both calm and not wise.
If john is either not quiet or wise then paul is not happy and vice versa.
If someone is not creative then lucy is not patient.
If someone is not calm or not wise then fred is generous.
Everyone who is both happy and quiet is calm or rich.
If paul is happy or not funny then someone is not humble or not tall.
If someone is not curious then someone is not creative.
Everyone who is humble or brave is not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
Someone is either old or not humble.
Someone is both calm and rich.
Someone is either not old or strong.
Someone is not tall.
Someone is either not wise or not rich.
Alice is not happy. | Fred is not funny. | entailment | ((?[X]:(tall(X)))<=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~humble(X)&wise(X))=>(~curious(X)<~>~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(((patient(mary)|~humble(mary)))=>((~generous(mary)&calm(mary))))&
(![X]:(generous(X)=>(calm(X)&~wise(X))))&
(((~quiet(john)<~>wise(john)))<=>(~happy(paul)))&
((?[X]:(~creative(X)))=>(~patient(lucy)))&
((?[X]:((~calm(X)|~wise(X))))=>(generous(fred)))&
(![X]:((happy(X)&quiet(X))=>(calm(X)|rich(X))))&
(((happy(paul)|~funny(paul)))=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:(~creative(X))))&
(![X]:((humble(X)|brave(X))=>~rich(X)))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~happy(alice)) | ~funny(fred) | [
"p3",
"p5",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 512170598438936106059919
% SZS output start Proof for 512170598438936106059919
4. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (generous(X0) => (~wise(X0) & calm(X0))) [input p5]
9. ? [X0] : (~wise(X0) | ~calm(X0)) => generous(fred) [input p8]
15. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~generous(X0)) [input p14]
16. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p15]
23. funny(fred) [input hypothesis]
31. ! [X0] : ((~wise(X0) & calm(X0)) | ~generous(X0)) [ennf transformation 6]
33. generous(fred) | ! [X0] : (wise(X0) & calm(X0)) [ennf transformation 9]
41. ! [X0] : (~generous(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 15]
53. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 4]
54. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 53]
63. ! [X0] : (~generous(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 41]
64. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 64]
89. ~calm(X0) | patient(X0) [cnf transformation 54]
95. ~generous(X0) | calm(X0) [cnf transformation 31]
103. generous(fred) | wise(X0) [cnf transformation 33]
111. ~generous(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 63]
112. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 65]
126. funny(fred) [cnf transformation 23]
127. ~wise(X0) | ~funny(X0) [duplicate literal removal 112]
223. 22 <=> ! [X0] : wise(X0) [avatar definition]
224. wise(X0) <- (22) [avatar component clause 223]
226. 23 <=> generous(fred) [avatar definition]
228. generous(fred) <- (23) [avatar component clause 226]
229. 22 | 23 [avatar split clause 103,226,223]
269. ~generous(X0) | ~calm(X0) [subsumption resolution 111,89]
270. ~generous(X0) [subsumption resolution 269,95]
301. $false <- (23) [subsumption resolution 228,270]
302. ~23 [avatar contradiction clause 301]
322. ~funny(X0) <- (22) [resolution 127,224]
324. $false <- (22) [resolution 322,126]
327. ~22 [avatar contradiction clause 324]
328. $false [avatar sat refutation 229,302,327]
% SZS output end Proof for 512170598438936106059919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is humble or not rich then lucy is both happy and not generous and vice versa.
If fred is not brave or not calm then fred is either patient or humble.
If alice is tall or wise then mary is either not curious or not happy.
Everyone who is not tall is calm or creative and vice versa.
Everyone who is not kind is both wise and not kind.
If lucy is both old and not calm then someone is not generous or not quiet.
Everyone who is brave is both not strong and not humble and vice versa.
Everyone who is not calm or not brave is both curious and not old and vice versa.
If someone is either not tall or curious then susan is not patient or wise and vice versa.
Everyone who is both not kind and humble is calm.
Everyone who is either humble or not tall is not kind or not wise.
Everyone who is kind or not quiet is both not generous and not curious and vice versa.
If someone is either rich or generous then someone is both quiet and not curious.
Everyone who is both not calm and not happy is either creative or not wise.
Everyone who is either patient or funny is both not strong and wise.
If paul is not strong or not kind then lucy is either not generous or quiet and vice versa.
Lucy is not strong or rich.
Someone is calm.
Someone is either not generous or rich.
Someone is strong or calm.
Someone is both not happy and rich.
Alice is wise.
Fred is both not humble and not strong.
Paul is both not humble and not tall. | Alice is not kind. | entailment | (((humble(susan)|~rich(susan)))<=>((happy(lucy)&~generous(lucy))))&
(((~brave(fred)|~calm(fred)))=>((patient(fred)<~>humble(fred))))&
(((tall(alice)|wise(alice)))=>((~curious(mary)<~>~happy(mary))))&
(![X]:(~tall(X)<=>(calm(X)|creative(X))))&
(![X]:(~kind(X)=>(wise(X)&~kind(X))))&
(((old(lucy)&~calm(lucy)))=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:(brave(X)<=>(~strong(X)&~humble(X))))&
(![X]:((~calm(X)|~brave(X))<=>(curious(X)&~old(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>((~patient(susan)|wise(susan))))&
(![X]:((~kind(X)&humble(X))=>calm(X)))&
(![X]:((humble(X)<~>~tall(X))=>(~kind(X)|~wise(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~generous(X)&~curious(X))))&
((?[X]:((rich(X)<~>generous(X))))=>(?[X]:((quiet(X)&~curious(X)))))&
(![X]:((~calm(X)&~happy(X))=>(creative(X)<~>~wise(X))))&
(![X]:((patient(X)<~>funny(X))=>(~strong(X)&wise(X))))&
(((~strong(paul)|~kind(paul)))<=>((~generous(lucy)<~>quiet(lucy))))&
((~strong(lucy)|rich(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((~happy(X)&rich(X))))&
(wise(alice))&
((~humble(fred)&~strong(fred)))&
((~humble(paul)&~tall(paul))) | ~kind(alice) | [
"p3",
"p6",
"p7",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6497818384024316733442692
% SZS output start Proof for 6497818384024316733442692
4. ! [X0] : (~tall(X0) <=> (creative(X0) | calm(X0))) [input p3]
7. ! [X0] : (brave(X0) <=> (~humble(X0) & ~strong(X0))) [input p6]
8. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~old(X0) & curious(X0))) [input p7]
11. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (~wise(X0) | ~kind(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) | kind(X0)) <=> (~curious(X0) & ~generous(X0))) [input p11]
22. wise(alice) [input p21]
25. kind(alice) [input hypothesis]
34. ! [X0] : ((~wise(X0) | ~kind(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 11]
35. ! [X0] : (~wise(X0) | ~kind(X0) | (humble(X0) <=> ~tall(X0))) [flattening 34]
44. ! [X0] : ((~tall(X0) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | tall(X0))) [nnf transformation 4]
45. ! [X0] : ((~tall(X0) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | tall(X0))) [flattening 44]
48. ! [X0] : ((brave(X0) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | ~brave(X0))) [nnf transformation 7]
49. ! [X0] : ((brave(X0) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | ~brave(X0))) [flattening 48]
50. ! [X0] : (((~brave(X0) | ~calm(X0)) | (old(X0) | ~curious(X0))) & ((~old(X0) & curious(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 8]
51. ! [X0] : ((~brave(X0) | ~calm(X0) | old(X0) | ~curious(X0)) & ((~old(X0) & curious(X0)) | (brave(X0) & calm(X0)))) [flattening 50]
57. ! [X0] : (~wise(X0) | ~kind(X0) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 35]
58. ! [X0] : (((~quiet(X0) | kind(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (quiet(X0) & ~kind(X0)))) [nnf transformation 12]
59. ! [X0] : ((~quiet(X0) | kind(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (quiet(X0) & ~kind(X0)))) [flattening 58]
91. ~tall(X0) | ~calm(X0) [cnf transformation 45]
97. ~brave(X0) | ~humble(X0) [cnf transformation 49]
99. curious(X0) | calm(X0) [cnf transformation 51]
100. curious(X0) | brave(X0) [cnf transformation 51]
112. ~kind(X0) | ~wise(X0) | humble(X0) | tall(X0) [cnf transformation 57]
115. ~kind(X0) | ~curious(X0) [cnf transformation 59]
141. wise(alice) [cnf transformation 22]
146. kind(alice) [cnf transformation 25]
189. 9 <=> wise(alice) [avatar definition]
190. wise(alice) <- (9) [avatar component clause 189]
202. 12 <=> tall(alice) [avatar definition]
203. tall(alice) <- (12) [avatar component clause 202]
317. 9 [avatar split clause 141,189]
325. ~curious(alice) [resolution 115,146]
330. brave(alice) [resolution 325,100]
331. calm(alice) [resolution 325,99]
419. ~wise(alice) | humble(alice) | tall(alice) [resolution 112,146]
421. humble(alice) | tall(alice) <- (9) [subsumption resolution 419,190]
552. ~humble(alice) [resolution 330,97]
555. tall(alice) <- (9) [subsumption resolution 421,552]
556. 12 | ~9 [avatar split clause 555,189,202]
557. ~calm(alice) <- (12) [resolution 203,91]
558. $false <- (12) [subsumption resolution 557,331]
559. ~12 [avatar contradiction clause 558]
560. $false [avatar sat refutation 317,556,559]
% SZS output end Proof for 6497818384024316733442692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either not curious or rich and vice versa.
Everyone who is not curious or not kind is either not brave or curious and vice versa.
If someone is either not generous or tall then someone is generous and vice versa.
Everyone who is either calm or old is patient and vice versa.
Everyone who is either not creative or wise is patient or brave.
If fred is brave then someone is either not old or not curious.
If john is either not old or not strong then someone is tall.
If someone is both not patient and tall then paul is not wise or not funny.
If fred is generous then someone is either happy or calm and vice versa.
Everyone who is not funny or strong is either happy or not funny.
If susan is tall then paul is not humble and vice versa.
Everyone who is not patient is either not tall or rich and vice versa.
Everyone who is both not brave and not generous is kind or not rich.
If someone is either calm or humble then paul is either not funny or not generous.
Everyone who is both not generous and funny is both happy and creative.
Everyone who is not patient is either not strong or not brave.
Someone is either rich or brave.
Lucy is not curious or not generous.
Susan is funny.
Paul is not happy or not strong.
Lucy is calm or curious.
Mary is quiet or old. | Mary is not wise. | neutral | (![X]:(~happy(X)<=>(~curious(X)<~>rich(X))))&
(![X]:((~curious(X)|~kind(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>old(X))<=>patient(X)))&
(![X]:((~creative(X)<~>wise(X))=>(patient(X)|brave(X))))&
((brave(fred))=>(?[X]:((~old(X)<~>~curious(X)))))&
(((~old(john)<~>~strong(john)))=>(?[X]:(tall(X))))&
((?[X]:((~patient(X)&tall(X))))=>((~wise(paul)|~funny(paul))))&
((generous(fred))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((~funny(X)|strong(X))=>(happy(X)<~>~funny(X))))&
((tall(susan))<=>(~humble(paul)))&
(![X]:(~patient(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((~brave(X)&~generous(X))=>(kind(X)|~rich(X))))&
((?[X]:((calm(X)<~>humble(X))))=>((~funny(paul)<~>~generous(paul))))&
(![X]:((~generous(X)&funny(X))=>(happy(X)&creative(X))))&
(![X]:(~patient(X)=>(~strong(X)<~>~brave(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((~curious(lucy)|~generous(lucy)))&
(funny(susan))&
((~happy(paul)|~strong(paul)))&
((calm(lucy)|curious(lucy)))&
((quiet(mary)|old(mary))) | ~wise(mary) | [] | null | 0 |
Everyone who is both funny and not tall is either not creative or not patient. Everyone who is both not creative and not curious is funny and vice versa. Everyone who is generous or not quiet is rich. Everyone who is not old is both not creative and strong and vice versa. Everyone who is not quiet is funny or not humble and vice versa. Everyone who is either funny or not tall is both not tall and not old and vice versa. If john is brave or strong then someone is both curious and not brave. If susan is not funny then alice is tall. If someone is both old and curious then someone is either not curious or brave and vice versa. If lucy is humble or calm then someone is either curious or rich and vice versa. Everyone who is not creative is either kind or not kind. Everyone who is both curious and rich is both not humble and humble and vice versa. Everyone who is both not strong and brave is patient or funny and vice versa. Everyone who is either not funny or old is both rich and not happy. If paul is either not quiet or patient then fred is both not rich and not wise and vice versa. Everyone who is curious or strong is both not kind and calm and vice versa. Someone is old. Paul is not wise. Fred is kind or not calm. Fred is either not quiet or not tall. Mary is not wise or not strong. Someone is either not calm or creative. Fred is both not kind and not generous. John is not brave. | John is not humble. | neutral | (![X]:((funny(X)&~tall(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((~creative(X)&~curious(X))<=>funny(X)))&
(![X]:((generous(X)|~quiet(X))=>rich(X)))&
(![X]:(~old(X)<=>(~creative(X)&strong(X))))&
(![X]:(~quiet(X)<=>(funny(X)|~humble(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~tall(X)&~old(X))))&
(((brave(john)|strong(john)))=>(?[X]:((curious(X)&~brave(X)))))&
((~funny(susan))=>(tall(alice)))&
((?[X]:((old(X)&curious(X))))<=>(?[X]:((~curious(X)<~>brave(X)))))&
(((humble(lucy)|calm(lucy)))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:(~creative(X)=>(kind(X)<~>~kind(X))))&
(![X]:((curious(X)&rich(X))<=>(~humble(X)&humble(X))))&
(![X]:((~strong(X)&brave(X))<=>(patient(X)|funny(X))))&
(![X]:((~funny(X)<~>old(X))=>(rich(X)&~happy(X))))&
(((~quiet(paul)<~>patient(paul)))<=>((~rich(fred)&~wise(fred))))&
(![X]:((curious(X)|strong(X))<=>(~kind(X)&calm(X))))&
(?[X]:(old(X)))&
(~wise(paul))&
((kind(fred)|~calm(fred)))&
((~quiet(fred)<~>~tall(fred)))&
((~wise(mary)|~strong(mary)))&
(?[X]:((~calm(X)<~>creative(X))))&
((~kind(fred)&~generous(fred)))&
(~brave(john)) | ~humble(john) | [] | null | 0 |
If someone is calm then someone is not patient and vice versa. If lucy is both not brave and brave then someone is both old and tall and vice versa. Everyone who is not brave or strong is not creative or not generous and vice versa. Everyone who is either humble or curious is both humble and wise and vice versa. Everyone who is either old or brave is both not tall and calm and vice versa. Everyone who is either not brave or strong is both calm and creative and vice versa. If john is either not happy or not creative then someone is generous or not rich. If someone is strong or rich then someone is not curious. If someone is either humble or old then someone is either not quiet or not rich. Everyone who is not happy is either not creative or not curious and vice versa. Everyone who is not strong or generous is quiet and vice versa. If paul is either quiet or generous then lucy is both creative and happy and vice versa. Everyone who is either strong or old is both brave and old and vice versa. Everyone who is humble is wise. Everyone who is humble or not strong is both not rich and brave and vice versa. If someone is both not happy and not strong then lucy is not tall or kind. Someone is not tall. Susan is either not creative or not rich. Mary is not quiet or funny. Someone is generous or not wise. Paul is both funny and not quiet. Mary is either curious or not rich. Lucy is either not humble or not calm. | Paul is not tall. | entailment | ((?[X]:(calm(X)))<=>(?[X]:(~patient(X))))&
(((~brave(lucy)&brave(lucy)))<=>(?[X]:((old(X)&tall(X)))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)|~generous(X))))&
(![X]:((humble(X)<~>curious(X))<=>(humble(X)&wise(X))))&
(![X]:((old(X)<~>brave(X))<=>(~tall(X)&calm(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(calm(X)&creative(X))))&
(((~happy(john)<~>~creative(john)))=>(?[X]:((generous(X)|~rich(X)))))&
((?[X]:((strong(X)|rich(X))))=>(?[X]:(~curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:(~happy(X)<=>(~creative(X)<~>~curious(X))))&
(![X]:((~strong(X)|generous(X))<=>quiet(X)))&
(((quiet(paul)<~>generous(paul)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>old(X))<=>(brave(X)&old(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((humble(X)|~strong(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~happy(X)&~strong(X))))=>((~tall(lucy)|kind(lucy))))&
(?[X]:(~tall(X)))&
((~creative(susan)<~>~rich(susan)))&
((~quiet(mary)|funny(mary)))&
(?[X]:((generous(X)|~wise(X))))&
((funny(paul)&~quiet(paul)))&
((curious(mary)<~>~rich(mary)))&
((~humble(lucy)<~>~calm(lucy))) | ~tall(paul) | [
"p1",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6831619568611819741799540
% SZS output start Proof for 6831619568611819741799540
2. (brave(lucy) & ~brave(lucy)) <=> ? [X0] : (tall(X0) & old(X0)) [input p1]
11. ! [X0] : ((generous(X0) | ~strong(X0)) <=> quiet(X0)) [input p10]
13. ! [X0] : ((strong(X0) <~> old(X0)) <=> (old(X0) & brave(X0))) [input p12]
21. ~quiet(paul) & funny(paul) [input p20]
24. tall(paul) [input hypothesis]
28. ~quiet(paul) [pure predicate removal 21]
40. ((brave(lucy) & ~brave(lucy)) | ! [X0] : (~tall(X0) | ~old(X0))) & (? [X0] : (tall(X0) & old(X0)) | (~brave(lucy) | brave(lucy))) [nnf transformation 2]
41. ((brave(lucy) & ~brave(lucy)) | ! [X0] : (~tall(X0) | ~old(X0))) & (? [X0] : (tall(X0) & old(X0)) | ~brave(lucy) | brave(lucy)) [flattening 40]
42. ((brave(lucy) & ~brave(lucy)) | ! [X0] : (~tall(X0) | ~old(X0))) & (? [X1] : (tall(X1) & old(X1)) | ~brave(lucy) | brave(lucy)) [rectify 41]
43. ? [X1] : (tall(X1) & old(X1)) => (tall(sK2) & old(sK2)) [choice axiom]
44. ((brave(lucy) & ~brave(lucy)) | ! [X0] : (~tall(X0) | ~old(X0))) & ((tall(sK2) & old(sK2)) | ~brave(lucy) | brave(lucy)) [skolemisation 42,43]
64. ! [X0] : (((generous(X0) | ~strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & strong(X0)))) [nnf transformation 11]
65. ! [X0] : ((generous(X0) | ~strong(X0) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & strong(X0)))) [flattening 64]
68. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [nnf transformation 13]
69. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [flattening 68]
83. ~brave(lucy) | ~tall(X0) | ~old(X0) [cnf transformation 44]
84. brave(lucy) | ~tall(X0) | ~old(X0) [cnf transformation 44]
119. quiet(X0) | strong(X0) [cnf transformation 65]
130. old(X0) | old(X0) | ~strong(X0) [cnf transformation 69]
144. ~quiet(paul) [cnf transformation 28]
149. tall(paul) [cnf transformation 24]
150. ~strong(X0) | old(X0) [duplicate literal removal 130]
171. 5 <=> ! [X0] : (~tall(X0) | ~old(X0)) [avatar definition]
172. ~tall(X0) | ~old(X0) <- (5) [avatar component clause 171]
174. 6 <=> brave(lucy) [avatar definition]
177. 5 | 6 [avatar split clause 84,174,171]
178. 5 | ~6 [avatar split clause 83,174,171]
246. 21 <=> quiet(paul) [avatar definition]
247. ~quiet(paul) <- (~21) [avatar component clause 246]
271. ~21 [avatar split clause 144,246]
292. strong(paul) <- (~21) [resolution 119,247]
296. old(paul) <- (~21) [resolution 150,292]
298. ~old(paul) <- (5) [resolution 172,149]
299. $false <- (5, ~21) [subsumption resolution 298,296]
300. ~5 | 21 [avatar contradiction clause 299]
301. $false [avatar sat refutation 177,178,271,300]
% SZS output end Proof for 6831619568611819741799540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either wise or creative then fred is both not strong and not happy and vice versa.
If alice is not quiet or rich then someone is both calm and not old and vice versa.
Everyone who is both patient and creative is both curious and not patient.
If someone is both tall and patient then someone is either not strong or not old and vice versa.
If someone is both not brave and brave then someone is both quiet and not generous.
Everyone who is not funny or rich is humble or happy.
Everyone who is not old or old is both not brave and calm.
If lucy is not wise then someone is not wise or curious.
Everyone who is either creative or not calm is rich and vice versa.
Everyone who is creative is either not rich or generous.
If lucy is either not quiet or not rich then susan is not happy or not wise.
Everyone who is both wise and not wise is either not generous or rich and vice versa.
If paul is either not curious or not strong then someone is either not strong or not wise and vice versa.
Everyone who is not tall is both strong and not calm.
Everyone who is either not brave or not humble is either patient or not tall.
If someone is curious or strong then someone is not brave and vice versa.
Someone is either not humble or happy.
Alice is either not generous or not old.
Someone is wise.
John is not rich or not tall.
Lucy is both not humble and not wise.
Someone is either not curious or happy.
Fred is not brave or rich. | Fred is rich. | contradiction | (((wise(alice)<~>creative(alice)))<=>((~strong(fred)&~happy(fred))))&
(((~quiet(alice)|rich(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((patient(X)&creative(X))=>(curious(X)&~patient(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((~strong(X)<~>~old(X)))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:((~funny(X)|rich(X))=>(humble(X)|happy(X))))&
(![X]:((~old(X)|old(X))=>(~brave(X)&calm(X))))&
((~wise(lucy))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((creative(X)<~>~calm(X))<=>rich(X)))&
(![X]:(creative(X)=>(~rich(X)<~>generous(X))))&
(((~quiet(lucy)<~>~rich(lucy)))=>((~happy(susan)|~wise(susan))))&
(![X]:((wise(X)&~wise(X))<=>(~generous(X)<~>rich(X))))&
(((~curious(paul)<~>~strong(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:(~tall(X)=>(strong(X)&~calm(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~brave(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
((~generous(alice)<~>~old(alice)))&
(?[X]:(wise(X)))&
((~rich(john)|~tall(john)))&
((~humble(lucy)&~wise(lucy)))&
(?[X]:((~curious(X)<~>happy(X))))&
((~brave(fred)|rich(fred))) | rich(fred) | [
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2727360786310841278754545
% SZS output start Proof for 2727360786310841278754545
7. ! [X0] : ((old(X0) | ~old(X0)) => (calm(X0) & ~brave(X0))) [input p6]
9. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> rich(X0)) [input p8]
10. ! [X0] : (creative(X0) => (~rich(X0) <~> generous(X0))) [input p9]
12. ! [X0] : ((~wise(X0) & wise(X0)) <=> (~generous(X0) <~> rich(X0))) [input p11]
24. rich(fred) [input hypothesis]
34. ! [X0] : ((calm(X0) & ~brave(X0)) | (~old(X0) & old(X0))) [ennf transformation 7]
36. ! [X0] : ((~rich(X0) <~> generous(X0)) | ~creative(X0)) [ennf transformation 10]
58. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ~rich(X0)) & (rich(X0) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 9]
59. ! [X0] : (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~creative(X0)) [nnf transformation 36]
61. ! [X0] : (((~wise(X0) & wise(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (wise(X0) | ~wise(X0)))) [nnf transformation 12]
62. ! [X0] : (((~wise(X0) & wise(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | wise(X0) | ~wise(X0))) [flattening 61]
106. calm(X0) | old(X0) [cnf transformation 34]
107. ~old(X0) | calm(X0) [cnf transformation 34]
109. rich(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 58]
111. ~calm(X0) | creative(X0) | ~rich(X0) [cnf transformation 58]
113. generous(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 59]
120. wise(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 62]
122. ~wise(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 62]
151. rich(fred) [cnf transformation 24]
230. calm(X0) [subsumption resolution 106,107]
245. ~rich(X0) | creative(X0) [subsumption resolution 111,230]
246. ~creative(X0) | rich(X0) [subsumption resolution 109,230]
247. ~creative(X0) | generous(X0) [subsumption resolution 113,246]
266. ~generous(X0) | ~rich(X0) [subsumption resolution 120,122]
349. creative(fred) [resolution 245,151]
351. generous(fred) [resolution 247,349]
353. ~rich(fred) [resolution 351,266]
354. $false [subsumption resolution 353,151]
% SZS output end Proof for 2727360786310841278754545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
If fred is both brave and rich then someone is either not old or not humble and vice versa.
Everyone who is not humble or tall is either calm or patient.
Everyone who is strong is wise and vice versa.
Fred is strong or quiet.
Lucy is humble or not tall.
Someone is creative or strong.
Alice is either strong or calm.
Lucy is either not brave or funny.
Fred is both patient and not happy. | Fred is not patient. | contradiction | (![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(((brave(fred)&rich(fred)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|tall(X))=>(calm(X)<~>patient(X))))&
(![X]:(strong(X)<=>wise(X)))&
((strong(fred)|quiet(fred)))&
((humble(lucy)|~tall(lucy)))&
(?[X]:((creative(X)|strong(X))))&
((strong(alice)<~>calm(alice)))&
((~brave(lucy)<~>funny(lucy)))&
((patient(fred)&~happy(fred))) | ~patient(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7267186825255217946288251
% SZS output start Proof for 7267186825255217946288251
21. ~happy(fred) & patient(fred) [input p20]
22. ~patient(fred) [input hypothesis]
134. patient(fred) [cnf transformation 21]
136. ~patient(fred) [cnf transformation 22]
259. $false [subsumption resolution 136,134]
% SZS output end Proof for 7267186825255217946288251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or patient is strong and vice versa.
Everyone who is old is either not brave or not tall and vice versa.
If someone is both not happy and brave then john is either happy or patient.
Everyone who is not calm or not rich is both old and not kind and vice versa.
Everyone who is kind or not quiet is both not patient and patient and vice versa.
Everyone who is not old is not quiet and vice versa.
Everyone who is either wise or happy is not patient and vice versa.
Everyone who is kind or old is calm.
Everyone who is wise or brave is not calm and vice versa.
Everyone who is rich or not funny is old and vice versa.
If mary is either calm or not happy then someone is both kind and not patient and vice versa.
Everyone who is not humble is both curious and not patient.
Everyone who is creative is either curious or not tall and vice versa.
Someone is both not brave and not kind.
Someone is either not generous or not wise.
Fred is either curious or rich.
Fred is kind or strong.
Paul is not rich or curious.
Paul is not calm or quiet.
Lucy is not humble. | Paul is not happy. | neutral | (![X]:((old(X)|patient(X))<=>strong(X)))&
(![X]:(old(X)<=>(~brave(X)<~>~tall(X))))&
((?[X]:((~happy(X)&brave(X))))=>((happy(john)<~>patient(john))))&
(![X]:((~calm(X)|~rich(X))<=>(old(X)&~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~patient(X)&patient(X))))&
(![X]:(~old(X)<=>~quiet(X)))&
(![X]:((wise(X)<~>happy(X))<=>~patient(X)))&
(![X]:((kind(X)|old(X))=>calm(X)))&
(![X]:((wise(X)|brave(X))<=>~calm(X)))&
(![X]:((rich(X)|~funny(X))<=>old(X)))&
(((calm(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((curious(fred)<~>rich(fred)))&
((kind(fred)|strong(fred)))&
((~rich(paul)|curious(paul)))&
((~calm(paul)|quiet(paul)))&
(~humble(lucy)) | ~happy(paul) | [] | null | 0 |
Everyone who is both funny and not funny is not humble or not calm and vice versa. If someone is not strong then fred is either not tall or not happy and vice versa. Everyone who is either not funny or old is both not calm and not strong and vice versa. If paul is either not quiet or not calm then john is curious or generous and vice versa. Everyone who is not old is both wise and humble. Everyone who is not strong is either not old or not humble and vice versa. Everyone who is not patient or not humble is either funny or old and vice versa. If alice is either rich or brave then someone is both tall and rich. Everyone who is not curious is not wise and vice versa. If someone is either funny or not brave then someone is either not creative or creative. If lucy is either not creative or old then someone is either not generous or not humble. Everyone who is strong or not wise is either not rich or rich and vice versa. If fred is either happy or not generous then someone is both quiet and not wise. If susan is funny or generous then paul is not happy or not wise. If someone is both patient and not wise then john is either not patient or not brave and vice versa. Someone is not humble or quiet. Fred is both not generous and brave. Fred is happy or generous. Susan is quiet. Lucy is not generous. Someone is either not curious or wise. | Fred is calm. | entailment | (![X]:((funny(X)&~funny(X))<=>(~humble(X)|~calm(X))))&
((?[X]:(~strong(X)))<=>((~tall(fred)<~>~happy(fred))))&
(![X]:((~funny(X)<~>old(X))<=>(~calm(X)&~strong(X))))&
(((~quiet(paul)<~>~calm(paul)))<=>((curious(john)|generous(john))))&
(![X]:(~old(X)=>(wise(X)&humble(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~patient(X)|~humble(X))<=>(funny(X)<~>old(X))))&
(((rich(alice)<~>brave(alice)))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:(~curious(X)<=>~wise(X)))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(((~creative(lucy)<~>old(lucy)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((strong(X)|~wise(X))<=>(~rich(X)<~>rich(X))))&
(((happy(fred)<~>~generous(fred)))=>(?[X]:((quiet(X)&~wise(X)))))&
(((funny(susan)|generous(susan)))=>((~happy(paul)|~wise(paul))))&
((?[X]:((patient(X)&~wise(X))))<=>((~patient(john)<~>~brave(john))))&
(?[X]:((~humble(X)|quiet(X))))&
((~generous(fred)&brave(fred)))&
((happy(fred)|generous(fred)))&
(quiet(susan))&
(~generous(lucy))&
(?[X]:((~curious(X)<~>wise(X)))) | calm(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 867966454653953954669832
% SZS output start Proof for 867966454653953954669832
1. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~calm(X0) | ~humble(X0))) [input p0]
22. ~calm(fred) [input hypothesis]
31. ! [X0] : (((~funny(X0) & funny(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (funny(X0) | ~funny(X0)))) [nnf transformation 1]
32. ! [X0] : (((~funny(X0) & funny(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | funny(X0) | ~funny(X0))) [flattening 31]
71. funny(X0) | calm(X0) [cnf transformation 32]
73. ~funny(X0) | calm(X0) [cnf transformation 32]
142. ~calm(fred) [cnf transformation 22]
145. calm(X0) [subsumption resolution 71,73]
280. $false [subsumption resolution 142,145]
% SZS output end Proof for 867966454653953954669832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or old is creative or not tall.
Everyone who is either not calm or not happy is creative.
Everyone who is either strong or not funny is not strong.
Everyone who is both calm and not calm is both not funny and creative and vice versa.
Everyone who is not old or not calm is old or tall and vice versa.
If someone is old or curious then someone is tall and vice versa.
If mary is both patient and not kind then someone is both not quiet and humble.
If alice is either not quiet or not happy then someone is both patient and not calm and vice versa.
If someone is not humble or not rich then paul is tall and vice versa.
Everyone who is both not rich and not creative is not calm or happy.
Everyone who is both humble and not humble is humble or not strong and vice versa.
If mary is curious then someone is both curious and not curious.
If someone is both generous and not brave then someone is not happy.
Everyone who is either not kind or not generous is both calm and not rich and vice versa.
Everyone who is not wise or quiet is old.
Paul is not creative.
John is both tall and not funny.
Someone is either not strong or not wise.
Lucy is not humble or not tall.
Someone is either calm or not humble.
Susan is humble or old.
Someone is not kind or not strong.
Someone is not creative or not rich. | Lucy is not humble. | entailment | (![X]:((humble(X)<~>old(X))=>(creative(X)|~tall(X))))&
(![X]:((~calm(X)<~>~happy(X))=>creative(X)))&
(![X]:((strong(X)<~>~funny(X))=>~strong(X)))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)&creative(X))))&
(![X]:((~old(X)|~calm(X))<=>(old(X)|tall(X))))&
((?[X]:((old(X)|curious(X))))<=>(?[X]:(tall(X))))&
(((patient(mary)&~kind(mary)))=>(?[X]:((~quiet(X)&humble(X)))))&
(((~quiet(alice)<~>~happy(alice)))<=>(?[X]:((patient(X)&~calm(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(tall(paul)))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)|happy(X))))&
(![X]:((humble(X)&~humble(X))<=>(humble(X)|~strong(X))))&
((curious(mary))=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(calm(X)&~rich(X))))&
(![X]:((~wise(X)|quiet(X))=>old(X)))&
(~creative(paul))&
((tall(john)&~funny(john)))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~humble(lucy)|~tall(lucy)))&
(?[X]:((calm(X)<~>~humble(X))))&
((humble(susan)|old(susan)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~creative(X)|~rich(X)))) | ~humble(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 156326320768082849156850
% SZS output start Proof for 156326320768082849156850
11. ! [X0] : ((~humble(X0) & humble(X0)) <=> (~strong(X0) | humble(X0))) [input p10]
24. humble(lucy) [input hypothesis]
60. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (humble(X0) | ~humble(X0)))) [nnf transformation 11]
61. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | humble(X0) | ~humble(X0))) [flattening 60]
108. ~humble(X0) | ~humble(X0) [cnf transformation 61]
131. humble(lucy) [cnf transformation 24]
133. ~humble(X0) [duplicate literal removal 108]
250. $false [subsumption resolution 131,133]
% SZS output end Proof for 156326320768082849156850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not humble then someone is not rich or not tall. Everyone who is both humble and tall is not humble or rich. Everyone who is not creative is not rich and vice versa. Everyone who is both old and not kind is wise and vice versa. If susan is both funny and not patient then fred is either not brave or not calm and vice versa. If someone is either wise or funny then john is wise or not patient and vice versa. If someone is not old then someone is not happy or not creative. If alice is not calm then someone is humble and vice versa. Everyone who is not generous is not patient or not calm. If paul is both not calm and not wise then someone is happy or generous and vice versa. Everyone who is not tall or patient is not creative or happy. Everyone who is calm or not strong is not patient or funny and vice versa. Everyone who is generous or not creative is both not humble and generous and vice versa. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Someone is both not calm and creative. Someone is either not strong or humble. Someone is not old. Someone is not happy or not humble. Someone is either not old or kind. Someone is both funny and old. Someone is either not old or not calm. Susan is either rich or old. | Susan is not old. | entailment | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(~humble(X)|rich(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:((old(X)&~kind(X))<=>wise(X)))&
(((funny(susan)&~patient(susan)))<=>((~brave(fred)<~>~calm(fred))))&
((?[X]:((wise(X)<~>funny(X))))<=>((wise(john)|~patient(john))))&
((?[X]:(~old(X)))=>(?[X]:((~happy(X)|~creative(X)))))&
((~calm(alice))<=>(?[X]:(humble(X))))&
(![X]:(~generous(X)=>(~patient(X)|~calm(X))))&
(((~calm(paul)&~wise(paul)))<=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~tall(X)|patient(X))=>(~creative(X)|happy(X))))&
(![X]:((calm(X)|~strong(X))<=>(~patient(X)|funny(X))))&
(![X]:((generous(X)|~creative(X))<=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:(~old(X)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((~old(X)<~>~calm(X))))&
((rich(susan)<~>old(susan))) | ~old(susan) | [
"p2",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6586058327095428219526876
% SZS output start Proof for 6586058327095428219526876
3. ! [X0] : (~creative(X0) <=> ~rich(X0)) [input p2]
13. ! [X0] : ((~creative(X0) | generous(X0)) <=> (generous(X0) & ~humble(X0))) [input p12]
15. ! [X0] : ((quiet(X0) & rich(X0)) <=> (~calm(X0) | ~humble(X0))) [input p14]
24. rich(susan) <~> old(susan) [input p23]
25. old(susan) [input hypothesis]
42. ! [X0] : ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))) [nnf transformation 3]
66. ! [X0] : (((~creative(X0) | generous(X0)) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | (creative(X0) & ~generous(X0)))) [nnf transformation 13]
67. ! [X0] : ((~creative(X0) | generous(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | (creative(X0) & ~generous(X0)))) [flattening 66]
73. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~quiet(X0) | ~rich(X0)))) [nnf transformation 15]
74. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~quiet(X0) | ~rich(X0))) [flattening 73]
93. (~old(susan) | ~rich(susan)) & (old(susan) | rich(susan)) [nnf transformation 24]
97. ~rich(X0) | creative(X0) [cnf transformation 42]
98. ~creative(X0) | rich(X0) [cnf transformation 42]
130. ~humble(X0) | creative(X0) [cnf transformation 67]
140. rich(X0) | humble(X0) [cnf transformation 74]
159. ~old(susan) | ~rich(susan) [cnf transformation 93]
160. old(susan) [cnf transformation 25]
351. 42 <=> rich(susan) [avatar definition]
353. ~rich(susan) <- (~42) [avatar component clause 351]
355. 43 <=> old(susan) [avatar definition]
358. ~42 | ~43 [avatar split clause 159,355,351]
360. 43 [avatar split clause 160,355]
373. humble(X0) | creative(X0) [resolution 140,97]
391. creative(X0) [subsumption resolution 373,130]
460. rich(X1) [resolution 391,98]
490. $false <- (~42) [resolution 460,353]
492. 42 [avatar contradiction clause 490]
494. $false [avatar sat refutation 358,360,492]
% SZS output end Proof for 6586058327095428219526876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not kind then someone is both not generous and patient and vice versa.
Everyone who is brave is calm and vice versa.
If someone is not strong then someone is either generous or funny.
If someone is brave then susan is brave or happy.
If someone is not patient or not creative then mary is either not tall or not calm.
If fred is both creative and wise then someone is both not wise and not curious.
Everyone who is not brave is brave or not humble and vice versa.
If someone is either not funny or brave then fred is not humble or funny and vice versa.
Everyone who is both curious and not tall is both quiet and not creative.
If john is wise then mary is not calm or funny.
If mary is either not rich or funny then lucy is either not quiet or strong and vice versa.
Everyone who is either brave or not kind is brave or happy and vice versa.
If someone is not funny or not curious then someone is not rich or strong.
Everyone who is kind is both not generous and not calm.
Everyone who is not funny or kind is either not quiet or humble.
Everyone who is wise is either funny or happy and vice versa.
Someone is patient.
Lucy is not generous or not strong.
Paul is tall or quiet.
John is not brave.
Lucy is not tall or not old. | Mary is not calm. | entailment | ((?[X]:((patient(X)|~kind(X))))<=>(?[X]:((~generous(X)&patient(X)))))&
(![X]:(brave(X)<=>calm(X)))&
((?[X]:(~strong(X)))=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:(brave(X)))=>((brave(susan)|happy(susan))))&
((?[X]:((~patient(X)|~creative(X))))=>((~tall(mary)<~>~calm(mary))))&
(((creative(fred)&wise(fred)))=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:(~brave(X)<=>(brave(X)|~humble(X))))&
((?[X]:((~funny(X)<~>brave(X))))<=>((~humble(fred)|funny(fred))))&
(![X]:((curious(X)&~tall(X))=>(quiet(X)&~creative(X))))&
((wise(john))=>((~calm(mary)|funny(mary))))&
(((~rich(mary)<~>funny(mary)))<=>((~quiet(lucy)<~>strong(lucy))))&
(![X]:((brave(X)<~>~kind(X))<=>(brave(X)|happy(X))))&
((?[X]:((~funny(X)|~curious(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(kind(X)=>(~generous(X)&~calm(X))))&
(![X]:((~funny(X)|kind(X))=>(~quiet(X)<~>humble(X))))&
(![X]:(wise(X)<=>(funny(X)<~>happy(X))))&
(?[X]:(patient(X)))&
((~generous(lucy)|~strong(lucy)))&
((tall(paul)|quiet(paul)))&
(~brave(john))&
((~tall(lucy)|~old(lucy))) | ~calm(mary) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5493816801598887127210564
% SZS output start Proof for 5493816801598887127210564
2. ! [X0] : (brave(X0) <=> calm(X0)) [input p1]
7. ! [X0] : (~brave(X0) <=> (~humble(X0) | brave(X0))) [input p6]
22. calm(mary) [input hypothesis]
47. ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 2]
55. ! [X0] : ((~brave(X0) | (humble(X0) & ~brave(X0))) & ((~humble(X0) | brave(X0)) | brave(X0))) [nnf transformation 7]
56. ! [X0] : ((~brave(X0) | (humble(X0) & ~brave(X0))) & (~humble(X0) | brave(X0) | brave(X0))) [flattening 55]
78. ~calm(X0) | brave(X0) [cnf transformation 47]
89. ~brave(X0) | ~brave(X0) [cnf transformation 56]
128. calm(mary) [cnf transformation 22]
132. ~brave(X0) [duplicate literal removal 89]
177. 11 <=> ! [X0] : ~brave(X0) [avatar definition]
178. ~brave(X0) <- (11) [avatar component clause 177]
196. 16 <=> calm(mary) [avatar definition]
198. calm(mary) <- (16) [avatar component clause 196]
224. 11 [avatar split clause 132,177]
313. 16 [avatar split clause 128,196]
316. brave(mary) <- (16) [resolution 78,198]
317. $false <- (11, 16) [subsumption resolution 316,178]
318. ~11 | ~16 [avatar contradiction clause 317]
319. $false [avatar sat refutation 224,313,318]
% SZS output end Proof for 5493816801598887127210564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and quiet is either not humble or quiet and vice versa.
If someone is either humble or not happy then someone is old and vice versa.
If someone is both strong and not patient then paul is rich or not wise.
If someone is not happy then someone is happy or calm and vice versa.
Everyone who is either funny or calm is either not funny or wise and vice versa.
If someone is both patient and rich then someone is not tall.
If fred is either tall or not tall then someone is not quiet and vice versa.
Everyone who is generous or funny is both not calm and not strong and vice versa.
If fred is not calm then someone is calm or creative.
If someone is not happy or humble then someone is tall or not quiet.
If paul is both not calm and not rich then lucy is not patient and vice versa.
Everyone who is not calm is either not patient or not wise and vice versa.
Everyone who is either happy or patient is either not quiet or not kind.
Everyone who is either calm or strong is not quiet or patient.
If someone is happy then someone is not patient or strong.
Paul is patient or humble.
Someone is strong or not funny.
Fred is rich or not rich. | Fred is not strong. | entailment | (![X]:((~humble(X)&quiet(X))<=>(~humble(X)<~>quiet(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(old(X))))&
((?[X]:((strong(X)&~patient(X))))=>((rich(paul)|~wise(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((funny(X)<~>calm(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:(~tall(X))))&
(((tall(fred)<~>~tall(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(~calm(X)&~strong(X))))&
((~calm(fred))=>(?[X]:((calm(X)|creative(X)))))&
((?[X]:((~happy(X)|humble(X))))=>(?[X]:((tall(X)|~quiet(X)))))&
(((~calm(paul)&~rich(paul)))<=>(~patient(lucy)))&
(![X]:(~calm(X)<=>(~patient(X)<~>~wise(X))))&
(![X]:((happy(X)<~>patient(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:((calm(X)<~>strong(X))=>(~quiet(X)|patient(X))))&
((?[X]:(happy(X)))=>(?[X]:((~patient(X)|strong(X)))))&
((patient(paul)|humble(paul)))&
(?[X]:((strong(X)|~funny(X))))&
((rich(fred)|~rich(fred))) | ~strong(fred) | [
"p2",
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8095542705497032929127057
% SZS output start Proof for 8095542705497032929127057
3. ? [X0] : (~patient(X0) & strong(X0)) => (~wise(paul) | rich(paul)) [input p2]
5. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~funny(X0) <~> wise(X0))) [input p4]
11. (~rich(paul) & ~calm(paul)) <=> ~patient(lucy) [input p10]
12. ! [X0] : (~calm(X0) <=> (~patient(X0) <~> ~wise(X0))) [input p11]
19. strong(fred) [input hypothesis]
26. (~wise(paul) | rich(paul)) | ! [X0] : (patient(X0) | ~strong(X0)) [ennf transformation 3]
27. ~wise(paul) | rich(paul) | ! [X0] : (patient(X0) | ~strong(X0)) [flattening 26]
46. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0)))) & (((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 5]
59. ((~rich(paul) & ~calm(paul)) | patient(lucy)) & (~patient(lucy) | (rich(paul) | calm(paul))) [nnf transformation 11]
60. ((~rich(paul) & ~calm(paul)) | patient(lucy)) & (~patient(lucy) | rich(paul) | calm(paul)) [flattening 59]
61. ! [X0] : ((~calm(X0) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) & (((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | calm(X0))) [nnf transformation 12]
79. ~wise(paul) | rich(paul) | patient(X0) | ~strong(X0) [cnf transformation 27]
83. wise(X0) | ~funny(X0) | calm(X0) | ~funny(X0) [cnf transformation 46]
86. ~wise(X0) | funny(X0) | funny(X0) | ~calm(X0) [cnf transformation 46]
87. calm(X0) | funny(X0) | wise(X0) | funny(X0) [cnf transformation 46]
90. ~calm(X0) | ~funny(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 46]
104. ~calm(paul) | patient(lucy) [cnf transformation 60]
105. ~rich(paul) | patient(lucy) [cnf transformation 60]
106. ~wise(X0) | ~patient(X0) | calm(X0) [cnf transformation 61]
109. ~calm(X0) | ~patient(X0) | wise(X0) [cnf transformation 61]
120. strong(fred) [cnf transformation 19]
123. wise(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 83]
124. ~wise(X0) | funny(X0) | ~calm(X0) [duplicate literal removal 86]
125. calm(X0) | funny(X0) | wise(X0) [duplicate literal removal 87]
126. ~calm(X0) | ~funny(X0) | ~wise(X0) [duplicate literal removal 90]
157. 7 <=> ! [X0] : (patient(X0) | ~strong(X0)) [avatar definition]
158. patient(X0) | ~strong(X0) <- (7) [avatar component clause 157]
160. 8 <=> rich(paul) [avatar definition]
164. 9 <=> wise(paul) [avatar definition]
167. 7 | 8 | ~9 [avatar split clause 79,164,160,157]
192. ~calm(X0) | ~wise(X0) [subsumption resolution 124,126]
193. calm(X0) | wise(X0) [subsumption resolution 123,125]
203. 18 <=> patient(lucy) [avatar definition]
205. patient(lucy) <- (18) [avatar component clause 203]
206. 18 | ~8 [avatar split clause 105,160,203]
208. 19 <=> calm(paul) [avatar definition]
210. ~calm(paul) <- (~19) [avatar component clause 208]
211. 18 | ~19 [avatar split clause 104,208,203]
213. ~patient(X0) | wise(X0) [subsumption resolution 109,193]
214. ~wise(X0) | ~patient(X0) [subsumption resolution 106,192]
215. ~patient(X0) [subsumption resolution 214,213]
228. wise(paul) <- (~19) [resolution 193,210]
232. 9 | 19 [avatar split clause 228,208,164]
233. ~strong(X0) <- (7) [subsumption resolution 158,215]
234. $false <- (7) [resolution 233,120]
235. ~7 [avatar contradiction clause 234]
236. $false <- (18) [subsumption resolution 205,215]
237. ~18 [avatar contradiction clause 236]
238. $false [avatar sat refutation 167,206,211,232,235,237]
% SZS output end Proof for 8095542705497032929127057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not creative is wise or generous.
Everyone who is both rich and happy is either happy or not happy.
Everyone who is not old is both not curious and old and vice versa.
Everyone who is patient is either kind or curious.
If someone is both strong and not kind then lucy is either not creative or quiet and vice versa.
Everyone who is both generous and strong is creative or wise and vice versa.
If fred is both not kind and curious then john is brave or not old.
If someone is both not quiet and not happy then john is wise or not brave.
If someone is not patient then someone is patient and vice versa.
If alice is either not calm or creative then someone is both happy and wise.
If lucy is not calm then john is both not quiet and not creative.
If paul is curious or calm then someone is not kind and vice versa.
Everyone who is both happy and brave is either brave or not strong and vice versa.
Everyone who is kind is both old and not old.
If fred is not generous then someone is both generous and not kind.
Everyone who is quiet is not creative and vice versa.
Someone is both not strong and humble.
Someone is either tall or not rich.
Lucy is tall or wise.
Someone is rich or strong.
Someone is patient or not strong.
Alice is either strong or old. | Fred is creative. | contradiction | (![X]:((~quiet(X)<~>~creative(X))=>(wise(X)|generous(X))))&
(![X]:((rich(X)&happy(X))=>(happy(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(~curious(X)&old(X))))&
(![X]:(patient(X)=>(kind(X)<~>curious(X))))&
((?[X]:((strong(X)&~kind(X))))<=>((~creative(lucy)<~>quiet(lucy))))&
(![X]:((generous(X)&strong(X))<=>(creative(X)|wise(X))))&
(((~kind(fred)&curious(fred)))=>((brave(john)|~old(john))))&
((?[X]:((~quiet(X)&~happy(X))))=>((wise(john)|~brave(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(patient(X))))&
(((~calm(alice)<~>creative(alice)))=>(?[X]:((happy(X)&wise(X)))))&
((~calm(lucy))=>((~quiet(john)&~creative(john))))&
(((curious(paul)|calm(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)&brave(X))<=>(brave(X)<~>~strong(X))))&
(![X]:(kind(X)=>(old(X)&~old(X))))&
((~generous(fred))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
((tall(lucy)|wise(lucy)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((patient(X)|~strong(X))))&
((strong(alice)<~>old(alice))) | creative(fred) | [
"p2",
"p4",
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 814298457948210612539434
% SZS output start Proof for 814298457948210612539434
3. ! [X0] : (~old(X0) <=> (old(X0) & ~curious(X0))) [input p2]
5. ? [X0] : (~kind(X0) & strong(X0)) <=> (~creative(lucy) <~> quiet(lucy)) [input p4]
6. ! [X0] : ((strong(X0) & generous(X0)) <=> (wise(X0) | creative(X0))) [input p5]
14. ! [X0] : (kind(X0) => (~old(X0) & old(X0))) [input p13]
16. ! [X0] : (quiet(X0) <=> ~creative(X0)) [input p15]
23. creative(fred) [input hypothesis]
37. ! [X0] : ((~old(X0) & old(X0)) | ~kind(X0)) [ennf transformation 14]
41. ! [X0] : ((~old(X0) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | old(X0))) [flattening 41]
44. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X0] : (kind(X0) | ~strong(X0))) [nnf transformation 5]
45. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [rectify 44]
46. ? [X0] : (~kind(X0) & strong(X0)) => (~kind(sK0) & strong(sK0)) [choice axiom]
47. ((~kind(sK0) & strong(sK0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [skolemisation 45,46]
48. ! [X0] : (((strong(X0) & generous(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((strong(X0) & generous(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~strong(X0) | ~generous(X0))) [flattening 48]
67. ! [X0] : ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))) [nnf transformation 16]
83. old(X0) | old(X0) [cnf transformation 42]
87. quiet(lucy) | ~creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
88. ~quiet(lucy) | creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
96. ~creative(X0) | strong(X0) [cnf transformation 49]
118. ~old(X0) | ~kind(X0) [cnf transformation 37]
121. ~creative(X0) | ~quiet(X0) [cnf transformation 67]
122. creative(X0) | quiet(X0) [cnf transformation 67]
131. creative(fred) [cnf transformation 23]
134. old(X0) [duplicate literal removal 83]
139. 1 <=> quiet(lucy) [avatar definition]
140. quiet(lucy) <- (1) [avatar component clause 139]
141. ~quiet(lucy) <- (~1) [avatar component clause 139]
143. 2 <=> creative(lucy) [avatar definition]
144. creative(lucy) <- (2) [avatar component clause 143]
145. ~creative(lucy) <- (~2) [avatar component clause 143]
159. 5 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
160. kind(X1) | ~strong(X1) <- (5) [avatar component clause 159]
161. 5 | 2 | ~1 [avatar split clause 88,139,143,159]
162. 5 | ~2 | 1 [avatar split clause 87,139,143,159]
254. ~kind(X0) [subsumption resolution 118,134]
310. strong(fred) [resolution 96,131]
318. quiet(lucy) <- (~2) [resolution 122,145]
321. $false <- (~1, ~2) [subsumption resolution 318,141]
322. 1 | 2 [avatar contradiction clause 321]
325. ~quiet(lucy) <- (2) [resolution 144,121]
328. $false <- (1, 2) [subsumption resolution 325,140]
329. ~1 | ~2 [avatar contradiction clause 328]
330. ~strong(X1) <- (5) [subsumption resolution 160,254]
339. $false <- (5) [resolution 330,310]
340. ~5 [avatar contradiction clause 339]
342. $false [avatar sat refutation 161,162,322,329,340]
% SZS output end Proof for 814298457948210612539434
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not calm is old or not patient. If someone is strong then someone is both not old and not wise. Everyone who is not happy or not generous is not funny and vice versa. Everyone who is either rich or not quiet is happy or patient and vice versa. Everyone who is both not patient and quiet is not creative or not strong and vice versa. Everyone who is either not generous or not funny is both generous and not brave. Everyone who is either not old or patient is both not funny and happy and vice versa. If someone is either wise or quiet then someone is either wise or not rich and vice versa. If someone is either not generous or not tall then john is creative. If alice is not funny or humble then someone is not tall and vice versa. Everyone who is happy or not creative is quiet or old. If mary is both not calm and kind then someone is both not curious and wise and vice versa. Everyone who is both funny and curious is brave and vice versa. Everyone who is not quiet or not creative is tall or brave. Everyone who is happy or not patient is not funny and vice versa. Everyone who is not wise is rich and vice versa. Mary is not humble or not calm. Lucy is brave or not happy. Fred is both calm and creative. Lucy is wise. Someone is humble or not generous. Lucy is not humble or calm. Alice is either not strong or generous. Someone is not old or wise. | Alice is not generous. | entailment | (![X]:((humble(X)&~calm(X))=>(old(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~happy(X)|~generous(X))<=>~funny(X)))&
(![X]:((rich(X)<~>~quiet(X))<=>(happy(X)|patient(X))))&
(![X]:((~patient(X)&quiet(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(generous(X)&~brave(X))))&
(![X]:((~old(X)<~>patient(X))<=>(~funny(X)&happy(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(creative(john)))&
(((~funny(alice)|humble(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((happy(X)|~creative(X))=>(quiet(X)|old(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:((funny(X)&curious(X))<=>brave(X)))&
(![X]:((~quiet(X)|~creative(X))=>(tall(X)|brave(X))))&
(![X]:((happy(X)|~patient(X))<=>~funny(X)))&
(![X]:(~wise(X)<=>rich(X)))&
((~humble(mary)|~calm(mary)))&
((brave(lucy)|~happy(lucy)))&
((calm(fred)&creative(fred)))&
(wise(lucy))&
(?[X]:((humble(X)|~generous(X))))&
((~humble(lucy)|calm(lucy)))&
((~strong(alice)<~>generous(alice)))&
(?[X]:((~old(X)|wise(X)))) | ~generous(alice) | [
"p1",
"p3",
"p6",
"p7",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2572305495433569285399724
% SZS output start Proof for 2572305495433569285399724
2. ? [X0] : strong(X0) => ? [X0] : (~wise(X0) & ~old(X0)) [input p1]
4. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (patient(X0) | happy(X0))) [input p3]
7. ! [X0] : ((~old(X0) <~> patient(X0)) <=> (happy(X0) & ~funny(X0))) [input p6]
8. ? [X0] : (wise(X0) <~> quiet(X0)) <=> ? [X0] : (wise(X0) <~> ~rich(X0)) [input p7]
16. ! [X0] : (~wise(X0) <=> rich(X0)) [input p15]
23. ~strong(alice) <~> generous(alice) [input p22]
25. generous(alice) [input hypothesis]
26. ? [X0] : strong(X0) => ? [X1] : (~wise(X1) & ~old(X1)) [rectify 2]
27. ? [X0] : (wise(X0) <~> quiet(X0)) <=> ? [X1] : (wise(X1) <~> ~rich(X1)) [rectify 8]
30. ? [X1] : (~wise(X1) & ~old(X1)) | ! [X0] : ~strong(X0) [ennf transformation 26]
37. ? [X0] : (~wise(X0) & ~old(X0)) | ! [X1] : ~strong(X1) [rectify 30]
38. ? [X0] : (~wise(X0) & ~old(X0)) => (~wise(sK0) & ~old(sK0)) [choice axiom]
39. (~wise(sK0) & ~old(sK0)) | ! [X1] : ~strong(X1) [skolemisation 37,38]
42. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~patient(X0) & ~happy(X0))) & ((patient(X0) | happy(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 4]
43. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~patient(X0) & ~happy(X0))) & (patient(X0) | happy(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 42]
47. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [flattening 47]
49. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (? [X1] : ((rich(X1) | ~wise(X1)) & (~rich(X1) | wise(X1))) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [nnf transformation 27]
50. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (? [X2] : ((rich(X2) | ~wise(X2)) & (~rich(X2) | wise(X2))) | ! [X3] : ((wise(X3) | ~quiet(X3)) & (quiet(X3) | ~wise(X3)))) [rectify 49]
51. ? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) => ((~quiet(sK1) | ~wise(sK1)) & (quiet(sK1) | wise(sK1))) [choice axiom]
52. ? [X2] : ((rich(X2) | ~wise(X2)) & (~rich(X2) | wise(X2))) => ((rich(sK2) | ~wise(sK2)) & (~rich(sK2) | wise(sK2))) [choice axiom]
53. (((~quiet(sK1) | ~wise(sK1)) & (quiet(sK1) | wise(sK1))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (((rich(sK2) | ~wise(sK2)) & (~rich(sK2) | wise(sK2))) | ! [X3] : ((wise(X3) | ~quiet(X3)) & (quiet(X3) | ~wise(X3)))) [skolemisation 50,52,51]
69. ! [X0] : ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))) [nnf transformation 16]
72. (~generous(alice) | strong(alice)) & (generous(alice) | ~strong(alice)) [nnf transformation 23]
76. ~old(sK0) | ~strong(X1) [cnf transformation 39]
77. ~wise(sK0) | ~strong(X1) [cnf transformation 39]
85. ~rich(X0) | quiet(X0) | ~happy(X0) [cnf transformation 43]
86. ~rich(X0) | quiet(X0) | ~patient(X0) [cnf transformation 43]
98. happy(X0) | patient(X0) | old(X0) [cnf transformation 48]
103. ~rich(sK2) | wise(sK2) | wise(X3) | ~quiet(X3) [cnf transformation 53]
105. rich(sK2) | ~wise(sK2) | wise(X3) | ~quiet(X3) [cnf transformation 53]
129. rich(X0) | wise(X0) [cnf transformation 69]
130. ~wise(X0) | ~rich(X0) [cnf transformation 69]
139. ~generous(alice) | strong(alice) [cnf transformation 72]
141. generous(alice) [cnf transformation 25]
144. 1 <=> ! [X1] : ~strong(X1) [avatar definition]
145. ~strong(X1) <- (1) [avatar component clause 144]
147. 2 <=> wise(sK0) [avatar definition]
149. ~wise(sK0) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 77,147,144]
152. 3 <=> old(sK0) [avatar definition]
154. ~old(sK0) <- (~3) [avatar component clause 152]
155. 1 | ~3 [avatar split clause 76,152,144]
157. 4 <=> ! [X1] : (wise(X1) | rich(X1)) [avatar definition]
158. rich(X1) | wise(X1) <- (4) [avatar component clause 157]
169. 7 <=> ! [X1] : (~rich(X1) | ~wise(X1)) [avatar definition]
170. ~rich(X1) | ~wise(X1) <- (7) [avatar component clause 169]
175. 8 <=> ! [X3] : (wise(X3) | ~quiet(X3)) [avatar definition]
176. ~quiet(X3) | wise(X3) <- (8) [avatar component clause 175]
178. 9 <=> wise(sK2) [avatar definition]
179. wise(sK2) <- (9) [avatar component clause 178]
180. ~wise(sK2) <- (~9) [avatar component clause 178]
182. 10 <=> rich(sK2) [avatar definition]
183. ~rich(sK2) <- (~10) [avatar component clause 182]
184. rich(sK2) <- (10) [avatar component clause 182]
185. 8 | ~9 | 10 [avatar split clause 105,182,178,175]
190. 8 | 9 | ~10 [avatar split clause 103,182,178,175]
247. 7 [avatar split clause 130,169]
248. 4 [avatar split clause 129,157]
282. 31 <=> strong(alice) [avatar definition]
284. strong(alice) <- (31) [avatar component clause 282]
286. 32 <=> generous(alice) [avatar definition]
289. 31 | ~32 [avatar split clause 139,286,282]
300. 32 [avatar split clause 141,286]
301. wise(sK2) <- (4, ~10) [resolution 158,183]
302. $false <- (4, ~9, ~10) [subsumption resolution 301,180]
303. ~4 | 9 | 10 [avatar contradiction clause 302]
305. ~wise(sK2) <- (7, 10) [resolution 170,184]
306. $false <- (7, 9, 10) [subsumption resolution 305,179]
307. ~7 | ~9 | ~10 [avatar contradiction clause 306]
335. quiet(X0) | ~happy(X0) | wise(X0) <- (4) [resolution 85,158]
336. ~happy(X0) | wise(X0) <- (4, 8) [subsumption resolution 335,176]
337. quiet(X0) | ~patient(X0) | wise(X0) <- (4) [resolution 86,158]
338. ~patient(X0) | wise(X0) <- (4, 8) [subsumption resolution 337,176]
342. patient(X0) | old(X0) | wise(X0) <- (4, 8) [resolution 98,336]
346. wise(X0) | old(X0) <- (4, 8) [subsumption resolution 342,338]
501. old(sK0) <- (~2, 4, 8) [resolution 346,149]
504. $false <- (~2, ~3, 4, 8) [subsumption resolution 501,154]
505. 2 | 3 | ~4 | ~8 [avatar contradiction clause 504]
506. $false <- (1, 31) [resolution 145,284]
507. ~1 | ~31 [avatar contradiction clause 506]
508. $false [avatar sat refutation 150,155,185,190,247,248,289,300,303,307,505,507]
% SZS output end Proof for 2572305495433569285399724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or brave then paul is patient or old and vice versa.
Everyone who is either not rich or not humble is not tall and vice versa.
If someone is curious or rich then someone is both not tall and happy.
If alice is old or not rich then fred is both not humble and kind and vice versa.
If someone is not rich then lucy is either calm or not tall and vice versa.
Everyone who is not funny is not humble or not quiet and vice versa.
If someone is not patient then paul is both not brave and old and vice versa.
If someone is either creative or not rich then someone is not tall or not funny.
Everyone who is not patient or curious is either old or not calm and vice versa.
Everyone who is brave or not curious is both not quiet and not rich and vice versa.
Everyone who is both not tall and not quiet is happy and vice versa.
If someone is not rich or curious then someone is not humble and vice versa.
Everyone who is not old or curious is both kind and generous.
If someone is both not humble and funny then someone is both not brave and not patient and vice versa.
If alice is calm then someone is not patient.
Everyone who is happy is patient and vice versa.
Fred is funny or generous.
John is not wise or not brave.
Someone is either not kind or not tall.
Someone is both not strong and not calm.
Paul is either not creative or tall.
Mary is both not generous and not quiet.
John is humble or creative.
Someone is either not old or generous. | Alice is quiet. | contradiction | (((~quiet(susan)<~>brave(susan)))<=>((patient(paul)|old(paul))))&
(![X]:((~rich(X)<~>~humble(X))<=>~tall(X)))&
((?[X]:((curious(X)|rich(X))))=>(?[X]:((~tall(X)&happy(X)))))&
(((old(alice)|~rich(alice)))<=>((~humble(fred)&kind(fred))))&
((?[X]:(~rich(X)))<=>((calm(lucy)<~>~tall(lucy))))&
(![X]:(~funny(X)<=>(~humble(X)|~quiet(X))))&
((?[X]:(~patient(X)))<=>((~brave(paul)&old(paul))))&
((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((~patient(X)|curious(X))<=>(old(X)<~>~calm(X))))&
(![X]:((brave(X)|~curious(X))<=>(~quiet(X)&~rich(X))))&
(![X]:((~tall(X)&~quiet(X))<=>happy(X)))&
((?[X]:((~rich(X)|curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~old(X)|curious(X))=>(kind(X)&generous(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((~brave(X)&~patient(X)))))&
((calm(alice))=>(?[X]:(~patient(X))))&
(![X]:(happy(X)<=>patient(X)))&
((funny(fred)|generous(fred)))&
((~wise(john)|~brave(john)))&
(?[X]:((~kind(X)<~>~tall(X))))&
(?[X]:((~strong(X)&~calm(X))))&
((~creative(paul)<~>tall(paul)))&
((~generous(mary)&~quiet(mary)))&
((humble(john)|creative(john)))&
(?[X]:((~old(X)<~>generous(X)))) | quiet(alice) | [
"p5",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1560014022131727722789117
% SZS output start Proof for 1560014022131727722789117
6. ! [X0] : (~funny(X0) <=> (~quiet(X0) | ~humble(X0))) [input p5]
10. ! [X0] : ((~curious(X0) | brave(X0)) <=> (~rich(X0) & ~quiet(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> happy(X0)) [input p10]
14. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X0] : (~patient(X0) & ~brave(X0)) [input p13]
16. ! [X0] : (happy(X0) <=> patient(X0)) [input p15]
25. quiet(alice) [input hypothesis]
29. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X1] : (~patient(X1) & ~brave(X1)) [rectify 14]
48. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | funny(X0))) [nnf transformation 6]
49. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | funny(X0))) [flattening 48]
61. ! [X0] : (((~curious(X0) | brave(X0)) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 10]
62. ! [X0] : ((~curious(X0) | brave(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [flattening 61]
63. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) | tall(X0)))) [nnf transformation 11]
64. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | quiet(X0) | tall(X0))) [flattening 63]
70. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X1] : (~patient(X1) & ~brave(X1)) | ! [X0] : (~funny(X0) | humble(X0))) [nnf transformation 29]
71. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X2] : (~patient(X2) & ~brave(X2)) | ! [X3] : (~funny(X3) | humble(X3))) [rectify 70]
72. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK6) & ~humble(sK6)) [choice axiom]
73. ? [X2] : (~patient(X2) & ~brave(X2)) => (~patient(sK7) & ~brave(sK7)) [choice axiom]
74. ((funny(sK6) & ~humble(sK6)) | ! [X1] : (patient(X1) | brave(X1))) & ((~patient(sK7) & ~brave(sK7)) | ! [X3] : (~funny(X3) | humble(X3))) [skolemisation 71,73,72]
77. ! [X0] : ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))) [nnf transformation 16]
111. ~funny(X0) | humble(X0) [cnf transformation 49]
124. ~brave(X0) | ~quiet(X0) [cnf transformation 62]
131. ~happy(X0) | ~quiet(X0) [cnf transformation 64]
141. ~humble(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
142. funny(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
145. ~patient(X0) | happy(X0) [cnf transformation 77]
157. quiet(alice) [cnf transformation 25]
275. 25 <=> ! [X1] : (patient(X1) | brave(X1)) [avatar definition]
276. patient(X1) | brave(X1) <- (25) [avatar component clause 275]
278. 26 <=> funny(sK6) [avatar definition]
280. funny(sK6) <- (26) [avatar component clause 278]
281. 25 | 26 [avatar split clause 142,278,275]
283. 27 <=> humble(sK6) [avatar definition]
285. ~humble(sK6) <- (~27) [avatar component clause 283]
286. 25 | ~27 [avatar split clause 141,283,275]
363. happy(X0) | brave(X0) <- (25) [resolution 276,145]
568. brave(X1) | ~quiet(X1) <- (25) [resolution 363,131]
570. ~quiet(X1) <- (25) [subsumption resolution 568,124]
634. $false <- (25) [resolution 570,157]
637. ~25 [avatar contradiction clause 634]
648. humble(sK6) <- (26) [resolution 280,111]
649. $false <- (26, ~27) [subsumption resolution 648,285]
650. ~26 | 27 [avatar contradiction clause 649]
651. $false [avatar sat refutation 281,286,637,650]
% SZS output end Proof for 1560014022131727722789117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not kind is not kind.
Everyone who is either not patient or not curious is wise or funny.
Everyone who is both not kind and rich is either not rich or wise.
If someone is not calm or generous then someone is not strong or rich and vice versa.
If someone is either creative or happy then mary is not patient and vice versa.
Everyone who is both calm and not kind is kind and vice versa.
If someone is old then fred is either not funny or not brave.
Everyone who is either funny or not happy is funny or quiet and vice versa.
Everyone who is both generous and not funny is not calm or old and vice versa.
If someone is not funny or not happy then lucy is creative.
If lucy is both funny and strong then someone is brave or not curious.
Everyone who is both happy and wise is both curious and old.
Everyone who is not calm is either not old or rich and vice versa.
If someone is both not quiet and wise then paul is both not kind and kind and vice versa.
If someone is either not tall or not calm then someone is creative or patient.
If lucy is rich then someone is tall or not generous.
Someone is not humble or happy.
John is not curious.
Alice is both patient and old.
Lucy is either quiet or curious.
Someone is either not creative or funny.
Lucy is old.
Fred is not calm or calm.
Paul is not quiet. | Mary is not generous. | contradiction | (![X]:((creative(X)&~kind(X))=>~kind(X)))&
(![X]:((~patient(X)<~>~curious(X))=>(wise(X)|funny(X))))&
(![X]:((~kind(X)&rich(X))=>(~rich(X)<~>wise(X))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:((~strong(X)|rich(X)))))&
((?[X]:((creative(X)<~>happy(X))))<=>(~patient(mary)))&
(![X]:((calm(X)&~kind(X))<=>kind(X)))&
((?[X]:(old(X)))=>((~funny(fred)<~>~brave(fred))))&
(![X]:((funny(X)<~>~happy(X))<=>(funny(X)|quiet(X))))&
(![X]:((generous(X)&~funny(X))<=>(~calm(X)|old(X))))&
((?[X]:((~funny(X)|~happy(X))))=>(creative(lucy)))&
(((funny(lucy)&strong(lucy)))=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((happy(X)&wise(X))=>(curious(X)&old(X))))&
(![X]:(~calm(X)<=>(~old(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~kind(paul)&kind(paul))))&
((?[X]:((~tall(X)<~>~calm(X))))=>(?[X]:((creative(X)|patient(X)))))&
((rich(lucy))=>(?[X]:((tall(X)|~generous(X)))))&
(?[X]:((~humble(X)|happy(X))))&
(~curious(john))&
((patient(alice)&old(alice)))&
((quiet(lucy)<~>curious(lucy)))&
(?[X]:((~creative(X)<~>funny(X))))&
(old(lucy))&
((~calm(fred)|calm(fred)))&
(~quiet(paul)) | ~generous(mary) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 11533884773722018258782
% SZS output start Proof for 11533884773722018258782
6. ! [X0] : ((~kind(X0) & calm(X0)) <=> kind(X0)) [input p5]
9. ! [X0] : ((~funny(X0) & generous(X0)) <=> (old(X0) | ~calm(X0))) [input p8]
25. ~generous(mary) [input hypothesis]
54. ! [X0] : (((~kind(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~calm(X0)))) [nnf transformation 6]
55. ! [X0] : (((~kind(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~calm(X0))) [flattening 54]
59. ! [X0] : (((~funny(X0) & generous(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (funny(X0) | ~generous(X0)))) [nnf transformation 9]
60. ! [X0] : (((~funny(X0) & generous(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | funny(X0) | ~generous(X0))) [flattening 59]
92. kind(X0) | kind(X0) | ~calm(X0) [cnf transformation 55]
94. ~kind(X0) | ~kind(X0) [cnf transformation 55]
104. generous(X0) | calm(X0) [cnf transformation 60]
134. ~generous(mary) [cnf transformation 25]
137. kind(X0) | ~calm(X0) [duplicate literal removal 92]
138. ~kind(X0) [duplicate literal removal 94]
194. ~calm(X0) [subsumption resolution 137,138]
210. generous(X0) [subsumption resolution 104,194]
258. $false [subsumption resolution 134,210]
% SZS output end Proof for 11533884773722018258782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not patient.
Everyone who is not old is humble and vice versa.
If someone is not tall then someone is either not happy or wise and vice versa.
Everyone who is either not happy or not funny is not patient.
If someone is brave then paul is tall or wise.
Everyone who is both not kind and wise is both quiet and humble and vice versa.
Everyone who is both not quiet and quiet is not humble or kind and vice versa.
If someone is not quiet or funny then someone is not creative or old and vice versa.
If susan is both humble and calm then someone is not curious or not strong.
Everyone who is either creative or quiet is both not patient and not generous.
Everyone who is either rich or not humble is old and vice versa.
Everyone who is either not happy or patient is both funny and not creative and vice versa.
Everyone who is either old or creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
Lucy is not patient.
John is not generous or generous.
Mary is tall or not strong.
Lucy is not calm or not humble.
Someone is generous or patient.
Alice is both generous and not rich.
Susan is not curious.
Lucy is humble or quiet. | Alice is not tall. | entailment | (![X]:(tall(X)=>~patient(X)))&
(![X]:(~old(X)<=>humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((~happy(X)<~>~funny(X))=>~patient(X)))&
((?[X]:(brave(X)))=>((tall(paul)|wise(paul))))&
(![X]:((~kind(X)&wise(X))<=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
(~patient(lucy))&
((~generous(john)|generous(john)))&
((tall(mary)|~strong(mary)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy))) | ~tall(alice) | [
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4973870942490446563794015
% SZS output start Proof for 4973870942490446563794015
14. ! [X0] : (rich(X0) <=> (old(X0) | tall(X0))) [input p13]
22. ~rich(alice) & generous(alice) [input p21]
25. tall(alice) [input hypothesis]
57. ! [X0] : ((rich(X0) | (~old(X0) & ~tall(X0))) & ((old(X0) | tall(X0)) | ~rich(X0))) [nnf transformation 14]
58. ! [X0] : ((rich(X0) | (~old(X0) & ~tall(X0))) & (old(X0) | tall(X0) | ~rich(X0))) [flattening 57]
109. ~tall(X0) | rich(X0) [cnf transformation 58]
129. ~rich(alice) [cnf transformation 22]
131. tall(alice) [cnf transformation 25]
251. rich(alice) [resolution 109,131]
252. $false [subsumption resolution 251,129]
% SZS output end Proof for 4973870942490446563794015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not rich then alice is both not brave and not wise and vice versa.
Everyone who is either not strong or not kind is both not brave and brave.
Everyone who is either wise or strong is either rich or humble and vice versa.
Everyone who is both not kind and not old is not patient and vice versa.
If fred is not strong or calm then john is not curious or rich and vice versa.
If susan is either strong or old then john is patient and vice versa.
Everyone who is both generous and not calm is funny or tall.
Everyone who is both calm and strong is not patient and vice versa.
If someone is tall then fred is generous or brave.
Everyone who is either not wise or not brave is either not wise or not generous and vice versa.
If someone is quiet then someone is not strong or generous.
If someone is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
Everyone who is not calm is both not rich and not curious.
If someone is both not old and curious then someone is either not funny or generous.
If someone is not calm then someone is not patient.
Someone is not curious.
Fred is not curious or not generous.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous.
Fred is either funny or wise.
Someone is either wise or not calm. | Fred is curious. | contradiction | ((?[X]:((~generous(X)&~rich(X))))<=>((~brave(alice)&~wise(alice))))&
(![X]:((~strong(X)<~>~kind(X))=>(~brave(X)&brave(X))))&
(![X]:((wise(X)<~>strong(X))<=>(rich(X)<~>humble(X))))&
(![X]:((~kind(X)&~old(X))<=>~patient(X)))&
(((~strong(fred)|calm(fred)))<=>((~curious(john)|rich(john))))&
(((strong(susan)<~>old(susan)))<=>(patient(john)))&
(![X]:((generous(X)&~calm(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&strong(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>((generous(fred)|brave(fred))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(![X]:(~calm(X)=>(~rich(X)&~curious(X))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(~patient(X))))&
(?[X]:(~curious(X)))&
((~curious(fred)|~generous(fred)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X))))&
((funny(fred)<~>wise(fred)))&
(?[X]:((wise(X)<~>~calm(X)))) | curious(fred) | [
"p1",
"p3",
"p7",
"p8",
"p9",
"p12",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1155657133005129648620529
% SZS output start Proof for 1155657133005129648620529
2. ! [X0] : ((~strong(X0) <~> ~kind(X0)) => (brave(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((~old(X0) & ~kind(X0)) <=> ~patient(X0)) [input p3]
8. ! [X0] : ((strong(X0) & calm(X0)) <=> ~patient(X0)) [input p7]
9. ? [X0] : tall(X0) => (brave(fred) | generous(fred)) [input p8]
10. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (~wise(X0) <~> ~generous(X0))) [input p9]
13. ! [X0] : (~tall(X0) => (~old(X0) | curious(X0))) [input p12]
16. ? [X0] : ~calm(X0) => ? [X0] : ~patient(X0) [input p15]
17. ? [X0] : ~curious(X0) [input p16]
18. ~generous(fred) | ~curious(fred) [input p17]
25. curious(fred) [input hypothesis]
29. ? [X0] : ~calm(X0) => ? [X1] : ~patient(X1) [rectify 16]
33. ! [X0] : ((brave(X0) & ~brave(X0)) | (~strong(X0) <=> ~kind(X0))) [ennf transformation 2]
36. (brave(fred) | generous(fred)) | ! [X0] : ~tall(X0) [ennf transformation 9]
37. brave(fred) | generous(fred) | ! [X0] : ~tall(X0) [flattening 36]
38. ! [X0] : ((~old(X0) | curious(X0)) | tall(X0)) [ennf transformation 13]
39. ! [X0] : (~old(X0) | curious(X0) | tall(X0)) [flattening 38]
42. ? [X1] : ~patient(X1) | ! [X0] : calm(X0) [ennf transformation 29]
48. ! [X0] : ((brave(X0) & ~brave(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) [nnf transformation 33]
50. ! [X0] : (((~old(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | (old(X0) | kind(X0)))) [nnf transformation 4]
51. ! [X0] : (((~old(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | old(X0) | kind(X0))) [flattening 50]
55. ! [X0] : (((strong(X0) & calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((strong(X0) & calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | ~calm(X0))) [flattening 55]
57. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) & (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 10]
67. ? [X0] : ~patient(X0) | ! [X1] : calm(X1) [rectify 42]
68. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
69. ~patient(sK4) | ! [X1] : calm(X1) [skolemisation 67,68]
70. ? [X0] : ~curious(X0) => ~curious(sK5) [choice axiom]
71. ~curious(sK5) [skolemisation 17,70]
88. ~brave(X0) | ~kind(X0) | strong(X0) [cnf transformation 48]
89. ~brave(X0) | ~strong(X0) | kind(X0) [cnf transformation 48]
90. ~kind(X0) | brave(X0) | strong(X0) [cnf transformation 48]
91. ~strong(X0) | brave(X0) | kind(X0) [cnf transformation 48]
100. ~patient(X0) | old(X0) | kind(X0) [cnf transformation 51]
101. ~kind(X0) | patient(X0) [cnf transformation 51]
102. ~old(X0) | patient(X0) [cnf transformation 51]
112. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 56]
114. patient(X0) | strong(X0) [cnf transformation 56]
115. brave(fred) | generous(fred) | ~tall(X0) [cnf transformation 37]
118. generous(X0) | wise(X0) | ~brave(X0) | wise(X0) [cnf transformation 57]
121. ~brave(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 57]
130. ~old(X0) | curious(X0) | tall(X0) [cnf transformation 39]
135. ~patient(sK4) | calm(X1) [cnf transformation 69]
136. ~curious(sK5) [cnf transformation 71]
137. ~generous(fred) | ~curious(fred) [cnf transformation 18]
148. curious(fred) [cnf transformation 25]
150. generous(X0) | wise(X0) | ~brave(X0) [duplicate literal removal 118]
151. ~wise(X0) | ~brave(X0) | generous(X0) [duplicate literal removal 121]
176. ~strong(X0) | kind(X0) [subsumption resolution 89,91]
177. ~kind(X0) | strong(X0) [subsumption resolution 88,90]
215. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
216. ~tall(X0) <- (13) [avatar component clause 215]
218. 14 <=> generous(fred) [avatar definition]
219. ~generous(fred) <- (~14) [avatar component clause 218]
222. 15 <=> brave(fred) [avatar definition]
224. brave(fred) <- (15) [avatar component clause 222]
225. 13 | 14 | 15 [avatar split clause 115,222,218,215]
226. ~brave(X0) | generous(X0) [subsumption resolution 150,151]
276. 27 <=> ! [X1] : calm(X1) [avatar definition]
277. calm(X1) <- (27) [avatar component clause 276]
279. 28 <=> patient(sK4) [avatar definition]
281. ~patient(sK4) <- (~28) [avatar component clause 279]
282. 27 | ~28 [avatar split clause 135,279,276]
284. 29 <=> curious(fred) [avatar definition]
287. ~29 | ~14 [avatar split clause 137,218,284]
324. 29 [avatar split clause 148,284]
329. strong(sK4) <- (~28) [resolution 114,281]
333. kind(sK4) <- (~28) [resolution 176,329]
340. generous(fred) <- (15) [resolution 226,224]
341. $false <- (~14, 15) [subsumption resolution 340,219]
342. 14 | ~15 [avatar contradiction clause 341]
344. patient(sK4) <- (~28) [resolution 333,101]
345. $false <- (~28) [subsumption resolution 344,281]
346. 28 [avatar contradiction clause 345]
353. old(X0) | kind(X0) | strong(X0) [resolution 100,114]
358. old(X0) | kind(X0) [subsumption resolution 353,176]
360. kind(X0) | patient(X0) [resolution 358,102]
361. patient(X0) [subsumption resolution 360,101]
363. ~strong(X0) | ~patient(X0) <- (27) [resolution 112,277]
367. ~strong(X0) <- (27) [subsumption resolution 363,361]
368. curious(X0) | tall(X0) | kind(X0) [resolution 130,358]
369. curious(X0) | kind(X0) <- (13) [subsumption resolution 368,216]
380. kind(sK5) <- (13) [resolution 369,136]
451. strong(sK5) <- (13) [resolution 380,177]
454. $false <- (13, 27) [subsumption resolution 451,367]
455. ~13 | ~27 [avatar contradiction clause 454]
456. $false [avatar sat refutation 225,282,287,324,342,346,455]
% SZS output end Proof for 1155657133005129648620529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich then susan is happy or not creative.
Everyone who is funny or calm is both wise and happy and vice versa.
If someone is either curious or not humble then susan is both not happy and happy.
Everyone who is both humble and not brave is creative or brave.
If mary is not wise then someone is not old and vice versa.
Everyone who is either wise or not strong is not curious or curious and vice versa.
If someone is not humble or old then someone is tall or not old and vice versa.
Everyone who is either not curious or not quiet is patient.
Everyone who is either not wise or generous is both not wise and not funny and vice versa.
Everyone who is both tall and not wise is not generous or tall and vice versa.
Everyone who is either patient or happy is either happy or wise.
Everyone who is either patient or humble is not funny or quiet and vice versa.
If susan is either not quiet or calm then someone is not kind and vice versa.
If someone is kind then mary is not calm and vice versa.
If someone is not wise or not creative then someone is either happy or old and vice versa.
Someone is either wise or old.
Someone is not old or generous.
Someone is either brave or not humble.
Lucy is kind.
Alice is both patient and not strong.
Someone is not happy or kind.
Mary is either not quiet or curious. | Mary is not calm. | entailment | ((~rich(lucy))=>((happy(susan)|~creative(susan))))&
(![X]:((funny(X)|calm(X))<=>(wise(X)&happy(X))))&
((?[X]:((curious(X)<~>~humble(X))))=>((~happy(susan)&happy(susan))))&
(![X]:((humble(X)&~brave(X))=>(creative(X)|brave(X))))&
((~wise(mary))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~strong(X))<=>(~curious(X)|curious(X))))&
((?[X]:((~humble(X)|old(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>patient(X)))&
(![X]:((~wise(X)<~>generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:((tall(X)&~wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((patient(X)<~>happy(X))=>(happy(X)<~>wise(X))))&
(![X]:((patient(X)<~>humble(X))<=>(~funny(X)|quiet(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(kind(X)))<=>(~calm(mary)))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((happy(X)<~>old(X)))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
(kind(lucy))&
((patient(alice)&~strong(alice)))&
(?[X]:((~happy(X)|kind(X))))&
((~quiet(mary)<~>curious(mary))) | ~calm(mary) | [
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1059182518343421135794260
% SZS output start Proof for 1059182518343421135794260
14. ? [X0] : kind(X0) <=> ~calm(mary) [input p13]
19. kind(lucy) [input p18]
23. calm(mary) [input hypothesis]
58. (? [X0] : kind(X0) | calm(mary)) & (~calm(mary) | ! [X0] : ~kind(X0)) [nnf transformation 14]
59. (? [X0] : kind(X0) | calm(mary)) & (~calm(mary) | ! [X1] : ~kind(X1)) [rectify 58]
60. ? [X0] : kind(X0) => kind(sK4) [choice axiom]
61. (kind(sK4) | calm(mary)) & (~calm(mary) | ! [X1] : ~kind(X1)) [skolemisation 59,60]
127. ~calm(mary) | ~kind(X1) [cnf transformation 61]
140. kind(lucy) [cnf transformation 19]
146. calm(mary) [cnf transformation 23]
236. 18 <=> calm(mary) [avatar definition]
245. 20 <=> ! [X1] : ~kind(X1) [avatar definition]
246. ~kind(X1) <- (20) [avatar component clause 245]
247. 20 | ~18 [avatar split clause 127,236,245]
296. 18 [avatar split clause 146,236]
297. $false <- (20) [resolution 246,140]
298. ~20 [avatar contradiction clause 297]
299. $false [avatar sat refutation 247,296,298]
% SZS output end Proof for 1059182518343421135794260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and strong then mary is not creative.
Everyone who is strong is generous or strong and vice versa.
If susan is both creative and not humble then lucy is both strong and patient.
If mary is not kind then fred is both generous and not patient.
Everyone who is both calm and quiet is not tall or rich and vice versa.
If john is not humble then fred is not rich or not creative.
Everyone who is both quiet and not strong is not strong and vice versa.
If someone is either quiet or not strong then mary is both tall and quiet.
If someone is either quiet or not humble then lucy is both not funny and not happy and vice versa.
Everyone who is patient or not funny is humble or patient.
Everyone who is not patient or old is either not patient or not funny and vice versa.
Everyone who is both curious and kind is both not rich and strong and vice versa.
Everyone who is either old or happy is not generous or old and vice versa.
Everyone who is not quiet or not strong is both not quiet and quiet and vice versa.
Everyone who is both happy and not brave is not patient.
Everyone who is either old or brave is happy and vice versa.
Someone is not tall or quiet.
John is generous or not curious.
Paul is creative or not calm.
Someone is kind or wise.
Mary is brave or tall.
Someone is either not humble or not calm.
Mary is not calm.
Someone is both wise and kind. | Fred is not curious. | neutral | (((~wise(mary)&strong(mary)))=>(~creative(mary)))&
(![X]:(strong(X)<=>(generous(X)|strong(X))))&
(((creative(susan)&~humble(susan)))=>((strong(lucy)&patient(lucy))))&
((~kind(mary))=>((generous(fred)&~patient(fred))))&
(![X]:((calm(X)&quiet(X))<=>(~tall(X)|rich(X))))&
((~humble(john))=>((~rich(fred)|~creative(fred))))&
(![X]:((quiet(X)&~strong(X))<=>~strong(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>((tall(mary)&quiet(mary))))&
((?[X]:((quiet(X)<~>~humble(X))))<=>((~funny(lucy)&~happy(lucy))))&
(![X]:((patient(X)|~funny(X))=>(humble(X)|patient(X))))&
(![X]:((~patient(X)|old(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)&strong(X))))&
(![X]:((old(X)<~>happy(X))<=>(~generous(X)|old(X))))&
(![X]:((~quiet(X)|~strong(X))<=>(~quiet(X)&quiet(X))))&
(![X]:((happy(X)&~brave(X))=>~patient(X)))&
(![X]:((old(X)<~>brave(X))<=>happy(X)))&
(?[X]:((~tall(X)|quiet(X))))&
((generous(john)|~curious(john)))&
((creative(paul)|~calm(paul)))&
(?[X]:((kind(X)|wise(X))))&
((brave(mary)|tall(mary)))&
(?[X]:((~humble(X)<~>~calm(X))))&
(~calm(mary))&
(?[X]:((wise(X)&kind(X)))) | ~curious(fred) | [] | null | 0 |
If someone is either kind or not quiet then someone is both kind and generous and vice versa.
Everyone who is not rich is not happy or quiet.
Everyone who is not brave is either not quiet or not patient and vice versa.
If someone is generous then john is both not humble and generous.
Everyone who is not creative is not tall or strong and vice versa.
Everyone who is tall or not happy is not strong or not tall.
Everyone who is not wise or funny is curious.
If someone is not kind or kind then mary is curious or wise and vice versa.
If someone is either not rich or not quiet then john is both curious and calm.
Everyone who is both old and wise is either not humble or not tall and vice versa.
Everyone who is generous is not patient or kind.
If someone is both generous and funny then someone is tall.
Everyone who is both wise and not kind is calm.
Everyone who is wise is rich and vice versa.
If lucy is both not kind and creative then lucy is both happy and not humble.
Fred is either funny or not funny.
John is funny.
John is either not tall or not kind.
Susan is both not wise and not funny.
Someone is not rich.
Someone is generous.
Someone is not patient or creative. | Fred is not quiet. | neutral | ((?[X]:((kind(X)<~>~quiet(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:(~rich(X)=>(~happy(X)|quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>~patient(X))))&
((?[X]:(generous(X)))=>((~humble(john)&generous(john))))&
(![X]:(~creative(X)<=>(~tall(X)|strong(X))))&
(![X]:((tall(X)|~happy(X))=>(~strong(X)|~tall(X))))&
(![X]:((~wise(X)|funny(X))=>curious(X)))&
((?[X]:((~kind(X)|kind(X))))<=>((curious(mary)|wise(mary))))&
((?[X]:((~rich(X)<~>~quiet(X))))=>((curious(john)&calm(john))))&
(![X]:((old(X)&wise(X))<=>(~humble(X)<~>~tall(X))))&
(![X]:(generous(X)=>(~patient(X)|kind(X))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:(tall(X))))&
(![X]:((wise(X)&~kind(X))=>calm(X)))&
(![X]:(wise(X)<=>rich(X)))&
(((~kind(lucy)&creative(lucy)))=>((happy(lucy)&~humble(lucy))))&
((funny(fred)<~>~funny(fred)))&
(funny(john))&
((~tall(john)<~>~kind(john)))&
((~wise(susan)&~funny(susan)))&
(?[X]:(~rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((~patient(X)|creative(X)))) | ~quiet(fred) | [] | null | 0 |
If someone is wise then john is either not patient or humble and vice versa. Everyone who is both strong and quiet is either humble or patient. Everyone who is not old or generous is both not generous and not calm. Everyone who is both not rich and not kind is both funny and not old and vice versa. If someone is either kind or funny then susan is either tall or not humble and vice versa. Everyone who is kind or not happy is brave. If someone is both not kind and not quiet then someone is both not tall and not generous. Everyone who is both quiet and not calm is both generous and not creative. If someone is not brave then someone is both curious and not curious and vice versa. If someone is either not kind or tall then someone is not rich. If someone is either calm or strong then mary is rich or curious. Everyone who is curious is not tall and vice versa. Everyone who is not happy is not wise or not kind and vice versa. If someone is calm or kind then someone is rich. Everyone who is either not rich or not patient is not humble or strong and vice versa. If alice is not old or calm then alice is not funny and vice versa. Mary is not tall. Someone is either tall or rich. Lucy is not creative or not strong. Someone is both not wise and not strong. Mary is not patient. Fred is either kind or not calm. Someone is both humble and creative. Fred is either old or not kind. | Alice is not funny. | neutral | ((?[X]:(wise(X)))<=>((~patient(john)<~>humble(john))))&
(![X]:((strong(X)&quiet(X))=>(humble(X)<~>patient(X))))&
(![X]:((~old(X)|generous(X))=>(~generous(X)&~calm(X))))&
(![X]:((~rich(X)&~kind(X))<=>(funny(X)&~old(X))))&
((?[X]:((kind(X)<~>funny(X))))<=>((tall(susan)<~>~humble(susan))))&
(![X]:((kind(X)|~happy(X))=>brave(X)))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((quiet(X)&~calm(X))=>(generous(X)&~creative(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~rich(X))))&
((?[X]:((calm(X)<~>strong(X))))=>((rich(mary)|curious(mary))))&
(![X]:(curious(X)<=>~tall(X)))&
(![X]:(~happy(X)<=>(~wise(X)|~kind(X))))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:(rich(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~humble(X)|strong(X))))&
(((~old(alice)|calm(alice)))<=>(~funny(alice)))&
(~tall(mary))&
(?[X]:((tall(X)<~>rich(X))))&
((~creative(lucy)|~strong(lucy)))&
(?[X]:((~wise(X)&~strong(X))))&
(~patient(mary))&
((kind(fred)<~>~calm(fred)))&
(?[X]:((humble(X)&creative(X))))&
((old(fred)<~>~kind(fred))) | ~funny(alice) | [] | null | 0 |
If mary is either not generous or humble then someone is not humble and vice versa.
If mary is both funny and generous then someone is wise or not strong.
If susan is not strong or not quiet then someone is not rich or curious.
Everyone who is wise is both not wise and not old and vice versa.
Everyone who is either not curious or not happy is both wise and not funny.
If someone is both creative and brave then alice is not old or brave and vice versa.
If paul is both old and not funny then lucy is either brave or tall.
Everyone who is old or patient is either not creative or humble.
Everyone who is either not rich or not strong is either generous or not tall.
Everyone who is both brave and not curious is curious and vice versa.
If someone is both patient and not wise then john is either not brave or not curious and vice versa.
If john is not old or not quiet then paul is either not curious or not calm.
Everyone who is either rich or not curious is both brave and wise and vice versa.
Everyone who is both patient and happy is not humble or not kind.
Everyone who is either not generous or not quiet is either tall or not strong and vice versa.
Everyone who is either rich or not happy is generous or creative and vice versa.
Someone is not humble.
Lucy is either creative or old.
John is not quiet or not old.
Lucy is either tall or happy.
Paul is either not old or old.
Someone is rich or not brave. | Mary is not rich. | contradiction | (((~generous(mary)<~>humble(mary)))<=>(?[X]:(~humble(X))))&
(((funny(mary)&generous(mary)))=>(?[X]:((wise(X)|~strong(X)))))&
(((~strong(susan)|~quiet(susan)))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:(wise(X)<=>(~wise(X)&~old(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(wise(X)&~funny(X))))&
((?[X]:((creative(X)&brave(X))))<=>((~old(alice)|brave(alice))))&
(((old(paul)&~funny(paul)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((old(X)|patient(X))=>(~creative(X)<~>humble(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(generous(X)<~>~tall(X))))&
(![X]:((brave(X)&~curious(X))<=>curious(X)))&
((?[X]:((patient(X)&~wise(X))))<=>((~brave(john)<~>~curious(john))))&
(((~old(john)|~quiet(john)))=>((~curious(paul)<~>~calm(paul))))&
(![X]:((rich(X)<~>~curious(X))<=>(brave(X)&wise(X))))&
(![X]:((patient(X)&happy(X))=>(~humble(X)|~kind(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((rich(X)<~>~happy(X))<=>(generous(X)|creative(X))))&
(?[X]:(~humble(X)))&
((creative(lucy)<~>old(lucy)))&
((~quiet(john)|~old(john)))&
((tall(lucy)<~>happy(lucy)))&
((~old(paul)<~>old(paul)))&
(?[X]:((rich(X)|~brave(X)))) | ~rich(mary) | [
"p3",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 111015945282823366296642
% SZS output start Proof for 111015945282823366296642
4. ! [X0] : (wise(X0) <=> (~old(X0) & ~wise(X0))) [input p3]
10. ! [X0] : ((~curious(X0) & brave(X0)) <=> curious(X0)) [input p9]
13. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> (wise(X0) & brave(X0))) [input p12]
23. ~rich(mary) [input hypothesis]
42. ! [X0] : ((wise(X0) | (old(X0) | wise(X0))) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 4]
43. ! [X0] : ((wise(X0) | old(X0) | wise(X0)) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [flattening 42]
53. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~brave(X0)))) [nnf transformation 10]
54. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~brave(X0))) [flattening 53]
60. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) | ~brave(X0))) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~wise(X0) | ~brave(X0)) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [flattening 60]
79. ~wise(X0) | ~wise(X0) [cnf transformation 43]
103. ~curious(X0) | ~curious(X0) [cnf transformation 54]
117. wise(X0) | rich(X0) | curious(X0) [cnf transformation 61]
143. ~rich(mary) [cnf transformation 23]
145. ~curious(X0) [duplicate literal removal 103]
146. ~wise(X0) [duplicate literal removal 79]
262. rich(X0) | curious(X0) [subsumption resolution 117,146]
263. rich(X0) [subsumption resolution 262,145]
284. $false [subsumption resolution 143,263]
% SZS output end Proof for 111015945282823366296642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or quiet is either not curious or not brave. If paul is brave or not strong then someone is quiet or happy. Everyone who is both strong and not old is funny and vice versa. Everyone who is both not happy and strong is either not humble or humble. Everyone who is not rich is strong or not brave. Everyone who is kind is not funny and vice versa. If fred is quiet then alice is both not funny and creative and vice versa. If alice is not quiet or calm then alice is both not strong and humble and vice versa. Everyone who is humble or not tall is both happy and not generous. If someone is either funny or not rich then someone is creative or happy. If someone is either not curious or not tall then mary is not creative or not old and vice versa. If susan is not rich then someone is tall and vice versa. Everyone who is both not rich and not brave is not old or happy and vice versa. If someone is not wise or not humble then someone is both humble and not wise. If alice is either strong or old then someone is calm or kind. If alice is quiet then john is either generous or humble. Someone is not old or humble. Lucy is both brave and not funny. Someone is either not calm or not creative. Someone is creative or tall. Paul is either curious or not wise. Lucy is either not tall or not generous. Alice is both not brave and not generous. Someone is not wise or strong. | Alice is creative. | neutral | (![X]:((~happy(X)|quiet(X))=>(~curious(X)<~>~brave(X))))&
(((brave(paul)|~strong(paul)))=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((strong(X)&~old(X))<=>funny(X)))&
(![X]:((~happy(X)&strong(X))=>(~humble(X)<~>humble(X))))&
(![X]:(~rich(X)=>(strong(X)|~brave(X))))&
(![X]:(kind(X)<=>~funny(X)))&
((quiet(fred))<=>((~funny(alice)&creative(alice))))&
(((~quiet(alice)|calm(alice)))<=>((~strong(alice)&humble(alice))))&
(![X]:((humble(X)|~tall(X))=>(happy(X)&~generous(X))))&
((?[X]:((funny(X)<~>~rich(X))))=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:((~curious(X)<~>~tall(X))))<=>((~creative(mary)|~old(mary))))&
((~rich(susan))<=>(?[X]:(tall(X))))&
(![X]:((~rich(X)&~brave(X))<=>(~old(X)|happy(X))))&
((?[X]:((~wise(X)|~humble(X))))=>(?[X]:((humble(X)&~wise(X)))))&
(((strong(alice)<~>old(alice)))=>(?[X]:((calm(X)|kind(X)))))&
((quiet(alice))=>((generous(john)<~>humble(john))))&
(?[X]:((~old(X)|humble(X))))&
((brave(lucy)&~funny(lucy)))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:((creative(X)|tall(X))))&
((curious(paul)<~>~wise(paul)))&
((~tall(lucy)<~>~generous(lucy)))&
((~brave(alice)&~generous(alice)))&
(?[X]:((~wise(X)|strong(X)))) | creative(alice) | [] | null | 0 |
If someone is kind then lucy is either not strong or creative. If someone is either not strong or not brave then john is not wise or not creative and vice versa. If someone is generous or happy then someone is both not strong and curious. Everyone who is curious is not wise and vice versa. Everyone who is not wise is both not quiet and not curious. Everyone who is kind or not creative is humble or not calm and vice versa. Everyone who is quiet or rich is either not generous or not old. If someone is both not creative and humble then someone is not happy. If someone is not patient then someone is both not patient and not brave and vice versa. If someone is generous or not quiet then someone is both not kind and rich. Everyone who is not brave is strong. If paul is either humble or quiet then alice is old or wise and vice versa. Everyone who is both old and kind is quiet or not generous and vice versa. Everyone who is not curious is tall and vice versa. Everyone who is either not humble or strong is kind or not curious and vice versa. Someone is calm. Paul is either not generous or calm. Someone is either not funny or calm. Someone is patient. Lucy is brave. Someone is either patient or not happy. | John is not tall. | contradiction | ((?[X]:(kind(X)))=>((~strong(lucy)<~>creative(lucy))))&
((?[X]:((~strong(X)<~>~brave(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:(~wise(X)=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)|~creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((quiet(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(((humble(paul)<~>quiet(paul)))<=>((old(alice)|wise(alice))))&
(![X]:((old(X)&kind(X))<=>(quiet(X)|~generous(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|~curious(X))))&
(?[X]:(calm(X)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:(patient(X)))&
(brave(lucy))&
(?[X]:((patient(X)<~>~happy(X)))) | ~tall(john) | [
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1856693756050847657450027
% SZS output start Proof for 1856693756050847657450027
4. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (~curious(X0) & ~quiet(X0))) [input p4]
14. ! [X0] : (~curious(X0) <=> tall(X0)) [input p13]
22. ~tall(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~quiet(X0)) | wise(X0)) [ennf transformation 5]
43. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 4]
62. ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0))) [nnf transformation 14]
88. ~curious(X0) | ~wise(X0) [cnf transformation 43]
89. curious(X0) | wise(X0) [cnf transformation 43]
91. ~curious(X0) | wise(X0) [cnf transformation 29]
120. tall(X0) | curious(X0) [cnf transformation 62]
137. ~tall(john) [cnf transformation 22]
197. wise(X0) [subsumption resolution 91,89]
298. curious(john) [resolution 120,137]
313. ~wise(john) [resolution 298,88]
314. $false [subsumption resolution 313,197]
% SZS output end Proof for 1856693756050847657450027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then john is either kind or brave and vice versa. If paul is both generous and not quiet then someone is both not happy and wise and vice versa. If susan is either kind or tall then lucy is either rich or generous. Everyone who is quiet is both not generous and calm. If someone is either not old or happy then mary is both not calm and generous and vice versa. Everyone who is either quiet or not funny is not humble or not creative and vice versa. Everyone who is curious is not generous or not humble and vice versa. Everyone who is not brave or kind is creative or not patient and vice versa. Everyone who is funny is either generous or calm and vice versa. Everyone who is wise or not calm is either creative or old and vice versa. Everyone who is either not humble or generous is not rich or brave and vice versa. If fred is both not tall and tall then someone is not funny. Everyone who is either tall or happy is quiet or tall and vice versa. Everyone who is either not generous or not kind is tall or not tall and vice versa. Everyone who is both not humble and creative is either not calm or brave. If someone is not curious then john is happy or not tall. Someone is not kind or not creative. Someone is either tall or generous. Lucy is not calm or rich. Someone is both not funny and not happy. Lucy is both brave and not generous. Someone is wise or brave. Someone is wise. | Fred is not kind. | neutral | ((?[X]:(~kind(X)))<=>((kind(john)<~>brave(john))))&
(((generous(paul)&~quiet(paul)))<=>(?[X]:((~happy(X)&wise(X)))))&
(((kind(susan)<~>tall(susan)))=>((rich(lucy)<~>generous(lucy))))&
(![X]:(quiet(X)=>(~generous(X)&calm(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>((~calm(mary)&generous(mary))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~humble(X)|~creative(X))))&
(![X]:(curious(X)<=>(~generous(X)|~humble(X))))&
(![X]:((~brave(X)|kind(X))<=>(creative(X)|~patient(X))))&
(![X]:(funny(X)<=>(generous(X)<~>calm(X))))&
(![X]:((wise(X)|~calm(X))<=>(creative(X)<~>old(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(~rich(X)|brave(X))))&
(((~tall(fred)&tall(fred)))=>(?[X]:(~funny(X))))&
(![X]:((tall(X)<~>happy(X))<=>(quiet(X)|tall(X))))&
(![X]:((~generous(X)<~>~kind(X))<=>(tall(X)|~tall(X))))&
(![X]:((~humble(X)&creative(X))=>(~calm(X)<~>brave(X))))&
((?[X]:(~curious(X)))=>((happy(john)|~tall(john))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((tall(X)<~>generous(X))))&
((~calm(lucy)|rich(lucy)))&
(?[X]:((~funny(X)&~happy(X))))&
((brave(lucy)&~generous(lucy)))&
(?[X]:((wise(X)|brave(X))))&
(?[X]:(wise(X))) | ~kind(fred) | [] | null | 0 |
If someone is both not wise and not tall then paul is tall.
If susan is not rich then someone is not creative or not kind and vice versa.
If susan is brave or tall then someone is both not quiet and patient and vice versa.
Everyone who is kind is either brave or tall.
Everyone who is either patient or not strong is happy and vice versa.
If susan is not generous then someone is both humble and not curious.
Everyone who is either happy or wise is both tall and not calm.
Everyone who is either rich or not brave is quiet.
Everyone who is wise or strong is both calm and not patient and vice versa.
If fred is both calm and strong then susan is either humble or kind and vice versa.
If someone is not tall or rich then mary is either not patient or not calm.
Everyone who is old is either not creative or curious and vice versa.
If someone is generous or quiet then john is humble or not happy and vice versa.
Everyone who is not happy is either wise or not strong.
Everyone who is either not strong or quiet is both generous and not tall.
Everyone who is generous is either tall or not quiet.
Someone is not old or curious.
John is curious.
Someone is either generous or quiet.
Someone is either generous or strong.
Alice is not old.
Someone is either not happy or rich.
Someone is not creative.
Mary is calm. | Mary is not strong. | entailment | ((?[X]:((~wise(X)&~tall(X))))=>(tall(paul)))&
((~rich(susan))<=>(?[X]:((~creative(X)|~kind(X)))))&
(((brave(susan)|tall(susan)))<=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(kind(X)=>(brave(X)<~>tall(X))))&
(![X]:((patient(X)<~>~strong(X))<=>happy(X)))&
((~generous(susan))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((happy(X)<~>wise(X))=>(tall(X)&~calm(X))))&
(![X]:((rich(X)<~>~brave(X))=>quiet(X)))&
(![X]:((wise(X)|strong(X))<=>(calm(X)&~patient(X))))&
(((calm(fred)&strong(fred)))<=>((humble(susan)<~>kind(susan))))&
((?[X]:((~tall(X)|rich(X))))=>((~patient(mary)<~>~calm(mary))))&
(![X]:(old(X)<=>(~creative(X)<~>curious(X))))&
((?[X]:((generous(X)|quiet(X))))<=>((humble(john)|~happy(john))))&
(![X]:(~happy(X)=>(wise(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(generous(X)&~tall(X))))&
(![X]:(generous(X)=>(tall(X)<~>~quiet(X))))&
(?[X]:((~old(X)|curious(X))))&
(curious(john))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(~old(alice))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
(calm(mary)) | ~strong(mary) | [
"p4",
"p6",
"p8",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1772121448994735429940262
% SZS output start Proof for 1772121448994735429940262
5. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> happy(X0)) [input p4]
7. ! [X0] : ((happy(X0) <~> wise(X0)) => (~calm(X0) & tall(X0))) [input p6]
9. ! [X0] : ((strong(X0) | wise(X0)) <=> (~patient(X0) & calm(X0))) [input p8]
14. ! [X0] : (~happy(X0) => (wise(X0) <~> ~strong(X0))) [input p13]
24. calm(mary) [input p23]
25. strong(mary) [input hypothesis]
30. ! [X0] : ((~calm(X0) & tall(X0)) | (happy(X0) <=> wise(X0))) [ennf transformation 7]
34. ! [X0] : ((wise(X0) <~> ~strong(X0)) | happy(X0)) [ennf transformation 14]
47. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~happy(X0)) & (happy(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 5]
50. ! [X0] : ((~calm(X0) & tall(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0)))) [nnf transformation 30]
52. ! [X0] : (((strong(X0) | wise(X0)) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | (~strong(X0) & ~wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((strong(X0) | wise(X0) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | (~strong(X0) & ~wise(X0)))) [flattening 52]
63. ! [X0] : (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | happy(X0)) [nnf transformation 34]
92. ~happy(X0) | patient(X0) | ~strong(X0) [cnf transformation 47]
99. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 50]
105. ~strong(X0) | ~patient(X0) [cnf transformation 53]
123. ~strong(X0) | wise(X0) | happy(X0) [cnf transformation 63]
141. calm(mary) [cnf transformation 24]
142. strong(mary) [cnf transformation 25]
238. 21 <=> patient(mary) [avatar definition]
242. 22 <=> calm(mary) [avatar definition]
244. calm(mary) <- (22) [avatar component clause 242]
317. 22 [avatar split clause 141,242]
319. ~patient(mary) [resolution 105,142]
385. 46 <=> happy(mary) [avatar definition]
386. happy(mary) <- (46) [avatar component clause 385]
389. 47 <=> wise(mary) [avatar definition]
393. happy(mary) | ~wise(mary) <- (22) [resolution 99,244]
449. wise(mary) | happy(mary) [resolution 123,142]
460. ~47 | 46 | ~22 [avatar split clause 393,242,385,389]
461. 46 | 47 [avatar split clause 449,389,385]
506. patient(mary) | ~strong(mary) <- (46) [resolution 386,92]
510. patient(mary) <- (46) [subsumption resolution 506,142]
511. 21 | ~46 [avatar split clause 510,385,238]
512. ~21 [avatar split clause 319,238]
513. $false [avatar sat refutation 317,460,461,511,512]
% SZS output end Proof for 1772121448994735429940262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either quiet or not quiet and vice versa.
If susan is not humble then alice is either patient or tall.
Everyone who is old is both not kind and not rich.
Everyone who is both generous and not happy is either funny or not calm.
If someone is old then someone is not patient or funny.
If susan is either not rich or not quiet then fred is not kind.
If someone is brave then someone is both not kind and not funny and vice versa.
Everyone who is not creative is kind.
Everyone who is patient or not rich is either not curious or brave.
If paul is both not patient and calm then mary is old.
If susan is both not quiet and not wise then someone is both calm and old.
If someone is quiet or kind then someone is either not strong or not quiet.
Everyone who is strong or not strong is not old and vice versa.
Everyone who is not strong or strong is curious or tall.
Everyone who is either not wise or curious is either generous or not funny and vice versa.
Everyone who is happy is both not creative and not happy and vice versa.
Susan is not curious.
Someone is kind.
Lucy is either not strong or not happy.
Paul is not quiet or not rich.
Fred is old or not tall.
Someone is tall.
Alice is both not curious and not quiet. | Alice is patient. | neutral | (![X]:(~funny(X)<=>(quiet(X)<~>~quiet(X))))&
((~humble(susan))=>((patient(alice)<~>tall(alice))))&
(![X]:(old(X)=>(~kind(X)&~rich(X))))&
(![X]:((generous(X)&~happy(X))=>(funny(X)<~>~calm(X))))&
((?[X]:(old(X)))=>(?[X]:((~patient(X)|funny(X)))))&
(((~rich(susan)<~>~quiet(susan)))=>(~kind(fred)))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:(~creative(X)=>kind(X)))&
(![X]:((patient(X)|~rich(X))=>(~curious(X)<~>brave(X))))&
(((~patient(paul)&calm(paul)))=>(old(mary)))&
(((~quiet(susan)&~wise(susan)))=>(?[X]:((calm(X)&old(X)))))&
((?[X]:((quiet(X)|kind(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((strong(X)|~strong(X))<=>~old(X)))&
(![X]:((~strong(X)|strong(X))=>(curious(X)|tall(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(generous(X)<~>~funny(X))))&
(![X]:(happy(X)<=>(~creative(X)&~happy(X))))&
(~curious(susan))&
(?[X]:(kind(X)))&
((~strong(lucy)<~>~happy(lucy)))&
((~quiet(paul)|~rich(paul)))&
((old(fred)|~tall(fred)))&
(?[X]:(tall(X)))&
((~curious(alice)&~quiet(alice))) | patient(alice) | [] | null | 0 |
Everyone who is both rich and creative is both calm and not calm.
Everyone who is brave or not rich is both creative and not wise and vice versa.
If someone is humble then susan is either not rich or patient.
Everyone who is both not tall and not funny is brave or patient.
Everyone who is either not happy or happy is not generous or tall and vice versa.
Everyone who is both creative and kind is not quiet or quiet.
Everyone who is tall or old is not wise or funny and vice versa.
If mary is not happy then someone is either calm or patient and vice versa.
Everyone who is not strong is strong.
Everyone who is both rich and not funny is not wise or not calm and vice versa.
Everyone who is either wise or calm is generous or humble.
Everyone who is old or not humble is happy or tall.
Everyone who is patient is either old or not wise and vice versa.
If alice is both old and tall then fred is not calm or not humble and vice versa.
If susan is either creative or not old then mary is not curious.
Everyone who is both not generous and not wise is both not tall and rich and vice versa.
Someone is either not strong or patient.
Someone is either not tall or not kind.
Someone is wise.
Someone is not generous or not strong.
Someone is strong or brave.
Susan is both tall and not wise.
Fred is either not kind or not rich.
Susan is both not humble and kind. | Mary is not patient. | neutral | (![X]:((rich(X)&creative(X))=>(calm(X)&~calm(X))))&
(![X]:((brave(X)|~rich(X))<=>(creative(X)&~wise(X))))&
((?[X]:(humble(X)))=>((~rich(susan)<~>patient(susan))))&
(![X]:((~tall(X)&~funny(X))=>(brave(X)|patient(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~generous(X)|tall(X))))&
(![X]:((creative(X)&kind(X))=>(~quiet(X)|quiet(X))))&
(![X]:((tall(X)|old(X))<=>(~wise(X)|funny(X))))&
((~happy(mary))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:(~strong(X)=>strong(X)))&
(![X]:((rich(X)&~funny(X))<=>(~wise(X)|~calm(X))))&
(![X]:((wise(X)<~>calm(X))=>(generous(X)|humble(X))))&
(![X]:((old(X)|~humble(X))=>(happy(X)|tall(X))))&
(![X]:(patient(X)<=>(old(X)<~>~wise(X))))&
(((old(alice)&tall(alice)))<=>((~calm(fred)|~humble(fred))))&
(((creative(susan)<~>~old(susan)))=>(~curious(mary)))&
(![X]:((~generous(X)&~wise(X))<=>(~tall(X)&rich(X))))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((strong(X)|brave(X))))&
((tall(susan)&~wise(susan)))&
((~kind(fred)<~>~rich(fred)))&
((~humble(susan)&kind(susan))) | ~patient(mary) | [] | null | 0 |
Everyone who is both not creative and not funny is kind and vice versa. Everyone who is both patient and curious is not tall. Everyone who is brave or humble is not strong and vice versa. If susan is both not humble and brave then someone is both happy and not generous and vice versa. Everyone who is both quiet and not quiet is not old or not calm and vice versa. If susan is calm then fred is kind and vice versa. Everyone who is wise or not curious is either strong or quiet. Everyone who is not brave or kind is generous. If mary is either not generous or creative then paul is patient. Everyone who is kind is not strong and vice versa. If someone is not brave then lucy is quiet or not creative and vice versa. Everyone who is happy is not old. Everyone who is both old and kind is kind. Everyone who is funny is not humble. Everyone who is both not calm and tall is not wise or not old and vice versa. If someone is both not tall and not rich then someone is either not calm or generous. Someone is not strong or not wise. Someone is both not curious and not tall. Someone is either not happy or not quiet. Someone is either patient or rich. Someone is either generous or quiet. Mary is both not patient and rich. | Susan is patient. | neutral | (![X]:((~creative(X)&~funny(X))<=>kind(X)))&
(![X]:((patient(X)&curious(X))=>~tall(X)))&
(![X]:((brave(X)|humble(X))<=>~strong(X)))&
(((~humble(susan)&brave(susan)))<=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((quiet(X)&~quiet(X))<=>(~old(X)|~calm(X))))&
((calm(susan))<=>(kind(fred)))&
(![X]:((wise(X)|~curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:((~brave(X)|kind(X))=>generous(X)))&
(((~generous(mary)<~>creative(mary)))=>(patient(paul)))&
(![X]:(kind(X)<=>~strong(X)))&
((?[X]:(~brave(X)))<=>((quiet(lucy)|~creative(lucy))))&
(![X]:(happy(X)=>~old(X)))&
(![X]:((old(X)&kind(X))=>kind(X)))&
(![X]:(funny(X)=>~humble(X)))&
(![X]:((~calm(X)&tall(X))<=>(~wise(X)|~old(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((~calm(X)<~>generous(X)))))&
(?[X]:((~strong(X)|~wise(X))))&
(?[X]:((~curious(X)&~tall(X))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:((generous(X)<~>quiet(X))))&
((~patient(mary)&rich(mary))) | patient(susan) | [] | null | 0 |
Everyone who is both humble and not humble is either kind or not funny and vice versa. Everyone who is either not generous or not calm is not kind or creative and vice versa. Everyone who is either not creative or not old is happy or patient. If someone is both wise and not patient then john is either not strong or rich and vice versa. If lucy is not curious or funny then someone is either not old or patient and vice versa. If susan is kind or not patient then someone is quiet or not calm. If someone is not quiet or brave then someone is not patient. If fred is not funny then someone is not brave or not kind and vice versa. Everyone who is not kind or patient is not old and vice versa. If someone is not generous then someone is not funny or not old and vice versa. If susan is quiet then alice is either not patient or happy and vice versa. Everyone who is either old or strong is either patient or not calm and vice versa. Everyone who is creative or old is both calm and not old. Everyone who is rich or generous is either not patient or patient and vice versa. Everyone who is both not generous and patient is both curious and not calm. Everyone who is both kind and not funny is not happy or not generous and vice versa. John is both not patient and not calm. Paul is humble. Someone is either not kind or not generous. Someone is either rich or not funny. Paul is not creative or creative. Fred is brave or not humble. Someone is both not quiet and not happy. Someone is not calm or not brave. | John is funny. | entailment | (![X]:((humble(X)&~humble(X))<=>(kind(X)<~>~funny(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~kind(X)|creative(X))))&
(![X]:((~creative(X)<~>~old(X))=>(happy(X)|patient(X))))&
((?[X]:((wise(X)&~patient(X))))<=>((~strong(john)<~>rich(john))))&
(((~curious(lucy)|funny(lucy)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((kind(susan)|~patient(susan)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:((~quiet(X)|brave(X))))=>(?[X]:(~patient(X))))&
((~funny(fred))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~kind(X)|patient(X))<=>~old(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~funny(X)|~old(X)))))&
((quiet(susan))<=>((~patient(alice)<~>happy(alice))))&
(![X]:((old(X)<~>strong(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((creative(X)|old(X))=>(calm(X)&~old(X))))&
(![X]:((rich(X)|generous(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((~generous(X)&patient(X))=>(curious(X)&~calm(X))))&
(![X]:((kind(X)&~funny(X))<=>(~happy(X)|~generous(X))))&
((~patient(john)&~calm(john)))&
(humble(paul))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((rich(X)<~>~funny(X))))&
((~creative(paul)|creative(paul)))&
((brave(fred)|~humble(fred)))&
(?[X]:((~quiet(X)&~happy(X))))&
(?[X]:((~calm(X)|~brave(X)))) | funny(john) | [
"p0",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 947297460101840437648680
% SZS output start Proof for 947297460101840437648680
1. ! [X0] : ((~humble(X0) & humble(X0)) <=> (kind(X0) <~> ~funny(X0))) [input p0]
9. ! [X0] : ((patient(X0) | ~kind(X0)) <=> ~old(X0)) [input p8]
13. ! [X0] : ((old(X0) | creative(X0)) => (~old(X0) & calm(X0))) [input p12]
17. ~calm(john) & ~patient(john) [input p16]
25. ~funny(john) [input hypothesis]
32. ! [X0] : ((~old(X0) & calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 13]
35. ! [X0] : (((~humble(X0) & humble(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (humble(X0) | ~humble(X0)))) [nnf transformation 1]
36. ! [X0] : (((~humble(X0) & humble(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | humble(X0) | ~humble(X0))) [flattening 35]
58. ! [X0] : (((patient(X0) | ~kind(X0)) | old(X0)) & (~old(X0) | (~patient(X0) & kind(X0)))) [nnf transformation 9]
59. ! [X0] : ((patient(X0) | ~kind(X0) | old(X0)) & (~old(X0) | (~patient(X0) & kind(X0)))) [flattening 58]
84. humble(X0) | kind(X0) | funny(X0) [cnf transformation 36]
86. ~humble(X0) | kind(X0) | funny(X0) [cnf transformation 36]
116. ~kind(X0) | patient(X0) | old(X0) [cnf transformation 59]
135. ~old(X0) | ~old(X0) [cnf transformation 32]
149. ~patient(john) [cnf transformation 17]
161. ~funny(john) [cnf transformation 25]
164. ~old(X0) [duplicate literal removal 135]
165. funny(X0) | kind(X0) [subsumption resolution 84,86]
355. kind(john) [resolution 165,161]
367. patient(john) | old(john) [resolution 116,355]
372. old(john) [subsumption resolution 367,149]
373. $false [subsumption resolution 372,164]
% SZS output end Proof for 947297460101840437648680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or funny then mary is not quiet or not kind and vice versa.
Everyone who is either funny or not kind is not old or funny and vice versa.
Everyone who is either not tall or not old is not curious.
If susan is generous or not tall then lucy is both quiet and not tall.
If susan is not rich then alice is not rich or not curious and vice versa.
Everyone who is not strong is not old.
Everyone who is not quiet is both patient and not patient and vice versa.
Everyone who is either not kind or not generous is both not old and happy and vice versa.
If john is both not creative and not strong then mary is not wise.
If paul is not happy then someone is strong or creative.
Everyone who is either not wise or not generous is quiet or curious.
If someone is either humble or patient then mary is funny.
Everyone who is either tall or generous is not happy.
If fred is funny then lucy is either not old or not happy.
Everyone who is not patient or not rich is either happy or not tall.
Everyone who is either not funny or not old is not happy or not wise and vice versa.
Fred is not creative or brave.
Someone is either not generous or funny.
Paul is either not happy or not wise.
Someone is strong.
Lucy is both quiet and old.
Someone is not wise. | Mary is not strong. | neutral | ((?[X]:((~happy(X)<~>funny(X))))<=>((~quiet(mary)|~kind(mary))))&
(![X]:((funny(X)<~>~kind(X))<=>(~old(X)|funny(X))))&
(![X]:((~tall(X)<~>~old(X))=>~curious(X)))&
(((generous(susan)|~tall(susan)))=>((quiet(lucy)&~tall(lucy))))&
((~rich(susan))<=>((~rich(alice)|~curious(alice))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:(~quiet(X)<=>(patient(X)&~patient(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~old(X)&happy(X))))&
(((~creative(john)&~strong(john)))=>(~wise(mary)))&
((~happy(paul))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(quiet(X)|curious(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(funny(mary)))&
(![X]:((tall(X)<~>generous(X))=>~happy(X)))&
((funny(fred))=>((~old(lucy)<~>~happy(lucy))))&
(![X]:((~patient(X)|~rich(X))=>(happy(X)<~>~tall(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(~happy(X)|~wise(X))))&
((~creative(fred)|brave(fred)))&
(?[X]:((~generous(X)<~>funny(X))))&
((~happy(paul)<~>~wise(paul)))&
(?[X]:(strong(X)))&
((quiet(lucy)&old(lucy)))&
(?[X]:(~wise(X))) | ~strong(mary) | [] | null | 0 |
Everyone who is quiet is either not kind or humble. Everyone who is not funny is both not rich and curious. Everyone who is both happy and not creative is not happy and vice versa. If someone is either not old or creative then someone is both old and not old. Everyone who is both creative and funny is curious. Everyone who is either tall or not curious is both generous and not strong and vice versa. If lucy is not curious or not strong then john is both old and not tall. If someone is not humble or not funny then alice is either old or kind. If someone is both not generous and not funny then lucy is not brave or not humble and vice versa. If fred is not patient or funny then someone is both not funny and not brave. If alice is both not creative and not rich then paul is not patient or not brave and vice versa. If fred is both kind and not curious then john is humble or calm. Everyone who is both strong and not happy is both quiet and funny and vice versa. Everyone who is not patient or quiet is quiet or happy. Everyone who is not patient is not curious. Mary is both happy and not kind. Someone is either humble or not calm. Someone is quiet or brave. Someone is either curious or strong. | John is not curious. | contradiction | (![X]:(quiet(X)=>(~kind(X)<~>humble(X))))&
(![X]:(~funny(X)=>(~rich(X)&curious(X))))&
(![X]:((happy(X)&~creative(X))<=>~happy(X)))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((creative(X)&funny(X))=>curious(X)))&
(![X]:((tall(X)<~>~curious(X))<=>(generous(X)&~strong(X))))&
(((~curious(lucy)|~strong(lucy)))=>((old(john)&~tall(john))))&
((?[X]:((~humble(X)|~funny(X))))=>((old(alice)<~>kind(alice))))&
((?[X]:((~generous(X)&~funny(X))))<=>((~brave(lucy)|~humble(lucy))))&
(((~patient(fred)|funny(fred)))=>(?[X]:((~funny(X)&~brave(X)))))&
(((~creative(alice)&~rich(alice)))<=>((~patient(paul)|~brave(paul))))&
(((kind(fred)&~curious(fred)))=>((humble(john)|calm(john))))&
(![X]:((strong(X)&~happy(X))<=>(quiet(X)&funny(X))))&
(![X]:((~patient(X)|quiet(X))=>(quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
((happy(mary)&~kind(mary)))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((curious(X)<~>strong(X)))) | ~curious(john) | [
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3021279097854782180504511
% SZS output start Proof for 3021279097854782180504511
2. ! [X0] : (~funny(X0) => (curious(X0) & ~rich(X0))) [input p1]
3. ! [X0] : ((~creative(X0) & happy(X0)) <=> ~happy(X0)) [input p2]
5. ! [X0] : ((funny(X0) & creative(X0)) => curious(X0)) [input p4]
20. ~curious(john) [input hypothesis]
23. ! [X0] : ((curious(X0) & ~rich(X0)) | funny(X0)) [ennf transformation 2]
25. ! [X0] : (curious(X0) | (~funny(X0) | ~creative(X0))) [ennf transformation 5]
26. ! [X0] : (curious(X0) | ~funny(X0) | ~creative(X0)) [flattening 25]
36. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | (creative(X0) | ~happy(X0)))) [nnf transformation 3]
37. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | creative(X0) | ~happy(X0))) [flattening 36]
67. curious(X0) | funny(X0) [cnf transformation 23]
68. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 37]
69. happy(X0) | happy(X0) [cnf transformation 37]
75. curious(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 26]
119. ~curious(john) [cnf transformation 20]
120. ~happy(X0) | creative(X0) [duplicate literal removal 68]
121. happy(X0) [duplicate literal removal 69]
122. creative(X0) [subsumption resolution 120,121]
134. curious(X0) | ~funny(X0) [subsumption resolution 75,122]
135. curious(X0) [subsumption resolution 134,67]
255. $false [subsumption resolution 119,135]
% SZS output end Proof for 3021279097854782180504511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or quiet then someone is not patient or calm and vice versa.
If someone is quiet or not happy then lucy is either wise or kind.
If someone is not wise then someone is not funny or not strong.
If fred is either creative or rich then lucy is both not wise and not generous.
If paul is not patient or rich then someone is both patient and not generous and vice versa.
If paul is not generous or creative then someone is not brave or not creative.
Everyone who is not calm is either generous or curious and vice versa.
Everyone who is both kind and not patient is happy or not humble.
Everyone who is not patient is wise or not funny.
Everyone who is either not strong or rich is not curious.
If someone is either humble or happy then lucy is patient and vice versa.
If susan is either generous or rich then susan is creative or humble and vice versa.
Everyone who is either not curious or not calm is creative.
If lucy is not strong or not wise then paul is both happy and humble.
Everyone who is not strong or not brave is either tall or not quiet.
If mary is either kind or not funny then paul is not calm and vice versa.
Alice is not curious or not humble.
Alice is rich or happy.
Susan is not calm or not wise.
John is either not patient or wise.
Mary is not humble.
Someone is either not generous or not calm.
Paul is quiet.
Someone is brave. | Paul is quiet. | entailment | ((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((quiet(X)|~happy(X))))=>((wise(lucy)<~>kind(lucy))))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)|~strong(X)))))&
(((creative(fred)<~>rich(fred)))=>((~wise(lucy)&~generous(lucy))))&
(((~patient(paul)|rich(paul)))<=>(?[X]:((patient(X)&~generous(X)))))&
(((~generous(paul)|creative(paul)))=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:(~calm(X)<=>(generous(X)<~>curious(X))))&
(![X]:((kind(X)&~patient(X))=>(happy(X)|~humble(X))))&
(![X]:(~patient(X)=>(wise(X)|~funny(X))))&
(![X]:((~strong(X)<~>rich(X))=>~curious(X)))&
((?[X]:((humble(X)<~>happy(X))))<=>(patient(lucy)))&
(((generous(susan)<~>rich(susan)))<=>((creative(susan)|humble(susan))))&
(![X]:((~curious(X)<~>~calm(X))=>creative(X)))&
(((~strong(lucy)|~wise(lucy)))=>((happy(paul)&humble(paul))))&
(![X]:((~strong(X)|~brave(X))=>(tall(X)<~>~quiet(X))))&
(((kind(mary)<~>~funny(mary)))<=>(~calm(paul)))&
((~curious(alice)|~humble(alice)))&
((rich(alice)|happy(alice)))&
((~calm(susan)|~wise(susan)))&
((~patient(john)<~>wise(john)))&
(~humble(mary))&
(?[X]:((~generous(X)<~>~calm(X))))&
(quiet(paul))&
(?[X]:(brave(X))) | quiet(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8919671863514429758321426
% SZS output start Proof for 8919671863514429758321426
23. quiet(paul) [input p22]
25. ~quiet(paul) [input hypothesis]
134. quiet(paul) [cnf transformation 23]
136. ~quiet(paul) [cnf transformation 25]
377. $false [subsumption resolution 136,134]
% SZS output end Proof for 8919671863514429758321426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is not humble and vice versa. Everyone who is not kind or not generous is happy and vice versa. If lucy is both not old and creative then john is both not generous and not patient and vice versa. If alice is humble or old then lucy is patient and vice versa. If someone is both not old and happy then someone is not generous or not kind. If someone is either brave or rich then someone is not creative or happy and vice versa. If lucy is brave then mary is not old or not quiet and vice versa. Everyone who is happy or not calm is not wise or funny. If susan is wise or humble then susan is either wise or not rich. Everyone who is both funny and happy is both not funny and happy and vice versa. Everyone who is happy is either not wise or calm and vice versa. If someone is not rich or patient then lucy is quiet or wise and vice versa. Everyone who is both curious and kind is either not generous or curious. Everyone who is either funny or brave is both not tall and not happy. If someone is either generous or funny then alice is not generous and vice versa. If paul is not creative then mary is not curious or generous. Mary is either old or not curious. Someone is either calm or not old. Mary is not curious or funny. Someone is either creative or not happy. Lucy is not creative or old. Someone is either not quiet or kind. Fred is both not quiet and generous. | Lucy is curious. | neutral | ((?[X]:((creative(X)|quiet(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)|~generous(X))<=>happy(X)))&
(((~old(lucy)&creative(lucy)))<=>((~generous(john)&~patient(john))))&
(((humble(alice)|old(alice)))<=>(patient(lucy)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((~generous(X)|~kind(X)))))&
((?[X]:((brave(X)<~>rich(X))))<=>(?[X]:((~creative(X)|happy(X)))))&
((brave(lucy))<=>((~old(mary)|~quiet(mary))))&
(![X]:((happy(X)|~calm(X))=>(~wise(X)|funny(X))))&
(((wise(susan)|humble(susan)))=>((wise(susan)<~>~rich(susan))))&
(![X]:((funny(X)&happy(X))<=>(~funny(X)&happy(X))))&
(![X]:(happy(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((quiet(lucy)|wise(lucy))))&
(![X]:((curious(X)&kind(X))=>(~generous(X)<~>curious(X))))&
(![X]:((funny(X)<~>brave(X))=>(~tall(X)&~happy(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>(~generous(alice)))&
((~creative(paul))=>((~curious(mary)|generous(mary))))&
((old(mary)<~>~curious(mary)))&
(?[X]:((calm(X)<~>~old(X))))&
((~curious(mary)|funny(mary)))&
(?[X]:((creative(X)<~>~happy(X))))&
((~creative(lucy)|old(lucy)))&
(?[X]:((~quiet(X)<~>kind(X))))&
((~quiet(fred)&generous(fred))) | curious(lucy) | [] | null | 0 |
If lucy is wise or happy then paul is both patient and humble.
Everyone who is both not creative and brave is quiet or wise.
Everyone who is either old or not kind is both patient and humble and vice versa.
Everyone who is not calm or strong is not quiet and vice versa.
If someone is old then alice is either wise or not calm and vice versa.
Everyone who is patient is both brave and not generous and vice versa.
Everyone who is either old or funny is funny or not wise.
If paul is either brave or not funny then john is both strong and not strong.
If lucy is both patient and not strong then someone is either not rich or not humble and vice versa.
Everyone who is not patient or patient is both humble and patient.
Everyone who is both not curious and not strong is kind or not funny.
Everyone who is both not curious and not wise is brave or not happy and vice versa.
Everyone who is not quiet is either curious or generous.
If someone is not creative then paul is either not quiet or not tall and vice versa.
Everyone who is funny or not strong is both patient and brave.
If mary is not old then someone is kind or quiet and vice versa.
Someone is either not tall or not quiet.
Someone is either not generous or not rich.
Mary is old or happy.
Someone is quiet.
Someone is not quiet or not rich. | Alice is tall. | neutral | (((wise(lucy)|happy(lucy)))=>((patient(paul)&humble(paul))))&
(![X]:((~creative(X)&brave(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)|strong(X))<=>~quiet(X)))&
((?[X]:(old(X)))<=>((wise(alice)<~>~calm(alice))))&
(![X]:(patient(X)<=>(brave(X)&~generous(X))))&
(![X]:((old(X)<~>funny(X))=>(funny(X)|~wise(X))))&
(((brave(paul)<~>~funny(paul)))=>((strong(john)&~strong(john))))&
(((patient(lucy)&~strong(lucy)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~patient(X)|patient(X))=>(humble(X)&patient(X))))&
(![X]:((~curious(X)&~strong(X))=>(kind(X)|~funny(X))))&
(![X]:((~curious(X)&~wise(X))<=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~generous(X)<~>~rich(X))))&
((old(mary)|happy(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)|~rich(X)))) | tall(alice) | [] | null | 0 |
If someone is both humble and generous then mary is both brave and not quiet and vice versa. Everyone who is not strong is not wise and vice versa. Everyone who is not quiet or not happy is both creative and not funny. If someone is both quiet and not patient then fred is not humble. Everyone who is both creative and tall is not kind or not happy and vice versa. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. If susan is both curious and generous then someone is curious and vice versa. Everyone who is both generous and not humble is not strong and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Everyone who is either strong or creative is both generous and curious. If someone is either not wise or not rich then someone is rich or not funny. Someone is not happy. Someone is not quiet or not old. Mary is either not patient or not wise. Someone is not funny or kind. Alice is strong. | Lucy is kind. | entailment | ((?[X]:((humble(X)&generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)|~old(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(strong(alice)) | kind(lucy) | [
"p1",
"p4",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8813586630915487169267132
% SZS output start Proof for 8813586630915487169267132
2. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p1]
5. ! [X0] : ((tall(X0) & creative(X0)) <=> (~happy(X0) | ~kind(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p5]
9. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p8]
11. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p10]
20. ~kind(lucy) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 6]
32. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 2]
33. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 5]
34. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 33]
42. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 9]
43. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 42]
49. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 11]
50. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 49]
69. ~wise(X0) | strong(X0) [cnf transformation 32]
70. ~strong(X0) | wise(X0) [cnf transformation 32]
79. kind(X0) | tall(X0) [cnf transformation 34]
83. ~generous(X0) | wise(X0) [cnf transformation 24]
98. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 43]
107. strong(X0) | generous(X0) [cnf transformation 50]
127. ~kind(lucy) [cnf transformation 20]
189. ~strong(X0) | kind(X0) [subsumption resolution 98,79]
265. generous(X0) | wise(X0) [resolution 107,70]
266. wise(X0) [subsumption resolution 265,83]
267. strong(X0) [resolution 266,69]
271. kind(X0) [resolution 189,267]
279. $false [resolution 271,127]
% SZS output end Proof for 8813586630915487169267132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is rich or calm and vice versa.
If mary is both quiet and not tall then someone is kind and vice versa.
Everyone who is creative is not tall or not rich and vice versa.
If mary is quiet or funny then john is creative.
If fred is curious or not kind then someone is both not old and kind.
If someone is calm or generous then alice is either rich or not brave and vice versa.
Everyone who is both quiet and not happy is both kind and not rich and vice versa.
Everyone who is both not patient and not calm is not calm or funny and vice versa.
Everyone who is both calm and not old is both humble and tall.
Everyone who is either not calm or not rich is both happy and not tall and vice versa.
Everyone who is humble is not curious or old.
If alice is not humble then someone is quiet.
Everyone who is both not curious and not humble is not old.
If fred is humble or kind then susan is either wise or not calm.
If someone is either not generous or not strong then mary is either creative or not calm.
If lucy is patient then paul is old or not patient.
Paul is either not happy or brave.
Lucy is not patient.
Someone is not tall or not calm.
Paul is not generous.
Someone is not wise.
Susan is both humble and not wise. | Fred is not wise. | neutral | (![X]:(funny(X)<=>(rich(X)|calm(X))))&
(((quiet(mary)&~tall(mary)))<=>(?[X]:(kind(X))))&
(![X]:(creative(X)<=>(~tall(X)|~rich(X))))&
(((quiet(mary)|funny(mary)))=>(creative(john)))&
(((curious(fred)|~kind(fred)))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:((calm(X)|generous(X))))<=>((rich(alice)<~>~brave(alice))))&
(![X]:((quiet(X)&~happy(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)&~calm(X))<=>(~calm(X)|funny(X))))&
(![X]:((calm(X)&~old(X))=>(humble(X)&tall(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>(happy(X)&~tall(X))))&
(![X]:(humble(X)=>(~curious(X)|old(X))))&
((~humble(alice))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&~humble(X))=>~old(X)))&
(((humble(fred)|kind(fred)))=>((wise(susan)<~>~calm(susan))))&
((?[X]:((~generous(X)<~>~strong(X))))=>((creative(mary)<~>~calm(mary))))&
((patient(lucy))=>((old(paul)|~patient(paul))))&
((~happy(paul)<~>brave(paul)))&
(~patient(lucy))&
(?[X]:((~tall(X)|~calm(X))))&
(~generous(paul))&
(?[X]:(~wise(X)))&
((humble(susan)&~wise(susan))) | ~wise(fred) | [] | null | 0 |
If paul is not wise or not rich then susan is not tall or funny and vice versa.
Everyone who is either rich or not creative is both not tall and kind and vice versa.
Everyone who is both tall and generous is curious.
If someone is either not calm or strong then someone is not patient and vice versa.
If someone is not patient or not happy then susan is not humble or funny and vice versa.
Everyone who is both not strong and not old is rich.
Everyone who is both strong and creative is both brave and not tall and vice versa.
Everyone who is not curious is not curious or not rich and vice versa.
If someone is either kind or not funny then someone is either wise or kind and vice versa.
Everyone who is creative is not happy or not strong and vice versa.
Everyone who is not rich is either not brave or tall.
Everyone who is either not calm or strong is patient and vice versa.
Everyone who is patient or strong is not quiet.
If someone is both not calm and tall then paul is both kind and curious.
If john is not creative then someone is either strong or not quiet.
If someone is both happy and not quiet then someone is not creative or not happy.
Mary is both not old and not happy.
Someone is both tall and old.
Someone is not creative.
Fred is both not curious and not strong.
Someone is generous or curious.
Someone is both not calm and funny.
Someone is kind or creative.
Someone is both not brave and not wise. | John is not curious. | neutral | (((~wise(paul)|~rich(paul)))<=>((~tall(susan)|funny(susan))))&
(![X]:((rich(X)<~>~creative(X))<=>(~tall(X)&kind(X))))&
(![X]:((tall(X)&generous(X))=>curious(X)))&
((?[X]:((~calm(X)<~>strong(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((~patient(X)|~happy(X))))<=>((~humble(susan)|funny(susan))))&
(![X]:((~strong(X)&~old(X))=>rich(X)))&
(![X]:((strong(X)&creative(X))<=>(brave(X)&~tall(X))))&
(![X]:(~curious(X)<=>(~curious(X)|~rich(X))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~strong(X))))&
(![X]:(~rich(X)=>(~brave(X)<~>tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>patient(X)))&
(![X]:((patient(X)|strong(X))=>~quiet(X)))&
((?[X]:((~calm(X)&tall(X))))=>((kind(paul)&curious(paul))))&
((~creative(john))=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~creative(X)|~happy(X)))))&
((~old(mary)&~happy(mary)))&
(?[X]:((tall(X)&old(X))))&
(?[X]:(~creative(X)))&
((~curious(fred)&~strong(fred)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~brave(X)&~wise(X)))) | ~curious(john) | [] | null | 0 |
Everyone who is either not strong or wise is patient and vice versa. Everyone who is creative or not old is funny. If alice is either tall or not generous then someone is not strong or generous and vice versa. Everyone who is not quiet is both not curious and brave and vice versa. If alice is strong then fred is not calm or not kind and vice versa. If fred is both not wise and curious then susan is both not brave and not happy and vice versa. If john is not calm then someone is either curious or rich. Everyone who is wise or not quiet is both not rich and creative. If someone is both calm and patient then alice is not happy or quiet. If susan is not brave or humble then alice is not happy or not generous and vice versa. Everyone who is either humble or quiet is either not patient or curious and vice versa. Everyone who is both not patient and not brave is not curious or not tall and vice versa. Everyone who is either not happy or humble is not rich and vice versa. Everyone who is strong is not curious and vice versa. Everyone who is either old or strong is either not funny or patient and vice versa. Everyone who is both rich and kind is both not quiet and brave. Someone is not old or creative. Someone is both strong and not happy. Someone is either not strong or humble. Someone is either not kind or brave. John is creative. Susan is humble or not wise. Mary is either not curious or brave. John is both creative and patient. | Alice is funny. | entailment | (![X]:((~strong(X)<~>wise(X))<=>patient(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
(((tall(alice)<~>~generous(alice)))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(~quiet(X)<=>(~curious(X)&brave(X))))&
((strong(alice))<=>((~calm(fred)|~kind(fred))))&
(((~wise(fred)&curious(fred)))<=>((~brave(susan)&~happy(susan))))&
((~calm(john))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&creative(X))))&
((?[X]:((calm(X)&patient(X))))=>((~happy(alice)|quiet(alice))))&
(((~brave(susan)|humble(susan)))<=>((~happy(alice)|~generous(alice))))&
(![X]:((humble(X)<~>quiet(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~rich(X)))&
(![X]:(strong(X)<=>~curious(X)))&
(![X]:((old(X)<~>strong(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((rich(X)&kind(X))=>(~quiet(X)&brave(X))))&
(?[X]:((~old(X)|creative(X))))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(creative(john))&
((humble(susan)|~wise(susan)))&
((~curious(mary)<~>brave(mary)))&
((creative(john)&patient(john))) | funny(alice) | [
"p0",
"p1",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1477427730331876646165937
% SZS output start Proof for 1477427730331876646165937
1. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : ((~old(X0) | creative(X0)) => funny(X0)) [input p1]
8. ! [X0] : ((~quiet(X0) | wise(X0)) => (creative(X0) & ~rich(X0))) [input p7]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~tall(X0) | ~curious(X0))) [input p11]
14. ! [X0] : (strong(X0) <=> ~curious(X0)) [input p13]
15. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p14]
25. ~funny(alice) [input hypothesis]
26. ! [X0] : (funny(X0) | (old(X0) & ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((creative(X0) & ~rich(X0)) | (quiet(X0) & ~wise(X0))) [ennf transformation 8]
33. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0)) & (patient(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 1]
50. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | brave(X0) | patient(X0))) [flattening 50]
53. ! [X0] : ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))) [nnf transformation 14]
54. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 15]
66. patient(X0) | wise(X0) | strong(X0) [cnf transformation 33]
70. ~creative(X0) | funny(X0) [cnf transformation 26]
71. funny(X0) | old(X0) [cnf transformation 26]
92. ~wise(X0) | creative(X0) [cnf transformation 28]
108. ~patient(X0) | curious(X0) [cnf transformation 51]
116. ~curious(X0) | ~strong(X0) [cnf transformation 53]
120. ~patient(X0) | funny(X0) | strong(X0) | ~old(X0) [cnf transformation 54]
124. ~strong(X0) | ~old(X0) | patient(X0) | funny(X0) [cnf transformation 54]
141. ~funny(alice) [cnf transformation 25]
175. 8 <=> strong(alice) [avatar definition]
176. ~strong(alice) <- (~8) [avatar component clause 175]
177. strong(alice) <- (8) [avatar component clause 175]
243. ~strong(X0) | patient(X0) | funny(X0) [subsumption resolution 124,71]
245. ~patient(X0) | funny(X0) | strong(X0) [subsumption resolution 120,71]
394. funny(X0) | strong(X0) | wise(X0) | strong(X0) [resolution 245,66]
395. funny(X0) | strong(X0) | wise(X0) [duplicate literal removal 394]
491. strong(alice) | wise(alice) [resolution 395,141]
558. wise(alice) <- (~8) [subsumption resolution 491,176]
564. 44 <=> patient(alice) [avatar definition]
566. patient(alice) <- (44) [avatar component clause 564]
573. creative(alice) <- (~8) [resolution 558,92]
616. funny(alice) <- (~8) [resolution 573,70]
617. $false <- (~8) [subsumption resolution 616,141]
618. 8 [avatar contradiction clause 617]
626. patient(alice) | funny(alice) <- (8) [resolution 177,243]
630. patient(alice) <- (8) [subsumption resolution 626,141]
631. 44 | ~8 [avatar split clause 630,175,564]
637. curious(alice) <- (44) [resolution 566,108]
651. ~strong(alice) <- (44) [resolution 637,116]
653. $false <- (8, 44) [subsumption resolution 651,177]
654. ~8 | ~44 [avatar contradiction clause 653]
655. $false [avatar sat refutation 618,631,654]
% SZS output end Proof for 1477427730331876646165937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or curious is both not rich and rich and vice versa.
If someone is both not patient and strong then someone is either not wise or patient.
If mary is curious then fred is both quiet and not creative and vice versa.
Everyone who is both creative and not quiet is not humble.
Everyone who is not old or not brave is not tall and vice versa.
If someone is not brave then john is not creative or wise.
Everyone who is either not patient or not generous is both not quiet and curious and vice versa.
If susan is both curious and rich then john is calm or funny.
Everyone who is not patient is both creative and curious and vice versa.
If susan is either humble or funny then mary is quiet or not strong.
Everyone who is not wise is either not brave or creative.
Everyone who is not strong or funny is not funny or not strong and vice versa.
If fred is either not quiet or not funny then someone is not kind or not funny.
Everyone who is kind is both funny and kind.
If someone is not old or not rich then someone is either curious or patient.
Everyone who is either not humble or rich is both quiet and funny.
John is calm or patient.
Someone is both tall and not strong.
Alice is either calm or happy.
Paul is calm or curious.
Someone is both calm and humble.
Someone is either quiet or not generous. | John is not strong. | entailment | (![X]:((~brave(X)|curious(X))<=>(~rich(X)&rich(X))))&
((?[X]:((~patient(X)&strong(X))))=>(?[X]:((~wise(X)<~>patient(X)))))&
((curious(mary))<=>((quiet(fred)&~creative(fred))))&
(![X]:((creative(X)&~quiet(X))=>~humble(X)))&
(![X]:((~old(X)|~brave(X))<=>~tall(X)))&
((?[X]:(~brave(X)))=>((~creative(john)|wise(john))))&
(![X]:((~patient(X)<~>~generous(X))<=>(~quiet(X)&curious(X))))&
(((curious(susan)&rich(susan)))=>((calm(john)|funny(john))))&
(![X]:(~patient(X)<=>(creative(X)&curious(X))))&
(((humble(susan)<~>funny(susan)))=>((quiet(mary)|~strong(mary))))&
(![X]:(~wise(X)=>(~brave(X)<~>creative(X))))&
(![X]:((~strong(X)|funny(X))<=>(~funny(X)|~strong(X))))&
(((~quiet(fred)<~>~funny(fred)))=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(kind(X)=>(funny(X)&kind(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((curious(X)<~>patient(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(quiet(X)&funny(X))))&
((calm(john)|patient(john)))&
(?[X]:((tall(X)&~strong(X))))&
((calm(alice)<~>happy(alice)))&
((calm(paul)|curious(paul)))&
(?[X]:((calm(X)&humble(X))))&
(?[X]:((quiet(X)<~>~generous(X)))) | ~strong(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9217307883683859346299812
% SZS output start Proof for 9217307883683859346299812
12. ! [X0] : ((funny(X0) | ~strong(X0)) <=> (~strong(X0) | ~funny(X0))) [input p11]
23. strong(john) [input hypothesis]
58. ! [X0] : (((funny(X0) | ~strong(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (~funny(X0) & strong(X0)))) [nnf transformation 12]
59. ! [X0] : ((funny(X0) | ~strong(X0) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | (~funny(X0) & strong(X0)))) [flattening 58]
104. ~strong(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 59]
105. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 59]
127. strong(john) [cnf transformation 23]
128. ~strong(X0) | ~funny(X0) [duplicate literal removal 104]
129. funny(X0) | ~strong(X0) [duplicate literal removal 105]
177. ~strong(X0) [subsumption resolution 128,129]
213. $false [subsumption resolution 127,177]
% SZS output end Proof for 9217307883683859346299812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is wise or not quiet then someone is both funny and not happy.
If someone is either wise or tall then mary is not creative or curious and vice versa.
If someone is not patient then someone is either kind or generous.
If someone is rich then john is either rich or not strong.
If someone is not tall or funny then someone is both calm and not old.
Everyone who is either not tall or not generous is either quiet or wise and vice versa.
If fred is either funny or brave then paul is not patient.
If someone is both not quiet and creative then someone is either brave or wise.
If someone is not old then paul is either not strong or creative and vice versa.
Everyone who is not happy or strong is either not funny or not creative and vice versa.
Everyone who is not brave is not tall or not calm and vice versa.
Everyone who is both curious and not patient is not brave and vice versa.
If someone is not patient or patient then john is not brave and vice versa.
Everyone who is both not patient and not generous is curious.
If mary is either not wise or humble then paul is either funny or not rich.
Everyone who is curious is funny and vice versa.
Someone is either creative or wise.
Someone is either not quiet or generous.
Someone is not calm or not happy.
Fred is not wise.
Someone is both humble and kind.
John is patient or not old.
Someone is either curious or not funny.
Someone is either rich or brave. | John is not curious. | contradiction | (((wise(mary)|~quiet(mary)))=>(?[X]:((funny(X)&~happy(X)))))&
((?[X]:((wise(X)<~>tall(X))))<=>((~creative(mary)|curious(mary))))&
((?[X]:(~patient(X)))=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:(rich(X)))=>((rich(john)<~>~strong(john))))&
((?[X]:((~tall(X)|funny(X))))=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(quiet(X)<~>wise(X))))&
(((funny(fred)<~>brave(fred)))=>(~patient(paul)))&
((?[X]:((~quiet(X)&creative(X))))=>(?[X]:((brave(X)<~>wise(X)))))&
((?[X]:(~old(X)))<=>((~strong(paul)<~>creative(paul))))&
(![X]:((~happy(X)|strong(X))<=>(~funny(X)<~>~creative(X))))&
(![X]:(~brave(X)<=>(~tall(X)|~calm(X))))&
(![X]:((curious(X)&~patient(X))<=>~brave(X)))&
((?[X]:((~patient(X)|patient(X))))<=>(~brave(john)))&
(![X]:((~patient(X)&~generous(X))=>curious(X)))&
(((~wise(mary)<~>humble(mary)))=>((funny(paul)<~>~rich(paul))))&
(![X]:(curious(X)<=>funny(X)))&
(?[X]:((creative(X)<~>wise(X))))&
(?[X]:((~quiet(X)<~>generous(X))))&
(?[X]:((~calm(X)|~happy(X))))&
(~wise(fred))&
(?[X]:((humble(X)&kind(X))))&
((patient(john)|~old(john)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((rich(X)<~>brave(X)))) | ~curious(john) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 820352894393930926392924
% SZS output start Proof for 820352894393930926392924
12. ! [X0] : ((~patient(X0) & curious(X0)) <=> ~brave(X0)) [input p11]
13. ? [X0] : (patient(X0) | ~patient(X0)) <=> ~brave(john) [input p12]
25. ~curious(john) [input hypothesis]
67. ! [X0] : (((~patient(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | (patient(X0) | ~curious(X0)))) [nnf transformation 12]
68. ! [X0] : (((~patient(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | patient(X0) | ~curious(X0))) [flattening 67]
69. (? [X0] : (patient(X0) | ~patient(X0)) | brave(john)) & (~brave(john) | ! [X0] : (~patient(X0) & patient(X0))) [nnf transformation 13]
70. (? [X0] : (patient(X0) | ~patient(X0)) | brave(john)) & (~brave(john) | ! [X1] : (~patient(X1) & patient(X1))) [rectify 69]
71. ? [X0] : (patient(X0) | ~patient(X0)) => (patient(sK6) | ~patient(sK6)) [choice axiom]
72. ((patient(sK6) | ~patient(sK6)) | brave(john)) & (~brave(john) | ! [X1] : (~patient(X1) & patient(X1))) [skolemisation 70,71]
135. brave(X0) | curious(X0) [cnf transformation 68]
137. ~brave(john) | patient(X1) [cnf transformation 72]
138. ~brave(john) | ~patient(X1) [cnf transformation 72]
160. ~curious(john) [cnf transformation 25]
210. 11 <=> ! [X1] : patient(X1) [avatar definition]
211. patient(X1) <- (11) [avatar component clause 210]
300. 31 <=> ! [X1] : ~patient(X1) [avatar definition]
301. ~patient(X1) <- (31) [avatar component clause 300]
303. 32 <=> brave(john) [avatar definition]
305. ~brave(john) <- (~32) [avatar component clause 303]
306. 31 | ~32 [avatar split clause 138,303,300]
307. 11 | ~32 [avatar split clause 137,303,210]
378. curious(john) <- (~32) [resolution 135,305]
382. $false <- (~32) [subsumption resolution 378,160]
383. 32 [avatar contradiction clause 382]
386. $false <- (11, 31) [subsumption resolution 211,301]
387. ~11 | ~31 [avatar contradiction clause 386]
388. $false [avatar sat refutation 306,307,383,387]
% SZS output end Proof for 820352894393930926392924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or brave is both not wise and brave.
If fred is tall then paul is not brave or not tall.
Everyone who is not quiet or not wise is funny.
If alice is quiet or not humble then someone is happy and vice versa.
Everyone who is not calm or strong is both not creative and not happy and vice versa.
If someone is humble or not calm then someone is both generous and not humble.
Everyone who is either not strong or not curious is tall and vice versa.
If someone is not calm or old then john is both brave and not wise and vice versa.
Everyone who is not funny or brave is not creative.
If john is both not generous and not rich then lucy is rich.
If someone is both not calm and old then someone is both not patient and not curious and vice versa.
If paul is either not kind or wise then john is both not kind and funny.
Everyone who is tall is not strong and vice versa.
If john is both not kind and not wise then fred is not curious or quiet.
Everyone who is humble is either not rich or not calm and vice versa.
Everyone who is strong or kind is either not generous or strong.
Mary is not brave or not creative.
Fred is both not kind and not calm.
Someone is not strong.
Someone is both not old and funny.
Someone is either creative or kind.
Someone is not tall. | Lucy is not curious. | contradiction | (![X]:((quiet(X)<~>brave(X))=>(~wise(X)&brave(X))))&
((tall(fred))=>((~brave(paul)|~tall(paul))))&
(![X]:((~quiet(X)|~wise(X))=>funny(X)))&
(((quiet(alice)|~humble(alice)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|strong(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((~calm(X)|old(X))))<=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|brave(X))=>~creative(X)))&
(((~generous(john)&~rich(john)))=>(rich(lucy)))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((~kind(paul)<~>wise(paul)))=>((~kind(john)&funny(john))))&
(![X]:(tall(X)<=>~strong(X)))&
(((~kind(john)&~wise(john)))=>((~curious(fred)|quiet(fred))))&
(![X]:(humble(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((strong(X)|kind(X))=>(~generous(X)<~>strong(X))))&
((~brave(mary)|~creative(mary)))&
((~kind(fred)&~calm(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&funny(X))))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:(~tall(X))) | ~curious(lucy) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 935831185282578790526996
% SZS output start Proof for 935831185282578790526996
7. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> tall(X0)) [input p6]
13. ! [X0] : (tall(X0) <=> ~strong(X0)) [input p12]
23. ~curious(lucy) [input hypothesis]
52. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | ~tall(X0)) & (tall(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 7]
64. ! [X0] : ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0))) [nnf transformation 13]
94. ~strong(X0) | tall(X0) | curious(X0) [cnf transformation 52]
96. ~tall(X0) | strong(X0) | curious(X0) [cnf transformation 52]
110. ~strong(X0) | ~tall(X0) [cnf transformation 64]
111. strong(X0) | tall(X0) [cnf transformation 64]
129. ~curious(lucy) [cnf transformation 23]
296. tall(X0) | curious(X0) | tall(X0) [resolution 94,111]
297. curious(X0) | tall(X0) [duplicate literal removal 296]
300. tall(lucy) [resolution 297,129]
308. strong(lucy) | curious(lucy) [resolution 96,300]
312. strong(lucy) [subsumption resolution 308,129]
412. ~tall(lucy) [resolution 312,110]
414. $false [subsumption resolution 412,300]
% SZS output end Proof for 935831185282578790526996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or happy is both not strong and not happy and vice versa.
If someone is not funny then fred is both not strong and not rich.
If someone is happy or not funny then susan is wise or calm.
Everyone who is funny or not curious is both not creative and kind.
Everyone who is funny or curious is both not strong and not wise and vice versa.
If lucy is both wise and calm then fred is strong and vice versa.
Everyone who is both not funny and not old is either curious or not old and vice versa.
If someone is both not brave and not kind then someone is not happy or brave.
If john is kind then mary is not tall.
Everyone who is not generous or not patient is wise or not rich.
Everyone who is either brave or tall is curious or creative and vice versa.
If mary is either not happy or not brave then mary is quiet or not strong and vice versa.
Everyone who is not happy or not funny is either calm or not rich.
Everyone who is both tall and funny is both not wise and old.
Someone is both not brave and not quiet.
Lucy is both tall and not wise.
Someone is both patient and not generous.
Someone is not tall or funny.
Someone is calm.
Someone is calm or old.
Someone is patient. | John is not kind. | contradiction | (![X]:((tall(X)<~>happy(X))<=>(~strong(X)&~happy(X))))&
((?[X]:(~funny(X)))=>((~strong(fred)&~rich(fred))))&
((?[X]:((happy(X)|~funny(X))))=>((wise(susan)|calm(susan))))&
(![X]:((funny(X)|~curious(X))=>(~creative(X)&kind(X))))&
(![X]:((funny(X)|curious(X))<=>(~strong(X)&~wise(X))))&
(((wise(lucy)&calm(lucy)))<=>(strong(fred)))&
(![X]:((~funny(X)&~old(X))<=>(curious(X)<~>~old(X))))&
((?[X]:((~brave(X)&~kind(X))))=>(?[X]:((~happy(X)|brave(X)))))&
((kind(john))=>(~tall(mary)))&
(![X]:((~generous(X)|~patient(X))=>(wise(X)|~rich(X))))&
(![X]:((brave(X)<~>tall(X))<=>(curious(X)|creative(X))))&
(((~happy(mary)<~>~brave(mary)))<=>((quiet(mary)|~strong(mary))))&
(![X]:((~happy(X)|~funny(X))=>(calm(X)<~>~rich(X))))&
(![X]:((tall(X)&funny(X))=>(~wise(X)&old(X))))&
(?[X]:((~brave(X)&~quiet(X))))&
((tall(lucy)&~wise(lucy)))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((~tall(X)|funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((calm(X)|old(X))))&
(?[X]:(patient(X))) | ~kind(john) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8037753750978856169968007
% SZS output start Proof for 8037753750978856169968007
4. ! [X0] : ((~curious(X0) | funny(X0)) => (kind(X0) & ~creative(X0))) [input p3]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (curious(X0) <~> ~old(X0))) [input p6]
22. ~kind(john) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~creative(X0)) | (curious(X0) & ~funny(X0))) [ennf transformation 4]
44. ! [X0] : (((~old(X0) & ~funny(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (old(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((~old(X0) & ~funny(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | old(X0) | funny(X0))) [flattening 44]
76. ~funny(X0) | kind(X0) [cnf transformation 30]
77. kind(X0) | curious(X0) [cnf transformation 30]
87. old(X0) | ~curious(X0) | old(X0) | funny(X0) [cnf transformation 45]
90. ~old(X0) | ~old(X0) | ~curious(X0) [cnf transformation 45]
121. ~kind(john) [cnf transformation 22]
122. old(X0) | ~curious(X0) | funny(X0) [duplicate literal removal 87]
123. ~old(X0) | ~curious(X0) [duplicate literal removal 90]
163. ~curious(X0) | funny(X0) [subsumption resolution 122,123]
177. 12 <=> kind(john) [avatar definition]
179. ~kind(john) <- (~12) [avatar component clause 177]
228. ~12 [avatar split clause 121,177]
229. curious(john) <- (~12) [resolution 77,179]
233. funny(john) <- (~12) [resolution 163,229]
235. kind(john) <- (~12) [resolution 233,76]
236. $false <- (~12) [subsumption resolution 235,179]
237. 12 [avatar contradiction clause 236]
238. $false [avatar sat refutation 228,237]
% SZS output end Proof for 8037753750978856169968007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is curious and vice versa.
Everyone who is not curious or wise is both not creative and not calm.
If mary is either patient or not quiet then lucy is generous or not brave and vice versa.
Everyone who is either calm or quiet is not curious and vice versa.
Everyone who is not rich is old.
Everyone who is not quiet or not strong is both not patient and not curious and vice versa.
If lucy is either humble or not humble then lucy is either not wise or not rich.
If someone is not wise or not quiet then someone is not curious and vice versa.
If someone is wise or humble then lucy is either not kind or tall and vice versa.
Everyone who is both old and wise is either not strong or humble and vice versa.
Everyone who is not old or tall is both humble and not old.
If someone is either quiet or patient then susan is either not humble or tall.
Everyone who is happy is either not curious or creative.
Everyone who is either not kind or wise is not humble or not kind.
If alice is quiet then someone is both rich and not patient.
Someone is either not happy or not curious.
Someone is either not brave or wise.
Someone is not generous.
Mary is either not old or funny.
John is both not kind and patient.
Someone is not calm.
Paul is either not creative or creative.
Someone is either quiet or not quiet. | Mary is quiet. | entailment | (![X]:(humble(X)<=>curious(X)))&
(![X]:((~curious(X)|wise(X))=>(~creative(X)&~calm(X))))&
(((patient(mary)<~>~quiet(mary)))<=>((generous(lucy)|~brave(lucy))))&
(![X]:((calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((~quiet(X)|~strong(X))<=>(~patient(X)&~curious(X))))&
(((humble(lucy)<~>~humble(lucy)))=>((~wise(lucy)<~>~rich(lucy))))&
((?[X]:((~wise(X)|~quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|humble(X))))<=>((~kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)&wise(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|tall(X))=>(humble(X)&~old(X))))&
((?[X]:((quiet(X)<~>patient(X))))=>((~humble(susan)<~>tall(susan))))&
(![X]:(happy(X)=>(~curious(X)<~>creative(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~humble(X)|~kind(X))))&
((quiet(alice))=>(?[X]:((rich(X)&~patient(X)))))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(~generous(X)))&
((~old(mary)<~>funny(mary)))&
((~kind(john)&patient(john)))&
(?[X]:(~calm(X)))&
((~creative(paul)<~>creative(paul)))&
(?[X]:((quiet(X)<~>~quiet(X)))) | quiet(mary) | [
"p1",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 605850034661276064440738
% SZS output start Proof for 605850034661276064440738
2. ! [X0] : ((wise(X0) | ~curious(X0)) => (~calm(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> ~curious(X0)) [input p3]
6. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> (~curious(X0) & ~patient(X0))) [input p5]
24. ~quiet(mary) [input hypothesis]
26. ! [X0] : ((~calm(X0) & ~creative(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 2]
38. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) | ~quiet(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [nnf transformation 6]
40. ! [X0] : ((~strong(X0) | ~quiet(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [flattening 39]
77. ~calm(X0) | curious(X0) [cnf transformation 26]
87. quiet(X0) | calm(X0) | curious(X0) [cnf transformation 38]
92. ~curious(X0) | quiet(X0) [cnf transformation 40]
142. ~quiet(mary) [cnf transformation 24]
170. quiet(X0) | curious(X0) [subsumption resolution 87,77]
173. quiet(X0) [subsumption resolution 92,170]
280. $false [subsumption resolution 142,173]
% SZS output end Proof for 605850034661276064440738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble then mary is both not rich and calm and vice versa. If someone is not brave or kind then lucy is both not kind and not strong and vice versa. Everyone who is rich or not funny is either patient or not rich. If lucy is not curious then someone is both happy and calm. Everyone who is both calm and not happy is either not wise or tall. Everyone who is old or not tall is not funny and vice versa. Everyone who is not patient is tall or brave and vice versa. If someone is both strong and not old then john is both creative and funny. If someone is not old then fred is either quiet or not rich. Everyone who is both generous and not tall is both not rich and humble. If lucy is either tall or brave then john is either not wise or funny. If someone is both generous and not old then someone is wise. Everyone who is not humble or wise is either not wise or tall. If someone is either not rich or not wise then john is not calm or kind and vice versa. Everyone who is either not kind or old is both not humble and not brave and vice versa. If susan is either humble or creative then fred is both not curious and not brave. John is not quiet or wise. Someone is either not calm or not curious. Someone is not kind or not curious. Susan is calm. Fred is not quiet or not funny. John is both patient and not humble. Fred is both creative and funny. Someone is generous or not generous. | John is not tall. | entailment | ((?[X]:(~humble(X)))<=>((~rich(mary)&calm(mary))))&
((?[X]:((~brave(X)|kind(X))))<=>((~kind(lucy)&~strong(lucy))))&
(![X]:((rich(X)|~funny(X))=>(patient(X)<~>~rich(X))))&
((~curious(lucy))=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((calm(X)&~happy(X))=>(~wise(X)<~>tall(X))))&
(![X]:((old(X)|~tall(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(tall(X)|brave(X))))&
((?[X]:((strong(X)&~old(X))))=>((creative(john)&funny(john))))&
((?[X]:(~old(X)))=>((quiet(fred)<~>~rich(fred))))&
(![X]:((generous(X)&~tall(X))=>(~rich(X)&humble(X))))&
(((tall(lucy)<~>brave(lucy)))=>((~wise(john)<~>funny(john))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:(wise(X))))&
(![X]:((~humble(X)|wise(X))=>(~wise(X)<~>tall(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((~calm(john)|kind(john))))&
(![X]:((~kind(X)<~>old(X))<=>(~humble(X)&~brave(X))))&
(((humble(susan)<~>creative(susan)))=>((~curious(fred)&~brave(fred))))&
((~quiet(john)|wise(john)))&
(?[X]:((~calm(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(calm(susan))&
((~quiet(fred)|~funny(fred)))&
((patient(john)&~humble(john)))&
((creative(fred)&funny(fred)))&
(?[X]:((generous(X)|~generous(X)))) | ~tall(john) | [
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5287996378986067121891357
% SZS output start Proof for 5287996378986067121891357
7. ! [X0] : (~patient(X0) <=> (brave(X0) | tall(X0))) [input p6]
22. ~humble(john) & patient(john) [input p21]
25. tall(john) [input hypothesis]
54. ! [X0] : ((~patient(X0) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | patient(X0))) [nnf transformation 7]
55. ! [X0] : ((~patient(X0) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | patient(X0))) [flattening 54]
94. ~tall(X0) | ~patient(X0) [cnf transformation 55]
133. patient(john) [cnf transformation 22]
138. tall(john) [cnf transformation 25]
324. ~patient(john) [resolution 94,138]
326. $false [subsumption resolution 324,133]
% SZS output end Proof for 5287996378986067121891357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not quiet is humble and vice versa.
Everyone who is both not tall and strong is either calm or kind.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Everyone who is old is tall or curious.
If someone is wise then mary is not rich or not humble.
Everyone who is either curious or not generous is humble and vice versa.
Susan is tall.
Someone is either curious or rich.
Someone is not quiet or brave.
John is either not strong or not generous.
Fred is curious or not strong.
Someone is both not creative and not rich. | Alice is strong. | entailment | (![X]:((~funny(X)<~>~quiet(X))<=>humble(X)))&
(![X]:((~tall(X)&strong(X))=>(calm(X)<~>kind(X))))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(![X]:(old(X)=>(tall(X)|curious(X))))&
((?[X]:(wise(X)))=>((~rich(mary)|~humble(mary))))&
(![X]:((curious(X)<~>~generous(X))<=>humble(X)))&
(tall(susan))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~quiet(X)|brave(X))))&
((~strong(john)<~>~generous(john)))&
((curious(fred)|~strong(fred)))&
(?[X]:((~creative(X)&~rich(X)))) | strong(alice) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2055862823530605157790792
% SZS output start Proof for 2055862823530605157790792
6. ? [X0] : (~strong(X0) | ~tall(X0)) <=> humble(john) [input p5]
11. ? [X0] : humble(X0) => ~humble(john) [input p10]
22. ~strong(alice) [input hypothesis]
31. ~humble(john) | ! [X0] : ~humble(X0) [ennf transformation 11]
48. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X0] : (strong(X0) & tall(X0))) [nnf transformation 6]
49. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [rectify 48]
50. ? [X0] : (~strong(X0) | ~tall(X0)) => (~strong(sK4) | ~tall(sK4)) [choice axiom]
51. ((~strong(sK4) | ~tall(sK4)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [skolemisation 49,50]
87. humble(john) | strong(X1) [cnf transformation 51]
110. ~humble(john) | ~humble(X0) [cnf transformation 31]
129. ~strong(alice) [cnf transformation 22]
194. 16 <=> humble(john) [avatar definition]
195. humble(john) <- (16) [avatar component clause 194]
207. 19 <=> ! [X1] : strong(X1) [avatar definition]
208. strong(X1) <- (19) [avatar component clause 207]
209. 19 | 16 [avatar split clause 87,194,207]
280. 35 <=> ! [X0] : ~humble(X0) [avatar definition]
281. ~humble(X0) <- (35) [avatar component clause 280]
282. 35 | ~16 [avatar split clause 110,194,280]
333. $false <- (19) [resolution 208,129]
334. ~19 [avatar contradiction clause 333]
337. $false <- (16, 35) [subsumption resolution 195,281]
338. ~16 | ~35 [avatar contradiction clause 337]
339. $false [avatar sat refutation 209,282,334,338]
% SZS output end Proof for 2055862823530605157790792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not tall is both not strong and old and vice versa.
If someone is not funny then john is both not strong and not funny.
Everyone who is both not curious and kind is calm and vice versa.
If someone is not tall or not patient then someone is not kind.
Everyone who is both not kind and not patient is quiet and vice versa.
If someone is both not strong and not tall then paul is not patient or curious and vice versa.
If someone is both not patient and funny then lucy is either curious or rich and vice versa.
If mary is either strong or not rich then paul is either strong or quiet.
Everyone who is either tall or not kind is old and vice versa.
If paul is both not old and not strong then someone is both strong and not generous.
Everyone who is not curious is both not curious and curious and vice versa.
If someone is both not quiet and happy then someone is both happy and not humble and vice versa.
If someone is both old and generous then fred is either not generous or not funny.
Everyone who is not quiet is funny or humble.
Everyone who is both patient and not brave is either funny or patient and vice versa.
Everyone who is either funny or not tall is either brave or tall.
Someone is not humble or not tall.
Someone is either rich or quiet.
Someone is not brave or not generous.
Someone is both patient and happy.
Someone is both not quiet and strong.
Lucy is creative.
Someone is wise.
Fred is either not generous or tall. | John is calm. | contradiction | (![X]:((~old(X)<~>~tall(X))<=>(~strong(X)&old(X))))&
((?[X]:(~funny(X)))=>((~strong(john)&~funny(john))))&
(![X]:((~curious(X)&kind(X))<=>calm(X)))&
((?[X]:((~tall(X)|~patient(X))))=>(?[X]:(~kind(X))))&
(![X]:((~kind(X)&~patient(X))<=>quiet(X)))&
((?[X]:((~strong(X)&~tall(X))))<=>((~patient(paul)|curious(paul))))&
((?[X]:((~patient(X)&funny(X))))<=>((curious(lucy)<~>rich(lucy))))&
(((strong(mary)<~>~rich(mary)))=>((strong(paul)<~>quiet(paul))))&
(![X]:((tall(X)<~>~kind(X))<=>old(X)))&
(((~old(paul)&~strong(paul)))=>(?[X]:((strong(X)&~generous(X)))))&
(![X]:(~curious(X)<=>(~curious(X)&curious(X))))&
((?[X]:((~quiet(X)&happy(X))))<=>(?[X]:((happy(X)&~humble(X)))))&
((?[X]:((old(X)&generous(X))))=>((~generous(fred)<~>~funny(fred))))&
(![X]:(~quiet(X)=>(funny(X)|humble(X))))&
(![X]:((patient(X)&~brave(X))<=>(funny(X)<~>patient(X))))&
(![X]:((funny(X)<~>~tall(X))=>(brave(X)<~>tall(X))))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((rich(X)<~>quiet(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~quiet(X)&strong(X))))&
(creative(lucy))&
(?[X]:(wise(X)))&
((~generous(fred)<~>tall(fred))) | calm(john) | [
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3061227475504307867311347
% SZS output start Proof for 3061227475504307867311347
3. ! [X0] : ((kind(X0) & ~curious(X0)) <=> calm(X0)) [input p2]
11. ! [X0] : (~curious(X0) <=> (curious(X0) & ~curious(X0))) [input p10]
25. calm(john) [input hypothesis]
28. ! [X0] : (calm(X0) => (kind(X0) & ~curious(X0))) [unused predicate definition removal 3]
32. ! [X0] : ((kind(X0) & ~curious(X0)) | ~calm(X0)) [ennf transformation 28]
61. ! [X0] : ((~curious(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | curious(X0))) [nnf transformation 11]
62. ! [X0] : ((~curious(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | curious(X0))) [flattening 61]
92. ~calm(X0) | ~curious(X0) [cnf transformation 32]
121. curious(X0) | curious(X0) [cnf transformation 62]
150. calm(john) [cnf transformation 25]
155. curious(X0) [duplicate literal removal 121]
347. ~curious(john) [resolution 92,150]
348. $false [subsumption resolution 347,155]
% SZS output end Proof for 3061227475504307867311347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or old then mary is either not brave or not patient and vice versa.
Everyone who is calm or not humble is calm and vice versa.
Everyone who is not patient or curious is both strong and not tall and vice versa.
Everyone who is either not humble or not tall is not rich and vice versa.
Everyone who is both not strong and not calm is either curious or not tall and vice versa.
Everyone who is either not quiet or not curious is both not tall and not generous and vice versa.
Everyone who is both not generous and not funny is not humble and vice versa.
If susan is not brave then mary is either humble or not quiet.
If someone is either not old or curious then someone is either quiet or not rich and vice versa.
If susan is both rich and not humble then susan is creative.
Everyone who is both not creative and not humble is both creative and not happy and vice versa.
Everyone who is both funny and not old is not curious and vice versa.
If someone is either not brave or humble then alice is not kind or not happy.
Everyone who is not patient or tall is both generous and not generous.
If someone is calm or happy then someone is not kind and vice versa.
If john is strong or not kind then someone is either not brave or not generous.
Susan is not wise or calm.
Alice is humble.
Alice is old or rich.
Someone is both not brave and curious.
Someone is both happy and humble.
Susan is not calm or not happy.
Paul is either funny or tall.
Fred is either not strong or old. | Susan is not rich. | entailment | ((?[X]:((tall(X)<~>old(X))))<=>((~brave(mary)<~>~patient(mary))))&
(![X]:((calm(X)|~humble(X))<=>calm(X)))&
(![X]:((~patient(X)|curious(X))<=>(strong(X)&~tall(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>~rich(X)))&
(![X]:((~strong(X)&~calm(X))<=>(curious(X)<~>~tall(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~tall(X)&~generous(X))))&
(![X]:((~generous(X)&~funny(X))<=>~humble(X)))&
((~brave(susan))=>((humble(mary)<~>~quiet(mary))))&
((?[X]:((~old(X)<~>curious(X))))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((rich(susan)&~humble(susan)))=>(creative(susan)))&
(![X]:((~creative(X)&~humble(X))<=>(creative(X)&~happy(X))))&
(![X]:((funny(X)&~old(X))<=>~curious(X)))&
((?[X]:((~brave(X)<~>humble(X))))=>((~kind(alice)|~happy(alice))))&
(![X]:((~patient(X)|tall(X))=>(generous(X)&~generous(X))))&
((?[X]:((calm(X)|happy(X))))<=>(?[X]:(~kind(X))))&
(((strong(john)|~kind(john)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
((~wise(susan)|calm(susan)))&
(humble(alice))&
((old(alice)|rich(alice)))&
(?[X]:((~brave(X)&curious(X))))&
(?[X]:((happy(X)&humble(X))))&
((~calm(susan)|~happy(susan)))&
((funny(paul)<~>tall(paul)))&
((~strong(fred)<~>old(fred))) | ~rich(susan) | [
"p1",
"p3",
"p9",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6049596919209352685159071
% SZS output start Proof for 6049596919209352685159071
2. ! [X0] : ((~humble(X0) | calm(X0)) <=> calm(X0)) [input p1]
4. ! [X0] : ((~humble(X0) <~> ~tall(X0)) <=> ~rich(X0)) [input p3]
10. (~humble(susan) & rich(susan)) => creative(susan) [input p9]
11. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> (~happy(X0) & creative(X0))) [input p10]
14. ! [X0] : ((tall(X0) | ~patient(X0)) => (~generous(X0) & generous(X0))) [input p13]
22. ~happy(susan) | ~calm(susan) [input p21]
25. rich(susan) [input hypothesis]
30. creative(susan) | (humble(susan) | ~rich(susan)) [ennf transformation 10]
31. creative(susan) | humble(susan) | ~rich(susan) [flattening 30]
34. ! [X0] : ((~generous(X0) & generous(X0)) | (~tall(X0) & patient(X0))) [ennf transformation 14]
40. ! [X0] : (((~humble(X0) | calm(X0)) | ~calm(X0)) & (calm(X0) | (humble(X0) & ~calm(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | calm(X0) | ~calm(X0)) & (calm(X0) | (humble(X0) & ~calm(X0)))) [flattening 40]
44. ! [X0] : ((((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | rich(X0)) & (~rich(X0) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0))))) [nnf transformation 4]
57. ! [X0] : (((~humble(X0) & ~creative(X0)) | (happy(X0) | ~creative(X0))) & ((~happy(X0) & creative(X0)) | (humble(X0) | creative(X0)))) [nnf transformation 11]
58. ! [X0] : (((~humble(X0) & ~creative(X0)) | happy(X0) | ~creative(X0)) & ((~happy(X0) & creative(X0)) | humble(X0) | creative(X0))) [flattening 57]
85. humble(X0) | calm(X0) [cnf transformation 41]
93. ~rich(X0) | ~humble(X0) | tall(X0) [cnf transformation 44]
121. creative(susan) | humble(susan) | ~rich(susan) [cnf transformation 31]
124. ~creative(X0) | happy(X0) | ~creative(X0) [cnf transformation 58]
132. generous(X0) | ~tall(X0) [cnf transformation 34]
134. ~generous(X0) | ~tall(X0) [cnf transformation 34]
148. ~happy(susan) | ~calm(susan) [cnf transformation 22]
153. rich(susan) [cnf transformation 25]
155. ~creative(X0) | happy(X0) [duplicate literal removal 124]
240. 18 <=> rich(susan) [avatar definition]
241. rich(susan) <- (18) [avatar component clause 240]
244. 19 <=> humble(susan) [avatar definition]
245. ~humble(susan) <- (~19) [avatar component clause 244]
248. 20 <=> creative(susan) [avatar definition]
250. creative(susan) <- (20) [avatar component clause 248]
251. ~18 | 19 | 20 [avatar split clause 121,248,244,240]
268. ~tall(X0) [subsumption resolution 132,134]
324. 37 <=> calm(susan) [avatar definition]
328. 38 <=> happy(susan) [avatar definition]
330. ~happy(susan) <- (~38) [avatar component clause 328]
331. ~37 | ~38 [avatar split clause 148,328,324]
343. 18 [avatar split clause 153,240]
370. ~humble(susan) | tall(susan) <- (18) [resolution 93,241]
374. ~humble(susan) <- (18) [subsumption resolution 370,268]
375. ~19 | ~18 [avatar split clause 374,240,244]
376. calm(susan) <- (~19) [resolution 245,85]
379. 37 | 19 [avatar split clause 376,244,324]
380. happy(susan) <- (20) [resolution 250,155]
381. $false <- (20, ~38) [subsumption resolution 380,330]
382. ~20 | 38 [avatar contradiction clause 381]
383. $false [avatar sat refutation 251,331,343,375,379,382]
% SZS output end Proof for 6049596919209352685159071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not happy or not humble then alice is not wise or humble.
Everyone who is either quiet or not happy is either not rich or not creative and vice versa.
If john is kind then fred is calm.
Everyone who is both not humble and not rich is either not patient or not old.
Everyone who is not wise or not kind is humble.
Everyone who is either not creative or not curious is not generous.
If alice is brave then lucy is both tall and not creative and vice versa.
Everyone who is both creative and not happy is curious or strong.
If fred is either not tall or patient then someone is either wise or not humble.
Everyone who is not happy or not brave is happy and vice versa.
Everyone who is both strong and kind is not creative.
If paul is either not humble or not creative then someone is both not patient and not kind.
If john is not brave or funny then someone is strong or curious and vice versa.
If someone is brave then mary is both old and patient.
Everyone who is not happy is either funny or not brave and vice versa.
Everyone who is both not creative and not curious is not patient or not old.
Someone is not patient or quiet.
Mary is wise or kind.
Lucy is funny.
Paul is tall or generous.
Someone is not strong or generous.
Mary is either old or not generous. | John is funny. | entailment | (((~happy(alice)<~>~humble(alice)))=>((~wise(alice)|humble(alice))))&
(![X]:((quiet(X)<~>~happy(X))<=>(~rich(X)<~>~creative(X))))&
((kind(john))=>(calm(fred)))&
(![X]:((~humble(X)&~rich(X))=>(~patient(X)<~>~old(X))))&
(![X]:((~wise(X)|~kind(X))=>humble(X)))&
(![X]:((~creative(X)<~>~curious(X))=>~generous(X)))&
((brave(alice))<=>((tall(lucy)&~creative(lucy))))&
(![X]:((creative(X)&~happy(X))=>(curious(X)|strong(X))))&
(((~tall(fred)<~>patient(fred)))=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((~happy(X)|~brave(X))<=>happy(X)))&
(![X]:((strong(X)&kind(X))=>~creative(X)))&
(((~humble(paul)<~>~creative(paul)))=>(?[X]:((~patient(X)&~kind(X)))))&
(((~brave(john)|funny(john)))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:(brave(X)))=>((old(mary)&patient(mary))))&
(![X]:(~happy(X)<=>(funny(X)<~>~brave(X))))&
(![X]:((~creative(X)&~curious(X))=>(~patient(X)|~old(X))))&
(?[X]:((~patient(X)|quiet(X))))&
((wise(mary)|kind(mary)))&
(funny(lucy))&
((tall(paul)|generous(paul)))&
(?[X]:((~strong(X)|generous(X))))&
((old(mary)<~>~generous(mary))) | funny(john) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8490185782572975112339553
% SZS output start Proof for 8490185782572975112339553
10. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> happy(X0)) [input p9]
15. ! [X0] : (~happy(X0) <=> (funny(X0) <~> ~brave(X0))) [input p14]
23. ~funny(john) [input hypothesis]
49. ! [X0] : (((~brave(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [nnf transformation 10]
50. ! [X0] : ((~brave(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [flattening 49]
59. ! [X0] : ((~happy(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0)))) & (((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | happy(X0))) [nnf transformation 15]
89. happy(X0) | happy(X0) [cnf transformation 50]
91. ~brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
106. ~happy(X0) | funny(X0) | brave(X0) [cnf transformation 59]
115. ~funny(john) [cnf transformation 23]
116. happy(X0) [duplicate literal removal 89]
117. ~brave(X0) | ~happy(X0) [duplicate literal removal 91]
195. 16 <=> brave(john) [avatar definition]
196. brave(john) <- (16) [avatar component clause 195]
199. 17 <=> funny(john) [avatar definition]
200. ~funny(john) <- (~17) [avatar component clause 199]
230. funny(X0) | brave(X0) [subsumption resolution 106,116]
273. ~17 [avatar split clause 115,199]
284. brave(john) <- (~17) [resolution 230,200]
287. 16 | 17 [avatar split clause 284,199,195]
289. ~happy(john) <- (16) [resolution 196,117]
290. $false <- (16) [subsumption resolution 289,116]
291. ~16 [avatar contradiction clause 290]
292. $false [avatar sat refutation 273,287,291]
% SZS output end Proof for 8490185782572975112339553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or brave then someone is both tall and funny. Everyone who is happy or patient is kind or not old and vice versa. Everyone who is either not wise or brave is not humble and vice versa. If mary is old or not kind then someone is funny. If someone is not happy then lucy is either not funny or not old and vice versa. Everyone who is both rich and not curious is curious and vice versa. If someone is either old or creative then john is not kind. Everyone who is both not strong and humble is both not humble and not creative. Everyone who is not brave is both not old and not kind. Everyone who is tall is both happy and not rich. If alice is not quiet or old then susan is quiet and vice versa. Everyone who is wise is not tall and vice versa. If mary is not brave then someone is not curious. If fred is not rich or not happy then mary is both brave and not humble. If someone is both not tall and not wise then susan is both not old and creative. Everyone who is both not funny and not humble is not happy or not wise and vice versa. Fred is both not strong and not brave. John is not patient or not tall. Alice is not rich. Alice is both calm and strong. Someone is not brave or humble. Mary is quiet or not creative. Someone is both not tall and kind. Someone is either tall or humble. | Fred is not funny. | entailment | ((?[X]:((old(X)<~>brave(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((happy(X)|patient(X))<=>(kind(X)|~old(X))))&
(![X]:((~wise(X)<~>brave(X))<=>~humble(X)))&
(((old(mary)|~kind(mary)))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))<=>((~funny(lucy)<~>~old(lucy))))&
(![X]:((rich(X)&~curious(X))<=>curious(X)))&
((?[X]:((old(X)<~>creative(X))))=>(~kind(john)))&
(![X]:((~strong(X)&humble(X))=>(~humble(X)&~creative(X))))&
(![X]:(~brave(X)=>(~old(X)&~kind(X))))&
(![X]:(tall(X)=>(happy(X)&~rich(X))))&
(((~quiet(alice)|old(alice)))<=>(quiet(susan)))&
(![X]:(wise(X)<=>~tall(X)))&
((~brave(mary))=>(?[X]:(~curious(X))))&
(((~rich(fred)|~happy(fred)))=>((brave(mary)&~humble(mary))))&
((?[X]:((~tall(X)&~wise(X))))=>((~old(susan)&creative(susan))))&
(![X]:((~funny(X)&~humble(X))<=>(~happy(X)|~wise(X))))&
((~strong(fred)&~brave(fred)))&
((~patient(john)|~tall(john)))&
(~rich(alice))&
((calm(alice)&strong(alice)))&
(?[X]:((~brave(X)|humble(X))))&
((quiet(mary)|~creative(mary)))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((tall(X)<~>humble(X)))) | ~funny(fred) | [
"p2",
"p7",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5689235419414353892385126
% SZS output start Proof for 5689235419414353892385126
3. ! [X0] : ((~wise(X0) <~> brave(X0)) <=> ~humble(X0)) [input p2]
8. ! [X0] : ((humble(X0) & ~strong(X0)) => (~creative(X0) & ~humble(X0))) [input p7]
16. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (~wise(X0) | ~happy(X0))) [input p15]
17. ~brave(fred) & ~strong(fred) [input p16]
25. funny(fred) [input hypothesis]
31. ! [X0] : ((~creative(X0) & ~humble(X0)) | (~humble(X0) | strong(X0))) [ennf transformation 8]
32. ! [X0] : ((~creative(X0) & ~humble(X0)) | ~humble(X0) | strong(X0)) [flattening 31]
44. ! [X0] : ((((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | humble(X0)) & (~humble(X0) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0))))) [nnf transformation 3]
59. ! [X0] : (((~humble(X0) & ~funny(X0)) | (wise(X0) & happy(X0))) & ((~wise(X0) | ~happy(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 16]
60. ! [X0] : (((~humble(X0) & ~funny(X0)) | (wise(X0) & happy(X0))) & (~wise(X0) | ~happy(X0) | humble(X0) | funny(X0))) [flattening 59]
78. ~wise(X0) | brave(X0) | humble(X0) [cnf transformation 44]
91. ~humble(X0) | ~humble(X0) | strong(X0) [cnf transformation 32]
111. ~funny(X0) | wise(X0) [cnf transformation 60]
114. ~strong(fred) [cnf transformation 17]
115. ~brave(fred) [cnf transformation 17]
125. funny(fred) [cnf transformation 25]
126. ~humble(X0) | strong(X0) [duplicate literal removal 91]
272. wise(fred) [resolution 111,125]
354. brave(fred) | humble(fred) [resolution 78,272]
356. humble(fred) [subsumption resolution 354,115]
396. strong(fred) [resolution 356,126]
399. $false [subsumption resolution 396,114]
% SZS output end Proof for 5689235419414353892385126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is either creative or not old then someone is not rich.
Everyone who is not rich or quiet is both curious and not wise and vice versa.
If john is old then lucy is both not tall and strong.
If alice is creative or not rich then lucy is both patient and not patient and vice versa.
Everyone who is calm is patient and vice versa.
Everyone who is not patient is kind.
If someone is creative then someone is not curious or not kind and vice versa.
Everyone who is both not generous and not strong is either not humble or not rich.
Everyone who is both calm and strong is either not strong or not rich.
Everyone who is either rich or not funny is either brave or not calm and vice versa.
If lucy is not strong or humble then paul is not brave or not generous and vice versa.
Everyone who is either not wise or kind is rich and vice versa.
Everyone who is either not strong or not tall is not old or not happy and vice versa.
Everyone who is not rich or quiet is creative.
Everyone who is both not happy and not strong is generous or wise and vice versa.
If someone is calm or creative then someone is either happy or not wise and vice versa.
Someone is brave.
Someone is not generous.
Alice is curious.
Someone is generous or funny.
Susan is both quiet and not happy.
Paul is both not kind and not strong.
John is either curious or not generous.
Someone is either not calm or calm. | Alice is not kind. | contradiction | (((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(((creative(alice)|~rich(alice)))<=>((patient(lucy)&~patient(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((~generous(X)&~strong(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((calm(X)&strong(X))=>(~strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(brave(X)<~>~calm(X))))&
(((~strong(lucy)|humble(lucy)))<=>((~brave(paul)|~generous(paul))))&
(![X]:((~wise(X)<~>kind(X))<=>rich(X)))&
(![X]:((~strong(X)<~>~tall(X))<=>(~old(X)|~happy(X))))&
(![X]:((~rich(X)|quiet(X))=>creative(X)))&
(![X]:((~happy(X)&~strong(X))<=>(generous(X)|wise(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(?[X]:(brave(X)))&
(?[X]:(~generous(X)))&
(curious(alice))&
(?[X]:((generous(X)|funny(X))))&
((quiet(susan)&~happy(susan)))&
((~kind(paul)&~strong(paul)))&
((curious(john)<~>~generous(john)))&
(?[X]:((~calm(X)<~>calm(X)))) | ~kind(alice) | [
"p1",
"p3",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 93994278954924004925395
% SZS output start Proof for 93994278954924004925395
2. ! [X0] : ((quiet(X0) | ~rich(X0)) <=> (~wise(X0) & curious(X0))) [input p1]
4. (~rich(alice) | creative(alice)) <=> (~patient(lucy) & patient(lucy)) [input p3]
12. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> rich(X0)) [input p11]
14. ! [X0] : ((quiet(X0) | ~rich(X0)) => creative(X0)) [input p13]
19. curious(alice) [input p18]
25. ~kind(alice) [input hypothesis]
35. ! [X0] : (creative(X0) | (~quiet(X0) & rich(X0))) [ennf transformation 14]
39. ! [X0] : (((quiet(X0) | ~rich(X0)) | (wise(X0) | ~curious(X0))) & ((~wise(X0) & curious(X0)) | (~quiet(X0) & rich(X0)))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | ~rich(X0) | wise(X0) | ~curious(X0)) & ((~wise(X0) & curious(X0)) | (~quiet(X0) & rich(X0)))) [flattening 39]
41. ((~rich(alice) | creative(alice)) | (patient(lucy) | ~patient(lucy))) & ((~patient(lucy) & patient(lucy)) | (rich(alice) & ~creative(alice))) [nnf transformation 4]
42. (~rich(alice) | creative(alice) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | (rich(alice) & ~creative(alice))) [flattening 41]
54. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~rich(X0)) & (rich(X0) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 12]
78. ~wise(X0) | rich(X0) [cnf transformation 40]
80. ~curious(X0) | ~rich(X0) | wise(X0) | quiet(X0) [cnf transformation 40]
83. patient(lucy) | ~creative(alice) [cnf transformation 42]
84. patient(lucy) | rich(alice) [cnf transformation 42]
85. ~patient(lucy) | ~creative(alice) [cnf transformation 42]
86. ~patient(lucy) | rich(alice) [cnf transformation 42]
112. kind(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 54]
121. ~quiet(X0) | creative(X0) [cnf transformation 35]
135. curious(alice) [cnf transformation 19]
145. ~kind(alice) [cnf transformation 25]
172. 6 <=> rich(alice) [avatar definition]
174. rich(alice) <- (6) [avatar component clause 172]
176. 7 <=> patient(lucy) [avatar definition]
179. 6 | ~7 [avatar split clause 86,176,172]
181. 8 <=> creative(alice) [avatar definition]
183. ~creative(alice) <- (~8) [avatar component clause 181]
184. ~8 | ~7 [avatar split clause 85,176,181]
185. 6 | 7 [avatar split clause 84,176,172]
186. ~8 | 7 [avatar split clause 83,176,181]
227. ~wise(X0) | kind(X0) [subsumption resolution 112,78]
399. ~rich(alice) | wise(alice) | quiet(alice) [resolution 80,135]
402. wise(alice) | quiet(alice) <- (6) [subsumption resolution 399,174]
404. 40 <=> quiet(alice) [avatar definition]
406. quiet(alice) <- (40) [avatar component clause 404]
408. 41 <=> wise(alice) [avatar definition]
410. wise(alice) <- (41) [avatar component clause 408]
411. 40 | 41 | ~6 [avatar split clause 402,172,408,404]
431. creative(alice) <- (40) [resolution 406,121]
433. $false <- (~8, 40) [subsumption resolution 431,183]
434. 8 | ~40 [avatar contradiction clause 433]
467. kind(alice) <- (41) [resolution 410,227]
470. $false <- (41) [subsumption resolution 467,145]
471. ~41 [avatar contradiction clause 470]
472. $false [avatar sat refutation 179,184,185,186,411,434,471]
% SZS output end Proof for 93994278954924004925395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not brave is both calm and strong.
Everyone who is not humble is not kind or patient.
Everyone who is either happy or not patient is not happy.
If someone is wise then someone is either not old or not humble and vice versa.
Everyone who is funny or creative is both not happy and wise and vice versa.
Everyone who is either not rich or not strong is either wise or funny and vice versa.
Everyone who is patient or not strong is not humble or not kind.
If john is not generous then someone is both strong and funny and vice versa.
If someone is not brave then lucy is both quiet and calm.
Everyone who is either not tall or not quiet is both not happy and funny and vice versa.
If paul is both curious and not patient then someone is tall and vice versa.
Everyone who is both not kind and creative is both patient and not rich.
If someone is not generous then someone is not wise and vice versa.
If susan is either wise or brave then someone is either not quiet or curious.
If someone is either calm or old then someone is either not old or curious and vice versa.
Everyone who is not creative is not strong and vice versa.
Paul is either generous or not quiet.
Someone is humble.
Someone is not creative or old.
Someone is either not calm or wise.
Someone is either not creative or not curious.
John is both not humble and funny.
Someone is quiet or curious.
Someone is humble or not calm. | John is not kind. | contradiction | (![X]:((wise(X)|~brave(X))=>(calm(X)&strong(X))))&
(![X]:(~humble(X)=>(~kind(X)|patient(X))))&
(![X]:((happy(X)<~>~patient(X))=>~happy(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((funny(X)|creative(X))<=>(~happy(X)&wise(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(wise(X)<~>funny(X))))&
(![X]:((patient(X)|~strong(X))=>(~humble(X)|~kind(X))))&
((~generous(john))<=>(?[X]:((strong(X)&funny(X)))))&
((?[X]:(~brave(X)))=>((quiet(lucy)&calm(lucy))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(~happy(X)&funny(X))))&
(((curious(paul)&~patient(paul)))<=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&creative(X))=>(patient(X)&~rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~wise(X))))&
(((wise(susan)<~>brave(susan)))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((calm(X)<~>old(X))))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:(~creative(X)<=>~strong(X)))&
((generous(paul)<~>~quiet(paul)))&
(?[X]:(humble(X)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~calm(X)<~>wise(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~humble(john)&funny(john)))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:((humble(X)|~calm(X)))) | ~kind(john) | [
"p0",
"p4",
"p5",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 921070622680657095126184
% SZS output start Proof for 921070622680657095126184
1. ! [X0] : ((~brave(X0) | wise(X0)) => (strong(X0) & calm(X0))) [input p0]
5. ! [X0] : ((creative(X0) | funny(X0)) <=> (wise(X0) & ~happy(X0))) [input p4]
6. ! [X0] : ((~rich(X0) <~> ~strong(X0)) <=> (wise(X0) <~> funny(X0))) [input p5]
12. ! [X0] : ((creative(X0) & ~kind(X0)) => (~rich(X0) & patient(X0))) [input p11]
16. ! [X0] : (~creative(X0) <=> ~strong(X0)) [input p15]
22. funny(john) & ~humble(john) [input p21]
25. ~kind(john) [input hypothesis]
29. ! [X0] : ((strong(X0) & calm(X0)) | (brave(X0) & ~wise(X0))) [ennf transformation 1]
36. ! [X0] : ((~rich(X0) & patient(X0)) | (~creative(X0) | kind(X0))) [ennf transformation 12]
37. ! [X0] : ((~rich(X0) & patient(X0)) | ~creative(X0) | kind(X0)) [flattening 36]
45. ! [X0] : (((creative(X0) | funny(X0)) | (~wise(X0) | happy(X0))) & ((wise(X0) & ~happy(X0)) | (~creative(X0) & ~funny(X0)))) [nnf transformation 5]
46. ! [X0] : ((creative(X0) | funny(X0) | ~wise(X0) | happy(X0)) & ((wise(X0) & ~happy(X0)) | (~creative(X0) & ~funny(X0)))) [flattening 45]
47. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [nnf transformation 6]
72. ! [X0] : ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))) [nnf transformation 16]
90. ~wise(X0) | strong(X0) [cnf transformation 29]
101. ~funny(X0) | wise(X0) [cnf transformation 46]
106. ~funny(X0) | ~wise(X0) | ~strong(X0) | rich(X0) [cnf transformation 47]
129. ~rich(X0) | ~creative(X0) | kind(X0) [cnf transformation 37]
144. ~strong(X0) | creative(X0) [cnf transformation 72]
155. funny(john) [cnf transformation 22]
158. ~kind(john) [cnf transformation 25]
186. ~funny(X0) | ~wise(X0) | rich(X0) [subsumption resolution 106,90]
187. ~funny(X0) | rich(X0) [subsumption resolution 186,101]
378. wise(john) [resolution 101,155]
379. strong(john) [resolution 378,90]
386. creative(john) [resolution 379,144]
389. rich(john) [resolution 187,155]
444. ~creative(john) | kind(john) [resolution 129,389]
446. kind(john) [subsumption resolution 444,386]
447. $false [subsumption resolution 446,158]
% SZS output end Proof for 921070622680657095126184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or not brave is both quiet and generous and vice versa. Everyone who is not brave is either calm or funny and vice versa. If fred is not kind then someone is both calm and not generous. If someone is not funny then paul is not strong or not patient and vice versa. If paul is not quiet then paul is quiet or creative and vice versa. Everyone who is either not old or tall is not tall or strong. Everyone who is both not strong and not wise is either not humble or not quiet. If fred is not humble or humble then someone is both not patient and not old and vice versa. If someone is humble then someone is not calm and vice versa. Everyone who is either not old or happy is not kind. If someone is not patient then someone is generous or not calm and vice versa. Everyone who is generous is not wise or funny. Everyone who is happy or not humble is strong and vice versa. If someone is both not wise and rich then paul is either calm or wise and vice versa. Everyone who is both not strong and not rich is not curious and vice versa. If fred is calm then lucy is not funny and vice versa. Someone is strong. Someone is not tall. Someone is both patient and not kind. Susan is rich. Someone is either creative or funny. Alice is not generous. Someone is not patient. Someone is calm. | Paul is not creative. | contradiction | (![X]:((~strong(X)<~>~brave(X))<=>(quiet(X)&generous(X))))&
(![X]:(~brave(X)<=>(calm(X)<~>funny(X))))&
((~kind(fred))=>(?[X]:((calm(X)&~generous(X)))))&
((?[X]:(~funny(X)))<=>((~strong(paul)|~patient(paul))))&
((~quiet(paul))<=>((quiet(paul)|creative(paul))))&
(![X]:((~old(X)<~>tall(X))=>(~tall(X)|strong(X))))&
(![X]:((~strong(X)&~wise(X))=>(~humble(X)<~>~quiet(X))))&
(((~humble(fred)|humble(fred)))<=>(?[X]:((~patient(X)&~old(X)))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((~old(X)<~>happy(X))=>~kind(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:(generous(X)=>(~wise(X)|funny(X))))&
(![X]:((happy(X)|~humble(X))<=>strong(X)))&
((?[X]:((~wise(X)&rich(X))))<=>((calm(paul)<~>wise(paul))))&
(![X]:((~strong(X)&~rich(X))<=>~curious(X)))&
((calm(fred))<=>(~funny(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(~tall(X)))&
(?[X]:((patient(X)&~kind(X))))&
(rich(susan))&
(?[X]:((creative(X)<~>funny(X))))&
(~generous(alice))&
(?[X]:(~patient(X)))&
(?[X]:(calm(X))) | ~creative(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8567220370218979994851443
% SZS output start Proof for 8567220370218979994851443
5. ~quiet(paul) <=> (creative(paul) | quiet(paul)) [input p4]
25. ~creative(paul) [input hypothesis]
46. (~quiet(paul) | (~creative(paul) & ~quiet(paul))) & ((creative(paul) | quiet(paul)) | quiet(paul)) [nnf transformation 5]
47. (~quiet(paul) | (~creative(paul) & ~quiet(paul))) & (creative(paul) | quiet(paul) | quiet(paul)) [flattening 46]
101. creative(paul) | quiet(paul) | quiet(paul) [cnf transformation 47]
102. ~quiet(paul) | ~quiet(paul) [cnf transformation 47]
142. ~creative(paul) [cnf transformation 25]
144. creative(paul) | quiet(paul) [duplicate literal removal 101]
145. ~quiet(paul) [duplicate literal removal 102]
179. 8 <=> creative(paul) [avatar definition]
183. 9 <=> quiet(paul) [avatar definition]
187. ~9 [avatar split clause 145,183]
188. 9 | 8 [avatar split clause 144,179,183]
287. ~8 [avatar split clause 142,179]
288. $false [avatar sat refutation 187,188,287]
% SZS output end Proof for 8567220370218979994851443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or not humble then someone is not wise and vice versa.
If someone is not tall or not calm then susan is not happy.
If alice is both wise and not quiet then someone is wise and vice versa.
If someone is funny then lucy is either not happy or not tall and vice versa.
If someone is old then fred is both rich and not strong.
Everyone who is not kind or not generous is both old and not generous.
If alice is both not wise and not happy then john is either not quiet or not tall and vice versa.
If fred is either creative or patient then paul is both not happy and not brave.
Everyone who is patient or not creative is either generous or not old.
Everyone who is rich is not old or old and vice versa.
Everyone who is rich is both strong and kind and vice versa.
Everyone who is both generous and strong is either funny or old and vice versa.
Everyone who is either not old or wise is either rich or not old.
If lucy is both curious and wise then susan is old and vice versa.
Susan is curious or not quiet.
Someone is happy.
Someone is both rich and not calm.
John is both tall and not brave.
Paul is patient or not humble.
Someone is brave or not humble. | Fred is not creative. | contradiction | ((?[X]:((curious(X)<~>~humble(X))))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(~happy(susan)))&
(((wise(alice)&~quiet(alice)))<=>(?[X]:(wise(X))))&
((?[X]:(funny(X)))<=>((~happy(lucy)<~>~tall(lucy))))&
((?[X]:(old(X)))=>((rich(fred)&~strong(fred))))&
(![X]:((~kind(X)|~generous(X))=>(old(X)&~generous(X))))&
(((~wise(alice)&~happy(alice)))<=>((~quiet(john)<~>~tall(john))))&
(((creative(fred)<~>patient(fred)))=>((~happy(paul)&~brave(paul))))&
(![X]:((patient(X)|~creative(X))=>(generous(X)<~>~old(X))))&
(![X]:(rich(X)<=>(~old(X)|old(X))))&
(![X]:(rich(X)<=>(strong(X)&kind(X))))&
(![X]:((generous(X)&strong(X))<=>(funny(X)<~>old(X))))&
(![X]:((~old(X)<~>wise(X))=>(rich(X)<~>~old(X))))&
(((curious(lucy)&wise(lucy)))<=>(old(susan)))&
((curious(susan)|~quiet(susan)))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)&~calm(X))))&
((tall(john)&~brave(john)))&
((patient(paul)|~humble(paul)))&
(?[X]:((brave(X)|~humble(X)))) | ~creative(fred) | [
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1688215651346650280478662
% SZS output start Proof for 1688215651346650280478662
5. ? [X0] : old(X0) => (~strong(fred) & rich(fred)) [input p4]
6. ! [X0] : ((~generous(X0) | ~kind(X0)) => (~generous(X0) & old(X0))) [input p5]
9. ! [X0] : ((~creative(X0) | patient(X0)) => (generous(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : (rich(X0) <=> (old(X0) | ~old(X0))) [input p9]
11. ! [X0] : (rich(X0) <=> (kind(X0) & strong(X0))) [input p10]
21. ~creative(fred) [input hypothesis]
24. (~strong(fred) & rich(fred)) | ! [X0] : ~old(X0) [ennf transformation 5]
25. ! [X0] : ((~generous(X0) & old(X0)) | (generous(X0) & kind(X0))) [ennf transformation 6]
27. ! [X0] : ((generous(X0) <~> ~old(X0)) | (creative(X0) & ~patient(X0))) [ennf transformation 9]
46. ! [X0] : (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (creative(X0) & ~patient(X0))) [nnf transformation 27]
47. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 10]
48. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | ~rich(X0))) [flattening 47]
49. ! [X0] : ((rich(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 11]
50. ! [X0] : ((rich(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | ~rich(X0))) [flattening 49]
76. ~strong(fred) | ~old(X0) [cnf transformation 24]
78. generous(X0) | old(X0) [cnf transformation 25]
94. old(X0) | ~generous(X0) | creative(X0) [cnf transformation 46]
96. rich(X0) | old(X0) [cnf transformation 48]
97. ~old(X0) | rich(X0) [cnf transformation 48]
98. strong(X0) | ~rich(X0) [cnf transformation 50]
122. ~creative(fred) [cnf transformation 21]
200. 18 <=> ! [X0] : ~old(X0) [avatar definition]
201. ~old(X0) <- (18) [avatar component clause 200]
203. 19 <=> strong(fred) [avatar definition]
205. ~strong(fred) <- (~19) [avatar component clause 203]
206. 18 | ~19 [avatar split clause 76,203,200]
235. 25 <=> creative(fred) [avatar definition]
236. ~creative(fred) <- (~25) [avatar component clause 235]
250. creative(X0) | old(X0) [subsumption resolution 94,78]
254. rich(X0) [subsumption resolution 96,97]
256. strong(X0) [subsumption resolution 98,254]
305. ~25 [avatar split clause 122,235]
307. old(fred) <- (~25) [resolution 250,236]
308. $false <- (18, ~25) [subsumption resolution 307,201]
309. ~18 | 25 [avatar contradiction clause 308]
310. $false <- (~19) [subsumption resolution 205,256]
311. 19 [avatar contradiction clause 310]
312. $false [avatar sat refutation 206,305,309,311]
% SZS output end Proof for 1688215651346650280478662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is calm and vice versa.
Everyone who is not strong is not happy or not funny and vice versa.
Everyone who is funny is both calm and not tall.
Everyone who is not rich is both kind and wise.
Everyone who is not quiet or not kind is patient or not happy and vice versa.
If someone is either creative or quiet then someone is rich and vice versa.
Everyone who is either calm or old is either funny or tall.
Everyone who is either patient or not happy is either wise or not strong and vice versa.
Everyone who is both not generous and funny is strong.
If john is either not curious or not generous then john is not quiet and vice versa.
If mary is calm or wise then lucy is both quiet and not patient.
Everyone who is both not creative and tall is either kind or quiet and vice versa.
If fred is both rich and not curious then alice is either not strong or funny.
Everyone who is not tall is both generous and humble.
If someone is both brave and happy then someone is not curious or not patient.
Fred is both humble and not old.
Alice is either not patient or wise.
Mary is creative or not creative.
Someone is generous or happy.
Lucy is creative.
Alice is either not humble or not calm.
Someone is both generous and not patient.
Someone is generous or not patient. | Alice is funny. | contradiction | ((?[X]:(~strong(X)))<=>(?[X]:(calm(X))))&
(![X]:(~strong(X)<=>(~happy(X)|~funny(X))))&
(![X]:(funny(X)=>(calm(X)&~tall(X))))&
(![X]:(~rich(X)=>(kind(X)&wise(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(patient(X)|~happy(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:((calm(X)<~>old(X))=>(funny(X)<~>tall(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((~generous(X)&funny(X))=>strong(X)))&
(((~curious(john)<~>~generous(john)))<=>(~quiet(john)))&
(((calm(mary)|wise(mary)))=>((quiet(lucy)&~patient(lucy))))&
(![X]:((~creative(X)&tall(X))<=>(kind(X)<~>quiet(X))))&
(((rich(fred)&~curious(fred)))=>((~strong(alice)<~>funny(alice))))&
(![X]:(~tall(X)=>(generous(X)&humble(X))))&
((?[X]:((brave(X)&happy(X))))=>(?[X]:((~curious(X)|~patient(X)))))&
((humble(fred)&~old(fred)))&
((~patient(alice)<~>wise(alice)))&
((creative(mary)|~creative(mary)))&
(?[X]:((generous(X)|happy(X))))&
(creative(lucy))&
((~humble(alice)<~>~calm(alice)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((generous(X)|~patient(X)))) | funny(alice) | [
"p2",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5714232342252856603855759
% SZS output start Proof for 5714232342252856603855759
3. ! [X0] : (funny(X0) => (~tall(X0) & calm(X0))) [input p2]
14. ! [X0] : (~tall(X0) => (humble(X0) & generous(X0))) [input p13]
21. ~humble(alice) <~> ~calm(alice) [input p20]
24. funny(alice) [input hypothesis]
29. ! [X0] : ((~tall(X0) & calm(X0)) | ~funny(X0)) [ennf transformation 3]
37. ! [X0] : ((humble(X0) & generous(X0)) | tall(X0)) [ennf transformation 14]
61. (calm(alice) | humble(alice)) & (~calm(alice) | ~humble(alice)) [nnf transformation 21]
71. ~funny(X0) | calm(X0) [cnf transformation 29]
72. ~tall(X0) | ~funny(X0) [cnf transformation 29]
113. humble(X0) | tall(X0) [cnf transformation 37]
121. ~calm(alice) | ~humble(alice) [cnf transformation 61]
126. funny(alice) [cnf transformation 24]
222. 21 <=> funny(alice) [avatar definition]
223. funny(alice) <- (21) [avatar component clause 222]
246. 26 <=> humble(alice) [avatar definition]
247. ~humble(alice) <- (~26) [avatar component clause 246]
250. 27 <=> calm(alice) [avatar definition]
251. ~calm(alice) <- (~27) [avatar component clause 250]
254. ~26 | ~27 [avatar split clause 121,250,246]
264. 21 [avatar split clause 126,222]
271. calm(alice) <- (21) [resolution 71,223]
272. $false <- (21, ~27) [subsumption resolution 271,251]
273. ~21 | 27 [avatar contradiction clause 272]
281. tall(alice) <- (~26) [resolution 113,247]
289. ~funny(alice) <- (~26) [resolution 281,72]
290. $false <- (21, ~26) [subsumption resolution 289,223]
291. ~21 | 26 [avatar contradiction clause 290]
292. $false [avatar sat refutation 254,264,273,291]
% SZS output end Proof for 5714232342252856603855759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not happy and not wise is not calm.
Everyone who is either not rich or not patient is not humble or happy and vice versa.
Everyone who is either happy or rich is both quiet and strong and vice versa.
If alice is either not humble or generous then someone is not old or not tall.
Everyone who is not humble or tall is both strong and quiet and vice versa.
Everyone who is both not humble and patient is not rich or generous.
If mary is not happy then mary is either not humble or not strong and vice versa.
Everyone who is either creative or curious is both not kind and old.
If mary is both creative and rich then someone is not old or brave and vice versa.
If someone is both creative and humble then susan is patient or generous and vice versa.
Everyone who is both not creative and not brave is tall or not funny.
If someone is rich then someone is not tall and vice versa.
If lucy is not patient then alice is both wise and not curious.
If fred is both old and patient then susan is not patient or not quiet and vice versa.
If lucy is not funny or quiet then someone is brave and vice versa.
If alice is creative or not quiet then fred is either creative or calm and vice versa.
Fred is both not generous and old.
Mary is both patient and tall.
Paul is not humble or patient.
Someone is either not patient or not strong.
Someone is creative.
Someone is curious or rich.
Someone is either not happy or creative. | Lucy is brave. | contradiction | (![X]:((~happy(X)&~wise(X))=>~calm(X)))&
(![X]:((~rich(X)<~>~patient(X))<=>(~humble(X)|happy(X))))&
(![X]:((happy(X)<~>rich(X))<=>(quiet(X)&strong(X))))&
(((~humble(alice)<~>generous(alice)))=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~humble(X)|tall(X))<=>(strong(X)&quiet(X))))&
(![X]:((~humble(X)&patient(X))=>(~rich(X)|generous(X))))&
((~happy(mary))<=>((~humble(mary)<~>~strong(mary))))&
(![X]:((creative(X)<~>curious(X))=>(~kind(X)&old(X))))&
(((creative(mary)&rich(mary)))<=>(?[X]:((~old(X)|brave(X)))))&
((?[X]:((creative(X)&humble(X))))<=>((patient(susan)|generous(susan))))&
(![X]:((~creative(X)&~brave(X))=>(tall(X)|~funny(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~tall(X))))&
((~patient(lucy))=>((wise(alice)&~curious(alice))))&
(((old(fred)&patient(fred)))<=>((~patient(susan)|~quiet(susan))))&
(((~funny(lucy)|quiet(lucy)))<=>(?[X]:(brave(X))))&
(((creative(alice)|~quiet(alice)))<=>((creative(fred)<~>calm(fred))))&
((~generous(fred)&old(fred)))&
((patient(mary)&tall(mary)))&
((~humble(paul)|patient(paul)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:(creative(X)))&
(?[X]:((curious(X)|rich(X))))&
(?[X]:((~happy(X)<~>creative(X)))) | brave(lucy) | [
"p1",
"p4",
"p6",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3187092758373806197883701
% SZS output start Proof for 3187092758373806197883701
2. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (happy(X0) | ~humble(X0))) [input p1]
5. ! [X0] : ((tall(X0) | ~humble(X0)) <=> (quiet(X0) & strong(X0))) [input p4]
7. ~happy(mary) <=> (~humble(mary) <~> ~strong(mary)) [input p6]
9. (rich(mary) & creative(mary)) <=> ? [X0] : (brave(X0) | ~old(X0)) [input p8]
18. tall(mary) & patient(mary) [input p17]
24. brave(lucy) [input hypothesis]
36. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~happy(X0) & humble(X0))) & ((happy(X0) | ~humble(X0)) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 2]
37. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~happy(X0) & humble(X0))) & (happy(X0) | ~humble(X0) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [flattening 36]
43. ! [X0] : (((tall(X0) | ~humble(X0)) | (~quiet(X0) | ~strong(X0))) & ((quiet(X0) & strong(X0)) | (~tall(X0) & humble(X0)))) [nnf transformation 5]
44. ! [X0] : ((tall(X0) | ~humble(X0) | ~quiet(X0) | ~strong(X0)) & ((quiet(X0) & strong(X0)) | (~tall(X0) & humble(X0)))) [flattening 43]
45. (~happy(mary) | ((~humble(mary) | strong(mary)) & (~strong(mary) | humble(mary)))) & (((strong(mary) | humble(mary)) & (~strong(mary) | ~humble(mary))) | happy(mary)) [nnf transformation 7]
47. ((rich(mary) & creative(mary)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X0] : (brave(X0) | ~old(X0)) | (~rich(mary) | ~creative(mary))) [nnf transformation 9]
48. ((rich(mary) & creative(mary)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X0] : (brave(X0) | ~old(X0)) | ~rich(mary) | ~creative(mary)) [flattening 47]
49. ((rich(mary) & creative(mary)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X1] : (brave(X1) | ~old(X1)) | ~rich(mary) | ~creative(mary)) [rectify 48]
50. ? [X1] : (brave(X1) | ~old(X1)) => (brave(sK1) | ~old(sK1)) [choice axiom]
51. ((rich(mary) & creative(mary)) | ! [X0] : (~brave(X0) & old(X0))) & ((brave(sK1) | ~old(sK1)) | ~rich(mary) | ~creative(mary)) [skolemisation 49,50]
83. ~patient(X0) | ~rich(X0) | humble(X0) [cnf transformation 37]
84. ~patient(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 37]
96. ~tall(X0) | strong(X0) [cnf transformation 44]
101. ~strong(mary) | ~humble(mary) | happy(mary) [cnf transformation 45]
111. rich(mary) | ~brave(X0) [cnf transformation 51]
137. patient(mary) [cnf transformation 18]
138. tall(mary) [cnf transformation 18]
146. brave(lucy) [cnf transformation 24]
167. 5 <=> strong(mary) [avatar definition]
171. 6 <=> happy(mary) [avatar definition]
172. happy(mary) <- (6) [avatar component clause 171]
177. 7 <=> humble(mary) [avatar definition]
181. 6 | ~7 | ~5 [avatar split clause 101,167,177,171]
183. 8 <=> ! [X0] : ~brave(X0) [avatar definition]
184. ~brave(X0) <- (8) [avatar component clause 183]
186. 9 <=> rich(mary) [avatar definition]
188. rich(mary) <- (9) [avatar component clause 186]
189. 8 | 9 [avatar split clause 111,186,183]
355. $false <- (8) [resolution 184,146]
356. ~8 [avatar contradiction clause 355]
362. strong(mary) [resolution 96,138]
368. ~rich(mary) | humble(mary) [resolution 83,137]
371. humble(mary) <- (9) [subsumption resolution 368,188]
383. 5 [avatar split clause 362,167]
384. 7 | ~9 [avatar split clause 371,186,177]
385. ~rich(mary) | ~happy(mary) [resolution 84,137]
388. ~happy(mary) <- (9) [subsumption resolution 385,188]
389. $false <- (6, 9) [subsumption resolution 388,172]
390. ~6 | ~9 [avatar contradiction clause 389]
400. $false [avatar sat refutation 181,189,356,383,384,390]
% SZS output end Proof for 3187092758373806197883701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and kind is not rich.
If someone is humble then mary is both creative and tall.
If fred is strong or humble then mary is tall or wise.
If someone is either not creative or not quiet then paul is patient.
If lucy is both humble and old then someone is not curious or curious.
If someone is not happy or curious then someone is either not strong or calm and vice versa.
If paul is curious then someone is either tall or funny.
If susan is not quiet then fred is either not brave or not calm.
Everyone who is calm or rich is humble and vice versa.
Everyone who is not brave or calm is both not happy and funny.
Everyone who is both not generous and funny is happy or brave and vice versa.
If fred is not creative or quiet then someone is patient and vice versa.
Everyone who is generous is either not patient or rich and vice versa.
Everyone who is happy is not funny or not brave.
Everyone who is not humble is both not calm and happy and vice versa.
Everyone who is either not funny or curious is both not patient and strong and vice versa.
Lucy is both brave and not wise.
Someone is not rich.
Someone is both funny and not rich.
John is brave or rich.
Mary is either not calm or old.
Mary is either strong or not calm.
John is tall or old.
Paul is either generous or humble. | Mary is not happy. | entailment | (![X]:((strong(X)&kind(X))=>~rich(X)))&
((?[X]:(humble(X)))=>((creative(mary)&tall(mary))))&
(((strong(fred)|humble(fred)))=>((tall(mary)|wise(mary))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(patient(paul)))&
(((humble(lucy)&old(lucy)))=>(?[X]:((~curious(X)|curious(X)))))&
((?[X]:((~happy(X)|curious(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((curious(paul))=>(?[X]:((tall(X)<~>funny(X)))))&
((~quiet(susan))=>((~brave(fred)<~>~calm(fred))))&
(![X]:((calm(X)|rich(X))<=>humble(X)))&
(![X]:((~brave(X)|calm(X))=>(~happy(X)&funny(X))))&
(![X]:((~generous(X)&funny(X))<=>(happy(X)|brave(X))))&
(((~creative(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>rich(X))))&
(![X]:(happy(X)=>(~funny(X)|~brave(X))))&
(![X]:(~humble(X)<=>(~calm(X)&happy(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~patient(X)&strong(X))))&
((brave(lucy)&~wise(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:((funny(X)&~rich(X))))&
((brave(john)|rich(john)))&
((~calm(mary)<~>old(mary)))&
((strong(mary)<~>~calm(mary)))&
((tall(john)|old(john)))&
((generous(paul)<~>humble(paul))) | ~happy(mary) | [
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5256490969780822204255704
% SZS output start Proof for 5256490969780822204255704
10. ! [X0] : ((calm(X0) | ~brave(X0)) => (funny(X0) & ~happy(X0))) [input p9]
11. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (brave(X0) | happy(X0))) [input p10]
14. ! [X0] : (happy(X0) => (~brave(X0) | ~funny(X0))) [input p13]
25. happy(mary) [input hypothesis]
36. ! [X0] : ((funny(X0) & ~happy(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 10]
37. ! [X0] : ((~brave(X0) | ~funny(X0)) | ~happy(X0)) [ennf transformation 14]
38. ! [X0] : (~brave(X0) | ~funny(X0) | ~happy(X0)) [flattening 37]
53. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~funny(X0) | generous(X0))) [flattening 53]
92. ~happy(X0) | brave(X0) [cnf transformation 36]
94. funny(X0) | brave(X0) [cnf transformation 36]
100. funny(X0) | ~brave(X0) [cnf transformation 54]
108. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 38]
131. happy(mary) [cnf transformation 25]
233. funny(X0) [subsumption resolution 100,94]
254. ~brave(X0) | ~happy(X0) [subsumption resolution 108,233]
255. ~happy(X0) [subsumption resolution 254,92]
295. $false [subsumption resolution 131,255]
% SZS output end Proof for 5256490969780822204255704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or patient is both humble and not strong. If paul is not rich then someone is both not rich and kind. If someone is both not quiet and strong then lucy is tall or kind. Everyone who is kind is either not strong or not rich. Everyone who is both calm and rich is either not brave or not calm. Everyone who is rich is curious and vice versa. If mary is strong then mary is not wise and vice versa. If john is both not rich and not calm then someone is wise or generous and vice versa. Everyone who is not brave is both not kind and not rich and vice versa. Everyone who is not creative is not generous or not brave and vice versa. Everyone who is both not strong and brave is both not kind and not quiet. If someone is both calm and generous then someone is old or not funny. Everyone who is funny is both calm and not tall. Everyone who is not rich is both kind and wise. Everyone who is not quiet or not kind is patient or not happy and vice versa. If someone is either creative or quiet then someone is rich and vice versa. Paul is not funny. Someone is either not funny or calm. Fred is old. Someone is either not quiet or not patient. John is both not generous and not creative. Someone is quiet. | Fred is not kind. | entailment | (![X]:((wise(X)|patient(X))=>(humble(X)&~strong(X))))&
((~rich(paul))=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((~quiet(X)&strong(X))))=>((tall(lucy)|kind(lucy))))&
(![X]:(kind(X)=>(~strong(X)<~>~rich(X))))&
(![X]:((calm(X)&rich(X))=>(~brave(X)<~>~calm(X))))&
(![X]:(rich(X)<=>curious(X)))&
((strong(mary))<=>(~wise(mary)))&
(((~rich(john)&~calm(john)))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(~brave(X)<=>(~kind(X)&~rich(X))))&
(![X]:(~creative(X)<=>(~generous(X)|~brave(X))))&
(![X]:((~strong(X)&brave(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((old(X)|~funny(X)))))&
(![X]:(funny(X)=>(calm(X)&~tall(X))))&
(![X]:(~rich(X)=>(kind(X)&wise(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(patient(X)|~happy(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(rich(X))))&
(~funny(paul))&
(?[X]:((~funny(X)<~>calm(X))))&
(old(fred))&
(?[X]:((~quiet(X)<~>~patient(X))))&
((~generous(john)&~creative(john)))&
(?[X]:(quiet(X))) | ~kind(fred) | [
"p0",
"p3",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8805105520331507179845842
% SZS output start Proof for 8805105520331507179845842
1. ! [X0] : ((patient(X0) | wise(X0)) => (~strong(X0) & humble(X0))) [input p0]
4. ! [X0] : (kind(X0) => (~strong(X0) <~> ~rich(X0))) [input p3]
9. ! [X0] : (~brave(X0) <=> (~rich(X0) & ~kind(X0))) [input p8]
11. ! [X0] : ((brave(X0) & ~strong(X0)) => (~quiet(X0) & ~kind(X0))) [input p10]
14. ! [X0] : (~rich(X0) => (wise(X0) & kind(X0))) [input p13]
23. kind(fred) [input hypothesis]
28. ! [X0] : ((patient(X0) | wise(X0)) => ~strong(X0)) [pure predicate removal 1]
29. ! [X0] : (~strong(X0) | (~patient(X0) & ~wise(X0))) [ennf transformation 28]
33. ! [X0] : ((~strong(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 4]
36. ! [X0] : ((~quiet(X0) & ~kind(X0)) | (~brave(X0) | strong(X0))) [ennf transformation 11]
37. ! [X0] : ((~quiet(X0) & ~kind(X0)) | ~brave(X0) | strong(X0)) [flattening 36]
39. ! [X0] : ((wise(X0) & kind(X0)) | rich(X0)) [ennf transformation 14]
42. ! [X0] : (((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | ~kind(X0)) [nnf transformation 33]
51. ! [X0] : ((~brave(X0) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | brave(X0))) [nnf transformation 9]
52. ! [X0] : ((~brave(X0) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | brave(X0))) [flattening 51]
70. ~strong(X0) | ~wise(X0) [cnf transformation 29]
75. ~kind(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 42]
88. ~kind(X0) | brave(X0) [cnf transformation 52]
94. ~kind(X0) | ~brave(X0) | strong(X0) [cnf transformation 37]
99. rich(X0) | wise(X0) [cnf transformation 39]
116. kind(fred) [cnf transformation 23]
180. ~kind(X0) | strong(X0) [subsumption resolution 94,88]
250. strong(fred) [resolution 180,116]
253. ~strong(fred) | ~rich(fred) [resolution 75,116]
256. ~rich(fred) [subsumption resolution 253,250]
259. ~wise(fred) [resolution 250,70]
276. wise(fred) [resolution 256,99]
277. $false [subsumption resolution 276,259]
% SZS output end Proof for 8805105520331507179845842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not brave then susan is not tall.
Everyone who is either humble or calm is not creative or generous and vice versa.
Everyone who is either not happy or calm is brave and vice versa.
Everyone who is curious or not rich is both not wise and not old.
Everyone who is not generous or generous is both not calm and not creative and vice versa.
Everyone who is either not patient or funny is both not curious and not kind and vice versa.
If lucy is both not patient and not wise then john is either happy or not humble.
Everyone who is not strong or not happy is brave.
Everyone who is both not generous and funny is wise or not humble and vice versa.
Everyone who is strong or not funny is strong or quiet.
If alice is not calm or not strong then someone is not strong or not humble.
If someone is both tall and patient then alice is either calm or not brave and vice versa.
Everyone who is both not brave and quiet is curious or not humble.
Everyone who is both not kind and generous is both old and happy.
If mary is either calm or not wise then alice is both not wise and not kind.
If someone is both brave and not patient then paul is either strong or not happy and vice versa.
Fred is either not brave or not strong.
Susan is both not brave and not creative.
Fred is either strong or not strong.
Someone is either tall or not strong.
Fred is kind or not rich.
Someone is not curious. | Paul is not humble. | contradiction | ((?[X]:((brave(X)&~brave(X))))=>(~tall(susan)))&
(![X]:((humble(X)<~>calm(X))<=>(~creative(X)|generous(X))))&
(![X]:((~happy(X)<~>calm(X))<=>brave(X)))&
(![X]:((curious(X)|~rich(X))=>(~wise(X)&~old(X))))&
(![X]:((~generous(X)|generous(X))<=>(~calm(X)&~creative(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(~curious(X)&~kind(X))))&
(((~patient(lucy)&~wise(lucy)))=>((happy(john)<~>~humble(john))))&
(![X]:((~strong(X)|~happy(X))=>brave(X)))&
(![X]:((~generous(X)&funny(X))<=>(wise(X)|~humble(X))))&
(![X]:((strong(X)|~funny(X))=>(strong(X)|quiet(X))))&
(((~calm(alice)|~strong(alice)))=>(?[X]:((~strong(X)|~humble(X)))))&
((?[X]:((tall(X)&patient(X))))<=>((calm(alice)<~>~brave(alice))))&
(![X]:((~brave(X)&quiet(X))=>(curious(X)|~humble(X))))&
(![X]:((~kind(X)&generous(X))=>(old(X)&happy(X))))&
(((calm(mary)<~>~wise(mary)))=>((~wise(alice)&~kind(alice))))&
((?[X]:((brave(X)&~patient(X))))<=>((strong(paul)<~>~happy(paul))))&
((~brave(fred)<~>~strong(fred)))&
((~brave(susan)&~creative(susan)))&
((strong(fred)<~>~strong(fred)))&
(?[X]:((tall(X)<~>~strong(X))))&
((kind(fred)|~rich(fred)))&
(?[X]:(~curious(X))) | ~humble(paul) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7242993566354058736722006
% SZS output start Proof for 7242993566354058736722006
2. ! [X0] : ((humble(X0) <~> calm(X0)) <=> (generous(X0) | ~creative(X0))) [input p1]
5. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (~creative(X0) & ~calm(X0))) [input p4]
23. ~humble(paul) [input hypothesis]
37. ! [X0] : ((((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))))) [flattening 37]
40. ! [X0] : (((generous(X0) | ~generous(X0)) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 5]
41. ! [X0] : ((generous(X0) | ~generous(X0) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | (~generous(X0) & generous(X0)))) [flattening 40]
68. creative(X0) | humble(X0) | calm(X0) [cnf transformation 38]
80. ~calm(X0) | generous(X0) [cnf transformation 41]
81. ~generous(X0) | ~calm(X0) [cnf transformation 41]
82. ~creative(X0) | generous(X0) [cnf transformation 41]
83. ~generous(X0) | ~creative(X0) [cnf transformation 41]
133. ~humble(paul) [cnf transformation 23]
134. ~creative(X0) [subsumption resolution 82,83]
135. ~calm(X0) [subsumption resolution 80,81]
265. humble(X0) | calm(X0) [resolution 68,134]
266. humble(X0) [subsumption resolution 265,135]
267. $false [resolution 266,133]
% SZS output end Proof for 7242993566354058736722006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both funny and not generous then susan is either wise or creative. Everyone who is kind is both not calm and tall and vice versa. Everyone who is not brave or creative is not happy. Everyone who is both brave and rich is quiet or not old and vice versa. Everyone who is both not quiet and funny is quiet or humble. Everyone who is not quiet or calm is creative or not patient and vice versa. If mary is not generous then someone is not old and vice versa. Everyone who is old is quiet. Everyone who is not strong or generous is not happy. If fred is either old or wise then alice is both not calm and not happy. If john is either happy or not brave then someone is not curious or not rich and vice versa. If alice is either creative or not wise then someone is curious and vice versa. Everyone who is rich is not strong or not humble. Everyone who is both strong and rich is not generous or not kind. If susan is funny then someone is not wise or happy and vice versa. Everyone who is both not curious and humble is old or not strong and vice versa. Lucy is either humble or not wise. Alice is both brave and not creative. Someone is either old or not calm. | Alice is not calm. | neutral | (((funny(paul)&~generous(paul)))=>((wise(susan)<~>creative(susan))))&
(![X]:(kind(X)<=>(~calm(X)&tall(X))))&
(![X]:((~brave(X)|creative(X))=>~happy(X)))&
(![X]:((brave(X)&rich(X))<=>(quiet(X)|~old(X))))&
(![X]:((~quiet(X)&funny(X))=>(quiet(X)|humble(X))))&
(![X]:((~quiet(X)|calm(X))<=>(creative(X)|~patient(X))))&
((~generous(mary))<=>(?[X]:(~old(X))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:((~strong(X)|generous(X))=>~happy(X)))&
(((old(fred)<~>wise(fred)))=>((~calm(alice)&~happy(alice))))&
(((happy(john)<~>~brave(john)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(((creative(alice)<~>~wise(alice)))<=>(?[X]:(curious(X))))&
(![X]:(rich(X)=>(~strong(X)|~humble(X))))&
(![X]:((strong(X)&rich(X))=>(~generous(X)|~kind(X))))&
((funny(susan))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~strong(X))))&
((humble(lucy)<~>~wise(lucy)))&
((brave(alice)&~creative(alice)))&
(?[X]:((old(X)<~>~calm(X)))) | ~calm(alice) | [] | null | 0 |
If someone is not old or not rich then susan is both not brave and brave. Everyone who is not funny is generous or not brave and vice versa. If john is not quiet then susan is curious and vice versa. If someone is not old or rich then someone is either old or generous. Everyone who is happy or not strong is wise or not generous. Everyone who is either not kind or brave is rich or not patient. If paul is not happy or not funny then paul is both not kind and quiet and vice versa. If mary is either not strong or not patient then paul is both kind and wise and vice versa. Everyone who is either not funny or not old is either not rich or not patient and vice versa. Everyone who is either old or not brave is wise or tall and vice versa. Everyone who is not calm or happy is curious or not curious and vice versa. If someone is not curious then someone is happy or not wise. If someone is both not kind and old then john is not rich. Everyone who is either strong or humble is both wise and not funny. If someone is rich then mary is either brave or not rich. If fred is either calm or not curious then john is both not creative and old. Someone is either patient or not quiet. John is either not creative or not wise. Someone is old or creative. Someone is not tall. Paul is both humble and patient. Someone is both brave and not strong. John is either humble or brave. | Paul is strong. | entailment | ((?[X]:((~old(X)|~rich(X))))=>((~brave(susan)&brave(susan))))&
(![X]:(~funny(X)<=>(generous(X)|~brave(X))))&
((~quiet(john))<=>(curious(susan)))&
((?[X]:((~old(X)|rich(X))))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:((happy(X)|~strong(X))=>(wise(X)|~generous(X))))&
(![X]:((~kind(X)<~>brave(X))=>(rich(X)|~patient(X))))&
(((~happy(paul)|~funny(paul)))<=>((~kind(paul)&quiet(paul))))&
(((~strong(mary)<~>~patient(mary)))<=>((kind(paul)&wise(paul))))&
(![X]:((~funny(X)<~>~old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>(wise(X)|tall(X))))&
(![X]:((~calm(X)|happy(X))<=>(curious(X)|~curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((happy(X)|~wise(X)))))&
((?[X]:((~kind(X)&old(X))))=>(~rich(john)))&
(![X]:((strong(X)<~>humble(X))=>(wise(X)&~funny(X))))&
((?[X]:(rich(X)))=>((brave(mary)<~>~rich(mary))))&
(((calm(fred)<~>~curious(fred)))=>((~creative(john)&old(john))))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~creative(john)<~>~wise(john)))&
(?[X]:((old(X)|creative(X))))&
(?[X]:(~tall(X)))&
((humble(paul)&patient(paul)))&
(?[X]:((brave(X)&~strong(X))))&
((humble(john)<~>brave(john))) | strong(paul) | [
"p0",
"p6",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 78193226963270507111652
% SZS output start Proof for 78193226963270507111652
1. ? [X0] : (~rich(X0) | ~old(X0)) => (brave(susan) & ~brave(susan)) [input p0]
7. (~funny(paul) | ~happy(paul)) <=> (quiet(paul) & ~kind(paul)) [input p6]
13. ? [X0] : (old(X0) & ~kind(X0)) => ~rich(john) [input p12]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => (~funny(X0) & wise(X0))) [input p13]
21. patient(paul) & humble(paul) [input p20]
24. ~strong(paul) [input hypothesis]
27. (brave(susan) & ~brave(susan)) | ! [X0] : (rich(X0) & old(X0)) [ennf transformation 1]
34. ~rich(john) | ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 13]
35. ! [X0] : ((~funny(X0) & wise(X0)) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
46. ((~funny(paul) | ~happy(paul)) | (~quiet(paul) | kind(paul))) & ((quiet(paul) & ~kind(paul)) | (funny(paul) & happy(paul))) [nnf transformation 7]
47. (~funny(paul) | ~happy(paul) | ~quiet(paul) | kind(paul)) & ((quiet(paul) & ~kind(paul)) | (funny(paul) & happy(paul))) [flattening 46]
58. ! [X0] : ((~funny(X0) & wise(X0)) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 35]
72. ~brave(susan) | old(X0) [cnf transformation 27]
73. ~brave(susan) | rich(X0) [cnf transformation 27]
74. brave(susan) | old(X0) [cnf transformation 27]
75. brave(susan) | rich(X0) [cnf transformation 27]
90. ~kind(paul) | funny(paul) [cnf transformation 47]
119. ~rich(john) | ~old(X0) | kind(X0) [cnf transformation 34]
123. ~humble(X0) | strong(X0) | ~funny(X0) [cnf transformation 58]
136. humble(paul) [cnf transformation 21]
142. ~strong(paul) [cnf transformation 24]
144. 1 <=> ! [X0] : rich(X0) [avatar definition]
145. rich(X0) <- (1) [avatar component clause 144]
147. 2 <=> brave(susan) [avatar definition]
150. 1 | 2 [avatar split clause 75,147,144]
152. 3 <=> ! [X0] : old(X0) [avatar definition]
153. old(X0) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 74,147,152]
155. 1 | ~2 [avatar split clause 73,147,144]
156. 3 | ~2 [avatar split clause 72,147,152]
183. 9 <=> kind(paul) [avatar definition]
184. ~kind(paul) <- (~9) [avatar component clause 183]
195. 12 <=> funny(paul) [avatar definition]
196. funny(paul) <- (12) [avatar component clause 195]
201. 12 | ~9 [avatar split clause 90,183,195]
235. 19 <=> ! [X0] : (~old(X0) | kind(X0)) [avatar definition]
236. ~old(X0) | kind(X0) <- (19) [avatar component clause 235]
238. 20 <=> rich(john) [avatar definition]
240. ~rich(john) <- (~20) [avatar component clause 238]
241. 19 | ~20 [avatar split clause 119,238,235]
311. $false <- (1, ~20) [resolution 240,145]
312. ~1 | 20 [avatar contradiction clause 311]
313. kind(X0) <- (3, 19) [subsumption resolution 236,153]
314. $false <- (3, ~9, 19) [resolution 313,184]
315. ~3 | 9 | ~19 [avatar contradiction clause 314]
378. strong(paul) | ~funny(paul) [resolution 123,136]
380. ~funny(paul) [subsumption resolution 378,142]
381. $false <- (12) [subsumption resolution 380,196]
382. ~12 [avatar contradiction clause 381]
383. $false [avatar sat refutation 150,154,155,156,201,241,312,315,382]
% SZS output end Proof for 78193226963270507111652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and calm is rich or not brave and vice versa.
If someone is not wise or not kind then someone is either not patient or humble.
Everyone who is strong or not quiet is brave.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
If someone is creative or not patient then someone is both rich and not rich and vice versa.
Everyone who is funny or curious is either not rich or not tall and vice versa.
Everyone who is both strong and not patient is both not kind and not curious.
If susan is either patient or curious then someone is strong or brave.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Everyone who is not curious is either not brave or creative and vice versa.
If alice is curious then someone is not old.
Someone is both calm and not creative.
Mary is either not quiet or brave.
Someone is curious.
Susan is happy or generous.
Someone is either quiet or rich.
Susan is not strong or not quiet. | Lucy is rich. | entailment | (![X]:((~funny(X)&calm(X))<=>(rich(X)|~brave(X))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((strong(X)|~quiet(X))=>brave(X)))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((funny(X)|curious(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((strong(X)&~patient(X))=>(~kind(X)&~curious(X))))&
(((patient(susan)<~>curious(susan)))=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(~curious(X)<=>(~brave(X)<~>creative(X))))&
((curious(alice))=>(?[X]:(~old(X))))&
(?[X]:((calm(X)&~creative(X))))&
((~quiet(mary)<~>brave(mary)))&
(?[X]:(curious(X)))&
((happy(susan)|generous(susan)))&
(?[X]:((quiet(X)<~>rich(X))))&
((~strong(susan)|~quiet(susan))) | rich(lucy) | [
"p4",
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6208727655282427891542508
% SZS output start Proof for 6208727655282427891542508
5. ! [X0] : ((~rich(X0) | kind(X0)) <=> happy(X0)) [input p4]
6. ? [X0] : (~patient(X0) | creative(X0)) <=> ? [X0] : (~rich(X0) & rich(X0)) [input p5]
12. ? [X0] : happy(X0) <=> (curious(lucy) & ~wise(lucy)) [input p11]
13. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p12]
23. ~rich(lucy) [input hypothesis]
25. ? [X0] : (~patient(X0) | creative(X0)) <=> ? [X1] : (~rich(X1) & rich(X1)) [rectify 6]
43. ! [X0] : (((~rich(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((~rich(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [flattening 43]
45. (? [X0] : (~patient(X0) | creative(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X1] : (~rich(X1) & rich(X1)) | ! [X0] : (patient(X0) & ~creative(X0))) [nnf transformation 25]
46. (? [X0] : (~patient(X0) | creative(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X2] : (~rich(X2) & rich(X2)) | ! [X3] : (patient(X3) & ~creative(X3))) [rectify 45]
47. ? [X0] : (~patient(X0) | creative(X0)) => (~patient(sK1) | creative(sK1)) [choice axiom]
48. ? [X2] : (~rich(X2) & rich(X2)) => (~rich(sK2) & rich(sK2)) [choice axiom]
49. ((~patient(sK1) | creative(sK1)) | ! [X1] : (rich(X1) | ~rich(X1))) & ((~rich(sK2) & rich(sK2)) | ! [X3] : (patient(X3) & ~creative(X3))) [skolemisation 46,48,47]
64. (? [X0] : happy(X0) | (~curious(lucy) | wise(lucy))) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [nnf transformation 12]
65. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [flattening 64]
66. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [rectify 65]
67. ? [X0] : happy(X0) => happy(sK7) [choice axiom]
68. (happy(sK7) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [skolemisation 66,67]
69. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 13]
70. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 69]
98. happy(X0) | rich(X0) [cnf transformation 44]
101. rich(sK2) | patient(X3) [cnf transformation 49]
103. ~rich(sK2) | patient(X3) [cnf transformation 49]
125. ~wise(lucy) | ~happy(X1) [cnf transformation 68]
131. ~patient(X0) | wise(X0) [cnf transformation 70]
150. ~rich(lucy) [cnf transformation 23]
164. 4 <=> ! [X1] : wise(X1) [avatar definition]
165. wise(X1) <- (4) [avatar component clause 164]
170. 5 <=> ! [X3] : patient(X3) [avatar definition]
171. patient(X3) <- (5) [avatar component clause 170]
173. 6 <=> rich(sK2) [avatar definition]
176. 5 | ~6 [avatar split clause 103,173,170]
181. 5 | 6 [avatar split clause 101,173,170]
255. 23 <=> wise(lucy) [avatar definition]
256. ~wise(lucy) <- (~23) [avatar component clause 255]
268. 26 <=> ! [X1] : ~happy(X1) [avatar definition]
269. ~happy(X1) <- (26) [avatar component clause 268]
271. 26 | ~23 [avatar split clause 125,255,268]
330. $false <- (4, ~23) [resolution 256,165]
331. ~4 | 23 [avatar contradiction clause 330]
349. wise(X0) <- (5) [resolution 131,171]
350. 4 | ~5 [avatar split clause 349,170,164]
352. rich(X0) <- (26) [resolution 269,98]
363. $false <- (26) [resolution 352,150]
368. ~26 [avatar contradiction clause 363]
369. $false [avatar sat refutation 176,181,271,331,350,368]
% SZS output end Proof for 6208727655282427891542508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or quiet is both not wise and not quiet. If fred is both tall and strong then someone is happy or not kind and vice versa. Everyone who is both generous and not curious is curious. If someone is either not brave or not wise then alice is calm. Everyone who is tall or not strong is not calm or not brave and vice versa. Everyone who is not wise is either calm or curious and vice versa. If lucy is both wise and calm then someone is either not brave or not quiet. If paul is both quiet and not brave then lucy is either strong or not generous. Everyone who is not funny or not tall is not humble or curious and vice versa. If someone is either not generous or quiet then susan is both wise and generous and vice versa. If someone is old or not calm then john is quiet. Everyone who is rich is both funny and not wise and vice versa. If someone is either creative or generous then someone is brave or not kind and vice versa. Everyone who is both humble and kind is either old or brave and vice versa. Everyone who is both kind and generous is either quiet or funny and vice versa. Someone is strong or not rich. Someone is wise or not patient. Someone is both happy and not generous. Alice is wise. Someone is both happy and not curious. Fred is both kind and not humble. Someone is strong or old. Someone is happy or not patient. | Alice is brave. | contradiction | (![X]:((humble(X)|quiet(X))=>(~wise(X)&~quiet(X))))&
(((tall(fred)&strong(fred)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((generous(X)&~curious(X))=>curious(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>(calm(alice)))&
(![X]:((tall(X)|~strong(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>curious(X))))&
(((wise(lucy)&calm(lucy)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((quiet(paul)&~brave(paul)))=>((strong(lucy)<~>~generous(lucy))))&
(![X]:((~funny(X)|~tall(X))<=>(~humble(X)|curious(X))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((wise(susan)&generous(susan))))&
((?[X]:((old(X)|~calm(X))))=>(quiet(john)))&
(![X]:(rich(X)<=>(funny(X)&~wise(X))))&
((?[X]:((creative(X)<~>generous(X))))<=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((humble(X)&kind(X))<=>(old(X)<~>brave(X))))&
(![X]:((kind(X)&generous(X))<=>(quiet(X)<~>funny(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((happy(X)&~generous(X))))&
(wise(alice))&
(?[X]:((happy(X)&~curious(X))))&
((kind(fred)&~humble(fred)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((happy(X)|~patient(X)))) | brave(alice) | [
"p0",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 654236169815092170535787
% SZS output start Proof for 654236169815092170535787
1. ! [X0] : ((quiet(X0) | humble(X0)) => (~quiet(X0) & ~wise(X0))) [input p0]
11. ? [X0] : (~calm(X0) | old(X0)) => quiet(john) [input p10]
14. ! [X0] : ((kind(X0) & humble(X0)) <=> (old(X0) <~> brave(X0))) [input p13]
19. wise(alice) [input p18]
24. brave(alice) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 1]
37. quiet(john) | ! [X0] : (calm(X0) & ~old(X0)) [ennf transformation 11]
65. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~kind(X0) | ~humble(X0)))) [nnf transformation 14]
66. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ~kind(X0) | ~humble(X0))) [flattening 65]
77. ~wise(X0) | ~humble(X0) [cnf transformation 29]
80. ~quiet(X0) | ~quiet(X0) [cnf transformation 29]
111. quiet(john) | ~old(X0) [cnf transformation 37]
123. humble(X0) | old(X0) | ~brave(X0) [cnf transformation 66]
135. wise(alice) [cnf transformation 19]
141. brave(alice) [cnf transformation 24]
143. ~quiet(X0) [duplicate literal removal 80]
219. ~old(X0) [subsumption resolution 111,143]
252. ~brave(X0) | humble(X0) [subsumption resolution 123,219]
269. ~humble(alice) [resolution 77,135]
273. humble(alice) [resolution 252,141]
274. $false [subsumption resolution 273,269]
% SZS output end Proof for 654236169815092170535787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then alice is not curious or humble and vice versa.
If someone is either not tall or calm then paul is both funny and rich and vice versa.
If alice is kind then lucy is happy and vice versa.
If paul is not creative then fred is either quiet or not happy and vice versa.
Everyone who is both happy and funny is both happy and strong and vice versa.
If mary is old then someone is curious or patient.
Everyone who is strong is both tall and humble and vice versa.
If john is creative then susan is not creative.
Everyone who is both wise and happy is not old.
Everyone who is either happy or quiet is not brave.
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
John is both tall and not strong.
Someone is either not patient or not happy.
Fred is both not wise and strong.
Fred is humble.
Mary is both not patient and not kind.
Someone is either creative or old.
Susan is curious.
Someone is either calm or tall. | Alice is tall. | entailment | ((?[X]:(humble(X)))<=>((~curious(alice)|humble(alice))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((funny(paul)&rich(paul))))&
((kind(alice))<=>(happy(lucy)))&
((~creative(paul))<=>((quiet(fred)<~>~happy(fred))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
((old(mary))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(strong(X)<=>(tall(X)&humble(X))))&
((creative(john))=>(~creative(susan)))&
(![X]:((wise(X)&happy(X))=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))=>~brave(X)))&
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((~wise(fred)&strong(fred)))&
(humble(fred))&
((~patient(mary)&~kind(mary)))&
(?[X]:((creative(X)<~>old(X))))&
(curious(susan))&
(?[X]:((calm(X)<~>tall(X)))) | tall(alice) | [
"p6",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1234806905771809205311942
% SZS output start Proof for 1234806905771809205311942
7. ! [X0] : (strong(X0) <=> (humble(X0) & tall(X0))) [input p6]
11. ? [X0] : (rich(X0) | brave(X0)) => (~happy(john) & ~funny(john)) [input p10]
12. ! [X0] : (tall(X0) <=> ~brave(X0)) [input p11]
14. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) & generous(X0))) [input p13]
17. ~strong(john) & tall(john) [input p16]
25. ~tall(alice) [input hypothesis]
31. (~happy(john) & ~funny(john)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 11]
48. ! [X0] : ((strong(X0) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | ~strong(X0))) [nnf transformation 7]
49. ! [X0] : ((strong(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~strong(X0))) [flattening 48]
51. ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))) [nnf transformation 12]
53. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 53]
89. ~strong(X0) | humble(X0) [cnf transformation 49]
90. ~tall(X0) | ~humble(X0) | strong(X0) [cnf transformation 49]
95. ~funny(john) | ~brave(X0) [cnf transformation 31]
100. brave(X0) | tall(X0) [cnf transformation 51]
105. humble(X0) | funny(X0) | strong(X0) [cnf transformation 54]
118. tall(john) [cnf transformation 17]
119. ~strong(john) [cnf transformation 17]
132. ~tall(alice) [cnf transformation 25]
236. 23 <=> ! [X0] : ~brave(X0) [avatar definition]
237. ~brave(X0) <- (23) [avatar component clause 236]
240. 24 <=> funny(john) [avatar definition]
242. ~funny(john) <- (~24) [avatar component clause 240]
244. 23 | ~24 [avatar split clause 95,240,236]
246. funny(X0) | humble(X0) [subsumption resolution 105,89]
306. humble(john) <- (~24) [resolution 246,242]
308. ~humble(john) | strong(john) [resolution 90,118]
311. strong(john) <- (~24) [subsumption resolution 308,306]
312. $false <- (~24) [subsumption resolution 311,119]
313. 24 [avatar contradiction clause 312]
326. tall(X0) <- (23) [resolution 237,100]
331. $false <- (23) [resolution 326,132]
336. ~23 [avatar contradiction clause 331]
337. $false [avatar sat refutation 244,313,336]
% SZS output end Proof for 1234806905771809205311942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not generous or not patient then someone is happy and vice versa.
Everyone who is not generous or not quiet is old.
Everyone who is either not old or humble is both happy and not funny and vice versa.
Everyone who is both funny and calm is strong and vice versa.
If mary is both tall and not quiet then someone is both wise and not calm and vice versa.
Everyone who is both patient and strong is not kind.
If someone is both not quiet and not happy then fred is both not old and patient and vice versa.
Everyone who is either patient or not tall is both patient and generous.
Everyone who is generous is kind or not patient and vice versa.
If mary is not creative then susan is either generous or rich.
Everyone who is calm is either funny or not patient and vice versa.
Everyone who is humble is both not happy and not quiet.
If mary is either not funny or funny then someone is wise or not tall.
Everyone who is creative is humble or not kind.
If mary is not brave then paul is both not curious and calm.
Everyone who is happy is curious.
Someone is either not quiet or not strong.
Someone is both not rich and curious.
Susan is either old or not calm.
Alice is either creative or not generous.
Someone is both curious and wise.
Susan is not happy or not kind.
Fred is both not quiet and not tall.
Mary is not generous. | Fred is not strong. | contradiction | (((~generous(susan)<~>~patient(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>old(X)))&
(![X]:((~old(X)<~>humble(X))<=>(happy(X)&~funny(X))))&
(![X]:((funny(X)&calm(X))<=>strong(X)))&
(((tall(mary)&~quiet(mary)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((patient(X)&strong(X))=>~kind(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((~old(fred)&patient(fred))))&
(![X]:((patient(X)<~>~tall(X))=>(patient(X)&generous(X))))&
(![X]:(generous(X)<=>(kind(X)|~patient(X))))&
((~creative(mary))=>((generous(susan)<~>rich(susan))))&
(![X]:(calm(X)<=>(funny(X)<~>~patient(X))))&
(![X]:(humble(X)=>(~happy(X)&~quiet(X))))&
(((~funny(mary)<~>funny(mary)))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(creative(X)=>(humble(X)|~kind(X))))&
((~brave(mary))=>((~curious(paul)&calm(paul))))&
(![X]:(happy(X)=>curious(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)&curious(X))))&
((old(susan)<~>~calm(susan)))&
((creative(alice)<~>~generous(alice)))&
(?[X]:((curious(X)&wise(X))))&
((~happy(susan)|~kind(susan)))&
((~quiet(fred)&~tall(fred)))&
(~generous(mary)) | ~strong(fred) | [
"p1",
"p2",
"p3",
"p6",
"p7",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2749564151245698940806420
% SZS output start Proof for 2749564151245698940806420
2. ! [X0] : ((~quiet(X0) | ~generous(X0)) => old(X0)) [input p1]
3. ! [X0] : ((~old(X0) <~> humble(X0)) <=> (~funny(X0) & happy(X0))) [input p2]
4. ! [X0] : ((calm(X0) & funny(X0)) <=> strong(X0)) [input p3]
7. ? [X0] : (~happy(X0) & ~quiet(X0)) <=> (patient(fred) & ~old(fred)) [input p6]
8. ! [X0] : ((patient(X0) <~> ~tall(X0)) => (generous(X0) & patient(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> (funny(X0) <~> ~patient(X0))) [input p10]
12. ! [X0] : (humble(X0) => (~quiet(X0) & ~happy(X0))) [input p11]
23. ~tall(fred) & ~quiet(fred) [input p22]
25. ~strong(fred) [input hypothesis]
30. ! [X0] : (old(X0) | (quiet(X0) & generous(X0))) [ennf transformation 2]
33. ! [X0] : ((generous(X0) & patient(X0)) | (patient(X0) <=> ~tall(X0))) [ennf transformation 8]
35. ! [X0] : ((~quiet(X0) & ~happy(X0)) | ~humble(X0)) [ennf transformation 12]
43. ! [X0] : ((((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0))))) [flattening 43]
45. ! [X0] : (((calm(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | (~calm(X0) | ~funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((calm(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | ~calm(X0) | ~funny(X0))) [flattening 45]
52. (? [X0] : (~happy(X0) & ~quiet(X0)) | (~patient(fred) | old(fred))) & ((patient(fred) & ~old(fred)) | ! [X0] : (happy(X0) | quiet(X0))) [nnf transformation 7]
53. (? [X0] : (~happy(X0) & ~quiet(X0)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X0] : (happy(X0) | quiet(X0))) [flattening 52]
54. (? [X0] : (~happy(X0) & ~quiet(X0)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X1] : (happy(X1) | quiet(X1))) [rectify 53]
55. ? [X0] : (~happy(X0) & ~quiet(X0)) => (~happy(sK2) & ~quiet(sK2)) [choice axiom]
56. ((~happy(sK2) & ~quiet(sK2)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X1] : (happy(X1) | quiet(X1))) [skolemisation 54,55]
57. ! [X0] : ((generous(X0) & patient(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) [nnf transformation 33]
61. ! [X0] : ((calm(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~calm(X0))) [nnf transformation 11]
79. old(X0) | quiet(X0) [cnf transformation 30]
84. ~old(X0) | humble(X0) | funny(X0) | ~happy(X0) [cnf transformation 44]
86. ~calm(X0) | strong(X0) | ~funny(X0) [cnf transformation 46]
94. ~old(fred) | happy(X1) | quiet(X1) [cnf transformation 56]
99. patient(X0) | patient(X0) | tall(X0) [cnf transformation 57]
109. ~funny(X0) | ~patient(X0) | calm(X0) [cnf transformation 61]
111. ~humble(X0) | ~happy(X0) [cnf transformation 35]
125. ~quiet(fred) [cnf transformation 23]
126. ~tall(fred) [cnf transformation 23]
128. ~strong(fred) [cnf transformation 25]
131. tall(X0) | patient(X0) [duplicate literal removal 99]
175. 10 <=> old(fred) [avatar definition]
176. ~old(fred) <- (~10) [avatar component clause 175]
177. old(fred) <- (10) [avatar component clause 175]
179. 11 <=> patient(fred) [avatar definition]
180. patient(fred) <- (11) [avatar component clause 179]
193. 14 <=> ! [X1] : (happy(X1) | quiet(X1)) [avatar definition]
194. quiet(X1) | happy(X1) <- (14) [avatar component clause 193]
196. 14 | ~10 [avatar split clause 94,175,193]
262. quiet(fred) <- (~10) [resolution 79,176]
264. $false <- (~10) [subsumption resolution 262,125]
265. 10 [avatar contradiction clause 264]
267. patient(fred) [resolution 131,126]
271. happy(fred) <- (14) [resolution 194,125]
344. humble(fred) | funny(fred) | ~happy(fred) <- (10) [resolution 84,177]
348. humble(fred) | funny(fred) <- (10, 14) [subsumption resolution 344,271]
350. 36 <=> funny(fred) [avatar definition]
352. funny(fred) <- (36) [avatar component clause 350]
354. 37 <=> humble(fred) [avatar definition]
356. humble(fred) <- (37) [avatar component clause 354]
357. 36 | 37 | ~10 | ~14 [avatar split clause 348,193,175,354,350]
363. ~patient(fred) | calm(fred) <- (36) [resolution 352,109]
366. calm(fred) <- (11, 36) [subsumption resolution 363,180]
372. strong(fred) | ~funny(fred) <- (11, 36) [resolution 366,86]
373. ~funny(fred) <- (11, 36) [subsumption resolution 372,128]
374. $false <- (11, 36) [subsumption resolution 373,352]
375. ~11 | ~36 [avatar contradiction clause 374]
381. 11 [avatar split clause 267,179]
386. ~happy(fred) <- (37) [resolution 356,111]
387. $false <- (14, 37) [subsumption resolution 386,271]
388. ~14 | ~37 [avatar contradiction clause 387]
389. $false [avatar sat refutation 196,265,357,375,381,388]
% SZS output end Proof for 2749564151245698940806420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.