premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is strong or not rich then susan is not rich or curious and vice versa.
If someone is not calm then paul is curious or creative.
Everyone who is not wise or curious is both not generous and kind and vice versa.
If john is both not old and happy then john is not generous or wise and vice versa.
Everyone who is not kind or not patient is both not funny and funny and vice versa.
Everyone who is either rich or not tall is both not quiet and tall.
Everyone who is not calm is both not happy and tall.
Everyone who is either not generous or calm is funny and vice versa.
Everyone who is happy is either tall or not creative.
If someone is either creative or brave then fred is not creative or not quiet and vice versa.
Everyone who is not wise or not rich is both not old and tall and vice versa.
If someone is both not tall and quiet then someone is both not wise and not rich.
Everyone who is both patient and happy is either not strong or not happy and vice versa.
Everyone who is both brave and curious is either quiet or not brave and vice versa.
Everyone who is wise is either kind or rich and vice versa.
Someone is either not generous or not tall.
Someone is both wise and not funny.
Paul is either calm or wise.
Someone is either not curious or funny.
Someone is not rich or creative.
Mary is either not quiet or not patient. | Fred is tall. | entailment | ((?[X]:((strong(X)|~rich(X))))<=>((~rich(susan)|curious(susan))))&
((?[X]:(~calm(X)))=>((curious(paul)|creative(paul))))&
(![X]:((~wise(X)|curious(X))<=>(~generous(X)&kind(X))))&
(((~old(john)&happy(john)))<=>((~generous(john)|wise(john))))&
(![X]:((~kind(X)|~patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((rich(X)<~>~tall(X))=>(~quiet(X)&tall(X))))&
(![X]:(~calm(X)=>(~happy(X)&tall(X))))&
(![X]:((~generous(X)<~>calm(X))<=>funny(X)))&
(![X]:(happy(X)=>(tall(X)<~>~creative(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~creative(fred)|~quiet(fred))))&
(![X]:((~wise(X)|~rich(X))<=>(~old(X)&tall(X))))&
((?[X]:((~tall(X)&quiet(X))))=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:((patient(X)&happy(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(kind(X)<~>rich(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((wise(X)&~funny(X))))&
((calm(paul)<~>wise(paul)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((~rich(X)|creative(X))))&
((~quiet(mary)<~>~patient(mary))) | tall(fred) | [
"p4",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 384439235214281933295337
% SZS output start Proof for 384439235214281933295337
5. ! [X0] : ((~patient(X0) | ~kind(X0)) <=> (funny(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((rich(X0) <~> ~tall(X0)) => (tall(X0) & ~quiet(X0))) [input p5]
11. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (tall(X0) & ~old(X0))) [input p10]
15. ! [X0] : (wise(X0) <=> (kind(X0) <~> rich(X0))) [input p14]
22. ~tall(fred) [input hypothesis]
26. ! [X0] : ((tall(X0) & ~quiet(X0)) | (rich(X0) <=> ~tall(X0))) [ennf transformation 6]
39. ! [X0] : (((~patient(X0) | ~kind(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (patient(X0) & kind(X0)))) [nnf transformation 5]
40. ! [X0] : ((~patient(X0) | ~kind(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (patient(X0) & kind(X0)))) [flattening 39]
41. ! [X0] : ((tall(X0) & ~quiet(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) [nnf transformation 26]
49. ! [X0] : (((~rich(X0) | ~wise(X0)) | (~tall(X0) | old(X0))) & ((tall(X0) & ~old(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 11]
50. ! [X0] : ((~rich(X0) | ~wise(X0) | ~tall(X0) | old(X0)) & ((tall(X0) & ~old(X0)) | (rich(X0) & wise(X0)))) [flattening 49]
58. ! [X0] : ((wise(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | ~wise(X0))) [nnf transformation 15]
86. ~funny(X0) | kind(X0) [cnf transformation 40]
88. funny(X0) | kind(X0) [cnf transformation 40]
94. tall(X0) | rich(X0) | tall(X0) [cnf transformation 41]
111. tall(X0) | wise(X0) [cnf transformation 50]
129. ~rich(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 58]
143. ~tall(fred) [cnf transformation 22]
148. tall(X0) | rich(X0) [duplicate literal removal 94]
208. kind(X0) [subsumption resolution 86,88]
255. ~wise(X0) | ~rich(X0) [subsumption resolution 129,208]
305. wise(fred) [resolution 111,143]
308. rich(fred) [resolution 148,143]
318. ~rich(fred) [resolution 255,305]
321. $false [subsumption resolution 318,308]
% SZS output end Proof for 384439235214281933295337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not quiet then alice is both not quiet and not wise and vice versa. If mary is not kind or not wise then alice is either old or not calm. Everyone who is not rich is old. Everyone who is happy or not quiet is not curious or curious and vice versa. If lucy is not old then alice is not old and vice versa. If lucy is either calm or not generous then someone is calm or not rich. Everyone who is either not quiet or tall is both generous and happy and vice versa. If someone is calm or not funny then someone is either not rich or not kind and vice versa. Everyone who is not strong is either patient or old. Everyone who is not patient or not curious is old or not curious and vice versa. Everyone who is quiet or old is both not funny and rich and vice versa. If fred is both rich and not strong then someone is both not old and not rich. Everyone who is both not creative and not brave is humble. If mary is both wise and tall then alice is either not kind or generous. If paul is either not creative or kind then alice is generous or creative. If fred is not generous or not humble then fred is strong. Someone is quiet or not strong. Fred is both not generous and patient. Alice is not generous or generous. Someone is not funny or old. Paul is brave or generous. Someone is both not funny and not tall. Someone is both patient and curious. Someone is curious. | Paul is not creative. | neutral | ((?[X]:((~old(X)|~quiet(X))))<=>((~quiet(alice)&~wise(alice))))&
(((~kind(mary)|~wise(mary)))=>((old(alice)<~>~calm(alice))))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((happy(X)|~quiet(X))<=>(~curious(X)|curious(X))))&
((~old(lucy))<=>(~old(alice)))&
(((calm(lucy)<~>~generous(lucy)))=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((~quiet(X)<~>tall(X))<=>(generous(X)&happy(X))))&
((?[X]:((calm(X)|~funny(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:(~strong(X)=>(patient(X)<~>old(X))))&
(![X]:((~patient(X)|~curious(X))<=>(old(X)|~curious(X))))&
(![X]:((quiet(X)|old(X))<=>(~funny(X)&rich(X))))&
(((rich(fred)&~strong(fred)))=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((~creative(X)&~brave(X))=>humble(X)))&
(((wise(mary)&tall(mary)))=>((~kind(alice)<~>generous(alice))))&
(((~creative(paul)<~>kind(paul)))=>((generous(alice)|creative(alice))))&
(((~generous(fred)|~humble(fred)))=>(strong(fred)))&
(?[X]:((quiet(X)|~strong(X))))&
((~generous(fred)&patient(fred)))&
((~generous(alice)|generous(alice)))&
(?[X]:((~funny(X)|old(X))))&
((brave(paul)|generous(paul)))&
(?[X]:((~funny(X)&~tall(X))))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:(curious(X))) | ~creative(paul) | [] | null | 0 |
Everyone who is both patient and wise is both funny and not creative. Everyone who is either not funny or wise is either brave or not rich. Everyone who is not quiet is both not brave and curious. If susan is both not curious and calm then someone is both not patient and not rich and vice versa. If someone is both creative and curious then someone is patient or not funny and vice versa. If someone is humble or not quiet then someone is both rich and old and vice versa. If susan is either not funny or not generous then fred is both not calm and not happy. Everyone who is creative or not strong is not creative. Everyone who is creative is tall. Everyone who is both patient and not kind is kind or not generous and vice versa. Everyone who is both not kind and not creative is either curious or not humble and vice versa. If someone is quiet or not kind then someone is either not humble or not patient and vice versa. Everyone who is both brave and not rich is either curious or not wise and vice versa. Everyone who is both wise and not rich is both not happy and not kind. Everyone who is either curious or kind is not old and vice versa. If mary is both not happy and not humble then fred is both calm and not strong. Someone is either not quiet or not generous. Fred is both not wise and not kind. Mary is strong. Someone is either not rich or not brave. Paul is both not old and not quiet. Alice is humble or not tall. Fred is not patient. Lucy is not curious or patient. | Fred is not funny. | contradiction | (![X]:((patient(X)&wise(X))=>(funny(X)&~creative(X))))&
(![X]:((~funny(X)<~>wise(X))=>(brave(X)<~>~rich(X))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(((~happy(mary)&~humble(mary)))=>((calm(fred)&~strong(fred))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((~wise(fred)&~kind(fred)))&
(strong(mary))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~old(paul)&~quiet(paul)))&
((humble(alice)|~tall(alice)))&
(~patient(fred))&
((~curious(lucy)|patient(lucy))) | ~funny(fred) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6966437155214369357508247
% SZS output start Proof for 6966437155214369357508247
5. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p4]
8. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p7]
25. ~funny(fred) [input hypothesis]
26. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 5]
34. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 8]
46. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 26]
47. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 46]
48. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK1) & creative(sK1)) [choice axiom]
49. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK2) | patient(sK2)) [choice axiom]
50. ((curious(sK1) & creative(sK1)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK2) | patient(sK2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 47,49,48]
89. creative(sK1) | funny(X1) [cnf transformation 50]
101. ~creative(X0) | ~creative(X0) [cnf transformation 34]
147. ~funny(fred) [cnf transformation 25]
150. ~creative(X0) [duplicate literal removal 101]
175. 6 <=> ! [X1] : funny(X1) [avatar definition]
176. funny(X1) <- (6) [avatar component clause 175]
187. 9 <=> creative(sK1) [avatar definition]
189. creative(sK1) <- (9) [avatar component clause 187]
190. 6 | 9 [avatar split clause 89,187,175]
332. $false <- (6) [resolution 176,147]
333. ~6 [avatar contradiction clause 332]
334. $false <- (9) [subsumption resolution 189,150]
335. ~9 [avatar contradiction clause 334]
336. $false [avatar sat refutation 190,333,335]
% SZS output end Proof for 6966437155214369357508247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or happy then someone is both generous and kind and vice versa.
If someone is both not funny and creative then someone is either not patient or creative and vice versa.
Everyone who is both not patient and curious is both kind and not rich and vice versa.
Everyone who is both not brave and not rich is not creative or not happy.
Everyone who is not rich or not happy is either not patient or not happy.
Everyone who is not curious is generous or not happy and vice versa.
If someone is either kind or creative then john is creative.
If someone is both not strong and not happy then someone is both not happy and wise.
Everyone who is not funny or happy is either brave or not strong and vice versa.
If susan is either kind or not generous then someone is either not happy or not creative.
If susan is either not wise or strong then someone is either not creative or wise and vice versa.
If lucy is not old then someone is not humble.
Everyone who is either not happy or patient is either wise or curious and vice versa.
If someone is either generous or not tall then mary is either funny or not wise and vice versa.
If fred is either creative or happy then john is either curious or generous.
Everyone who is happy or calm is both tall and not patient and vice versa.
Paul is rich.
Someone is both not creative and generous.
John is either not humble or not old.
Someone is not strong.
Lucy is either strong or quiet.
Paul is old or not funny.
Someone is calm or not humble.
Alice is both not old and tall. | Susan is happy. | entailment | ((?[X]:((~rich(X)<~>happy(X))))<=>(?[X]:((generous(X)&kind(X)))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:((~patient(X)&curious(X))<=>(kind(X)&~rich(X))))&
(![X]:((~brave(X)&~rich(X))=>(~creative(X)|~happy(X))))&
(![X]:((~rich(X)|~happy(X))=>(~patient(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(generous(X)|~happy(X))))&
((?[X]:((kind(X)<~>creative(X))))=>(creative(john)))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~funny(X)|happy(X))<=>(brave(X)<~>~strong(X))))&
(((kind(susan)<~>~generous(susan)))=>(?[X]:((~happy(X)<~>~creative(X)))))&
(((~wise(susan)<~>strong(susan)))<=>(?[X]:((~creative(X)<~>wise(X)))))&
((~old(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~happy(X)<~>patient(X))<=>(wise(X)<~>curious(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>((funny(mary)<~>~wise(mary))))&
(((creative(fred)<~>happy(fred)))=>((curious(john)<~>generous(john))))&
(![X]:((happy(X)|calm(X))<=>(tall(X)&~patient(X))))&
(rich(paul))&
(?[X]:((~creative(X)&generous(X))))&
((~humble(john)<~>~old(john)))&
(?[X]:(~strong(X)))&
((strong(lucy)<~>quiet(lucy)))&
((old(paul)|~funny(paul)))&
(?[X]:((calm(X)|~humble(X))))&
((~old(alice)&tall(alice))) | happy(susan) | [
"p4",
"p5",
"p7",
"p10",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 964286405548463044568554
% SZS output start Proof for 964286405548463044568554
5. ! [X0] : ((~happy(X0) | ~rich(X0)) => (~patient(X0) <~> ~happy(X0))) [input p4]
6. ! [X0] : (~curious(X0) <=> (~happy(X0) | generous(X0))) [input p5]
8. ? [X0] : (~happy(X0) & ~strong(X0)) => ? [X0] : (wise(X0) & ~happy(X0)) [input p7]
11. (~wise(susan) <~> strong(susan)) <=> ? [X0] : (~creative(X0) <~> wise(X0)) [input p10]
13. ! [X0] : ((~happy(X0) <~> patient(X0)) <=> (wise(X0) <~> curious(X0))) [input p12]
16. ! [X0] : ((calm(X0) | happy(X0)) <=> (~patient(X0) & tall(X0))) [input p15]
18. ? [X0] : (generous(X0) & ~creative(X0)) [input p17]
25. ~happy(susan) [input hypothesis]
28. ? [X0] : (~happy(X0) & ~strong(X0)) => ? [X1] : (wise(X1) & ~happy(X1)) [rectify 8]
31. ! [X0] : ((~patient(X0) <~> ~happy(X0)) | (happy(X0) & rich(X0))) [ennf transformation 5]
33. ? [X1] : (wise(X1) & ~happy(X1)) | ! [X0] : (happy(X0) | strong(X0)) [ennf transformation 28]
49. ! [X0] : (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (happy(X0) & rich(X0))) [nnf transformation 31]
50. ! [X0] : ((~curious(X0) | (happy(X0) & ~generous(X0))) & ((~happy(X0) | generous(X0)) | curious(X0))) [nnf transformation 6]
51. ! [X0] : ((~curious(X0) | (happy(X0) & ~generous(X0))) & (~happy(X0) | generous(X0) | curious(X0))) [flattening 50]
53. ? [X0] : (wise(X0) & ~happy(X0)) | ! [X1] : (happy(X1) | strong(X1)) [rectify 33]
54. ? [X0] : (wise(X0) & ~happy(X0)) => (wise(sK4) & ~happy(sK4)) [choice axiom]
55. (wise(sK4) & ~happy(sK4)) | ! [X1] : (happy(X1) | strong(X1)) [skolemisation 53,54]
61. (((~strong(susan) | wise(susan)) & (strong(susan) | ~wise(susan))) | ! [X0] : ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (? [X0] : ((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | ((~wise(susan) | ~strong(susan)) & (strong(susan) | wise(susan)))) [nnf transformation 11]
62. (((~strong(susan) | wise(susan)) & (strong(susan) | ~wise(susan))) | ! [X0] : ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (? [X1] : ((~wise(X1) | creative(X1)) & (wise(X1) | ~creative(X1))) | ((~wise(susan) | ~strong(susan)) & (strong(susan) | wise(susan)))) [rectify 61]
63. ? [X1] : ((~wise(X1) | creative(X1)) & (wise(X1) | ~creative(X1))) => ((~wise(sK6) | creative(sK6)) & (wise(sK6) | ~creative(sK6))) [choice axiom]
64. (((~strong(susan) | wise(susan)) & (strong(susan) | ~wise(susan))) | ! [X0] : ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(sK6) | creative(sK6)) & (wise(sK6) | ~creative(sK6))) | ((~wise(susan) | ~strong(susan)) & (strong(susan) | wise(susan)))) [skolemisation 62,63]
67. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [nnf transformation 13]
73. ! [X0] : (((calm(X0) | happy(X0)) | (patient(X0) | ~tall(X0))) & ((~patient(X0) & tall(X0)) | (~calm(X0) & ~happy(X0)))) [nnf transformation 16]
74. ! [X0] : ((calm(X0) | happy(X0) | patient(X0) | ~tall(X0)) & ((~patient(X0) & tall(X0)) | (~calm(X0) & ~happy(X0)))) [flattening 73]
75. ? [X0] : (generous(X0) & ~creative(X0)) => (generous(sK9) & ~creative(sK9)) [choice axiom]
76. generous(sK9) & ~creative(sK9) [skolemisation 18,75]
103. happy(X0) | patient(X0) | happy(X0) [cnf transformation 49]
105. ~curious(X0) | ~generous(X0) [cnf transformation 51]
106. ~curious(X0) | happy(X0) [cnf transformation 51]
109. ~happy(sK4) | happy(X1) | strong(X1) [cnf transformation 55]
110. wise(sK4) | happy(X1) | strong(X1) [cnf transformation 55]
127. ~strong(susan) | wise(susan) | wise(X0) | creative(X0) [cnf transformation 64]
134. patient(X0) | ~happy(X0) | curious(X0) | ~wise(X0) [cnf transformation 67]
136. ~patient(X0) | happy(X0) | curious(X0) | ~wise(X0) [cnf transformation 67]
152. ~patient(X0) | ~happy(X0) [cnf transformation 74]
156. ~creative(sK9) [cnf transformation 76]
157. generous(sK9) [cnf transformation 76]
167. ~happy(susan) [cnf transformation 25]
168. patient(X0) | happy(X0) [duplicate literal removal 103]
244. 18 <=> ! [X1] : (happy(X1) | strong(X1)) [avatar definition]
245. strong(X1) | happy(X1) <- (18) [avatar component clause 244]
247. 19 <=> wise(sK4) [avatar definition]
249. wise(sK4) <- (19) [avatar component clause 247]
250. 18 | 19 [avatar split clause 110,247,244]
252. 20 <=> happy(sK4) [avatar definition]
255. 18 | ~20 [avatar split clause 109,252,244]
280. 26 <=> wise(susan) [avatar definition]
282. wise(susan) <- (26) [avatar component clause 280]
284. 27 <=> strong(susan) [avatar definition]
286. ~strong(susan) <- (~27) [avatar component clause 284]
289. 28 <=> ! [X0] : (wise(X0) | creative(X0)) [avatar definition]
290. wise(X0) | creative(X0) <- (28) [avatar component clause 289]
291. 28 | 26 | ~27 [avatar split clause 127,284,280,289]
315. happy(X0) | curious(X0) | ~wise(X0) [subsumption resolution 136,168]
316. ~wise(X0) | happy(X0) [subsumption resolution 315,106]
318. ~wise(X0) | curious(X0) | patient(X0) [subsumption resolution 134,316]
418. happy(susan) <- (18, ~27) [resolution 245,286]
419. $false <- (18, ~27) [subsumption resolution 418,167]
420. ~18 | 27 [avatar contradiction clause 419]
421. happy(sK4) <- (19) [resolution 316,249]
424. 20 | ~19 [avatar split clause 421,247,252]
427. happy(susan) <- (26) [resolution 282,316]
428. $false <- (26) [subsumption resolution 427,167]
429. ~26 [avatar contradiction clause 428]
433. creative(X1) | happy(X1) <- (28) [resolution 290,316]
551. curious(X0) | patient(X0) | creative(X0) <- (28) [resolution 318,290]
692. happy(sK9) <- (28) [resolution 433,156]
721. ~generous(X4) | creative(X4) | patient(X4) <- (28) [resolution 551,105]
747. creative(sK9) | patient(sK9) <- (28) [resolution 721,157]
767. patient(sK9) <- (28) [subsumption resolution 747,156]
864. ~happy(sK9) <- (28) [resolution 767,152]
876. $false <- (28) [subsumption resolution 864,692]
877. ~28 [avatar contradiction clause 876]
878. $false [avatar sat refutation 250,255,291,420,424,429,877]
% SZS output end Proof for 964286405548463044568554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is tall is not tall.
If john is either humble or not strong then fred is either patient or calm and vice versa.
Everyone who is either not kind or not humble is not kind.
If mary is both rich and funny then someone is not quiet or funny.
If someone is kind then someone is both not wise and happy.
If someone is either wise or happy then john is both quiet and not humble.
Everyone who is both not humble and strong is not curious.
Everyone who is not tall is both rich and quiet and vice versa.
If someone is both not generous and not wise then someone is either not kind or not quiet and vice versa.
If someone is both not patient and not tall then alice is both quiet and not brave and vice versa.
If lucy is either not humble or not funny then someone is strong and vice versa.
If john is both not tall and not generous then someone is strong or not rich.
If someone is not calm then someone is rich or kind.
Paul is funny.
Someone is both not happy and not old.
Paul is not patient.
Paul is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall. | Alice is patient. | neutral | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(tall(X)=>~tall(X)))&
(((humble(john)<~>~strong(john)))<=>((patient(fred)<~>calm(fred))))&
(![X]:((~kind(X)<~>~humble(X))=>~kind(X)))&
(((rich(mary)&funny(mary)))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((wise(X)<~>happy(X))))=>((quiet(john)&~humble(john))))&
(![X]:((~humble(X)&strong(X))=>~curious(X)))&
(![X]:(~tall(X)<=>(rich(X)&quiet(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)&~brave(alice))))&
(((~humble(lucy)<~>~funny(lucy)))<=>(?[X]:(strong(X))))&
(((~tall(john)&~generous(john)))=>(?[X]:((strong(X)|~rich(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(funny(paul))&
(?[X]:((~happy(X)&~old(X))))&
(~patient(paul))&
((old(paul)|~humble(paul)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X)))) | patient(alice) | [] | null | 0 |
If lucy is either not generous or happy then someone is both not strong and strong. If someone is not curious or kind then john is both not kind and not happy. If someone is both not kind and rich then lucy is either humble or not curious. Everyone who is not rich is curious and vice versa. Everyone who is old or not brave is rich and vice versa. Everyone who is not old or not humble is both not creative and rich and vice versa. Everyone who is wise is not tall or not rich and vice versa. If john is both generous and not kind then susan is not tall or not curious. If someone is not patient then someone is either old or not humble and vice versa. Everyone who is either not quiet or quiet is not strong or kind and vice versa. If someone is quiet then lucy is quiet or not calm. Everyone who is both not quiet and not brave is kind or generous and vice versa. If someone is curious then someone is not old. Everyone who is either not brave or patient is not strong. Everyone who is both patient and not patient is humble and vice versa. Someone is either not generous or funny. Someone is both not happy and not old. Someone is either wise or not calm. Alice is not funny. Someone is funny or patient. Someone is brave. Someone is quiet or creative. | John is not creative. | entailment | (((~generous(lucy)<~>happy(lucy)))=>(?[X]:((~strong(X)&strong(X)))))&
((?[X]:((~curious(X)|kind(X))))=>((~kind(john)&~happy(john))))&
((?[X]:((~kind(X)&rich(X))))=>((humble(lucy)<~>~curious(lucy))))&
(![X]:(~rich(X)<=>curious(X)))&
(![X]:((old(X)|~brave(X))<=>rich(X)))&
(![X]:((~old(X)|~humble(X))<=>(~creative(X)&rich(X))))&
(![X]:(wise(X)<=>(~tall(X)|~rich(X))))&
(((generous(john)&~kind(john)))=>((~tall(susan)|~curious(susan))))&
((?[X]:(~patient(X)))<=>(?[X]:((old(X)<~>~humble(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~strong(X)|kind(X))))&
((?[X]:(quiet(X)))=>((quiet(lucy)|~calm(lucy))))&
(![X]:((~quiet(X)&~brave(X))<=>(kind(X)|generous(X))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)<~>patient(X))=>~strong(X)))&
(![X]:((patient(X)&~patient(X))<=>humble(X)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((~happy(X)&~old(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(~funny(alice))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|creative(X)))) | ~creative(john) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7629853772815567260729057
% SZS output start Proof for 7629853772815567260729057
6. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (rich(X0) & ~creative(X0))) [input p5]
15. ! [X0] : ((~patient(X0) & patient(X0)) <=> humble(X0)) [input p14]
23. creative(john) [input hypothesis]
42. ! [X0] : (((~humble(X0) | ~old(X0)) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | (humble(X0) & old(X0)))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | ~old(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | (humble(X0) & old(X0)))) [flattening 42]
59. ! [X0] : (((~patient(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | (patient(X0) | ~patient(X0)))) [nnf transformation 15]
60. ! [X0] : (((~patient(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | patient(X0) | ~patient(X0))) [flattening 59]
91. ~creative(X0) | humble(X0) [cnf transformation 43]
119. patient(X0) | ~humble(X0) [cnf transformation 60]
120. ~patient(X0) | ~humble(X0) [cnf transformation 60]
131. creative(john) [cnf transformation 23]
243. ~humble(X0) [subsumption resolution 119,120]
286. humble(john) [resolution 91,131]
287. $false [subsumption resolution 286,243]
% SZS output end Proof for 7629853772815567260729057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not calm is not humble.
Everyone who is brave is both tall and not happy.
Everyone who is either not patient or calm is not generous or not rich.
Everyone who is both quiet and not old is not patient and vice versa.
If mary is both calm and not tall then someone is not rich.
Everyone who is either not generous or creative is either strong or not generous and vice versa.
Everyone who is not strong or not curious is happy and vice versa.
If someone is old or not happy then someone is either calm or curious and vice versa.
Everyone who is either rich or not calm is strong or not funny and vice versa.
Everyone who is either rich or not calm is both not patient and not old.
If someone is both not humble and not old then someone is not calm or not tall and vice versa.
Everyone who is not patient is either patient or happy and vice versa.
If someone is either patient or not patient then mary is either not humble or not quiet.
Everyone who is not generous or wise is both humble and creative.
Everyone who is either not strong or quiet is both not curious and old and vice versa.
If paul is either wise or not patient then someone is strong or quiet.
John is either rich or brave.
Someone is not kind or not funny.
John is not calm or humble.
Someone is both quiet and not old.
Someone is either not wise or brave.
Someone is happy or not tall.
Someone is either tall or generous. | Mary is not rich. | neutral | (![X]:((old(X)|~calm(X))=>~humble(X)))&
(![X]:(brave(X)=>(tall(X)&~happy(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~generous(X)|~rich(X))))&
(![X]:((quiet(X)&~old(X))<=>~patient(X)))&
(((calm(mary)&~tall(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~generous(X)<~>creative(X))<=>(strong(X)<~>~generous(X))))&
(![X]:((~strong(X)|~curious(X))<=>happy(X)))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>(strong(X)|~funny(X))))&
(![X]:((rich(X)<~>~calm(X))=>(~patient(X)&~old(X))))&
((?[X]:((~humble(X)&~old(X))))<=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:(~patient(X)<=>(patient(X)<~>happy(X))))&
((?[X]:((patient(X)<~>~patient(X))))=>((~humble(mary)<~>~quiet(mary))))&
(![X]:((~generous(X)|wise(X))=>(humble(X)&creative(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~curious(X)&old(X))))&
(((wise(paul)<~>~patient(paul)))=>(?[X]:((strong(X)|quiet(X)))))&
((rich(john)<~>brave(john)))&
(?[X]:((~kind(X)|~funny(X))))&
((~calm(john)|humble(john)))&
(?[X]:((quiet(X)&~old(X))))&
(?[X]:((~wise(X)<~>brave(X))))&
(?[X]:((happy(X)|~tall(X))))&
(?[X]:((tall(X)<~>generous(X)))) | ~rich(mary) | [] | null | 0 |
If someone is generous or not brave then someone is either kind or not quiet. Everyone who is both curious and not tall is either humble or not tall. Everyone who is both funny and not creative is either quiet or not calm. Everyone who is both not patient and patient is either funny or not rich. If someone is both creative and not old then someone is not calm. Everyone who is old is both not humble and not creative and vice versa. Everyone who is either creative or not curious is not calm. Everyone who is both not happy and not kind is either tall or curious. If fred is not brave or calm then someone is not funny. Everyone who is funny is either brave or patient. If susan is either tall or curious then someone is either strong or not funny and vice versa. If someone is not old or not creative then someone is not quiet or wise. Everyone who is both not old and tall is not tall. Everyone who is curious is both not old and not tall and vice versa. If mary is not funny then mary is either not rich or creative and vice versa. If someone is not generous then someone is either not old or calm. Fred is not happy. Someone is both creative and not calm. John is both not tall and not humble. Someone is not funny. Fred is creative. John is happy. Lucy is both rich and not humble. Someone is strong. | John is tall. | contradiction | ((?[X]:((generous(X)|~brave(X))))=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((curious(X)&~tall(X))=>(humble(X)<~>~tall(X))))&
(![X]:((funny(X)&~creative(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((~patient(X)&patient(X))=>(funny(X)<~>~rich(X))))&
((?[X]:((creative(X)&~old(X))))=>(?[X]:(~calm(X))))&
(![X]:(old(X)<=>(~humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~curious(X))=>~calm(X)))&
(![X]:((~happy(X)&~kind(X))=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((~old(X)&tall(X))=>~tall(X)))&
(![X]:(curious(X)<=>(~old(X)&~tall(X))))&
((~funny(mary))<=>((~rich(mary)<~>creative(mary))))&
((?[X]:(~generous(X)))=>(?[X]:((~old(X)<~>calm(X)))))&
(~happy(fred))&
(?[X]:((creative(X)&~calm(X))))&
((~tall(john)&~humble(john)))&
(?[X]:(~funny(X)))&
(creative(fred))&
(happy(john))&
((rich(lucy)&~humble(lucy)))&
(?[X]:(strong(X))) | tall(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8929886306270010058596386
% SZS output start Proof for 8929886306270010058596386
19. ~humble(john) & ~tall(john) [input p18]
25. tall(john) [input hypothesis]
124. ~tall(john) [cnf transformation 19]
132. tall(john) [cnf transformation 25]
235. $false [subsumption resolution 132,124]
% SZS output end Proof for 8929886306270010058596386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or kind is both not tall and happy and vice versa.
Everyone who is brave is both not funny and wise and vice versa.
Everyone who is both quiet and not creative is either happy or not kind.
If someone is not curious or not wise then lucy is not humble and vice versa.
If lucy is both humble and not humble then someone is either not curious or happy and vice versa.
If susan is tall then someone is not old or quiet and vice versa.
Everyone who is not funny is both not curious and not patient and vice versa.
If lucy is either curious or old then susan is happy and vice versa.
Everyone who is both quiet and strong is either not happy or patient.
Everyone who is either not tall or strong is either not patient or strong and vice versa.
If lucy is both not kind and happy then susan is generous and vice versa.
If someone is not funny then someone is funny or tall and vice versa.
Everyone who is both kind and not wise is either calm or happy and vice versa.
If alice is kind then someone is both not calm and not old.
Everyone who is not humble or tall is not rich and vice versa.
Someone is both not creative and not humble.
Paul is both not funny and old.
Someone is both curious and not calm.
Someone is both not patient and not quiet.
Lucy is either generous or not wise.
Someone is curious or not calm. | Alice is curious. | neutral | (![X]:((~rich(X)|kind(X))<=>(~tall(X)&happy(X))))&
(![X]:(brave(X)<=>(~funny(X)&wise(X))))&
(![X]:((quiet(X)&~creative(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(~humble(lucy)))&
(((humble(lucy)&~humble(lucy)))<=>(?[X]:((~curious(X)<~>happy(X)))))&
((tall(susan))<=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:(~funny(X)<=>(~curious(X)&~patient(X))))&
(((curious(lucy)<~>old(lucy)))<=>(happy(susan)))&
(![X]:((quiet(X)&strong(X))=>(~happy(X)<~>patient(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~patient(X)<~>strong(X))))&
(((~kind(lucy)&happy(lucy)))<=>(generous(susan)))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((kind(X)&~wise(X))<=>(calm(X)<~>happy(X))))&
((kind(alice))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((~humble(X)|tall(X))<=>~rich(X)))&
(?[X]:((~creative(X)&~humble(X))))&
((~funny(paul)&old(paul)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
((generous(lucy)<~>~wise(lucy)))&
(?[X]:((curious(X)|~calm(X)))) | curious(alice) | [] | 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. | Paul is not calm. | contradiction | (![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(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 518124948947307649743284
% SZS output start Proof for 518124948947307649743284
1. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~calm(X0) | ~humble(X0))) [input p0]
22. ~calm(paul) [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(paul) [cnf transformation 22]
145. calm(X0) [subsumption resolution 71,73]
280. $false [subsumption resolution 142,145]
% SZS output end Proof for 518124948947307649743284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is curious.
If susan is not happy or old then someone is not humble and vice versa.
Everyone who is both tall and kind is both generous and rich and vice versa.
If john is rich then lucy is both not funny and not rich and vice versa.
Everyone who is calm or humble is both creative and tall and vice versa.
If alice is either creative or not calm then paul is not tall or generous.
Everyone who is strong is either not patient or not kind and vice versa.
Everyone who is both patient and brave is not strong or patient and vice versa.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Susan is either not kind or kind.
Someone is wise or not patient.
Paul is either tall or not creative.
Alice is not quiet.
Someone is both not kind and calm.
Someone is either strong or old.
Someone is either not quiet or not old. | Fred is not creative. | contradiction | (![X]:(~generous(X)=>curious(X)))&
(((~happy(susan)|old(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((tall(X)&kind(X))<=>(generous(X)&rich(X))))&
((rich(john))<=>((~funny(lucy)&~rich(lucy))))&
(![X]:((calm(X)|humble(X))<=>(creative(X)&tall(X))))&
(((creative(alice)<~>~calm(alice)))=>((~tall(paul)|generous(paul))))&
(![X]:(strong(X)<=>(~patient(X)<~>~kind(X))))&
(![X]:((patient(X)&brave(X))<=>(~strong(X)|patient(X))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
((~kind(susan)<~>kind(susan)))&
(?[X]:((wise(X)|~patient(X))))&
((tall(paul)<~>~creative(paul)))&
(~quiet(alice))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~quiet(X)<~>~old(X)))) | ~creative(fred) | [
"p4",
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6458760719399957326642370
% SZS output start Proof for 6458760719399957326642370
5. ! [X0] : ((humble(X0) | calm(X0)) <=> (tall(X0) & creative(X0))) [input p4]
9. ! [X0] : ((old(X0) | ~calm(X0)) => brave(X0)) [input p8]
10. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> rich(X0)) [input p9]
15. ! [X0] : ((brave(X0) | creative(X0)) => (generous(X0) & ~happy(X0))) [input p14]
16. (~rich(mary) | brave(mary)) <=> (~generous(fred) | calm(fred)) [input p15]
24. ~creative(fred) [input hypothesis]
29. ! [X0] : (brave(X0) | (~old(X0) & calm(X0))) [ennf transformation 9]
36. ! [X0] : ((generous(X0) & ~happy(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 15]
46. ! [X0] : (((humble(X0) | calm(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((humble(X0) | calm(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 46]
52. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 10]
56. ((~rich(mary) | brave(mary)) | (generous(fred) & ~calm(fred))) & ((~generous(fred) | calm(fred)) | (rich(mary) & ~brave(mary))) [nnf transformation 16]
57. (~rich(mary) | brave(mary) | (generous(fred) & ~calm(fred))) & (~generous(fred) | calm(fred) | (rich(mary) & ~brave(mary))) [flattening 56]
79. ~calm(X0) | creative(X0) [cnf transformation 47]
96. ~old(X0) | brave(X0) [cnf transformation 29]
98. rich(X0) | old(X0) | rich(X0) [cnf transformation 52]
99. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 52]
110. ~brave(X0) | generous(X0) [cnf transformation 36]
111. ~generous(fred) | calm(fred) | ~brave(mary) [cnf transformation 57]
126. ~creative(fred) [cnf transformation 24]
128. rich(X0) | old(X0) [duplicate literal removal 98]
129. ~rich(X0) | old(X0) [duplicate literal removal 99]
183. old(X0) [subsumption resolution 128,129]
195. 14 <=> generous(fred) [avatar definition]
196. ~generous(fred) <- (~14) [avatar component clause 195]
199. 15 <=> brave(mary) [avatar definition]
200. ~brave(mary) <- (~15) [avatar component clause 199]
208. 17 <=> calm(fred) [avatar definition]
209. calm(fred) <- (17) [avatar component clause 208]
213. ~15 | 17 | ~14 [avatar split clause 111,195,208,199]
225. brave(X0) [resolution 96,183]
231. generous(X0) [resolution 110,225]
234. $false <- (~14) [resolution 231,196]
235. 14 [avatar contradiction clause 234]
236. $false <- (~15) [subsumption resolution 200,225]
237. 15 [avatar contradiction clause 236]
239. creative(fred) <- (17) [resolution 209,79]
240. $false <- (17) [subsumption resolution 239,126]
241. ~17 [avatar contradiction clause 240]
242. $false [avatar sat refutation 213,235,237,241]
% SZS output end Proof for 6458760719399957326642370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not humble is tall or rich.
Everyone who is either not humble or brave is generous and vice versa.
Everyone who is either not kind or kind is brave or wise and vice versa.
Everyone who is both not funny and not strong is calm and vice versa.
If someone is not funny then susan is either not brave or curious and vice versa.
If susan is not generous then someone is both patient and humble and vice versa.
If someone is old or strong then mary is funny and vice versa.
If john is not happy then susan is either curious or not brave.
Everyone who is quiet is both wise and not humble.
Everyone who is either not rich or rich is both not happy and not creative.
If someone is not tall or humble then someone is funny or not calm and vice versa.
Everyone who is both funny and creative is both not humble and brave and vice versa.
Everyone who is not brave is either funny or humble.
If paul is both not happy and not wise then fred is kind and vice versa.
Everyone who is both not curious and old is either not calm or humble and vice versa.
Everyone who is either generous or old is happy or not happy and vice versa.
Someone is either not kind or not curious.
Someone is either humble or not calm.
Alice is wise or not tall.
Someone is both not brave and patient.
Lucy is not kind. | John is rich. | neutral | (![X]:((~funny(X)&~humble(X))=>(tall(X)|rich(X))))&
(![X]:((~humble(X)<~>brave(X))<=>generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(brave(X)|wise(X))))&
(![X]:((~funny(X)&~strong(X))<=>calm(X)))&
((?[X]:(~funny(X)))<=>((~brave(susan)<~>curious(susan))))&
((~generous(susan))<=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:((old(X)|strong(X))))<=>(funny(mary)))&
((~happy(john))=>((curious(susan)<~>~brave(susan))))&
(![X]:(quiet(X)=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((wise(alice)|~tall(alice)))&
(?[X]:((~brave(X)&patient(X))))&
(~kind(lucy)) | rich(john) | [] | null | 0 |
Everyone who is patient or not patient is both not wise and patient and vice versa. Everyone who is not old or brave is either not kind or not generous. Everyone who is either not generous or not curious is both not old and funny. Everyone who is both quiet and not curious is not wise or brave and vice versa. Everyone who is not kind is both calm and humble and vice versa. If someone is patient then someone is both creative and generous. If paul is both calm and not old then someone is either calm or rich. If someone is not wise then fred is both not generous and not strong and vice versa. If someone is either rich or not funny then lucy is not tall. If mary is not old or patient then someone is happy or not wise. If someone is old or not wise then someone is either not happy or not humble. If mary is both not curious and calm then paul is old and vice versa. If someone is strong or old then paul is either not humble or not calm and vice versa. Everyone who is both kind and not tall is either humble or not calm. If susan is old or curious then paul is curious. Someone is rich or kind. Alice is wise or patient. John is either not patient or not humble. Lucy is old. Paul is kind. Someone is either wise or happy. Someone is either kind or wise. Someone is either rich or wise. | Fred is not quiet. | contradiction | (![X]:((patient(X)|~patient(X))<=>(~wise(X)&patient(X))))&
(![X]:((~old(X)|brave(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~generous(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((quiet(X)&~curious(X))<=>(~wise(X)|brave(X))))&
(![X]:(~kind(X)<=>(calm(X)&humble(X))))&
((?[X]:(patient(X)))=>(?[X]:((creative(X)&generous(X)))))&
(((calm(paul)&~old(paul)))=>(?[X]:((calm(X)<~>rich(X)))))&
((?[X]:(~wise(X)))<=>((~generous(fred)&~strong(fred))))&
((?[X]:((rich(X)<~>~funny(X))))=>(~tall(lucy)))&
(((~old(mary)|patient(mary)))=>(?[X]:((happy(X)|~wise(X)))))&
((?[X]:((old(X)|~wise(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
(((~curious(mary)&calm(mary)))<=>(old(paul)))&
((?[X]:((strong(X)|old(X))))<=>((~humble(paul)<~>~calm(paul))))&
(![X]:((kind(X)&~tall(X))=>(humble(X)<~>~calm(X))))&
(((old(susan)|curious(susan)))=>(curious(paul)))&
(?[X]:((rich(X)|kind(X))))&
((wise(alice)|patient(alice)))&
((~patient(john)<~>~humble(john)))&
(old(lucy))&
(kind(paul))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:((rich(X)<~>wise(X)))) | ~quiet(fred) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 852236033219553782763267
% SZS output start Proof for 852236033219553782763267
1. ! [X0] : ((~patient(X0) | patient(X0)) <=> (patient(X0) & ~wise(X0))) [input p0]
4. ! [X0] : ((~curious(X0) & quiet(X0)) <=> (brave(X0) | ~wise(X0))) [input p3]
24. ~quiet(fred) [input hypothesis]
39. ! [X0] : (((~patient(X0) | patient(X0)) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | (patient(X0) & ~patient(X0)))) [nnf transformation 1]
40. ! [X0] : ((~patient(X0) | patient(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | (patient(X0) & ~patient(X0)))) [flattening 39]
43. ! [X0] : (((~curious(X0) & quiet(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (curious(X0) | ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : (((~curious(X0) & quiet(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | curious(X0) | ~quiet(X0))) [flattening 43]
84. ~wise(X0) | ~patient(X0) [cnf transformation 40]
87. patient(X0) | patient(X0) [cnf transformation 40]
98. quiet(X0) | wise(X0) [cnf transformation 44]
144. ~quiet(fred) [cnf transformation 24]
145. patient(X0) [duplicate literal removal 87]
147. ~wise(X0) [subsumption resolution 84,145]
149. quiet(X0) [subsumption resolution 98,147]
244. $false [subsumption resolution 144,149]
% SZS output end Proof for 852236033219553782763267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet and generous is old or not creative and vice versa. Everyone who is both not old and not generous is either not happy or not generous. Everyone who is either brave or not tall is either not old or not rich and vice versa. Everyone who is creative is not strong or kind. If alice is not funny or rich then fred is patient. If alice is both old and not creative then someone is happy or not kind and vice versa. Everyone who is either not calm or generous is not old and vice versa. If alice is both not calm and creative then someone is not rich or strong and vice versa. Everyone who is both not kind and not creative is curious or kind and vice versa. If paul is not strong or not brave then alice is not quiet or happy and vice versa. If lucy is both kind and not curious then susan is brave or not curious. If someone is not wise then someone is both brave and quiet and vice versa. If susan is not wise then someone is both kind and not generous and vice versa. If john is either calm or not funny then mary is kind and vice versa. Someone is both not old and wise. Mary is both quiet and creative. Someone is either funny or not wise. Someone is either humble or not creative. | Lucy is not brave. | neutral | (![X]:((~quiet(X)&generous(X))<=>(old(X)|~creative(X))))&
(![X]:((~old(X)&~generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(creative(X)=>(~strong(X)|kind(X))))&
(((~funny(alice)|rich(alice)))=>(patient(fred)))&
(((old(alice)&~creative(alice)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>~old(X)))&
(((~calm(alice)&creative(alice)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)|kind(X))))&
(((~strong(paul)|~brave(paul)))<=>((~quiet(alice)|happy(alice))))&
(((kind(lucy)&~curious(lucy)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)&quiet(X)))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(?[X]:((~old(X)&wise(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>~creative(X)))) | ~brave(lucy) | [] | null | 0 |
If someone is not tall or tall then mary is kind and vice versa. If someone is not wise or not creative then someone is either not wise or wise and vice versa. Everyone who is both patient and not funny is rich and vice versa. Everyone who is both not brave and not kind is either not patient or not kind. Everyone who is either not calm or creative is either not patient or brave and vice versa. If someone is not calm or happy then fred is old or humble. Everyone who is either not calm or kind is humble and vice versa. If someone is either not brave or not wise then someone is both old and happy. Everyone who is both wise and calm is either not patient or not quiet. If susan is not rich then fred is happy and vice versa. Everyone who is either patient or happy is both rich and not quiet. Everyone who is not kind is either rich or not creative and vice versa. Everyone who is not strong is rich and vice versa. Everyone who is both curious and creative is both not creative and not wise and vice versa. If mary is both funny and not wise then someone is humble. If someone is not brave then someone is not quiet or tall. Alice is generous or not curious. Someone is both not creative and not patient. Someone is not wise. Alice is not happy or wise. Someone is both not generous and quiet. Someone is old. Someone is either rich or not patient. Someone is strong or not quiet. | Alice is not happy. | neutral | ((?[X]:((~tall(X)|tall(X))))<=>(kind(mary)))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((patient(X)&~funny(X))<=>rich(X)))&
(![X]:((~brave(X)&~kind(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>creative(X))<=>(~patient(X)<~>brave(X))))&
((?[X]:((~calm(X)|happy(X))))=>((old(fred)|humble(fred))))&
(![X]:((~calm(X)<~>kind(X))<=>humble(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>(?[X]:((old(X)&happy(X)))))&
(![X]:((wise(X)&calm(X))=>(~patient(X)<~>~quiet(X))))&
((~rich(susan))<=>(happy(fred)))&
(![X]:((patient(X)<~>happy(X))=>(rich(X)&~quiet(X))))&
(![X]:(~kind(X)<=>(rich(X)<~>~creative(X))))&
(![X]:(~strong(X)<=>rich(X)))&
(![X]:((curious(X)&creative(X))<=>(~creative(X)&~wise(X))))&
(((funny(mary)&~wise(mary)))=>(?[X]:(humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~quiet(X)|tall(X)))))&
((generous(alice)|~curious(alice)))&
(?[X]:((~creative(X)&~patient(X))))&
(?[X]:(~wise(X)))&
((~happy(alice)|wise(alice)))&
(?[X]:((~generous(X)&quiet(X))))&
(?[X]:(old(X)))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:((strong(X)|~quiet(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is either patient or not old is either not rich or not happy and vice versa.
Everyone who is either humble or not curious is either calm or not tall.
Everyone who is either not strong or old is either strong or brave and vice versa.
If paul is either not old or not patient then someone is calm.
Everyone who is creative or not brave is curious.
Everyone who is humble is both not strong and curious and vice versa.
Everyone who is either not strong or not creative is both calm and humble and vice versa.
If susan is humble or not old then paul is not brave.
Everyone who is quiet is either strong or not humble and vice versa.
Everyone who is happy or not brave is either not curious or not wise and vice versa.
Everyone who is both not quiet and not brave is not generous or not wise and vice versa.
If mary is either not tall or not wise then fred is not kind or brave and vice versa.
Everyone who is quiet is old or not brave.
Everyone who is not happy or brave is humble and vice versa.
Everyone who is patient or generous is either not rich or not wise and vice versa.
Everyone who is generous or old is not generous and vice versa.
Paul is both calm and not quiet.
Someone is either not patient or quiet.
Someone is not calm.
Someone is not humble or not quiet. | Paul is not tall. | contradiction | (![X]:((patient(X)<~>~old(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((humble(X)<~>~curious(X))=>(calm(X)<~>~tall(X))))&
(![X]:((~strong(X)<~>old(X))<=>(strong(X)<~>brave(X))))&
(((~old(paul)<~>~patient(paul)))=>(?[X]:(calm(X))))&
(![X]:((creative(X)|~brave(X))=>curious(X)))&
(![X]:(humble(X)<=>(~strong(X)&curious(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>(calm(X)&humble(X))))&
(((humble(susan)|~old(susan)))=>(~brave(paul)))&
(![X]:(quiet(X)<=>(strong(X)<~>~humble(X))))&
(![X]:((happy(X)|~brave(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(~generous(X)|~wise(X))))&
(((~tall(mary)<~>~wise(mary)))<=>((~kind(fred)|brave(fred))))&
(![X]:(quiet(X)=>(old(X)|~brave(X))))&
(![X]:((~happy(X)|brave(X))<=>humble(X)))&
(![X]:((patient(X)|generous(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((generous(X)|old(X))<=>~generous(X)))&
((calm(paul)&~quiet(paul)))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~humble(X)|~quiet(X)))) | ~tall(paul) | [
"p0",
"p1",
"p4",
"p9",
"p10",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3880985608271726704645416
% SZS output start Proof for 3880985608271726704645416
1. ! [X0] : ((patient(X0) <~> ~old(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((humble(X0) <~> ~curious(X0)) => (calm(X0) <~> ~tall(X0))) [input p1]
5. ! [X0] : ((~brave(X0) | creative(X0)) => curious(X0)) [input p4]
10. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~curious(X0) <~> ~wise(X0))) [input p9]
11. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (~wise(X0) | ~generous(X0))) [input p10]
14. ! [X0] : ((brave(X0) | ~happy(X0)) <=> humble(X0)) [input p13]
15. ! [X0] : ((generous(X0) | patient(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p14]
16. ! [X0] : ((old(X0) | generous(X0)) <=> ~generous(X0)) [input p15]
17. ~quiet(paul) & calm(paul) [input p16]
21. ~tall(paul) [input hypothesis]
22. ! [X0] : ((calm(X0) <~> ~tall(X0)) | (humble(X0) <=> ~curious(X0))) [ennf transformation 2]
24. ! [X0] : (curious(X0) | (brave(X0) & ~creative(X0))) [ennf transformation 5]
28. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [nnf transformation 1]
29. ! [X0] : (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) [nnf transformation 22]
39. ! [X0] : (((~brave(X0) | happy(X0)) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0)))) & (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | (brave(X0) & ~happy(X0)))) [nnf transformation 10]
40. ! [X0] : ((~brave(X0) | happy(X0) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0)))) & (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | (brave(X0) & ~happy(X0)))) [flattening 39]
41. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & ((~wise(X0) | ~generous(X0)) | (brave(X0) | quiet(X0)))) [nnf transformation 11]
42. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (wise(X0) & generous(X0))) & (~wise(X0) | ~generous(X0) | brave(X0) | quiet(X0))) [flattening 41]
45. ! [X0] : (((brave(X0) | ~happy(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 14]
46. ! [X0] : ((brave(X0) | ~happy(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & happy(X0)))) [flattening 45]
47. ! [X0] : (((generous(X0) | patient(X0)) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | (~generous(X0) & ~patient(X0)))) [nnf transformation 15]
48. ! [X0] : ((generous(X0) | patient(X0) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | (~generous(X0) & ~patient(X0)))) [flattening 47]
49. ! [X0] : (((old(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (~old(X0) & ~generous(X0)))) [nnf transformation 16]
50. ! [X0] : ((old(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (~old(X0) & ~generous(X0)))) [flattening 49]
58. ~happy(X0) | ~rich(X0) | ~old(X0) | ~patient(X0) [cnf transformation 28]
60. ~old(X0) | rich(X0) | happy(X0) | ~patient(X0) [cnf transformation 28]
62. ~happy(X0) | patient(X0) | ~old(X0) | rich(X0) [cnf transformation 28]
68. ~calm(X0) | tall(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 29]
81. brave(X0) | curious(X0) [cnf transformation 24]
97. ~wise(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 40]
98. ~wise(X0) | ~curious(X0) | brave(X0) [cnf transformation 40]
106. ~brave(X0) | generous(X0) [cnf transformation 42]
115. humble(X0) | happy(X0) [cnf transformation 46]
120. ~patient(X0) | rich(X0) | wise(X0) [cnf transformation 48]
123. ~rich(X0) | patient(X0) | generous(X0) | wise(X0) [cnf transformation 48]
124. ~generous(X0) | ~generous(X0) [cnf transformation 50]
126. old(X0) | generous(X0) | generous(X0) [cnf transformation 50]
127. calm(paul) [cnf transformation 17]
133. ~tall(paul) [cnf transformation 21]
134. ~generous(X0) [duplicate literal removal 124]
135. generous(X0) | old(X0) [duplicate literal removal 126]
143. 1 <=> patient(paul) [avatar definition]
144. ~patient(paul) <- (~1) [avatar component clause 143]
145. patient(paul) <- (1) [avatar component clause 143]
163. 5 <=> brave(paul) [avatar definition]
164. brave(paul) <- (5) [avatar component clause 163]
165. ~brave(paul) <- (~5) [avatar component clause 163]
175. ~wise(X0) | brave(X0) [subsumption resolution 98,81]
210. generous(X0) | curious(X0) [resolution 106,81]
211. curious(X0) [subsumption resolution 210,134]
216. old(X1) [resolution 135,134]
232. 14 <=> humble(paul) [avatar definition]
233. ~humble(paul) <- (~14) [avatar component clause 232]
239. happy(paul) <- (~14) [resolution 233,115]
270. ~rich(paul) | ~old(paul) | ~patient(paul) <- (~14) [resolution 58,239]
272. ~patient(X0) | happy(X0) | rich(X0) [resolution 60,216]
277. patient(paul) | ~old(paul) | rich(paul) <- (~14) [resolution 62,239]
280. ~old(paul) | rich(paul) <- (~1, ~14) [subsumption resolution 277,144]
281. rich(paul) <- (~1, ~14) [subsumption resolution 280,216]
300. tall(paul) | ~curious(paul) | ~humble(paul) [resolution 68,127]
386. patient(paul) | generous(paul) | wise(paul) <- (~1, ~14) [resolution 123,281]
387. generous(paul) | wise(paul) <- (~1, ~14) [subsumption resolution 386,144]
388. wise(paul) <- (~1, ~14) [subsumption resolution 387,134]
419. brave(paul) <- (~1, ~14) [resolution 388,175]
423. $false <- (~1, ~5, ~14) [subsumption resolution 419,165]
424. 1 | 5 | 14 [avatar contradiction clause 423]
427. 27 <=> rich(paul) [avatar definition]
428. ~rich(paul) <- (~27) [avatar component clause 427]
431. ~rich(paul) | ~patient(paul) <- (~14) [subsumption resolution 270,216]
432. ~1 | ~27 | 14 [avatar split clause 431,232,427,143]
433. happy(paul) | rich(paul) <- (1) [resolution 145,272]
434. rich(paul) | wise(paul) <- (1) [resolution 145,120]
435. wise(paul) <- (1, ~27) [subsumption resolution 434,428]
439. ~curious(paul) | ~happy(paul) <- (1, ~27) [resolution 435,97]
447. ~happy(paul) <- (1, ~27) [subsumption resolution 439,211]
450. rich(paul) <- (1, ~27) [subsumption resolution 433,447]
451. $false <- (1, ~27) [subsumption resolution 450,428]
452. ~1 | 27 [avatar contradiction clause 451]
453. ~curious(paul) | ~humble(paul) [subsumption resolution 300,133]
454. ~humble(paul) [subsumption resolution 453,211]
455. ~14 [avatar split clause 454,232]
462. generous(paul) <- (5) [resolution 164,106]
481. $false <- (5) [subsumption resolution 462,134]
482. ~5 [avatar contradiction clause 481]
483. $false [avatar sat refutation 424,432,452,455,482]
% SZS output end Proof for 3880985608271726704645416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not patient is tall and vice versa. Everyone who is creative is not funny or not generous. Everyone who is not old or humble is either humble or generous. Everyone who is calm or happy is kind and vice versa. Everyone who is quiet is both not generous and not kind. Everyone who is both kind and generous is rich or not brave and vice versa. If alice is both not brave and funny then someone is humble or not funny. If someone is both not rich and generous then someone is patient and vice versa. Everyone who is not strong is not humble and vice versa. If someone is strong or rich then paul is wise and vice versa. If someone is calm or not patient then someone is rich or funny. Everyone who is strong or brave is either not creative or not brave and vice versa. If someone is either tall or not humble then lucy is both not rich and not strong. If john is both generous and calm then someone is calm or kind. Everyone who is either not old or patient is not rich. Everyone who is not funny or not humble is both not patient and not curious and vice versa. John is either not strong or not creative. Someone is either creative or not curious. Mary is not curious. Fred is not brave. Someone is either not quiet or not creative. Susan is not wise. Someone is rich. | Lucy is rich. | contradiction | (![X]:((kind(X)<~>~patient(X))<=>tall(X)))&
(![X]:(creative(X)=>(~funny(X)|~generous(X))))&
(![X]:((~old(X)|humble(X))=>(humble(X)<~>generous(X))))&
(![X]:((calm(X)|happy(X))<=>kind(X)))&
(![X]:(quiet(X)=>(~generous(X)&~kind(X))))&
(![X]:((kind(X)&generous(X))<=>(rich(X)|~brave(X))))&
(((~brave(alice)&funny(alice)))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:(patient(X))))&
(![X]:(~strong(X)<=>~humble(X)))&
((?[X]:((strong(X)|rich(X))))<=>(wise(paul)))&
((?[X]:((calm(X)|~patient(X))))=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((strong(X)|brave(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((tall(X)<~>~humble(X))))=>((~rich(lucy)&~strong(lucy))))&
(((generous(john)&calm(john)))=>(?[X]:((calm(X)|kind(X)))))&
(![X]:((~old(X)<~>patient(X))=>~rich(X)))&
(![X]:((~funny(X)|~humble(X))<=>(~patient(X)&~curious(X))))&
((~strong(john)<~>~creative(john)))&
(?[X]:((creative(X)<~>~curious(X))))&
(~curious(mary))&
(~brave(fred))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(~wise(susan))&
(?[X]:(rich(X))) | rich(lucy) | [
"p0",
"p2",
"p5",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5277803981941472526626328
% SZS output start Proof for 5277803981941472526626328
1. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> tall(X0)) [input p0]
3. ! [X0] : ((humble(X0) | ~old(X0)) => (humble(X0) <~> generous(X0))) [input p2]
6. ! [X0] : ((generous(X0) & kind(X0)) <=> (~brave(X0) | rich(X0))) [input p5]
13. ? [X0] : (tall(X0) <~> ~humble(X0)) => (~strong(lucy) & ~rich(lucy)) [input p12]
16. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (~curious(X0) & ~patient(X0))) [input p15]
23. ? [X0] : rich(X0) [input p22]
24. rich(lucy) [input hypothesis]
29. ! [X0] : ((humble(X0) <~> generous(X0)) | (~humble(X0) & old(X0))) [ennf transformation 3]
34. (~strong(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) <=> ~humble(X0)) [ennf transformation 13]
38. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | ~tall(X0)) & (tall(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 1]
39. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | (~humble(X0) & old(X0))) [nnf transformation 29]
42. ! [X0] : (((generous(X0) & kind(X0)) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 6]
43. ! [X0] : (((generous(X0) & kind(X0)) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | ~generous(X0) | ~kind(X0))) [flattening 42]
61. (~strong(lucy) & ~rich(lucy)) | ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 34]
65. ! [X0] : (((~humble(X0) | ~funny(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 16]
66. ! [X0] : ((~humble(X0) | ~funny(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (humble(X0) & funny(X0)))) [flattening 65]
74. ? [X0] : rich(X0) => rich(sK8) [choice axiom]
75. rich(sK8) [skolemisation 23,74]
79. ~tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 38]
84. ~generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 39]
91. ~rich(X0) | kind(X0) [cnf transformation 43]
93. ~rich(X0) | generous(X0) [cnf transformation 43]
113. ~rich(lucy) | tall(X0) | humble(X0) [cnf transformation 61]
120. ~patient(X0) | humble(X0) [cnf transformation 66]
133. rich(sK8) [cnf transformation 75]
134. rich(lucy) [cnf transformation 24]
137. ~humble(X0) | ~generous(X0) [duplicate literal removal 84]
214. 19 <=> ! [X0] : (tall(X0) | humble(X0)) [avatar definition]
215. humble(X0) | tall(X0) <- (19) [avatar component clause 214]
226. 22 <=> rich(lucy) [avatar definition]
229. 19 | ~22 [avatar split clause 113,226,214]
275. 22 [avatar split clause 134,226]
278. kind(sK8) [resolution 91,133]
282. generous(sK8) [resolution 93,133]
301. ~generous(X0) | tall(X0) <- (19) [resolution 215,137]
509. tall(sK8) <- (19) [resolution 301,282]
539. 61 <=> patient(sK8) [avatar definition]
540. patient(sK8) <- (61) [avatar component clause 539]
573. humble(sK8) <- (61) [resolution 540,120]
606. ~kind(sK8) | patient(sK8) <- (19) [resolution 509,79]
625. ~generous(sK8) <- (61) [resolution 573,137]
629. $false <- (61) [subsumption resolution 625,282]
630. ~61 [avatar contradiction clause 629]
631. patient(sK8) <- (19) [subsumption resolution 606,278]
632. 61 | ~19 [avatar split clause 631,214,539]
633. $false [avatar sat refutation 229,275,630,632]
% SZS output end Proof for 5277803981941472526626328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich is patient. If someone is either strong or brave then fred is not funny. Everyone who is creative or not wise is curious. Everyone who is not creative or not happy is both curious and wise. Everyone who is rich or not creative is both not kind and not curious and vice versa. If someone is not kind then paul is calm and vice versa. Everyone who is either not humble or quiet is not brave and vice versa. If susan is either not old or not funny then someone is either not wise or not quiet. If susan is not generous then someone is either not curious or not tall. If susan is not creative then someone is both not brave and strong and vice versa. If someone is either old or not tall then susan is either calm or not patient. Everyone who is both old and strong is not strong. Everyone who is either patient or kind is not brave or not wise and vice versa. If john is strong or not tall then someone is rich. Everyone who is happy is either not strong or not happy and vice versa. Alice is quiet or not humble. Someone is curious or rich. Mary is not calm. Lucy is not generous. John is both not humble and kind. Paul is calm or kind. John is either tall or not funny. Mary is either kind or not tall. | Lucy is not rich. | entailment | (![X]:((generous(X)<~>~rich(X))=>patient(X)))&
((?[X]:((strong(X)<~>brave(X))))=>(~funny(fred)))&
(![X]:((creative(X)|~wise(X))=>curious(X)))&
(![X]:((~creative(X)|~happy(X))=>(curious(X)&wise(X))))&
(![X]:((rich(X)|~creative(X))<=>(~kind(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(calm(paul)))&
(![X]:((~humble(X)<~>quiet(X))<=>~brave(X)))&
(((~old(susan)<~>~funny(susan)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
((~generous(susan))=>(?[X]:((~curious(X)<~>~tall(X)))))&
((~creative(susan))<=>(?[X]:((~brave(X)&strong(X)))))&
((?[X]:((old(X)<~>~tall(X))))=>((calm(susan)<~>~patient(susan))))&
(![X]:((old(X)&strong(X))=>~strong(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~brave(X)|~wise(X))))&
(((strong(john)|~tall(john)))=>(?[X]:(rich(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~happy(X))))&
((quiet(alice)|~humble(alice)))&
(?[X]:((curious(X)|rich(X))))&
(~calm(mary))&
(~generous(lucy))&
((~humble(john)&kind(john)))&
((calm(paul)|kind(paul)))&
((tall(john)<~>~funny(john)))&
((kind(mary)<~>~tall(mary))) | ~rich(lucy) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5447512961302842990987410
% SZS output start Proof for 5447512961302842990987410
3. ! [X0] : ((~wise(X0) | creative(X0)) => curious(X0)) [input p2]
4. ! [X0] : ((~happy(X0) | ~creative(X0)) => (wise(X0) & curious(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | rich(X0)) <=> (~curious(X0) & ~kind(X0))) [input p4]
24. rich(lucy) [input hypothesis]
27. ! [X0] : (curious(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 3]
28. ! [X0] : ((wise(X0) & curious(X0)) | (happy(X0) & creative(X0))) [ennf transformation 4]
37. ! [X0] : (((~creative(X0) | rich(X0)) | (curious(X0) | kind(X0))) & ((~curious(X0) & ~kind(X0)) | (creative(X0) & ~rich(X0)))) [nnf transformation 5]
38. ! [X0] : ((~creative(X0) | rich(X0) | curious(X0) | kind(X0)) & ((~curious(X0) & ~kind(X0)) | (creative(X0) & ~rich(X0)))) [flattening 37]
68. curious(X0) | ~creative(X0) [cnf transformation 27]
70. curious(X0) | creative(X0) [cnf transformation 28]
76. ~curious(X0) | ~rich(X0) [cnf transformation 38]
122. rich(lucy) [cnf transformation 24]
138. curious(X0) [subsumption resolution 70,68]
140. ~rich(X0) [subsumption resolution 76,138]
232. $false [subsumption resolution 122,140]
% SZS output end Proof for 5447512961302842990987410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not calm is either not patient or kind and vice versa. If susan is not quiet or not kind then someone is both not rich and not generous and vice versa. Everyone who is not brave or not strong is both tall and curious and vice versa. If someone is either kind or brave then someone is quiet or not curious. If alice is either not happy or tall then someone is both happy and not rich and vice versa. Everyone who is not patient or not rich is either not generous or brave. Everyone who is not generous is not rich or quiet. Everyone who is funny or happy is both not humble and not tall and vice versa. Everyone who is both patient and not creative is kind. Everyone who is either calm or happy is both creative and humble and vice versa. Everyone who is either funny or not kind is not rich or not funny and vice versa. If someone is both not calm and not funny then lucy is both not kind and old and vice versa. Everyone who is not rich is happy. If someone is both not curious and not wise then susan is both wise and not quiet. If someone is both not creative and not wise then paul is either not quiet or not creative. If someone is patient or not creative then someone is both not rich and old and vice versa. Someone is both not kind and calm. Paul is not calm or not tall. Someone is both calm and curious. Someone is quiet or creative. Someone is quiet. Someone is kind. Paul is both not funny and tall. Mary is both not strong and not brave. | Susan is not humble. | entailment | (![X]:((~creative(X)&~calm(X))<=>(~patient(X)<~>kind(X))))&
(((~quiet(susan)|~kind(susan)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~brave(X)|~strong(X))<=>(tall(X)&curious(X))))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((quiet(X)|~curious(X)))))&
(((~happy(alice)<~>tall(alice)))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~patient(X)|~rich(X))=>(~generous(X)<~>brave(X))))&
(![X]:(~generous(X)=>(~rich(X)|quiet(X))))&
(![X]:((funny(X)|happy(X))<=>(~humble(X)&~tall(X))))&
(![X]:((patient(X)&~creative(X))=>kind(X)))&
(![X]:((calm(X)<~>happy(X))<=>(creative(X)&humble(X))))&
(![X]:((funny(X)<~>~kind(X))<=>(~rich(X)|~funny(X))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~kind(lucy)&old(lucy))))&
(![X]:(~rich(X)=>happy(X)))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(susan)&~quiet(susan))))&
((?[X]:((~creative(X)&~wise(X))))=>((~quiet(paul)<~>~creative(paul))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((~rich(X)&old(X)))))&
(?[X]:((~kind(X)&calm(X))))&
((~calm(paul)|~tall(paul)))&
(?[X]:((calm(X)&curious(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:(quiet(X)))&
(?[X]:(kind(X)))&
((~funny(paul)&tall(paul)))&
((~strong(mary)&~brave(mary))) | ~humble(susan) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 13116238845390177936199
% SZS output start Proof for 13116238845390177936199
2. (~kind(susan) | ~quiet(susan)) <=> ? [X0] : (~generous(X0) & ~rich(X0)) [input p1]
3. ! [X0] : ((~strong(X0) | ~brave(X0)) <=> (curious(X0) & tall(X0))) [input p2]
6. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~generous(X0) <~> brave(X0))) [input p5]
8. ! [X0] : ((happy(X0) | funny(X0)) <=> (~tall(X0) & ~humble(X0))) [input p7]
11. ! [X0] : ((funny(X0) <~> ~kind(X0)) <=> (~funny(X0) | ~rich(X0))) [input p10]
13. ! [X0] : (~rich(X0) => happy(X0)) [input p12]
25. humble(susan) [input hypothesis]
31. ! [X0] : ((~generous(X0) <~> brave(X0)) | (rich(X0) & patient(X0))) [ennf transformation 6]
36. ! [X0] : (happy(X0) | rich(X0)) [ennf transformation 13]
39. ((~kind(susan) | ~quiet(susan)) | ! [X0] : (generous(X0) | rich(X0))) & (? [X0] : (~generous(X0) & ~rich(X0)) | (kind(susan) & quiet(susan))) [nnf transformation 2]
40. (~kind(susan) | ~quiet(susan) | ! [X0] : (generous(X0) | rich(X0))) & (? [X0] : (~generous(X0) & ~rich(X0)) | (kind(susan) & quiet(susan))) [flattening 39]
41. (~kind(susan) | ~quiet(susan) | ! [X0] : (generous(X0) | rich(X0))) & (? [X1] : (~generous(X1) & ~rich(X1)) | (kind(susan) & quiet(susan))) [rectify 40]
42. ? [X1] : (~generous(X1) & ~rich(X1)) => (~generous(sK0) & ~rich(sK0)) [choice axiom]
43. (~kind(susan) | ~quiet(susan) | ! [X0] : (generous(X0) | rich(X0))) & ((~generous(sK0) & ~rich(sK0)) | (kind(susan) & quiet(susan))) [skolemisation 41,42]
44. ! [X0] : (((~strong(X0) | ~brave(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (strong(X0) & brave(X0)))) [nnf transformation 3]
45. ! [X0] : ((~strong(X0) | ~brave(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (strong(X0) & brave(X0)))) [flattening 44]
54. ! [X0] : (((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (rich(X0) & patient(X0))) [nnf transformation 31]
55. ! [X0] : (((happy(X0) | funny(X0)) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | (~happy(X0) & ~funny(X0)))) [nnf transformation 8]
56. ! [X0] : ((happy(X0) | funny(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | (~happy(X0) & ~funny(X0)))) [flattening 55]
59. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [nnf transformation 11]
60. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [flattening 59]
88. ~rich(sK0) | kind(susan) [cnf transformation 43]
90. ~generous(sK0) | kind(susan) [cnf transformation 43]
92. tall(X0) | brave(X0) [cnf transformation 45]
108. ~brave(X0) | generous(X0) | rich(X0) [cnf transformation 54]
111. ~humble(X0) | ~happy(X0) [cnf transformation 56]
113. ~happy(X0) | ~tall(X0) [cnf transformation 56]
122. ~funny(X0) | ~rich(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 60]
125. ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 60]
132. happy(X0) | rich(X0) [cnf transformation 36]
150. humble(susan) [cnf transformation 25]
151. ~funny(X0) | ~rich(X0) | ~kind(X0) [duplicate literal removal 122]
152. ~kind(X0) | funny(X0) [duplicate literal removal 125]
154. 1 <=> ! [X0] : (generous(X0) | rich(X0)) [avatar definition]
155. generous(X0) | rich(X0) <- (1) [avatar component clause 154]
161. 3 <=> kind(susan) [avatar definition]
166. 4 <=> generous(sK0) [avatar definition]
168. ~generous(sK0) <- (~4) [avatar component clause 166]
169. 3 | ~4 [avatar split clause 90,166,161]
172. 5 <=> rich(sK0) [avatar definition]
174. ~rich(sK0) <- (~5) [avatar component clause 172]
175. 3 | ~5 [avatar split clause 88,172,161]
220. ~rich(X0) | ~kind(X0) [subsumption resolution 151,152]
301. ~happy(susan) [resolution 111,150]
306. rich(susan) [resolution 132,301]
307. ~tall(X0) | rich(X0) [resolution 132,113]
382. ~kind(susan) [resolution 306,220]
485. brave(X1) | rich(X1) [resolution 307,92]
550. ~3 [avatar split clause 382,161]
552. rich(sK0) <- (1, ~4) [resolution 155,168]
556. $false <- (1, ~4, ~5) [subsumption resolution 552,174]
557. ~1 | 4 | 5 [avatar contradiction clause 556]
633. rich(X0) | generous(X0) | rich(X0) [resolution 485,108]
635. rich(X0) | generous(X0) [duplicate literal removal 633]
636. 1 [avatar split clause 635,154]
637. $false [avatar sat refutation 169,175,550,557,636]
% SZS output end Proof for 13116238845390177936199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise then susan is not brave and vice versa. Everyone who is either not quiet or humble is both happy and kind and vice versa. If fred is both not calm and curious then alice is not kind and vice versa. Everyone who is tall is either calm or not humble. Everyone who is either not generous or curious is both not rich and not generous. Everyone who is either not kind or brave is both not patient and not happy and vice versa. Everyone who is not brave is both not kind and patient. Everyone who is curious or humble is not happy or funny and vice versa. If someone is not creative then someone is both not tall and not old. Everyone who is not funny is either not kind or not rich. If someone is not wise then fred is either tall or not quiet and vice versa. Everyone who is not humble is both not calm and not quiet. Everyone who is both happy and curious is not quiet or happy and vice versa. Everyone who is both not wise and not kind is not tall. Everyone who is wise is not old or not happy. John is rich or not tall. Someone is not curious or not strong. Fred is either humble or creative. | Mary is not rich. | neutral | ((~wise(mary))<=>(~brave(susan)))&
(![X]:((~quiet(X)<~>humble(X))<=>(happy(X)&kind(X))))&
(((~calm(fred)&curious(fred)))<=>(~kind(alice)))&
(![X]:(tall(X)=>(calm(X)<~>~humble(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~rich(X)&~generous(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~patient(X)&~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)&patient(X))))&
(![X]:((curious(X)|humble(X))<=>(~happy(X)|funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>~rich(X))))&
((?[X]:(~wise(X)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(~humble(X)=>(~calm(X)&~quiet(X))))&
(![X]:((happy(X)&curious(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~wise(X)&~kind(X))=>~tall(X)))&
(![X]:(wise(X)=>(~old(X)|~happy(X))))&
((rich(john)|~tall(john)))&
(?[X]:((~curious(X)|~strong(X))))&
((humble(fred)<~>creative(fred))) | ~rich(mary) | [] | null | 0 |
Everyone who is not humble or calm is both old and patient and vice versa.
If someone is not strong then someone is either not generous or quiet and vice versa.
Everyone who is not generous or patient is tall or not strong and vice versa.
Everyone who is quiet or not strong is not funny.
Everyone who is either brave or not brave is not strong or not calm.
If lucy is both quiet and generous then someone is not brave and vice versa.
Everyone who is either not patient or not generous is tall and vice versa.
If john is both generous and wise then john is wise or rich.
Everyone who is either not funny or not old is not patient or not generous and vice versa.
Everyone who is strong is not curious or not kind.
Everyone who is not calm is both rich and funny and vice versa.
If someone is either not creative or not wise then someone is not quiet.
If john is humble or creative then susan is not strong.
If someone is either not brave or not calm then someone is either not strong or not humble and vice versa.
If fred is either not creative or not kind then someone is not old and vice versa.
If someone is not rich or not humble then lucy is not brave and vice versa.
Someone is either strong or brave.
Susan is either creative or not calm.
Lucy is curious.
Someone is either not calm or not kind.
Alice is not kind.
Someone is curious or patient. | Fred is generous. | contradiction | (![X]:((~humble(X)|calm(X))<=>(old(X)&patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~generous(X)<~>quiet(X)))))&
(![X]:((~generous(X)|patient(X))<=>(tall(X)|~strong(X))))&
(![X]:((quiet(X)|~strong(X))=>~funny(X)))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)|~calm(X))))&
(((quiet(lucy)&generous(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>tall(X)))&
(((generous(john)&wise(john)))=>((wise(john)|rich(john))))&
(![X]:((~funny(X)<~>~old(X))<=>(~patient(X)|~generous(X))))&
(![X]:(strong(X)=>(~curious(X)|~kind(X))))&
(![X]:(~calm(X)<=>(rich(X)&funny(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(?[X]:(~quiet(X))))&
(((humble(john)|creative(john)))=>(~strong(susan)))&
((?[X]:((~brave(X)<~>~calm(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(((~creative(fred)<~>~kind(fred)))<=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(~brave(lucy)))&
(?[X]:((strong(X)<~>brave(X))))&
((creative(susan)<~>~calm(susan)))&
(curious(lucy))&
(?[X]:((~calm(X)<~>~kind(X))))&
(~kind(alice))&
(?[X]:((curious(X)|patient(X)))) | generous(fred) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8445005782610540737363297
% SZS output start Proof for 8445005782610540737363297
1. ! [X0] : ((calm(X0) | ~humble(X0)) <=> (patient(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (~strong(X0) | tall(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => ~funny(X0)) [input p3]
6. (generous(lucy) & quiet(lucy)) <=> ? [X0] : ~brave(X0) [input p5]
7. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> tall(X0)) [input p6]
9. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (~generous(X0) | ~patient(X0))) [input p8]
11. ! [X0] : (~calm(X0) <=> (funny(X0) & rich(X0))) [input p10]
16. ? [X0] : (~humble(X0) | ~rich(X0)) <=> ~brave(lucy) [input p15]
23. generous(fred) [input hypothesis]
27. ! [X0] : (~funny(X0) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
36. ! [X0] : (((calm(X0) | ~humble(X0)) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | ~humble(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [flattening 36]
43. ! [X0] : (((patient(X0) | ~generous(X0)) | (strong(X0) & ~tall(X0))) & ((~strong(X0) | tall(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 3]
44. ! [X0] : ((patient(X0) | ~generous(X0) | (strong(X0) & ~tall(X0))) & (~strong(X0) | tall(X0) | (~patient(X0) & generous(X0)))) [flattening 43]
46. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~generous(lucy) | ~quiet(lucy))) [nnf transformation 6]
47. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~generous(lucy) | ~quiet(lucy)) [flattening 46]
48. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~generous(lucy) | ~quiet(lucy)) [rectify 47]
49. ? [X1] : ~brave(X1) => ~brave(sK2) [choice axiom]
50. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (~brave(sK2) | ~generous(lucy) | ~quiet(lucy)) [skolemisation 48,49]
51. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ~tall(X0)) & (tall(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 7]
52. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 9]
53. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [flattening 52]
54. ! [X0] : ((~calm(X0) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | calm(X0))) [nnf transformation 11]
55. ! [X0] : ((~calm(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | calm(X0))) [flattening 54]
69. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X0] : (humble(X0) & rich(X0))) [nnf transformation 16]
70. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [rectify 69]
71. ? [X0] : (~humble(X0) | ~rich(X0)) => (~humble(sK7) | ~rich(sK7)) [choice axiom]
72. ((~humble(sK7) | ~rich(sK7)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [skolemisation 70,71]
83. ~calm(X0) | old(X0) [cnf transformation 37]
86. ~patient(X0) | ~humble(X0) | calm(X0) | ~old(X0) [cnf transformation 37]
93. ~tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 44]
95. ~funny(X0) | ~quiet(X0) [cnf transformation 27]
100. quiet(lucy) | brave(X0) [cnf transformation 50]
101. generous(lucy) | brave(X0) [cnf transformation 50]
102. tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 51]
104. ~generous(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 51]
107. ~generous(X0) | ~patient(X0) | ~old(X0) | funny(X0) [cnf transformation 53]
108. ~generous(X0) | ~patient(X0) | ~funny(X0) | old(X0) [cnf transformation 53]
115. funny(X0) | calm(X0) [cnf transformation 55]
116. ~rich(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 55]
133. ~brave(lucy) | rich(X1) [cnf transformation 72]
134. ~brave(lucy) | humble(X1) [cnf transformation 72]
145. generous(fred) [cnf transformation 23]
175. 7 <=> ! [X0] : brave(X0) [avatar definition]
176. brave(X0) <- (7) [avatar component clause 175]
178. 8 <=> generous(lucy) [avatar definition]
180. generous(lucy) <- (8) [avatar component clause 178]
181. 7 | 8 [avatar split clause 101,178,175]
183. 9 <=> quiet(lucy) [avatar definition]
186. 7 | 9 [avatar split clause 100,183,175]
193. ~tall(X0) | ~generous(X0) [subsumption resolution 104,93]
194. ~generous(X0) | patient(X0) [subsumption resolution 102,193]
195. ~funny(X0) | ~generous(X0) | old(X0) [subsumption resolution 108,194]
196. ~generous(X0) | ~old(X0) | funny(X0) [subsumption resolution 107,194]
279. 29 <=> brave(lucy) [avatar definition]
280. ~brave(lucy) <- (~29) [avatar component clause 279]
292. 32 <=> ! [X1] : humble(X1) [avatar definition]
293. humble(X1) <- (32) [avatar component clause 292]
294. 32 | ~29 [avatar split clause 134,279,292]
296. 33 <=> ! [X1] : rich(X1) [avatar definition]
297. rich(X1) <- (33) [avatar component clause 296]
298. 33 | ~29 [avatar split clause 133,279,296]
349. patient(fred) [resolution 194,145]
470. ~generous(X2) | old(X2) | calm(X2) [resolution 195,115]
473. ~generous(X2) | old(X2) [subsumption resolution 470,83]
479. ~old(fred) | funny(fred) [resolution 196,145]
480. ~old(lucy) | funny(lucy) <- (8) [resolution 196,180]
482. 54 <=> funny(fred) [avatar definition]
484. funny(fred) <- (54) [avatar component clause 482]
486. 55 <=> old(fred) [avatar definition]
489. 54 | ~55 [avatar split clause 479,486,482]
491. 56 <=> funny(lucy) [avatar definition]
493. funny(lucy) <- (56) [avatar component clause 491]
495. 57 <=> old(lucy) [avatar definition]
498. 56 | ~57 | ~8 [avatar split clause 480,178,495,491]
503. ~humble(fred) | calm(fred) | ~old(fred) [resolution 86,349]
530. old(fred) [resolution 473,145]
531. old(lucy) <- (8) [resolution 473,180]
536. 55 [avatar split clause 530,486]
538. 60 <=> calm(fred) [avatar definition]
542. 61 <=> humble(fred) [avatar definition]
544. ~humble(fred) <- (~61) [avatar component clause 542]
545. ~55 | 60 | ~61 [avatar split clause 503,542,538,486]
546. 57 | ~8 [avatar split clause 531,178,495]
557. ~quiet(lucy) <- (56) [resolution 493,95]
560. ~9 | ~56 [avatar split clause 557,491,183]
571. $false <- (7, ~29) [resolution 176,280]
572. ~7 | 29 [avatar contradiction clause 571]
577. ~funny(X0) | ~calm(X0) <- (33) [resolution 297,116]
586. ~calm(fred) <- (33, 54) [resolution 577,484]
587. ~60 | ~33 | ~54 [avatar split clause 586,482,296,538]
591. $false <- (32, ~61) [resolution 544,293]
592. ~32 | 61 [avatar contradiction clause 591]
593. $false [avatar sat refutation 181,186,294,298,489,498,536,545,546,560,572,587,592]
% SZS output end Proof for 8445005782610540737363297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is both curious and not wise then fred is both tall and curious.
If mary is not calm then mary is both not quiet and not kind and vice versa.
Everyone who is curious or wise is rich or calm.
If someone is not calm or tall then paul is curious and vice versa.
Everyone who is rich is either funny or strong.
If fred is both wise and humble then alice is either not strong or tall.
Everyone who is patient is either not wise or not strong.
Everyone who is not calm is both not tall and not quiet and vice versa.
If john is either kind or not curious then someone is either not humble or generous.
If someone is not happy then someone is happy or patient.
If someone is not kind or strong then mary is either humble or not tall.
Everyone who is not rich is not old or not calm.
Everyone who is wise or not wise is not calm and vice versa.
Everyone who is both not quiet and not brave is both funny and creative.
Everyone who is tall or calm is not strong or not old and vice versa.
Everyone who is either not curious or not brave is generous.
Fred is not patient.
Alice is both kind and not brave.
Someone is either not curious or wise.
Lucy is not generous.
Alice is not curious or not creative.
Mary is either creative or rich.
Paul is brave or quiet. | Lucy is curious. | neutral | (((curious(mary)&~wise(mary)))=>((tall(fred)&curious(fred))))&
((~calm(mary))<=>((~quiet(mary)&~kind(mary))))&
(![X]:((curious(X)|wise(X))=>(rich(X)|calm(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(curious(paul)))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((wise(fred)&humble(fred)))=>((~strong(alice)<~>tall(alice))))&
(![X]:(patient(X)=>(~wise(X)<~>~strong(X))))&
(![X]:(~calm(X)<=>(~tall(X)&~quiet(X))))&
(((kind(john)<~>~curious(john)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((humble(mary)<~>~tall(mary))))&
(![X]:(~rich(X)=>(~old(X)|~calm(X))))&
(![X]:((wise(X)|~wise(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~brave(X))=>(funny(X)&creative(X))))&
(![X]:((tall(X)|calm(X))<=>(~strong(X)|~old(X))))&
(![X]:((~curious(X)<~>~brave(X))=>generous(X)))&
(~patient(fred))&
((kind(alice)&~brave(alice)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~generous(lucy))&
((~curious(alice)|~creative(alice)))&
((creative(mary)<~>rich(mary)))&
((brave(paul)|quiet(paul))) | curious(lucy) | [] | null | 0 |
Everyone who is both rich and kind is generous.
If someone is both happy and humble then someone is generous or not old and vice versa.
Everyone who is calm is curious.
If john is not funny or not wise then mary is either not brave or not happy and vice versa.
Everyone who is either wise or strong is both creative and not wise and vice versa.
Everyone who is not brave is not creative or not patient and vice versa.
If someone is either not generous or brave then susan is either not humble or strong and vice versa.
Everyone who is both not patient and strong is both creative and not generous and vice versa.
Everyone who is rich or not humble is either not generous or not quiet and vice versa.
If someone is either funny or happy then someone is either wise or old and vice versa.
Everyone who is both calm and not kind is both not rich and strong.
If someone is creative then mary is both calm and happy.
Everyone who is brave or not quiet is both not patient and not rich.
Everyone who is either patient or tall is wise or humble.
Everyone who is both not quiet and not generous is creative or curious and vice versa.
If john is either generous or kind then someone is kind and vice versa.
Susan is either funny or quiet.
Alice is either not calm or not quiet.
Alice is both creative and old.
Someone is tall.
John is not happy or humble.
Someone is not brave or not wise. | Alice is patient. | contradiction | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((generous(X)|~old(X)))))&
(![X]:(calm(X)=>curious(X)))&
(((~funny(john)|~wise(john)))<=>((~brave(mary)<~>~happy(mary))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)&strong(X))<=>(creative(X)&~generous(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((calm(X)&~kind(X))=>(~rich(X)&strong(X))))&
((?[X]:(creative(X)))=>((calm(mary)&happy(mary))))&
(![X]:((brave(X)|~quiet(X))=>(~patient(X)&~rich(X))))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)|humble(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(creative(X)|curious(X))))&
(((generous(john)<~>kind(john)))<=>(?[X]:(kind(X))))&
((funny(susan)<~>quiet(susan)))&
((~calm(alice)<~>~quiet(alice)))&
((creative(alice)&old(alice)))&
(?[X]:(tall(X)))&
((~happy(john)|humble(john)))&
(?[X]:((~brave(X)|~wise(X)))) | patient(alice) | [
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6532598588201419142555570
% SZS output start Proof for 6532598588201419142555570
13. ! [X0] : ((~quiet(X0) | brave(X0)) => (~rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (curious(X0) | creative(X0))) [input p14]
19. old(alice) & creative(alice) [input p18]
23. patient(alice) [input hypothesis]
32. ! [X0] : ((~rich(X0) & ~patient(X0)) | (quiet(X0) & ~brave(X0))) [ennf transformation 13]
60. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~curious(X0) & ~creative(X0))) & ((curious(X0) | creative(X0)) | (generous(X0) | quiet(X0)))) [nnf transformation 15]
61. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~curious(X0) & ~creative(X0))) & (curious(X0) | creative(X0) | generous(X0) | quiet(X0))) [flattening 60]
125. ~patient(X0) | quiet(X0) [cnf transformation 32]
131. ~quiet(X0) | ~creative(X0) [cnf transformation 61]
143. creative(alice) [cnf transformation 19]
148. patient(alice) [cnf transformation 23]
313. 35 <=> quiet(alice) [avatar definition]
315. quiet(alice) <- (35) [avatar component clause 313]
331. quiet(alice) [resolution 125,148]
334. 35 [avatar split clause 331,313]
335. ~creative(alice) <- (35) [resolution 131,315]
336. $false <- (35) [subsumption resolution 335,143]
337. ~35 [avatar contradiction clause 336]
338. $false [avatar sat refutation 334,337]
% SZS output end Proof for 6532598588201419142555570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet then john is rich or curious.
If fred is either not old or not happy then someone is not patient and vice versa.
If someone is either creative or strong then someone is not strong or patient.
Everyone who is both not kind and kind is either patient or creative.
Everyone who is not kind is not rich.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
Everyone who is calm is both curious and humble.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
John is tall or funny.
Mary is both not patient and brave.
Someone is either quiet or humble.
Alice is either kind or curious.
Mary is kind.
Fred is not humble.
Fred is both quiet and not patient.
Fred is both not patient and funny. | Mary is not old. | entailment | ((?[X]:(~quiet(X)))=>((rich(john)|curious(john))))&
(((~old(fred)<~>~happy(fred)))<=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:((~kind(X)&kind(X))=>(patient(X)<~>creative(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
(![X]:(calm(X)=>(curious(X)&humble(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
((tall(john)|funny(john)))&
((~patient(mary)&brave(mary)))&
(?[X]:((quiet(X)<~>humble(X))))&
((kind(alice)<~>curious(alice)))&
(kind(mary))&
(~humble(fred))&
((quiet(fred)&~patient(fred)))&
((~patient(fred)&funny(fred))) | ~old(mary) | [
"p5",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1977899051119989482337235
% SZS output start Proof for 1977899051119989482337235
6. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p5]
7. ! [X0] : (happy(X0) <=> (brave(X0) & ~creative(X0))) [input p6]
9. ! [X0] : ((~calm(X0) | creative(X0)) <=> (brave(X0) | funny(X0))) [input p8]
10. ! [X0] : (~happy(X0) => (~calm(X0) <~> ~humble(X0))) [input p9]
14. ! [X0] : (calm(X0) => (humble(X0) & curious(X0))) [input p13]
25. old(mary) [input hypothesis]
35. ! [X0] : ((~calm(X0) <~> ~humble(X0)) | happy(X0)) [ennf transformation 10]
37. ! [X0] : ((humble(X0) & curious(X0)) | ~calm(X0)) [ennf transformation 14]
48. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 6]
49. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 48]
50. ! [X0] : ((happy(X0) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 7]
51. ! [X0] : ((happy(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [flattening 50]
56. ! [X0] : (((~calm(X0) | creative(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 9]
57. ! [X0] : ((~calm(X0) | creative(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | (calm(X0) & ~creative(X0)))) [flattening 56]
58. ! [X0] : (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | happy(X0)) [nnf transformation 35]
84. calm(X0) | happy(X0) [cnf transformation 49]
85. ~old(X0) | calm(X0) [cnf transformation 49]
86. ~creative(X0) | ~happy(X0) [cnf transformation 51]
87. ~happy(X0) | brave(X0) [cnf transformation 51]
96. ~brave(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
97. ~humble(X0) | ~calm(X0) | happy(X0) [cnf transformation 58]
108. ~calm(X0) | humble(X0) [cnf transformation 37]
126. old(mary) [cnf transformation 25]
195. ~humble(X0) | happy(X0) [subsumption resolution 97,84]
281. calm(mary) [resolution 85,126]
287. humble(X0) | happy(X0) [resolution 108,84]
290. happy(X0) [subsumption resolution 287,195]
296. brave(X0) [resolution 290,87]
320. ~calm(X0) | creative(X0) [resolution 96,296]
326. creative(mary) [resolution 320,281]
332. ~happy(mary) [resolution 326,86]
333. $false [subsumption resolution 332,290]
% SZS output end Proof for 1977899051119989482337235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either generous or curious is either not calm or not tall and vice versa.
If john is both generous and not calm then someone is not curious and vice versa.
Everyone who is both not generous and not creative is either kind or creative.
If paul is not rich then mary is not creative.
If alice is both humble and not wise then someone is happy and vice versa.
Everyone who is both generous and brave is either humble or not brave and vice versa.
Everyone who is not old or rich is either not calm or not humble and vice versa.
If susan is creative then someone is not generous or patient.
If john is not humble or creative then someone is both not funny and generous and vice versa.
If someone is both creative and funny then someone is funny or not wise and vice versa.
If lucy is either not tall or not patient then fred is not brave or wise.
If alice is either old or not curious then paul is not generous.
Everyone who is either not strong or patient is not creative and vice versa.
If john is either not kind or curious then someone is either humble or creative and vice versa.
Everyone who is both not quiet and not brave is tall.
If someone is rich then john is both not happy and happy and vice versa.
Someone is kind or tall.
Someone is not rich.
Someone is brave or curious.
John is not curious.
Someone is either generous or not generous.
Someone is not quiet or funny.
John is either not patient or quiet.
Paul is not humble. | Mary is creative. | contradiction | (![X]:((generous(X)<~>curious(X))<=>(~calm(X)<~>~tall(X))))&
(((generous(john)&~calm(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~generous(X)&~creative(X))=>(kind(X)<~>creative(X))))&
((~rich(paul))=>(~creative(mary)))&
(((humble(alice)&~wise(alice)))<=>(?[X]:(happy(X))))&
(![X]:((generous(X)&brave(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((~old(X)|rich(X))<=>(~calm(X)<~>~humble(X))))&
((creative(susan))=>(?[X]:((~generous(X)|patient(X)))))&
(((~humble(john)|creative(john)))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((creative(X)&funny(X))))<=>(?[X]:((funny(X)|~wise(X)))))&
(((~tall(lucy)<~>~patient(lucy)))=>((~brave(fred)|wise(fred))))&
(((old(alice)<~>~curious(alice)))=>(~generous(paul)))&
(![X]:((~strong(X)<~>patient(X))<=>~creative(X)))&
(((~kind(john)<~>curious(john)))<=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~quiet(X)&~brave(X))=>tall(X)))&
((?[X]:(rich(X)))<=>((~happy(john)&happy(john))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:(~rich(X)))&
(?[X]:((brave(X)|curious(X))))&
(~curious(john))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|funny(X))))&
((~patient(john)<~>quiet(john)))&
(~humble(paul)) | creative(mary) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4442657052676773891578942
% SZS output start Proof for 4442657052676773891578942
4. ~rich(paul) => ~creative(mary) [input p3]
16. ? [X0] : rich(X0) <=> (happy(john) & ~happy(john)) [input p15]
25. creative(mary) [input hypothesis]
29. ~creative(mary) | rich(paul) [ennf transformation 4]
71. (? [X0] : rich(X0) | (~happy(john) | happy(john))) & ((happy(john) & ~happy(john)) | ! [X0] : ~rich(X0)) [nnf transformation 16]
72. (? [X0] : rich(X0) | ~happy(john) | happy(john)) & ((happy(john) & ~happy(john)) | ! [X0] : ~rich(X0)) [flattening 71]
73. (? [X0] : rich(X0) | ~happy(john) | happy(john)) & ((happy(john) & ~happy(john)) | ! [X1] : ~rich(X1)) [rectify 72]
74. ? [X0] : rich(X0) => rich(sK7) [choice axiom]
75. (rich(sK7) | ~happy(john) | happy(john)) & ((happy(john) & ~happy(john)) | ! [X1] : ~rich(X1)) [skolemisation 73,74]
101. ~creative(mary) | rich(paul) [cnf transformation 29]
145. ~happy(john) | ~rich(X1) [cnf transformation 75]
146. happy(john) | ~rich(X1) [cnf transformation 75]
158. creative(mary) [cnf transformation 25]
181. 5 <=> rich(paul) [avatar definition]
183. rich(paul) <- (5) [avatar component clause 181]
185. 6 <=> creative(mary) [avatar definition]
188. 5 | ~6 [avatar split clause 101,185,181]
338. 39 <=> ! [X1] : ~rich(X1) [avatar definition]
339. ~rich(X1) <- (39) [avatar component clause 338]
341. 40 <=> happy(john) [avatar definition]
344. 39 | 40 [avatar split clause 146,341,338]
345. 39 | ~40 [avatar split clause 145,341,338]
384. 6 [avatar split clause 158,185]
386. $false <- (5, 39) [subsumption resolution 183,339]
387. ~5 | ~39 [avatar contradiction clause 386]
390. $false [avatar sat refutation 188,344,345,384,387]
% SZS output end Proof for 4442657052676773891578942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not wise and not old then susan is both not creative and not old and vice versa. If someone is either not happy or calm then john is both not old and not wise. If someone is both not patient and old then john is not creative or generous. Everyone who is quiet or not patient is either old or quiet and vice versa. Everyone who is creative is funny or not humble and vice versa. Everyone who is not brave is both kind and not patient. Everyone who is either not old or not wise is rich or not curious and vice versa. Everyone who is either happy or kind is either calm or tall and vice versa. If someone is both strong and not patient then lucy is curious or wise. If mary is not creative or not quiet then lucy is either brave or patient. Everyone who is both not generous and happy is either curious or strong. Everyone who is not creative or not wise is either not wise or not calm. Everyone who is patient is rich and vice versa. Everyone who is not calm is both patient and curious and vice versa. Everyone who is not curious is either not tall or humble and vice versa. If paul is either wise or curious then someone is either funny or not happy. Fred is not wise. Someone is both not generous and not calm. Someone is not happy or not tall. Someone is both tall and kind. Susan is both not tall and not rich. Someone is either not funny or creative. | John is funny. | neutral | (((~wise(lucy)&~old(lucy)))<=>((~creative(susan)&~old(susan))))&
((?[X]:((~happy(X)<~>calm(X))))=>((~old(john)&~wise(john))))&
((?[X]:((~patient(X)&old(X))))=>((~creative(john)|generous(john))))&
(![X]:((quiet(X)|~patient(X))<=>(old(X)<~>quiet(X))))&
(![X]:(creative(X)<=>(funny(X)|~humble(X))))&
(![X]:(~brave(X)=>(kind(X)&~patient(X))))&
(![X]:((~old(X)<~>~wise(X))<=>(rich(X)|~curious(X))))&
(![X]:((happy(X)<~>kind(X))<=>(calm(X)<~>tall(X))))&
((?[X]:((strong(X)&~patient(X))))=>((curious(lucy)|wise(lucy))))&
(((~creative(mary)|~quiet(mary)))=>((brave(lucy)<~>patient(lucy))))&
(![X]:((~generous(X)&happy(X))=>(curious(X)<~>strong(X))))&
(![X]:((~creative(X)|~wise(X))=>(~wise(X)<~>~calm(X))))&
(![X]:(patient(X)<=>rich(X)))&
(![X]:(~calm(X)<=>(patient(X)&curious(X))))&
(![X]:(~curious(X)<=>(~tall(X)<~>humble(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(~wise(fred))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:((~happy(X)|~tall(X))))&
(?[X]:((tall(X)&kind(X))))&
((~tall(susan)&~rich(susan)))&
(?[X]:((~funny(X)<~>creative(X)))) | funny(john) | [] | null | 0 |
Everyone who is not humble is not old.
If someone is curious or not strong then john is either creative or old and vice versa.
Everyone who is either old or not generous is either not tall or not quiet and vice versa.
Everyone who is both brave and rich is either not creative or not old.
Everyone who is not patient or not rich is not strong or not brave.
Everyone who is not tall or wise is not funny or quiet and vice versa.
Everyone who is humble or not wise is wise.
Everyone who is either not old or not calm is not curious.
If john is either patient or not tall then alice is generous or not quiet and vice versa.
If paul is both tall and humble then john is either brave or not rich and vice versa.
If someone is not happy or not old then someone is not strong or old and vice versa.
If someone is either not old or funny then paul is not creative or not tall.
If someone is either creative or funny then fred is either wise or not curious.
Everyone who is not tall or wise is either not humble or not old and vice versa.
If someone is not curious then someone is either strong or not creative and vice versa.
Everyone who is either humble or generous is both not humble and wise and vice versa.
Alice is either not patient or not tall.
John is both not curious and brave.
Susan is both tall and not funny.
Alice is either not curious or brave.
John is both strong and not funny.
Lucy is funny.
Someone is not strong. | Alice is creative. | neutral | (![X]:(~humble(X)=>~old(X)))&
((?[X]:((curious(X)|~strong(X))))<=>((creative(john)<~>old(john))))&
(![X]:((old(X)<~>~generous(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((brave(X)&rich(X))=>(~creative(X)<~>~old(X))))&
(![X]:((~patient(X)|~rich(X))=>(~strong(X)|~brave(X))))&
(![X]:((~tall(X)|wise(X))<=>(~funny(X)|quiet(X))))&
(![X]:((humble(X)|~wise(X))=>wise(X)))&
(![X]:((~old(X)<~>~calm(X))=>~curious(X)))&
(((patient(john)<~>~tall(john)))<=>((generous(alice)|~quiet(alice))))&
(((tall(paul)&humble(paul)))<=>((brave(john)<~>~rich(john))))&
((?[X]:((~happy(X)|~old(X))))<=>(?[X]:((~strong(X)|old(X)))))&
((?[X]:((~old(X)<~>funny(X))))=>((~creative(paul)|~tall(paul))))&
((?[X]:((creative(X)<~>funny(X))))=>((wise(fred)<~>~curious(fred))))&
(![X]:((~tall(X)|wise(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
((~patient(alice)<~>~tall(alice)))&
((~curious(john)&brave(john)))&
((tall(susan)&~funny(susan)))&
((~curious(alice)<~>brave(alice)))&
((strong(john)&~funny(john)))&
(funny(lucy))&
(?[X]:(~strong(X))) | creative(alice) | [] | null | 0 |
If john is not creative or tall then paul is either not rich or curious and vice versa. Everyone who is not quiet is either tall or not strong and vice versa. If lucy is both happy and humble then alice is either not strong or brave and vice versa. Everyone who is happy is patient or not old and vice versa. If paul is not wise then someone is both quiet and curious and vice versa. If lucy is either brave or not calm then alice is not creative or not calm. If someone is old then someone is not old or quiet and vice versa. If someone is either not generous or not tall then fred is not kind. If john is not kind or not patient then john is not kind or curious and vice versa. If fred is not funny or not happy then someone is humble or not humble. If someone is not wise then someone is both not happy and not brave. Everyone who is either not humble or generous is happy or calm and vice versa. Everyone who is not tall or quiet is creative or patient. Everyone who is curious is either happy or generous and vice versa. Everyone who is not funny or brave is happy or wise. If someone is curious or not wise then lucy is rich or brave. Someone is creative. Alice is either old or quiet. Someone is humble. Fred is rich or not strong. Someone is not tall or creative. Lucy is old. Susan is either creative or brave. Someone is either generous or patient. | Fred is not happy. | neutral | (((~creative(john)|tall(john)))<=>((~rich(paul)<~>curious(paul))))&
(![X]:(~quiet(X)<=>(tall(X)<~>~strong(X))))&
(((happy(lucy)&humble(lucy)))<=>((~strong(alice)<~>brave(alice))))&
(![X]:(happy(X)<=>(patient(X)|~old(X))))&
((~wise(paul))<=>(?[X]:((quiet(X)&curious(X)))))&
(((brave(lucy)<~>~calm(lucy)))=>((~creative(alice)|~calm(alice))))&
((?[X]:(old(X)))<=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(~kind(fred)))&
(((~kind(john)|~patient(john)))<=>((~kind(john)|curious(john))))&
(((~funny(fred)|~happy(fred)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((~humble(X)<~>generous(X))<=>(happy(X)|calm(X))))&
(![X]:((~tall(X)|quiet(X))=>(creative(X)|patient(X))))&
(![X]:(curious(X)<=>(happy(X)<~>generous(X))))&
(![X]:((~funny(X)|brave(X))=>(happy(X)|wise(X))))&
((?[X]:((curious(X)|~wise(X))))=>((rich(lucy)|brave(lucy))))&
(?[X]:(creative(X)))&
((old(alice)<~>quiet(alice)))&
(?[X]:(humble(X)))&
((rich(fred)|~strong(fred)))&
(?[X]:((~tall(X)|creative(X))))&
(old(lucy))&
((creative(susan)<~>brave(susan)))&
(?[X]:((generous(X)<~>patient(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is both humble and curious is humble and vice versa.
Everyone who is both not tall and humble is not rich or not generous and vice versa.
If mary is both happy and not old then someone is not humble.
If someone is happy then susan is both not curious and not generous.
Everyone who is generous or not brave is either not wise or tall.
If john is not patient then someone is either rich or kind.
Everyone who is either rich or humble is generous.
Everyone who is quiet is either happy or not tall and vice versa.
If someone is both not generous and brave then someone is tall and vice versa.
If susan is brave or not rich then paul is not quiet or generous and vice versa.
Everyone who is either not creative or curious is not kind.
Everyone who is not happy is both not curious and not tall and vice versa.
Everyone who is both not creative and brave is calm or tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
If lucy is old then someone is either not patient or not tall and vice versa.
Everyone who is calm is both wise and not funny.
Paul is either not funny or not rich.
Fred is both not humble and creative.
Someone is both not humble and rich.
Susan is both brave and not happy.
Someone is either creative or not wise.
Paul is either old or funny.
Someone is not wise. | John is not rich. | contradiction | (![X]:((humble(X)&curious(X))<=>humble(X)))&
(![X]:((~tall(X)&humble(X))<=>(~rich(X)|~generous(X))))&
(((happy(mary)&~old(mary)))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))=>((~curious(susan)&~generous(susan))))&
(![X]:((generous(X)|~brave(X))=>(~wise(X)<~>tall(X))))&
((~patient(john))=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((rich(X)<~>humble(X))=>generous(X)))&
(![X]:(quiet(X)<=>(happy(X)<~>~tall(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:(tall(X))))&
(((brave(susan)|~rich(susan)))<=>((~quiet(paul)|generous(paul))))&
(![X]:((~creative(X)<~>curious(X))=>~kind(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~tall(X))))&
(![X]:((~creative(X)&brave(X))<=>(calm(X)|tall(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
((old(lucy))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:(calm(X)=>(wise(X)&~funny(X))))&
((~funny(paul)<~>~rich(paul)))&
((~humble(fred)&creative(fred)))&
(?[X]:((~humble(X)&rich(X))))&
((brave(susan)&~happy(susan)))&
(?[X]:((creative(X)<~>~wise(X))))&
((old(paul)<~>funny(paul)))&
(?[X]:(~wise(X))) | ~rich(john) | [
"p0",
"p1",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 369653583896885312739665
% SZS output start Proof for 369653583896885312739665
1. ! [X0] : ((curious(X0) & humble(X0)) <=> humble(X0)) [input p0]
2. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (~generous(X0) | ~rich(X0))) [input p1]
4. ? [X0] : happy(X0) => (~generous(susan) & ~curious(susan)) [input p3]
12. ! [X0] : (~happy(X0) <=> (~tall(X0) & ~curious(X0))) [input p11]
24. ~rich(john) [input hypothesis]
28. (~generous(susan) & ~curious(susan)) | ! [X0] : ~happy(X0) [ennf transformation 4]
34. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (~curious(X0) | ~humble(X0)))) [nnf transformation 1]
35. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 34]
36. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~humble(X0) | tall(X0))) [flattening 36]
54. ! [X0] : ((~happy(X0) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [nnf transformation 12]
55. ! [X0] : ((~happy(X0) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [flattening 54]
75. ~humble(X0) | curious(X0) [cnf transformation 35]
79. rich(X0) | humble(X0) [cnf transformation 37]
80. generous(X0) | humble(X0) [cnf transformation 37]
82. ~curious(susan) | ~happy(X0) [cnf transformation 28]
83. ~generous(susan) | ~happy(X0) [cnf transformation 28]
105. ~curious(X0) | happy(X0) [cnf transformation 55]
135. ~rich(john) [cnf transformation 24]
150. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
151. ~happy(X0) <- (4) [avatar component clause 150]
153. 5 <=> generous(susan) [avatar definition]
155. ~generous(susan) <- (~5) [avatar component clause 153]
156. 4 | ~5 [avatar split clause 83,153,150]
158. 6 <=> curious(susan) [avatar definition]
160. ~curious(susan) <- (~6) [avatar component clause 158]
161. 4 | ~6 [avatar split clause 82,158,150]
268. humble(john) [resolution 79,135]
270. curious(john) [resolution 268,75]
271. humble(susan) <- (~5) [resolution 80,155]
273. curious(susan) <- (~5) [resolution 271,75]
274. $false <- (~5, ~6) [subsumption resolution 273,160]
275. 5 | 6 [avatar contradiction clause 274]
276. happy(john) [resolution 270,105]
277. $false <- (4) [subsumption resolution 276,151]
278. ~4 [avatar contradiction clause 277]
279. $false [avatar sat refutation 156,161,275,278]
% SZS output end Proof for 369653583896885312739665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both brave and creative and vice versa.
If fred is creative or not rich then someone is not calm.
Everyone who is both not tall and generous is not old and vice versa.
If susan is either not wise or not funny then someone is not rich or not patient and vice versa.
If alice is either quiet or funny then someone is not creative.
If paul is either wise or not calm then lucy is both funny and curious.
If someone is either not funny or not creative then paul is both not funny and strong.
Everyone who is not generous or not strong is both not quiet and funny.
If alice is both not humble and humble then john is quiet or not happy.
Everyone who is either not quiet or curious is not generous or not kind and vice versa.
Everyone who is not creative or not funny is both not creative and not happy and vice versa.
If paul is not old or happy then john is either not rich or strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
Someone is not happy.
Someone is both not creative and old.
Someone is not old.
Someone is not creative.
Someone is both not funny and wise.
Susan is quiet.
John is either patient or humble. | Susan is tall. | neutral | (![X]:(curious(X)<=>(brave(X)&creative(X))))&
(((creative(fred)|~rich(fred)))=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)&generous(X))<=>~old(X)))&
(((~wise(susan)<~>~funny(susan)))<=>(?[X]:((~rich(X)|~patient(X)))))&
(((quiet(alice)<~>funny(alice)))=>(?[X]:(~creative(X))))&
(((wise(paul)<~>~calm(paul)))=>((funny(lucy)&curious(lucy))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((~funny(paul)&strong(paul))))&
(![X]:((~generous(X)|~strong(X))=>(~quiet(X)&funny(X))))&
(((~humble(alice)&humble(alice)))=>((quiet(john)|~happy(john))))&
(![X]:((~quiet(X)<~>curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~creative(X)|~funny(X))<=>(~creative(X)&~happy(X))))&
(((~old(paul)|happy(paul)))<=>((~rich(john)<~>strong(john))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:(~old(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)&wise(X))))&
(quiet(susan))&
((patient(john)<~>humble(john))) | tall(susan) | [] | null | 0 |
If someone is both not funny and happy then paul is creative and vice versa.
Everyone who is either creative or not quiet is either not brave or not curious and vice versa.
Everyone who is not generous is wise or creative and vice versa.
Everyone who is not wise or not humble is not funny and vice versa.
If someone is kind then someone is not tall or generous.
Everyone who is not funny or not humble is not generous or humble.
Everyone who is not quiet or generous is either tall or old.
Everyone who is either curious or not curious is not rich or generous.
Everyone who is not creative is not happy or tall.
Everyone who is old or not humble is not old or creative and vice versa.
If someone is not calm or quiet then someone is not strong or funny and vice versa.
If alice is tall or not patient then someone is both not rich and not quiet and vice versa.
If someone is happy or not funny then susan is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
Someone is both not creative and not funny.
Susan is both curious and tall.
Someone is not patient.
Someone is rich or tall.
Someone is either patient or curious.
Lucy is calm or not generous.
Someone is both tall and not wise. | Lucy is not generous. | entailment | ((?[X]:((~funny(X)&happy(X))))<=>(creative(paul)))&
(![X]:((creative(X)<~>~quiet(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(~generous(X)<=>(wise(X)|creative(X))))&
(![X]:((~wise(X)|~humble(X))<=>~funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((~funny(X)|~humble(X))=>(~generous(X)|humble(X))))&
(![X]:((~quiet(X)|generous(X))=>(tall(X)<~>old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~rich(X)|generous(X))))&
(![X]:(~creative(X)=>(~happy(X)|tall(X))))&
(![X]:((old(X)|~humble(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(?[X]:((~creative(X)&~funny(X))))&
((curious(susan)&tall(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|tall(X))))&
(?[X]:((patient(X)<~>curious(X))))&
((calm(lucy)|~generous(lucy)))&
(?[X]:((tall(X)&~wise(X)))) | ~generous(lucy) | [
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7271536006437393704694623
% SZS output start Proof for 7271536006437393704694623
3. ! [X0] : (~generous(X0) <=> (creative(X0) | wise(X0))) [input p2]
6. ! [X0] : ((~humble(X0) | ~funny(X0)) => (humble(X0) | ~generous(X0))) [input p5]
10. ! [X0] : ((~humble(X0) | old(X0)) <=> (creative(X0) | ~old(X0))) [input p9]
24. generous(lucy) [input hypothesis]
28. ! [X0] : ((humble(X0) | ~generous(X0)) | (humble(X0) & funny(X0))) [ennf transformation 6]
29. ! [X0] : (humble(X0) | ~generous(X0) | (humble(X0) & funny(X0))) [flattening 28]
42. ! [X0] : ((~generous(X0) | (~creative(X0) & ~wise(X0))) & ((creative(X0) | wise(X0)) | generous(X0))) [nnf transformation 3]
43. ! [X0] : ((~generous(X0) | (~creative(X0) & ~wise(X0))) & (creative(X0) | wise(X0) | generous(X0))) [flattening 42]
48. ! [X0] : (((~humble(X0) | old(X0)) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 10]
49. ! [X0] : ((~humble(X0) | old(X0) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | (humble(X0) & ~old(X0)))) [flattening 48]
95. ~generous(X0) | ~creative(X0) [cnf transformation 43]
100. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 29]
108. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 49]
110. ~humble(X0) | old(X0) | old(X0) [cnf transformation 49]
147. generous(lucy) [cnf transformation 24]
148. ~old(X0) | creative(X0) [duplicate literal removal 108]
149. ~humble(X0) | old(X0) [duplicate literal removal 110]
152. ~generous(X0) | humble(X0) [duplicate literal removal 100]
299. 33 <=> generous(lucy) [avatar definition]
300. generous(lucy) <- (33) [avatar component clause 299]
303. 33 [avatar split clause 147,299]
306. ~creative(lucy) <- (33) [resolution 95,300]
308. humble(lucy) <- (33) [resolution 152,300]
310. old(lucy) <- (33) [resolution 308,149]
376. creative(lucy) <- (33) [resolution 310,148]
378. $false <- (33) [subsumption resolution 376,306]
379. ~33 [avatar contradiction clause 378]
380. $false [avatar sat refutation 303,379]
% SZS output end Proof for 7271536006437393704694623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or happy is both not tall and quiet and vice versa.
If someone is either not kind or not generous then fred is both happy and not creative.
If someone is either not brave or not funny then someone is either not curious or not strong and vice versa.
If someone is quiet then susan is both kind and not kind and vice versa.
Everyone who is not rich or not funny is not humble.
If someone is either calm or patient then someone is rich.
Everyone who is quiet is either tall or not rich and vice versa.
Everyone who is either not strong or calm is both strong and creative and vice versa.
If mary is both not brave and not old then someone is both not rich and quiet.
If mary is either not quiet or not curious then paul is not humble and vice versa.
Everyone who is both not wise and humble is brave and vice versa.
If alice is old or not brave then fred is either not curious or quiet.
If susan is either calm or not brave then someone is both kind and patient.
If someone is either not kind or calm then someone is both old and generous.
If fred is not humble then someone is not kind or not wise.
If alice is both not kind and not strong then lucy is both not wise and generous and vice versa.
John is curious or tall.
John is not generous.
Paul is both not quiet and old.
Someone is either old or curious.
Someone is either not happy or not kind. | Mary is not tall. | entailment | (![X]:((~humble(X)|happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~generous(X))))=>((happy(fred)&~creative(fred))))&
((?[X]:((~brave(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:(quiet(X)))<=>((kind(susan)&~kind(susan))))&
(![X]:((~rich(X)|~funny(X))=>~humble(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(rich(X))))&
(![X]:(quiet(X)<=>(tall(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>calm(X))<=>(strong(X)&creative(X))))&
(((~brave(mary)&~old(mary)))=>(?[X]:((~rich(X)&quiet(X)))))&
(((~quiet(mary)<~>~curious(mary)))<=>(~humble(paul)))&
(![X]:((~wise(X)&humble(X))<=>brave(X)))&
(((old(alice)|~brave(alice)))=>((~curious(fred)<~>quiet(fred))))&
(((calm(susan)<~>~brave(susan)))=>(?[X]:((kind(X)&patient(X)))))&
((?[X]:((~kind(X)<~>calm(X))))=>(?[X]:((old(X)&generous(X)))))&
((~humble(fred))=>(?[X]:((~kind(X)|~wise(X)))))&
(((~kind(alice)&~strong(alice)))<=>((~wise(lucy)&generous(lucy))))&
((curious(john)|tall(john)))&
(~generous(john))&
((~quiet(paul)&old(paul)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((~happy(X)<~>~kind(X)))) | ~tall(mary) | [
"p0",
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3055187283116826201122550
% SZS output start Proof for 3055187283116826201122550
1. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (quiet(X0) & ~tall(X0))) [input p0]
4. ? [X0] : quiet(X0) <=> (~kind(susan) & kind(susan)) [input p3]
5. ! [X0] : ((~funny(X0) | ~rich(X0)) => ~humble(X0)) [input p4]
7. ! [X0] : (quiet(X0) <=> (tall(X0) <~> ~rich(X0))) [input p6]
22. tall(mary) [input hypothesis]
27. ! [X0] : (~humble(X0) | (funny(X0) & rich(X0))) [ennf transformation 5]
35. ! [X0] : (((happy(X0) | ~humble(X0)) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | (~happy(X0) & humble(X0)))) [nnf transformation 1]
36. ! [X0] : ((happy(X0) | ~humble(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | (~happy(X0) & humble(X0)))) [flattening 35]
43. (? [X0] : quiet(X0) | (kind(susan) | ~kind(susan))) & ((~kind(susan) & kind(susan)) | ! [X0] : ~quiet(X0)) [nnf transformation 4]
44. (? [X0] : quiet(X0) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X0] : ~quiet(X0)) [flattening 43]
45. (? [X0] : quiet(X0) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
47. (quiet(sK2) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
52. ! [X0] : ((quiet(X0) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ~quiet(X0))) [nnf transformation 7]
80. quiet(X0) | humble(X0) [cnf transformation 36]
95. kind(susan) | ~quiet(X1) [cnf transformation 47]
96. ~kind(susan) | ~quiet(X1) [cnf transformation 47]
98. ~humble(X0) | rich(X0) [cnf transformation 27]
104. ~rich(X0) | quiet(X0) | ~tall(X0) [cnf transformation 52]
146. tall(mary) [cnf transformation 22]
204. 13 <=> ! [X1] : ~quiet(X1) [avatar definition]
205. ~quiet(X1) <- (13) [avatar component clause 204]
207. 14 <=> kind(susan) [avatar definition]
210. 13 | ~14 [avatar split clause 96,207,204]
211. 13 | 14 [avatar split clause 95,207,204]
380. humble(X0) <- (13) [resolution 80,205]
396. rich(X0) <- (13) [resolution 380,98]
424. quiet(X0) | ~tall(X0) <- (13) [resolution 104,396]
428. ~tall(X0) <- (13) [subsumption resolution 424,205]
434. $false <- (13) [resolution 428,146]
435. ~13 [avatar contradiction clause 434]
436. $false [avatar sat refutation 210,211,435]
% SZS output end Proof for 3055187283116826201122550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not kind is both quiet and not creative and vice versa.
If someone is either quiet or tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Susan is both happy and humble.
Alice is both tall and not old.
Someone is not old or not generous.
Fred is rich.
Alice is not generous or not kind.
Paul is curious.
Someone is not humble. | Fred is calm. | entailment | (![X]:((~calm(X)&~kind(X))<=>(quiet(X)&~creative(X))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
((happy(susan)&humble(susan)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X))))&
(rich(fred))&
((~generous(alice)|~kind(alice)))&
(curious(paul))&
(?[X]:(~humble(X))) | calm(fred) | [
"p0",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5177629576164985921864742
% SZS output start Proof for 5177629576164985921864742
1. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> (~creative(X0) & quiet(X0))) [input p0]
8. ! [X0] : ((wise(X0) & ~creative(X0)) <=> strong(X0)) [input p7]
9. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> (calm(X0) | old(X0))) [input p9]
11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10]
12. ! [X0] : (humble(X0) => (strong(X0) <~> ~patient(X0))) [input p11]
13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13]
15. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p14]
20. rich(fred) [input p19]
24. ~calm(fred) [input hypothesis]
30. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11]
31. ! [X0] : ((strong(X0) <~> ~patient(X0)) | ~humble(X0)) [ennf transformation 12]
33. ! [X0] : (((~kind(X0) & ~calm(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (kind(X0) | calm(X0)))) [nnf transformation 1]
34. ! [X0] : (((~kind(X0) & ~calm(X0)) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | kind(X0) | calm(X0))) [flattening 33]
44. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | (~wise(X0) | creative(X0)))) [nnf transformation 8]
45. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | ~wise(X0) | creative(X0))) [flattening 44]
46. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 9]
47. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 46]
48. ! [X0] : (((~quiet(X0) | ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (quiet(X0) & patient(X0)))) [nnf transformation 10]
49. ! [X0] : ((~quiet(X0) | ~patient(X0) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | (quiet(X0) & patient(X0)))) [flattening 48]
50. ! [X0] : (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ~humble(X0)) [nnf transformation 31]
51. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13]
52. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 51]
53. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14]
54. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 53]
55. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 15]
56. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 55]
64. ~creative(X0) | kind(X0) | calm(X0) [cnf transformation 34]
89. ~strong(X0) | wise(X0) [cnf transformation 45]
90. ~rich(X0) | funny(X0) [cnf transformation 47]
91. ~rich(X0) | happy(X0) [cnf transformation 47]
95. old(X0) | calm(X0) | patient(X0) [cnf transformation 49]
99. ~happy(X0) | funny(X0) [cnf transformation 30]
100. ~old(X0) | ~happy(X0) [cnf transformation 30]
101. ~humble(X0) | strong(X0) | ~patient(X0) [cnf transformation 50]
106. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 52]
113. ~brave(X0) | old(X0) | ~wise(X0) [cnf transformation 54]
114. ~brave(X0) | old(X0) | ~kind(X0) [cnf transformation 54]
117. ~funny(X0) | creative(X0) | humble(X0) [cnf transformation 56]
128. rich(fred) [cnf transformation 20]
132. ~calm(fred) [cnf transformation 24]
206. ~happy(X0) | brave(X0) [subsumption resolution 106,99]
243. funny(fred) [resolution 90,128]
245. happy(fred) [resolution 91,128]
251. brave(fred) [resolution 206,245]
318. ~happy(X0) | patient(X0) | calm(X0) [resolution 95,100]
385. old(fred) | ~wise(fred) [resolution 113,251]
407. old(fred) | ~kind(fred) [resolution 114,251]
424. 39 <=> kind(fred) [avatar definition]
426. ~kind(fred) <- (~39) [avatar component clause 424]
428. 40 <=> old(fred) [avatar definition]
430. old(fred) <- (40) [avatar component clause 428]
431. ~39 | 40 [avatar split clause 407,428,424]
460. 47 <=> wise(fred) [avatar definition]
463. ~47 | 40 [avatar split clause 385,428,460]
488. creative(fred) | humble(fred) [resolution 117,243]
574. 56 <=> humble(fred) [avatar definition]
576. humble(fred) <- (56) [avatar component clause 574]
578. 57 <=> creative(fred) [avatar definition]
580. creative(fred) <- (57) [avatar component clause 578]
581. 56 | 57 [avatar split clause 488,578,574]
636. patient(fred) | calm(fred) [resolution 318,245]
646. patient(fred) [subsumption resolution 636,132]
686. strong(fred) | ~patient(fred) <- (56) [resolution 576,101]
689. strong(fred) <- (56) [subsumption resolution 686,646]
848. wise(fred) <- (56) [resolution 689,89]
852. 47 | ~56 [avatar split clause 848,574,460]
864. ~happy(fred) <- (40) [resolution 430,100]
868. $false <- (40) [subsumption resolution 864,245]
869. ~40 [avatar contradiction clause 868]
871. kind(fred) | calm(fred) <- (57) [resolution 580,64]
873. calm(fred) <- (~39, 57) [subsumption resolution 871,426]
874. $false <- (~39, 57) [subsumption resolution 873,132]
875. 39 | ~57 [avatar contradiction clause 874]
876. $false [avatar sat refutation 431,463,581,852,869,875]
% SZS output end Proof for 5177629576164985921864742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is wise then lucy is both creative and not tall and vice versa.
Everyone who is either wise or quiet is either not strong or calm and vice versa.
Everyone who is either generous or not patient is not generous and vice versa.
Everyone who is either not funny or not old is both not rich and happy and vice versa.
Everyone who is not old or creative is not strong.
If someone is both not humble and not tall then someone is either creative or funny and vice versa.
Everyone who is wise is not happy or not creative and vice versa.
Everyone who is kind or happy is either generous or not happy and vice versa.
If paul is not funny or not calm then someone is both not old and humble and vice versa.
Everyone who is not creative or not curious is both strong and not rich.
If someone is both generous and calm then john is tall.
If someone is either not curious or not kind then paul is not creative or happy.
Everyone who is either not happy or generous is both old and humble.
Everyone who is rich is either not curious or not generous.
If someone is not quiet then john is both happy and not calm.
Mary is creative.
Someone is not happy or happy.
Paul is not happy or not patient.
Someone is both humble and rich.
Someone is patient or rich. | Paul is patient. | contradiction | ((wise(mary))<=>((creative(lucy)&~tall(lucy))))&
(![X]:((wise(X)<~>quiet(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((generous(X)<~>~patient(X))<=>~generous(X)))&
(![X]:((~funny(X)<~>~old(X))<=>(~rich(X)&happy(X))))&
(![X]:((~old(X)|creative(X))=>~strong(X)))&
((?[X]:((~humble(X)&~tall(X))))<=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:(wise(X)<=>(~happy(X)|~creative(X))))&
(![X]:((kind(X)|happy(X))<=>(generous(X)<~>~happy(X))))&
(((~funny(paul)|~calm(paul)))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((~creative(X)|~curious(X))=>(strong(X)&~rich(X))))&
((?[X]:((generous(X)&calm(X))))=>(tall(john)))&
((?[X]:((~curious(X)<~>~kind(X))))=>((~creative(paul)|happy(paul))))&
(![X]:((~happy(X)<~>generous(X))=>(old(X)&humble(X))))&
(![X]:(rich(X)=>(~curious(X)<~>~generous(X))))&
((?[X]:(~quiet(X)))=>((happy(john)&~calm(john))))&
(creative(mary))&
(?[X]:((~happy(X)|happy(X))))&
((~happy(paul)|~patient(paul)))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((patient(X)|rich(X)))) | patient(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1018657572572330309109913
% SZS output start Proof for 1018657572572330309109913
3. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> ~generous(X0)) [input p2]
21. patient(paul) [input hypothesis]
34. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | generous(X0)) & (~generous(X0) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 3]
71. ~generous(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 34]
73. ~patient(X0) | generous(X0) | generous(X0) [cnf transformation 34]
124. patient(paul) [cnf transformation 21]
127. ~generous(X0) | ~patient(X0) [duplicate literal removal 71]
128. ~patient(X0) | generous(X0) [duplicate literal removal 73]
144. ~patient(X0) [subsumption resolution 127,128]
243. $false [subsumption resolution 124,144]
% SZS output end Proof for 1018657572572330309109913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not old then someone is both generous and not curious and vice versa.
Everyone who is both wise and strong is not wise and vice versa.
Everyone who is not wise or not generous is both not creative and not kind.
Everyone who is patient is either kind or not brave.
If mary is either strong or creative then someone is quiet or old.
Everyone who is tall is both not calm and not funny and vice versa.
Everyone who is not brave or not curious is funny and vice versa.
If paul is not calm then mary is either patient or not creative and vice versa.
Everyone who is either creative or happy is rich and vice versa.
If fred is both not generous and happy then someone is either not quiet or calm.
Everyone who is quiet or funny is not curious or old.
If lucy is not rich or old then fred is both patient and not quiet and vice versa.
If someone is not strong then susan is either rich or old.
Everyone who is either not patient or not calm is quiet or not happy and vice versa.
If fred is both not humble and brave then someone is both brave and funny.
Everyone who is both creative and not calm is both tall and curious.
Mary is happy.
Someone is wise.
Someone is patient or strong.
Someone is both old and patient.
Someone is kind.
John is either not old or not creative.
Alice is either not patient or not rich.
Paul is either wise or kind. | Mary is not strong. | entailment | ((~old(john))<=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((wise(X)&strong(X))<=>~wise(X)))&
(![X]:((~wise(X)|~generous(X))=>(~creative(X)&~kind(X))))&
(![X]:(patient(X)=>(kind(X)<~>~brave(X))))&
(((strong(mary)<~>creative(mary)))=>(?[X]:((quiet(X)|old(X)))))&
(![X]:(tall(X)<=>(~calm(X)&~funny(X))))&
(![X]:((~brave(X)|~curious(X))<=>funny(X)))&
((~calm(paul))<=>((patient(mary)<~>~creative(mary))))&
(![X]:((creative(X)<~>happy(X))<=>rich(X)))&
(((~generous(fred)&happy(fred)))=>(?[X]:((~quiet(X)<~>calm(X)))))&
(![X]:((quiet(X)|funny(X))=>(~curious(X)|old(X))))&
(((~rich(lucy)|old(lucy)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:(~strong(X)))=>((rich(susan)<~>old(susan))))&
(![X]:((~patient(X)<~>~calm(X))<=>(quiet(X)|~happy(X))))&
(((~humble(fred)&brave(fred)))=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((creative(X)&~calm(X))=>(tall(X)&curious(X))))&
(happy(mary))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:(kind(X)))&
((~old(john)<~>~creative(john)))&
((~patient(alice)<~>~rich(alice)))&
((wise(paul)<~>kind(paul))) | ~strong(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5867261787454651828503678
% SZS output start Proof for 5867261787454651828503678
2. ! [X0] : ((strong(X0) & wise(X0)) <=> ~wise(X0)) [input p1]
25. strong(mary) [input hypothesis]
45. ! [X0] : (((strong(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 2]
46. ! [X0] : (((strong(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | ~strong(X0) | ~wise(X0))) [flattening 45]
75. ~wise(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 46]
76. wise(X0) | wise(X0) [cnf transformation 46]
129. strong(mary) [cnf transformation 25]
130. ~wise(X0) | ~strong(X0) [duplicate literal removal 75]
131. wise(X0) [duplicate literal removal 76]
150. ~strong(X0) [subsumption resolution 130,131]
246. $false [subsumption resolution 129,150]
% SZS output end Proof for 5867261787454651828503678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not brave or rich is either creative or patient.
If someone is either not calm or not generous then someone is either not quiet or kind.
Everyone who is humble is either humble or not wise and vice versa.
Everyone who is either not happy or not quiet is either creative or not curious and vice versa.
If someone is not calm or brave then fred is either strong or not kind and vice versa.
Everyone who is not patient or kind is either wise or old.
If someone is both wise and not calm then susan is both not creative and creative and vice versa.
Everyone who is not happy is both not happy and not curious.
If paul is not generous then john is either not curious or not happy.
If someone is funny or generous then someone is quiet.
If paul is both strong and not happy then someone is both not rich and not generous and vice versa.
Everyone who is both not quiet and not humble is either brave or not curious and vice versa.
Everyone who is happy is either kind or not generous.
Everyone who is not kind or not curious is not old and vice versa.
If someone is not tall then lucy is not humble or not generous and vice versa.
Someone is not curious or not happy.
Alice is both curious and not generous.
Alice is not kind.
Mary is either brave or not calm.
Someone is strong.
Someone is not strong.
Someone is not humble or quiet. | Lucy is not creative. | neutral | (![X]:((~brave(X)<~>rich(X))=>(creative(X)<~>patient(X))))&
((?[X]:((~calm(X)<~>~generous(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:(humble(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((strong(fred)<~>~kind(fred))))&
(![X]:((~patient(X)|kind(X))=>(wise(X)<~>old(X))))&
((?[X]:((wise(X)&~calm(X))))<=>((~creative(susan)&creative(susan))))&
(![X]:(~happy(X)=>(~happy(X)&~curious(X))))&
((~generous(paul))=>((~curious(john)<~>~happy(john))))&
((?[X]:((funny(X)|generous(X))))=>(?[X]:(quiet(X))))&
(((strong(paul)&~happy(paul)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(brave(X)<~>~curious(X))))&
(![X]:(happy(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)|~curious(X))<=>~old(X)))&
((?[X]:(~tall(X)))<=>((~humble(lucy)|~generous(lucy))))&
(?[X]:((~curious(X)|~happy(X))))&
((curious(alice)&~generous(alice)))&
(~kind(alice))&
((brave(mary)<~>~calm(mary)))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~humble(X)|quiet(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both humble and creative is either not humble or humble and vice versa. Everyone who is humble or funny is not brave and vice versa. If paul is both rich and patient then someone is either not brave or not tall. If someone is not rich or curious then someone is both generous and tall. Everyone who is both not brave and funny is both tall and not curious. If fred is either not happy or not patient then someone is not kind or not curious. If john is both not humble and funny then susan is both not tall and not creative and vice versa. Everyone who is not calm is not tall or strong. If mary is either not strong or funny then fred is both creative and funny. Everyone who is either not happy or not calm is tall. Everyone who is not creative is not strong or calm. Everyone who is both not rich and creative is both not patient and not old and vice versa. Everyone who is both not kind and not wise is not humble or funny. Everyone who is not brave is either old or not calm and vice versa. If lucy is humble then someone is both not happy and not kind. If someone is creative then john is both not curious and generous. Someone is both not tall and quiet. Fred is tall or wise. Someone is both creative and not generous. Someone is not quiet or not humble. Susan is not old or strong. Mary is both old and wise. Susan is humble. | Paul is not strong. | neutral | (![X]:((humble(X)&creative(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((humble(X)|funny(X))<=>~brave(X)))&
(((rich(paul)&patient(paul)))=>(?[X]:((~brave(X)<~>~tall(X)))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((~brave(X)&funny(X))=>(tall(X)&~curious(X))))&
(((~happy(fred)<~>~patient(fred)))=>(?[X]:((~kind(X)|~curious(X)))))&
(((~humble(john)&funny(john)))<=>((~tall(susan)&~creative(susan))))&
(![X]:(~calm(X)=>(~tall(X)|strong(X))))&
(((~strong(mary)<~>funny(mary)))=>((creative(fred)&funny(fred))))&
(![X]:((~happy(X)<~>~calm(X))=>tall(X)))&
(![X]:(~creative(X)=>(~strong(X)|calm(X))))&
(![X]:((~rich(X)&creative(X))<=>(~patient(X)&~old(X))))&
(![X]:((~kind(X)&~wise(X))=>(~humble(X)|funny(X))))&
(![X]:(~brave(X)<=>(old(X)<~>~calm(X))))&
((humble(lucy))=>(?[X]:((~happy(X)&~kind(X)))))&
((?[X]:(creative(X)))=>((~curious(john)&generous(john))))&
(?[X]:((~tall(X)&quiet(X))))&
((tall(fred)|wise(fred)))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((~quiet(X)|~humble(X))))&
((~old(susan)|strong(susan)))&
((old(mary)&wise(mary)))&
(humble(susan)) | ~strong(paul) | [] | null | 0 |
Everyone who is either strong or not funny is rich. If john is either strong or not curious then paul is either not calm or not curious and vice versa. If alice is either brave or not creative then alice is both curious and not generous. Everyone who is strong is old or rich and vice versa. Everyone who is not brave or happy is both not kind and funny. Everyone who is both not kind and happy is creative or not kind. Everyone who is either strong or not brave is either not old or not wise and vice versa. If someone is either old or not tall then someone is both generous and patient and vice versa. If susan is funny then someone is not rich or not wise and vice versa. Everyone who is both not patient and rich is happy or humble. Everyone who is both not strong and quiet is either curious or not strong. Everyone who is wise is both patient and quiet and vice versa. If john is quiet then paul is either creative or calm and vice versa. Everyone who is brave is both not creative and rich and vice versa. If someone is tall or rich then john is not brave or humble and vice versa. Everyone who is both quiet and not quiet is either not humble or calm and vice versa. Fred is either happy or not generous. Fred is both rich and kind. Mary is curious or not rich. Someone is not creative or generous. Paul is both not humble and not funny. Mary is both not wise and not quiet. Lucy is old or not rich. Someone is both not funny and calm. | John is not tall. | neutral | (![X]:((strong(X)<~>~funny(X))=>rich(X)))&
(((strong(john)<~>~curious(john)))<=>((~calm(paul)<~>~curious(paul))))&
(((brave(alice)<~>~creative(alice)))=>((curious(alice)&~generous(alice))))&
(![X]:(strong(X)<=>(old(X)|rich(X))))&
(![X]:((~brave(X)|happy(X))=>(~kind(X)&funny(X))))&
(![X]:((~kind(X)&happy(X))=>(creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
((funny(susan))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((~patient(X)&rich(X))=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&quiet(X))=>(curious(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(patient(X)&quiet(X))))&
((quiet(john))<=>((creative(paul)<~>calm(paul))))&
(![X]:(brave(X)<=>(~creative(X)&rich(X))))&
((?[X]:((tall(X)|rich(X))))<=>((~brave(john)|humble(john))))&
(![X]:((quiet(X)&~quiet(X))<=>(~humble(X)<~>calm(X))))&
((happy(fred)<~>~generous(fred)))&
((rich(fred)&kind(fred)))&
((curious(mary)|~rich(mary)))&
(?[X]:((~creative(X)|generous(X))))&
((~humble(paul)&~funny(paul)))&
((~wise(mary)&~quiet(mary)))&
((old(lucy)|~rich(lucy)))&
(?[X]:((~funny(X)&calm(X)))) | ~tall(john) | [] | null | 0 |
If someone is not old then someone is either not old or not rich and vice versa.
Everyone who is either tall or brave is both not humble and humble and vice versa.
If mary is either humble or kind then someone is both humble and generous.
If someone is not funny then paul is either not calm or not tall.
If fred is either brave or happy then someone is not funny or not generous and vice versa.
Everyone who is funny is both not funny and not generous and vice versa.
Everyone who is either curious or not strong is either not calm or old and vice versa.
Everyone who is not funny is either not curious or not happy.
If someone is happy or quiet then someone is both funny and calm and vice versa.
If mary is either funny or humble then susan is either not tall or not generous and vice versa.
If fred is not funny or patient then someone is not old and vice versa.
If paul is quiet or humble then someone is either not rich or not patient and vice versa.
Everyone who is not kind or rich is creative.
Everyone who is both calm and not creative is either generous or not calm.
Everyone who is either tall or wise is tall.
Everyone who is old or not rich is either wise or strong.
Alice is not old or not strong.
John is not funny.
Someone is either not rich or humble.
Someone is not humble.
Alice is wise.
Mary is calm. | Alice is not brave. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~humble(X)&humble(X))))&
(((humble(mary)<~>kind(mary)))=>(?[X]:((humble(X)&generous(X)))))&
((?[X]:(~funny(X)))=>((~calm(paul)<~>~tall(paul))))&
(((brave(fred)<~>happy(fred)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:(funny(X)<=>(~funny(X)&~generous(X))))&
(![X]:((curious(X)<~>~strong(X))<=>(~calm(X)<~>old(X))))&
(![X]:(~funny(X)=>(~curious(X)<~>~happy(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:((funny(X)&calm(X)))))&
(((funny(mary)<~>humble(mary)))<=>((~tall(susan)<~>~generous(susan))))&
(((~funny(fred)|patient(fred)))<=>(?[X]:(~old(X))))&
(((quiet(paul)|humble(paul)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~kind(X)|rich(X))=>creative(X)))&
(![X]:((calm(X)&~creative(X))=>(generous(X)<~>~calm(X))))&
(![X]:((tall(X)<~>wise(X))=>tall(X)))&
(![X]:((old(X)|~rich(X))=>(wise(X)<~>strong(X))))&
((~old(alice)|~strong(alice)))&
(~funny(john))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~humble(X)))&
(wise(alice))&
(calm(mary)) | ~brave(alice) | [
"p1",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8436008363064693648565711
% SZS output start Proof for 8436008363064693648565711
2. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (humble(X0) & ~humble(X0))) [input p1]
15. ! [X0] : ((tall(X0) <~> wise(X0)) => tall(X0)) [input p14]
21. wise(alice) [input p20]
23. ~brave(alice) [input hypothesis]
31. ! [X0] : (tall(X0) | (tall(X0) <=> wise(X0))) [ennf transformation 15]
38. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [flattening 38]
68. ! [X0] : (tall(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) [nnf transformation 31]
79. ~humble(X0) | brave(X0) | ~tall(X0) [cnf transformation 39]
81. humble(X0) | brave(X0) | ~tall(X0) [cnf transformation 39]
133. tall(X0) | tall(X0) | ~wise(X0) [cnf transformation 68]
143. wise(alice) [cnf transformation 21]
145. ~brave(alice) [cnf transformation 23]
146. ~wise(X0) | tall(X0) [duplicate literal removal 133]
175. ~tall(X0) | brave(X0) [subsumption resolution 79,81]
332. tall(alice) [resolution 146,143]
339. brave(alice) [resolution 175,332]
341. $false [subsumption resolution 339,145]
% SZS output end Proof for 8436008363064693648565711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and not generous then john is either not creative or generous and vice versa.
Everyone who is patient is both not humble and not creative.
Everyone who is quiet or tall is calm.
Everyone who is old or creative is calm or funny.
If fred is rich or not happy then susan is both not calm and funny.
Everyone who is both rich and not strong is both old and not curious.
If someone is both not strong and brave then someone is creative and vice versa.
Everyone who is funny is either not humble or strong and vice versa.
Everyone who is not brave or patient is either not calm or not patient and vice versa.
Everyone who is funny or not creative is not funny.
Everyone who is not kind or patient is creative or funny and vice versa.
If john is both patient and tall then alice is not quiet.
If fred is not rich then lucy is either not creative or not old.
Everyone who is not happy or creative is tall and vice versa.
Everyone who is not rich or quiet is either kind or not calm.
If someone is both rich and not curious then alice is humble and vice versa.
Someone is happy or not funny.
Susan is not brave.
Someone is quiet.
Alice is not generous or not brave.
Someone is strong or tall.
Alice is not tall.
Someone is not creative. | Susan is strong. | neutral | ((?[X]:((brave(X)&~generous(X))))<=>((~creative(john)<~>generous(john))))&
(![X]:(patient(X)=>(~humble(X)&~creative(X))))&
(![X]:((quiet(X)|tall(X))=>calm(X)))&
(![X]:((old(X)|creative(X))=>(calm(X)|funny(X))))&
(((rich(fred)|~happy(fred)))=>((~calm(susan)&funny(susan))))&
(![X]:((rich(X)&~strong(X))=>(old(X)&~curious(X))))&
((?[X]:((~strong(X)&brave(X))))<=>(?[X]:(creative(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>strong(X))))&
(![X]:((~brave(X)|patient(X))<=>(~calm(X)<~>~patient(X))))&
(![X]:((funny(X)|~creative(X))=>~funny(X)))&
(![X]:((~kind(X)|patient(X))<=>(creative(X)|funny(X))))&
(((patient(john)&tall(john)))=>(~quiet(alice)))&
((~rich(fred))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((~happy(X)|creative(X))<=>tall(X)))&
(![X]:((~rich(X)|quiet(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((rich(X)&~curious(X))))<=>(humble(alice)))&
(?[X]:((happy(X)|~funny(X))))&
(~brave(susan))&
(?[X]:(quiet(X)))&
((~generous(alice)|~brave(alice)))&
(?[X]:((strong(X)|tall(X))))&
(~tall(alice))&
(?[X]:(~creative(X))) | strong(susan) | [] | null | 0 |
Everyone who is both rich and not happy is either not generous or not happy and vice versa. Everyone who is both old and tall is wise or generous and vice versa. Everyone who is not brave or not rich is both funny and old. If alice is either not wise or tall then lucy is either not quiet or not tall. Everyone who is either rich or old is both calm and not creative and vice versa. Everyone who is curious is either happy or brave. If mary is rich or not humble then someone is either not creative or humble. Everyone who is either not old or funny is not generous or not curious and vice versa. If susan is both tall and calm then susan is both strong and not strong. Everyone who is either not tall or not old is strong and vice versa. Everyone who is not humble is either not kind or funny and vice versa. If mary is either kind or strong then someone is not funny. If someone is funny then someone is either tall or not wise and vice versa. If someone is creative or funny then mary is humble or patient and vice versa. Everyone who is both tall and curious is generous. If mary is both not old and not funny then someone is funny and vice versa. Someone is patient. John is not funny or curious. Paul is calm. Lucy is both creative and tall. Lucy is rich or not funny. Someone is curious. Someone is either strong or rich. | Alice is not brave. | contradiction | (![X]:((rich(X)&~happy(X))<=>(~generous(X)<~>~happy(X))))&
(![X]:((old(X)&tall(X))<=>(wise(X)|generous(X))))&
(![X]:((~brave(X)|~rich(X))=>(funny(X)&old(X))))&
(((~wise(alice)<~>tall(alice)))=>((~quiet(lucy)<~>~tall(lucy))))&
(![X]:((rich(X)<~>old(X))<=>(calm(X)&~creative(X))))&
(![X]:(curious(X)=>(happy(X)<~>brave(X))))&
(((rich(mary)|~humble(mary)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((~old(X)<~>funny(X))<=>(~generous(X)|~curious(X))))&
(((tall(susan)&calm(susan)))=>((strong(susan)&~strong(susan))))&
(![X]:((~tall(X)<~>~old(X))<=>strong(X)))&
(![X]:(~humble(X)<=>(~kind(X)<~>funny(X))))&
(((kind(mary)<~>strong(mary)))=>(?[X]:(~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((tall(X)<~>~wise(X)))))&
((?[X]:((creative(X)|funny(X))))<=>((humble(mary)|patient(mary))))&
(![X]:((tall(X)&curious(X))=>generous(X)))&
(((~old(mary)&~funny(mary)))<=>(?[X]:(funny(X))))&
(?[X]:(patient(X)))&
((~funny(john)|curious(john)))&
(calm(paul))&
((creative(lucy)&tall(lucy)))&
((rich(lucy)|~funny(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((strong(X)<~>rich(X)))) | ~brave(alice) | [
"p0",
"p1",
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3189168393486085607196893
% SZS output start Proof for 3189168393486085607196893
1. ! [X0] : ((~happy(X0) & rich(X0)) <=> (~generous(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((tall(X0) & old(X0)) <=> (generous(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | ~brave(X0)) => (old(X0) & funny(X0))) [input p2]
16. (~funny(mary) & ~old(mary)) <=> ? [X0] : funny(X0) [input p15]
24. ~brave(alice) [input hypothesis]
26. ! [X0] : ((old(X0) & funny(X0)) | (rich(X0) & brave(X0))) [ennf transformation 3]
35. ! [X0] : (((~happy(X0) & rich(X0)) | ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0)))) & (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | (happy(X0) | ~rich(X0)))) [nnf transformation 1]
36. ! [X0] : (((~happy(X0) & rich(X0)) | ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0)))) & (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | happy(X0) | ~rich(X0))) [flattening 35]
37. ! [X0] : (((tall(X0) & old(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (~tall(X0) | ~old(X0)))) [nnf transformation 2]
38. ! [X0] : (((tall(X0) & old(X0)) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | ~tall(X0) | ~old(X0))) [flattening 37]
63. ((~funny(mary) & ~old(mary)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (funny(mary) | old(mary))) [nnf transformation 16]
64. ((~funny(mary) & ~old(mary)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | funny(mary) | old(mary)) [flattening 63]
65. ((~funny(mary) & ~old(mary)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | funny(mary) | old(mary)) [rectify 64]
66. ? [X1] : funny(X1) => funny(sK5) [choice axiom]
67. ((~funny(mary) & ~old(mary)) | ! [X0] : ~funny(X0)) & (funny(sK5) | funny(mary) | old(mary)) [skolemisation 65,66]
76. happy(X0) | generous(X0) | happy(X0) | ~rich(X0) [cnf transformation 36]
79. ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 36]
83. ~generous(X0) | old(X0) [cnf transformation 38]
86. funny(X0) | brave(X0) [cnf transformation 26]
87. funny(X0) | rich(X0) [cnf transformation 26]
134. ~old(mary) | ~funny(X0) [cnf transformation 67]
135. ~funny(mary) | ~funny(X0) [cnf transformation 67]
145. ~brave(alice) [cnf transformation 24]
146. happy(X0) | generous(X0) | ~rich(X0) [duplicate literal removal 76]
147. ~happy(X0) | generous(X0) [duplicate literal removal 79]
148. ~rich(X0) | generous(X0) [subsumption resolution 146,147]
191. 8 <=> rich(mary) [avatar definition]
192. rich(mary) <- (8) [avatar component clause 191]
242. 18 <=> ! [X3] : ~funny(X3) [avatar definition]
243. ~funny(X3) <- (18) [avatar component clause 242]
273. 25 <=> funny(mary) [avatar definition]
275. ~funny(mary) <- (~25) [avatar component clause 273]
276. 18 | ~25 [avatar split clause 135,273,242]
278. 26 <=> old(mary) [avatar definition]
280. ~old(mary) <- (~26) [avatar component clause 278]
281. 18 | ~26 [avatar split clause 134,278,242]
311. brave(X0) <- (18) [resolution 86,243]
315. $false <- (18) [resolution 311,145]
316. ~18 [avatar contradiction clause 315]
321. rich(mary) <- (~25) [resolution 275,87]
323. 8 | 25 [avatar split clause 321,273,191]
327. generous(mary) <- (8) [resolution 148,192]
338. old(mary) <- (8) [resolution 327,83]
339. $false <- (8, ~26) [subsumption resolution 338,280]
340. ~8 | 26 [avatar contradiction clause 339]
341. $false [avatar sat refutation 276,281,316,323,340]
% SZS output end Proof for 3189168393486085607196893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not quiet or old and vice versa.
Everyone who is not patient is both not patient and tall.
If john is both not rich and happy then someone is both funny and not funny.
If susan is either happy or not generous then mary is not tall.
If someone is both not quiet and not rich then someone is tall and vice versa.
If someone is not creative or not kind then someone is funny.
Everyone who is happy is not funny or not old.
Everyone who is kind is both not curious and not happy.
Everyone who is not rich is both not quiet and not creative and vice versa.
Everyone who is happy or generous is not happy or patient.
Everyone who is either not calm or not quiet is patient or not patient and vice versa.
Everyone who is not creative is brave or strong.
Everyone who is either not kind or calm is both not quiet and not calm.
Everyone who is curious is both not happy and tall and vice versa.
Everyone who is not funny is generous or not generous and vice versa.
If someone is either happy or creative then alice is not brave and vice versa.
Someone is not old.
Someone is both not tall and not strong.
Someone is not curious or not happy.
Lucy is either not patient or not humble. | Lucy is old. | contradiction | (![X]:(~rich(X)<=>(~quiet(X)<~>old(X))))&
(![X]:(~patient(X)=>(~patient(X)&tall(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((funny(X)&~funny(X)))))&
(((happy(susan)<~>~generous(susan)))=>(~tall(mary)))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:(tall(X))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(funny(X))))&
(![X]:(happy(X)=>(~funny(X)|~old(X))))&
(![X]:(kind(X)=>(~curious(X)&~happy(X))))&
(![X]:(~rich(X)<=>(~quiet(X)&~creative(X))))&
(![X]:((happy(X)|generous(X))=>(~happy(X)|patient(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(patient(X)|~patient(X))))&
(![X]:(~creative(X)=>(brave(X)|strong(X))))&
(![X]:((~kind(X)<~>calm(X))=>(~quiet(X)&~calm(X))))&
(![X]:(curious(X)<=>(~happy(X)&tall(X))))&
(![X]:(~funny(X)<=>(generous(X)|~generous(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(~brave(alice)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)&~strong(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~patient(lucy)<~>~humble(lucy))) | old(lucy) | [
"p0",
"p4",
"p5",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4591908546137563027672918
% SZS output start Proof for 4591908546137563027672918
1. ! [X0] : (~rich(X0) <=> (~quiet(X0) <~> old(X0))) [input p0]
5. ? [X0] : (~rich(X0) & ~quiet(X0)) <=> ? [X0] : tall(X0) [input p4]
6. ? [X0] : (~kind(X0) | ~creative(X0)) => ? [X0] : funny(X0) [input p5]
9. ! [X0] : (~rich(X0) <=> (~creative(X0) & ~quiet(X0))) [input p8]
11. ! [X0] : ((~calm(X0) <~> ~quiet(X0)) <=> (~patient(X0) | patient(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> calm(X0)) => (~calm(X0) & ~quiet(X0))) [input p12]
15. ! [X0] : (~funny(X0) <=> (~generous(X0) | generous(X0))) [input p14]
21. old(lucy) [input hypothesis]
22. ? [X0] : (~rich(X0) & ~quiet(X0)) <=> ? [X1] : tall(X1) [rectify 5]
23. ? [X0] : (~kind(X0) | ~creative(X0)) => ? [X1] : funny(X1) [rectify 6]
29. ? [X1] : funny(X1) | ! [X0] : (kind(X0) & creative(X0)) [ennf transformation 23]
37. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~kind(X0) <=> calm(X0))) [ennf transformation 13]
40. ! [X0] : ((~rich(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | rich(X0))) [nnf transformation 1]
44. (? [X0] : (~rich(X0) & ~quiet(X0)) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : (rich(X0) | quiet(X0))) [nnf transformation 22]
45. (? [X0] : (~rich(X0) & ~quiet(X0)) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : (rich(X3) | quiet(X3))) [rectify 44]
46. ? [X0] : (~rich(X0) & ~quiet(X0)) => (~rich(sK1) & ~quiet(sK1)) [choice axiom]
47. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
48. ((~rich(sK1) & ~quiet(sK1)) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : (rich(X3) | quiet(X3))) [skolemisation 45,47,46]
49. ? [X0] : funny(X0) | ! [X1] : (kind(X1) & creative(X1)) [rectify 29]
50. ? [X0] : funny(X0) => funny(sK3) [choice axiom]
51. funny(sK3) | ! [X1] : (kind(X1) & creative(X1)) [skolemisation 49,50]
52. ! [X0] : ((~rich(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | rich(X0))) [nnf transformation 9]
53. ! [X0] : ((~rich(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | rich(X0))) [flattening 52]
54. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [nnf transformation 11]
55. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [flattening 54]
56. ! [X0] : ((~calm(X0) & ~quiet(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) [nnf transformation 37]
57. ! [X0] : ((~funny(X0) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | funny(X0))) [nnf transformation 15]
58. ! [X0] : ((~funny(X0) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | funny(X0))) [flattening 57]
73. ~old(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 40]
80. tall(sK2) | rich(X3) | quiet(X3) [cnf transformation 48]
81. ~quiet(sK1) | ~tall(X1) [cnf transformation 48]
84. funny(sK3) | kind(X1) [cnf transformation 51]
88. ~quiet(X0) | rich(X0) [cnf transformation 53]
97. quiet(X0) | calm(X0) | ~patient(X0) [cnf transformation 55]
98. quiet(X0) | calm(X0) | patient(X0) [cnf transformation 55]
103. ~calm(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 56]
106. ~funny(X0) | ~generous(X0) [cnf transformation 58]
107. ~funny(X0) | generous(X0) [cnf transformation 58]
118. old(lucy) [cnf transformation 21]
119. ~calm(X0) | ~kind(X0) [duplicate literal removal 103]
150. 7 <=> ! [X1] : ~tall(X1) [avatar definition]
151. ~tall(X1) <- (7) [avatar component clause 150]
158. 9 <=> quiet(sK1) [avatar definition]
160. ~quiet(sK1) <- (~9) [avatar component clause 158]
161. 7 | ~9 [avatar split clause 81,158,150]
163. 10 <=> ! [X3] : (rich(X3) | quiet(X3)) [avatar definition]
164. rich(X3) | quiet(X3) <- (10) [avatar component clause 163]
166. 11 <=> tall(sK2) [avatar definition]
168. tall(sK2) <- (11) [avatar component clause 166]
169. 10 | 11 [avatar split clause 80,166,163]
171. 12 <=> ! [X1] : kind(X1) [avatar definition]
172. kind(X1) <- (12) [avatar component clause 171]
174. 13 <=> funny(sK3) [avatar definition]
176. funny(sK3) <- (13) [avatar component clause 174]
177. 12 | 13 [avatar split clause 84,174,171]
182. calm(X0) | quiet(X0) [subsumption resolution 97,98]
185. ~funny(X0) [subsumption resolution 106,107]
227. $false <- (13) [subsumption resolution 176,185]
228. ~13 [avatar contradiction clause 227]
229. rich(X3) <- (10) [subsumption resolution 164,88]
239. quiet(X0) | ~kind(X0) [resolution 182,119]
240. quiet(X0) <- (12) [subsumption resolution 239,172]
241. $false <- (~9, 12) [resolution 240,160]
243. 9 | ~12 [avatar contradiction clause 241]
250. ~quiet(lucy) | ~rich(lucy) [resolution 73,118]
251. ~rich(lucy) <- (12) [subsumption resolution 250,240]
252. $false <- (10, 12) [subsumption resolution 251,229]
253. ~10 | ~12 [avatar contradiction clause 252]
254. $false <- (7, 11) [subsumption resolution 168,151]
255. ~7 | ~11 [avatar contradiction clause 254]
256. $false [avatar sat refutation 161,169,177,228,243,253,255]
% SZS output end Proof for 4591908546137563027672918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or wise is either wise or curious. If someone is both not humble and brave then fred is either wise or not wise. Everyone who is wise is either old or not curious. Everyone who is not curious is generous or not patient. Everyone who is not kind is both not curious and not generous. If someone is either not kind or not tall then someone is either curious or not wise and vice versa. Everyone who is funny or not wise is tall. If someone is both old and creative then someone is not strong or not patient and vice versa. If mary is tall or humble then someone is both strong and not curious and vice versa. Everyone who is not kind is happy and vice versa. If someone is both not rich and patient then susan is not old. If fred is both not happy and tall then someone is either not rich or not brave. Everyone who is either not brave or not wise is curious or calm. Everyone who is both not funny and not happy is not curious and vice versa. Everyone who is either funny or not humble is not tall. Lucy is not brave or wise. Someone is either kind or brave. Someone is either strong or curious. Someone is both not strong and funny. Someone is brave. Susan is rich or not humble. | Fred is patient. | neutral | (![X]:((patient(X)<~>wise(X))=>(wise(X)<~>curious(X))))&
((?[X]:((~humble(X)&brave(X))))=>((wise(fred)<~>~wise(fred))))&
(![X]:(wise(X)=>(old(X)<~>~curious(X))))&
(![X]:(~curious(X)=>(generous(X)|~patient(X))))&
(![X]:(~kind(X)=>(~curious(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~tall(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((funny(X)|~wise(X))=>tall(X)))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~strong(X)|~patient(X)))))&
(((tall(mary)|humble(mary)))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~kind(X)<=>happy(X)))&
((?[X]:((~rich(X)&patient(X))))=>(~old(susan)))&
(((~happy(fred)&tall(fred)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~brave(X)<~>~wise(X))=>(curious(X)|calm(X))))&
(![X]:((~funny(X)&~happy(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~humble(X))=>~tall(X)))&
((~brave(lucy)|wise(lucy)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:((strong(X)<~>curious(X))))&
(?[X]:((~strong(X)&funny(X))))&
(?[X]:(brave(X)))&
((rich(susan)|~humble(susan))) | patient(fred) | [] | null | 0 |
Everyone who is not quiet or not tall is either creative or not quiet.
If john is both not patient and not creative then someone is calm or humble.
Everyone who is either not strong or wise is tall and vice versa.
Everyone who is both not rich and not patient is both not wise and not calm and vice versa.
If paul is both calm and creative then someone is happy or quiet and vice versa.
If fred is rich then someone is either generous or not happy.
Everyone who is curious is either not curious or strong.
If someone is not funny then someone is both rich and not brave and vice versa.
Everyone who is both calm and humble is creative or not strong and vice versa.
If someone is either rich or not kind then someone is either not generous or not humble.
Everyone who is wise is both not brave and creative.
If alice is not strong then alice is either generous or curious.
Everyone who is either not kind or brave is kind or rich.
If paul is either calm or not funny then someone is both rich and strong and vice versa.
Everyone who is strong or rich is patient or not kind and vice versa.
Everyone who is not curious or creative is both not happy and not rich.
Fred is both patient and brave.
Someone is curious or not strong.
Someone is rich.
Someone is either wise or not quiet.
Someone is not curious.
John is either not funny or generous.
Alice is either not curious or rich.
Lucy is not calm. | Fred is tall. | contradiction | (![X]:((~quiet(X)|~tall(X))=>(creative(X)<~>~quiet(X))))&
(((~patient(john)&~creative(john)))=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>tall(X)))&
(![X]:((~rich(X)&~patient(X))<=>(~wise(X)&~calm(X))))&
(((calm(paul)&creative(paul)))<=>(?[X]:((happy(X)|quiet(X)))))&
((rich(fred))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(curious(X)=>(~curious(X)<~>strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((calm(X)&humble(X))<=>(creative(X)|~strong(X))))&
((?[X]:((rich(X)<~>~kind(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:(wise(X)=>(~brave(X)&creative(X))))&
((~strong(alice))=>((generous(alice)<~>curious(alice))))&
(![X]:((~kind(X)<~>brave(X))=>(kind(X)|rich(X))))&
(((calm(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((strong(X)|rich(X))<=>(patient(X)|~kind(X))))&
(![X]:((~curious(X)|creative(X))=>(~happy(X)&~rich(X))))&
((patient(fred)&brave(fred)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>~quiet(X))))&
(?[X]:(~curious(X)))&
((~funny(john)<~>generous(john)))&
((~curious(alice)<~>rich(alice)))&
(~calm(lucy)) | tall(fred) | [
"p2",
"p6",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7919578214748866785467891
% SZS output start Proof for 7919578214748866785467891
3. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> tall(X0)) [input p2]
7. ! [X0] : (curious(X0) => (~curious(X0) <~> strong(X0))) [input p6]
11. ! [X0] : (wise(X0) => (creative(X0) & ~brave(X0))) [input p10]
15. ! [X0] : ((rich(X0) | strong(X0)) <=> (~kind(X0) | patient(X0))) [input p14]
16. ! [X0] : ((creative(X0) | ~curious(X0)) => (~rich(X0) & ~happy(X0))) [input p15]
17. brave(fred) & patient(fred) [input p16]
25. tall(fred) [input hypothesis]
28. ! [X0] : (tall(X0) => (~strong(X0) <~> wise(X0))) [unused predicate definition removal 3]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | ~tall(X0)) [ennf transformation 28]
34. ! [X0] : ((~curious(X0) <~> strong(X0)) | ~curious(X0)) [ennf transformation 7]
36. ! [X0] : ((creative(X0) & ~brave(X0)) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 16]
44. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~tall(X0)) [nnf transformation 32]
55. ! [X0] : (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ~curious(X0)) [nnf transformation 34]
73. ! [X0] : (((rich(X0) | strong(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 15]
74. ! [X0] : ((rich(X0) | strong(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | (~rich(X0) & ~strong(X0)))) [flattening 73]
91. ~strong(X0) | wise(X0) | ~tall(X0) [cnf transformation 44]
104. strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
118. ~brave(X0) | ~wise(X0) [cnf transformation 36]
132. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 74]
136. ~rich(X0) | curious(X0) [cnf transformation 40]
138. patient(fred) [cnf transformation 17]
139. brave(fred) [cnf transformation 17]
150. tall(fred) [cnf transformation 25]
152. ~curious(X0) | strong(X0) [duplicate literal removal 104]
199. 11 <=> rich(fred) [avatar definition]
200. rich(fred) <- (11) [avatar component clause 199]
328. ~wise(fred) [resolution 118,139]
445. strong(fred) | rich(fred) [resolution 132,138]
482. 57 <=> strong(fred) [avatar definition]
484. strong(fred) <- (57) [avatar component clause 482]
485. 11 | 57 [avatar split clause 445,482,199]
488. curious(fred) <- (11) [resolution 200,136]
546. strong(fred) <- (11) [resolution 488,152]
547. 57 | ~11 [avatar split clause 546,199,482]
549. wise(fred) | ~tall(fred) <- (57) [resolution 484,91]
552. ~tall(fred) <- (57) [subsumption resolution 549,328]
553. $false <- (57) [subsumption resolution 552,150]
554. ~57 [avatar contradiction clause 553]
555. $false [avatar sat refutation 485,547,554]
% SZS output end Proof for 7919578214748866785467891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not humble is both not rich and not curious and vice versa.
Everyone who is not quiet is both wise and happy and vice versa.
Everyone who is not quiet is not strong or creative.
Everyone who is either patient or funny is both brave and not wise.
Everyone who is not kind is not patient or not happy.
If mary is not rich or not calm then mary is either tall or not kind.
Everyone who is not curious is brave or rich.
If john is not patient then someone is curious or not rich.
Everyone who is patient or not brave is not old or strong.
Everyone who is not calm or not brave is both not funny and funny and vice versa.
Everyone who is either not brave or happy is both not tall and not generous.
Everyone who is either not strong or not calm is patient or not funny.
Everyone who is kind is not calm or not happy.
If lucy is both creative and rich then paul is not calm or not wise.
Everyone who is either strong or generous is both not generous and curious and vice versa.
Everyone who is not rich is kind or curious and vice versa.
Paul is not funny.
Someone is both not happy and funny.
Someone is not patient or not tall.
Susan is not wise or generous.
John is either humble or not calm.
Fred is brave or not calm.
Someone is either rich or wise.
Someone is not calm or kind. | Paul is brave. | entailment | (![X]:((quiet(X)<~>~humble(X))<=>(~rich(X)&~curious(X))))&
(![X]:(~quiet(X)<=>(wise(X)&happy(X))))&
(![X]:(~quiet(X)=>(~strong(X)|creative(X))))&
(![X]:((patient(X)<~>funny(X))=>(brave(X)&~wise(X))))&
(![X]:(~kind(X)=>(~patient(X)|~happy(X))))&
(((~rich(mary)|~calm(mary)))=>((tall(mary)<~>~kind(mary))))&
(![X]:(~curious(X)=>(brave(X)|rich(X))))&
((~patient(john))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((patient(X)|~brave(X))=>(~old(X)|strong(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~funny(X)&funny(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~tall(X)&~generous(X))))&
(![X]:((~strong(X)<~>~calm(X))=>(patient(X)|~funny(X))))&
(![X]:(kind(X)=>(~calm(X)|~happy(X))))&
(((creative(lucy)&rich(lucy)))=>((~calm(paul)|~wise(paul))))&
(![X]:((strong(X)<~>generous(X))<=>(~generous(X)&curious(X))))&
(![X]:(~rich(X)<=>(kind(X)|curious(X))))&
(~funny(paul))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:((~patient(X)|~tall(X))))&
((~wise(susan)|generous(susan)))&
((humble(john)<~>~calm(john)))&
((brave(fred)|~calm(fred)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:((~calm(X)|kind(X)))) | brave(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5767955491835125132340422
% SZS output start Proof for 5767955491835125132340422
10. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (funny(X0) & ~funny(X0))) [input p9]
25. ~brave(paul) [input hypothesis]
51. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 10]
52. ! [X0] : ((~brave(X0) | ~calm(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (brave(X0) & calm(X0)))) [flattening 51]
91. ~funny(X0) | brave(X0) [cnf transformation 52]
93. funny(X0) | brave(X0) [cnf transformation 52]
123. ~brave(paul) [cnf transformation 25]
159. brave(X0) [subsumption resolution 91,93]
209. $false [subsumption resolution 123,159]
% SZS output end Proof for 5767955491835125132340422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then paul is not curious or not humble and vice versa.
If alice is not brave or curious then someone is not strong and vice versa.
Everyone who is not tall is both not kind and brave.
Everyone who is either strong or patient is not tall or not kind and vice versa.
If someone is not curious or funny then fred is old or quiet and vice versa.
Everyone who is creative is curious or not tall and vice versa.
If someone is either humble or patient then john is either calm or old and vice versa.
Everyone who is both not quiet and brave is either not quiet or not kind and vice versa.
Everyone who is both quiet and tall is happy.
Everyone who is either old or creative is both not happy and old.
If mary is both tall and not wise then alice is humble.
Everyone who is funny or curious is creative or not wise.
Everyone who is not generous or humble is not brave and vice versa.
Everyone who is both not funny and not rich is rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
Someone is both old and not rich.
John is not kind or calm.
John is both not humble and not happy.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Fred is either not calm or funny. | John is not generous. | entailment | ((?[X]:((~curious(X)<~>~old(X))))<=>((~curious(paul)|~humble(paul))))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~tall(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~tall(X)|~kind(X))))&
((?[X]:((~curious(X)|funny(X))))<=>((old(fred)|quiet(fred))))&
(![X]:(creative(X)<=>(curious(X)|~tall(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>((calm(john)<~>old(john))))&
(![X]:((~quiet(X)&brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((quiet(X)&tall(X))=>happy(X)))&
(![X]:((old(X)<~>creative(X))=>(~happy(X)&old(X))))&
(((tall(mary)&~wise(mary)))=>(humble(alice)))&
(![X]:((funny(X)|curious(X))=>(creative(X)|~wise(X))))&
(![X]:((~generous(X)|humble(X))<=>~brave(X)))&
(![X]:((~funny(X)&~rich(X))<=>rich(X)))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
(?[X]:((old(X)&~rich(X))))&
((~kind(john)|calm(john)))&
((~humble(john)&~happy(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
((~calm(fred)<~>funny(fred))) | ~generous(john) | [
"p2",
"p7",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1127431917050347969839864
% SZS output start Proof for 1127431917050347969839864
3. ! [X0] : (~tall(X0) => (brave(X0) & ~kind(X0))) [input p2]
8. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p7]
13. ! [X0] : ((humble(X0) | ~generous(X0)) <=> ~brave(X0)) [input p12]
16. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> kind(X0)) [input p15]
19. ~happy(john) & ~humble(john) [input p18]
24. generous(john) [input hypothesis]
25. ! [X0] : ((brave(X0) & ~kind(X0)) | tall(X0)) [ennf transformation 3]
56. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~brave(X0) | quiet(X0)))) [nnf transformation 8]
57. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ~brave(X0) | quiet(X0))) [flattening 56]
59. ! [X0] : (((humble(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) & generous(X0)))) [nnf transformation 13]
60. ! [X0] : ((humble(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~humble(X0) & generous(X0)))) [flattening 59]
67. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) | tall(X0)))) [nnf transformation 16]
68. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | ~quiet(X0) | tall(X0))) [flattening 67]
85. ~kind(X0) | tall(X0) [cnf transformation 25]
109. kind(X0) | quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 57]
111. ~quiet(X0) | ~quiet(X0) | kind(X0) [cnf transformation 57]
124. ~generous(X0) | humble(X0) | brave(X0) [cnf transformation 60]
132. ~tall(X0) | ~kind(X0) [cnf transformation 68]
137. ~humble(john) [cnf transformation 19]
145. generous(john) [cnf transformation 24]
149. kind(X0) | quiet(X0) | ~brave(X0) [duplicate literal removal 109]
150. ~quiet(X0) | kind(X0) [duplicate literal removal 111]
255. ~brave(X0) | kind(X0) [subsumption resolution 149,150]
280. ~kind(X0) [subsumption resolution 132,85]
351. humble(john) | brave(john) [resolution 124,145]
352. brave(john) [subsumption resolution 351,137]
358. kind(john) [resolution 352,255]
361. $false [subsumption resolution 358,280]
% SZS output end Proof for 1127431917050347969839864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not curious is both not funny and not generous.
Everyone who is both not humble and not wise is either not humble or not brave.
If fred is humble then paul is creative and vice versa.
Everyone who is either creative or not quiet is either calm or not happy and vice versa.
Everyone who is not funny or not happy is both not calm and not brave and vice versa.
If john is not curious or not generous then someone is both not tall and patient and vice versa.
If alice is both not creative and not old then someone is either not wise or not happy.
If someone is not wise then john is both not brave and not quiet.
If someone is both not kind and not old then someone is wise.
If someone is either happy or not creative then someone is funny and vice versa.
Everyone who is either not brave or humble is not old or happy.
Everyone who is either tall or wise is both not old and happy and vice versa.
If john is both tall and patient then someone is calm.
Everyone who is either patient or not generous is generous or strong and vice versa.
Everyone who is not curious is both not quiet and strong and vice versa.
Everyone who is either kind or not curious is both not rich and wise and vice versa.
Fred is either not old or not creative.
Someone is not rich or not kind.
Someone is either wise or not funny.
Someone is strong or old.
Someone is either not curious or not old.
Someone is both old and patient.
Someone is old or not quiet.
Someone is happy. | Alice is not generous. | neutral | (![X]:((~funny(X)<~>~curious(X))=>(~funny(X)&~generous(X))))&
(![X]:((~humble(X)&~wise(X))=>(~humble(X)<~>~brave(X))))&
((humble(fred))<=>(creative(paul)))&
(![X]:((creative(X)<~>~quiet(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~funny(X)|~happy(X))<=>(~calm(X)&~brave(X))))&
(((~curious(john)|~generous(john)))<=>(?[X]:((~tall(X)&patient(X)))))&
(((~creative(alice)&~old(alice)))=>(?[X]:((~wise(X)<~>~happy(X)))))&
((?[X]:(~wise(X)))=>((~brave(john)&~quiet(john))))&
((?[X]:((~kind(X)&~old(X))))=>(?[X]:(wise(X))))&
((?[X]:((happy(X)<~>~creative(X))))<=>(?[X]:(funny(X))))&
(![X]:((~brave(X)<~>humble(X))=>(~old(X)|happy(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~old(X)&happy(X))))&
(((tall(john)&patient(john)))=>(?[X]:(calm(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(generous(X)|strong(X))))&
(![X]:(~curious(X)<=>(~quiet(X)&strong(X))))&
(![X]:((kind(X)<~>~curious(X))<=>(~rich(X)&wise(X))))&
((~old(fred)<~>~creative(fred)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:((old(X)|~quiet(X))))&
(?[X]:(happy(X))) | ~generous(alice) | [] | null | 0 |
Everyone who is both tall and not curious is rich and vice versa. Everyone who is curious is wise or brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. Everyone who is not curious is creative or not patient and vice versa. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. Lucy is either not curious or brave. Susan is either funny or not calm. Fred is not kind. Paul is tall or brave. | Susan is happy. | neutral | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(wise(X)|brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul))) | happy(susan) | [] | null | 0 |
If mary is not humble or not strong then fred is not creative and vice versa.
If someone is both not wise and kind then someone is both not creative and old.
Everyone who is strong is both old and curious and vice versa.
If someone is curious then susan is not curious.
If lucy is old then someone is either curious or not quiet.
If paul is either tall or patient then someone is both funny and wise.
Everyone who is both happy and not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
Lucy is not wise or calm.
Susan is rich.
Susan is not calm.
Someone is both humble and rich. | Paul is not old. | neutral | (((~humble(mary)|~strong(mary)))<=>(~creative(fred)))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:(strong(X)<=>(old(X)&curious(X))))&
((?[X]:(curious(X)))=>(~curious(susan)))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(((tall(paul)<~>patient(paul)))=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((happy(X)&~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X)))) | ~old(paul) | [] | null | 0 |
If someone is not tall or tall then someone is generous and vice versa.
Everyone who is both not curious and not brave is tall.
If mary is both not quiet and funny then someone is not old or patient and vice versa.
If mary is not old then someone is both humble and not generous and vice versa.
Everyone who is either calm or happy is not old.
Everyone who is both curious and funny is not quiet.
Everyone who is not curious or brave is creative.
Everyone who is humble is both not tall and not calm.
Everyone who is both not wise and not generous is both not quiet and wise.
If someone is not tall then mary is not generous or generous and vice versa.
If someone is both brave and old then someone is not curious or funny and vice versa.
If someone is both not quiet and tall then someone is both generous and not tall and vice versa.
If someone is generous or not kind then someone is either not tall or creative and vice versa.
Everyone who is brave or not brave is quiet.
Everyone who is not calm or not curious is both generous and not tall and vice versa.
If someone is both not quiet and not tall then someone is both funny and not rich.
Someone is quiet or brave.
Someone is either curious or not strong.
Someone is not curious or not brave.
Someone is both generous and creative.
Someone is not funny or not rich.
Fred is kind.
Someone is not patient. | Mary is humble. | contradiction | ((?[X]:((~tall(X)|tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((~curious(X)&~brave(X))=>tall(X)))&
(((~quiet(mary)&funny(mary)))<=>(?[X]:((~old(X)|patient(X)))))&
((~old(mary))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:((calm(X)<~>happy(X))=>~old(X)))&
(![X]:((curious(X)&funny(X))=>~quiet(X)))&
(![X]:((~curious(X)|brave(X))=>creative(X)))&
(![X]:(humble(X)=>(~tall(X)&~calm(X))))&
(![X]:((~wise(X)&~generous(X))=>(~quiet(X)&wise(X))))&
((?[X]:(~tall(X)))<=>((~generous(mary)|generous(mary))))&
((?[X]:((brave(X)&old(X))))<=>(?[X]:((~curious(X)|funny(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:((generous(X)&~tall(X)))))&
((?[X]:((generous(X)|~kind(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((brave(X)|~brave(X))=>quiet(X)))&
(![X]:((~calm(X)|~curious(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~quiet(X)&~tall(X))))=>(?[X]:((funny(X)&~rich(X)))))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((~funny(X)|~rich(X))))&
(kind(fred))&
(?[X]:(~patient(X))) | humble(mary) | [
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 800104495696753942473759
% SZS output start Proof for 800104495696753942473759
8. ! [X0] : (humble(X0) => (~calm(X0) & ~tall(X0))) [input p7]
12. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : (~tall(X0) & generous(X0)) [input p11]
14. ! [X0] : ((~brave(X0) | brave(X0)) => quiet(X0)) [input p13]
15. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~tall(X0) & generous(X0))) [input p14]
24. humble(mary) [input hypothesis]
27. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : (~tall(X1) & generous(X1)) [rectify 12]
39. ! [X0] : ((~calm(X0) & ~tall(X0)) | ~humble(X0)) [ennf transformation 8]
40. ! [X0] : (quiet(X0) | (brave(X0) & ~brave(X0))) [ennf transformation 14]
67. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : (tall(X1) | ~generous(X1))) & (? [X1] : (~tall(X1) & generous(X1)) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 27]
68. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : (tall(X1) | ~generous(X1))) & (? [X2] : (~tall(X2) & generous(X2)) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 67]
69. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK7) & ~quiet(sK7)) [choice axiom]
70. ? [X2] : (~tall(X2) & generous(X2)) => (~tall(sK8) & generous(sK8)) [choice axiom]
71. ((tall(sK7) & ~quiet(sK7)) | ! [X1] : (tall(X1) | ~generous(X1))) & ((~tall(sK8) & generous(sK8)) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 68,70,69]
77. ! [X0] : (((~curious(X0) | ~calm(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 15]
78. ! [X0] : ((~curious(X0) | ~calm(X0) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | (curious(X0) & calm(X0)))) [flattening 77]
110. ~humble(X0) | ~tall(X0) [cnf transformation 39]
111. ~calm(X0) | ~humble(X0) [cnf transformation 39]
122. ~quiet(sK7) | tall(X1) | ~generous(X1) [cnf transformation 71]
130. quiet(X0) | ~brave(X0) [cnf transformation 40]
131. quiet(X0) | brave(X0) [cnf transformation 40]
132. calm(X0) | generous(X0) [cnf transformation 78]
146. humble(mary) [cnf transformation 24]
187. 10 <=> ! [X0] : (generous(X0) | ~humble(X0)) [avatar definition]
188. ~humble(X0) | generous(X0) <- (10) [avatar component clause 187]
205. 14 <=> generous(mary) [avatar definition]
206. generous(mary) <- (14) [avatar component clause 205]
245. 23 <=> ! [X1] : (tall(X1) | ~generous(X1)) [avatar definition]
246. ~generous(X1) | tall(X1) <- (23) [avatar component clause 245]
253. 25 <=> quiet(sK7) [avatar definition]
255. ~quiet(sK7) <- (~25) [avatar component clause 253]
256. 23 | ~25 [avatar split clause 122,253,245]
304. quiet(X0) [subsumption resolution 130,131]
334. ~tall(mary) [resolution 110,146]
335. generous(X0) | ~humble(X0) [resolution 132,111]
339. generous(mary) <- (10) [resolution 188,146]
340. 14 | ~10 [avatar split clause 339,187,205]
341. 10 [avatar split clause 335,187]
350. tall(mary) <- (14, 23) [resolution 246,206]
357. $false <- (14, 23) [subsumption resolution 350,334]
358. ~14 | ~23 [avatar contradiction clause 357]
361. $false <- (~25) [subsumption resolution 255,304]
362. 25 [avatar contradiction clause 361]
363. $false [avatar sat refutation 256,340,341,358,362]
% SZS output end Proof for 800104495696753942473759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and strong is not strong or not creative and vice versa.
Everyone who is not happy or not funny is both funny and strong and vice versa.
If someone is either old or not funny then john is rich or not quiet.
If alice is both kind and not funny then someone is patient and vice versa.
Everyone who is both humble and rich is kind or not tall.
If someone is not funny or not creative then john is both curious and not creative and vice versa.
If someone is not strong or not generous then someone is not rich or curious.
Everyone who is quiet or strong is not calm or brave and vice versa.
Everyone who is both not happy and not strong is either curious or not patient and vice versa.
Everyone who is either tall or not humble is not rich.
If john is happy or calm then paul is not calm or not rich.
Everyone who is both not happy and not wise is not humble or generous.
If john is wise or not curious then someone is wise.
Everyone who is either not happy or quiet is not tall and vice versa.
Everyone who is curious or not curious is not brave or funny.
Susan is either not quiet or not funny.
Mary is rich.
Someone is not old.
Someone is not calm or not funny.
Someone is not kind.
Alice is not curious or not wise.
Someone is wise or quiet. | Susan is quiet. | contradiction | (![X]:((curious(X)&strong(X))<=>(~strong(X)|~creative(X))))&
(![X]:((~happy(X)|~funny(X))<=>(funny(X)&strong(X))))&
((?[X]:((old(X)<~>~funny(X))))=>((rich(john)|~quiet(john))))&
(((kind(alice)&~funny(alice)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&rich(X))=>(kind(X)|~tall(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(john)&~creative(john))))&
((?[X]:((~strong(X)|~generous(X))))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((quiet(X)|strong(X))<=>(~calm(X)|brave(X))))&
(![X]:((~happy(X)&~strong(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((tall(X)<~>~humble(X))=>~rich(X)))&
(((happy(john)|calm(john)))=>((~calm(paul)|~rich(paul))))&
(![X]:((~happy(X)&~wise(X))=>(~humble(X)|generous(X))))&
(((wise(john)|~curious(john)))=>(?[X]:(wise(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>~tall(X)))&
(![X]:((curious(X)|~curious(X))=>(~brave(X)|funny(X))))&
((~quiet(susan)<~>~funny(susan)))&
(rich(mary))&
(?[X]:(~old(X)))&
(?[X]:((~calm(X)|~funny(X))))&
(?[X]:(~kind(X)))&
((~curious(alice)|~wise(alice)))&
(?[X]:((wise(X)|quiet(X)))) | quiet(susan) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7515469755163276274850490
% SZS output start Proof for 7515469755163276274850490
2. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (strong(X0) & funny(X0))) [input p1]
16. ~quiet(susan) <~> ~funny(susan) [input p15]
23. quiet(susan) [input hypothesis]
40. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~funny(X0) | ~happy(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | (funny(X0) & happy(X0)))) [flattening 40]
64. (funny(susan) | quiet(susan)) & (~funny(susan) | ~quiet(susan)) [nnf transformation 16]
79. funny(X0) | funny(X0) [cnf transformation 41]
117. ~funny(susan) | ~quiet(susan) [cnf transformation 64]
125. quiet(susan) [cnf transformation 23]
126. funny(X0) [duplicate literal removal 79]
196. ~quiet(susan) [subsumption resolution 117,126]
208. $false [subsumption resolution 125,196]
% SZS output end Proof for 7515469755163276274850490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and patient is kind. Everyone who is humble is either not old or not kind. If someone is both not curious and strong then fred is tall or not humble and vice versa. Everyone who is either brave or not wise is either not funny or wise and vice versa. If someone is not calm or not generous then mary is funny and vice versa. If someone is wise then alice is either generous or not old and vice versa. If paul is not wise then someone is not creative and vice versa. Everyone who is both not curious and not generous is both not kind and happy and vice versa. If mary is generous then susan is not old or not kind and vice versa. Everyone who is both old and not wise is both not humble and not rich. Everyone who is both happy and not curious is not happy or calm and vice versa. Everyone who is not happy is patient and vice versa. Everyone who is strong is either not brave or not curious. If someone is either quiet or humble then lucy is happy and vice versa. If lucy is both not generous and not old then someone is both not creative and old and vice versa. Everyone who is not wise or not happy is rich or humble. Alice is not kind. Someone is not humble or kind. Someone is curious. Mary is both not creative and not kind. Paul is not funny. Fred is both not wise and creative. Alice is not quiet or not patient. | Lucy is humble. | neutral | (![X]:((quiet(X)&patient(X))=>kind(X)))&
(![X]:(humble(X)=>(~old(X)<~>~kind(X))))&
((?[X]:((~curious(X)&strong(X))))<=>((tall(fred)|~humble(fred))))&
(![X]:((brave(X)<~>~wise(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>(funny(mary)))&
((?[X]:(wise(X)))<=>((generous(alice)<~>~old(alice))))&
((~wise(paul))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~kind(X)&happy(X))))&
((generous(mary))<=>((~old(susan)|~kind(susan))))&
(![X]:((old(X)&~wise(X))=>(~humble(X)&~rich(X))))&
(![X]:((happy(X)&~curious(X))<=>(~happy(X)|calm(X))))&
(![X]:(~happy(X)<=>patient(X)))&
(![X]:(strong(X)=>(~brave(X)<~>~curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))<=>(happy(lucy)))&
(((~generous(lucy)&~old(lucy)))<=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~wise(X)|~happy(X))=>(rich(X)|humble(X))))&
(~kind(alice))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(curious(X)))&
((~creative(mary)&~kind(mary)))&
(~funny(paul))&
((~wise(fred)&creative(fred)))&
((~quiet(alice)|~patient(alice))) | humble(lucy) | [] | null | 0 |
If someone is not rich then someone is either not humble or wise. Everyone who is not generous or not brave is not strong. Everyone who is brave is creative or not tall and vice versa. If someone is happy then susan is both calm and rich and vice versa. If someone is both not happy and generous then someone is either kind or not curious and vice versa. Everyone who is happy or generous is not strong or kind. Everyone who is either creative or not rich is either not humble or not wise. If lucy is both not wise and curious then someone is both not calm and kind. If someone is either not calm or rich then alice is wise or not generous and vice versa. If someone is not rich or curious then alice is either brave or funny and vice versa. Everyone who is not humble is both humble and not patient and vice versa. If lucy is either not rich or not generous then fred is either not kind or patient. If lucy is either not rich or generous then lucy is not generous or brave. Everyone who is not curious is either old or not tall. If someone is not humble then susan is creative. Everyone who is either generous or humble is creative or not patient. Alice is not old. Someone is not patient or not quiet. Someone is creative or tall. John is quiet. Fred is both quiet and not creative. Someone is both tall and happy. Someone is not wise or kind. | Susan is not calm. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((~generous(X)|~brave(X))=>~strong(X)))&
(![X]:(brave(X)<=>(creative(X)|~tall(X))))&
((?[X]:(happy(X)))<=>((calm(susan)&rich(susan))))&
((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((happy(X)|generous(X))=>(~strong(X)|kind(X))))&
(![X]:((creative(X)<~>~rich(X))=>(~humble(X)<~>~wise(X))))&
(((~wise(lucy)&curious(lucy)))=>(?[X]:((~calm(X)&kind(X)))))&
((?[X]:((~calm(X)<~>rich(X))))<=>((wise(alice)|~generous(alice))))&
((?[X]:((~rich(X)|curious(X))))<=>((brave(alice)<~>funny(alice))))&
(![X]:(~humble(X)<=>(humble(X)&~patient(X))))&
(((~rich(lucy)<~>~generous(lucy)))=>((~kind(fred)<~>patient(fred))))&
(((~rich(lucy)<~>generous(lucy)))=>((~generous(lucy)|brave(lucy))))&
(![X]:(~curious(X)=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))=>(creative(susan)))&
(![X]:((generous(X)<~>humble(X))=>(creative(X)|~patient(X))))&
(~old(alice))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((creative(X)|tall(X))))&
(quiet(john))&
((quiet(fred)&~creative(fred)))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~wise(X)|kind(X)))) | ~calm(susan) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8862581761191990965594524
% SZS output start Proof for 8862581761191990965594524
4. ? [X0] : happy(X0) <=> (rich(susan) & calm(susan)) [input p3]
22. ? [X0] : (happy(X0) & tall(X0)) [input p21]
24. ~calm(susan) [input hypothesis]
46. (? [X0] : happy(X0) | (~rich(susan) | ~calm(susan))) & ((rich(susan) & calm(susan)) | ! [X0] : ~happy(X0)) [nnf transformation 4]
47. (? [X0] : happy(X0) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X0] : ~happy(X0)) [flattening 46]
48. (? [X0] : happy(X0) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X1] : ~happy(X1)) [rectify 47]
49. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
50. (happy(sK1) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X1] : ~happy(X1)) [skolemisation 48,49]
78. ? [X0] : (happy(X0) & tall(X0)) => (happy(sK9) & tall(sK9)) [choice axiom]
79. happy(sK9) & tall(sK9) [skolemisation 22,78]
87. calm(susan) | ~happy(X1) [cnf transformation 50]
135. happy(sK9) [cnf transformation 79]
137. ~calm(susan) [cnf transformation 24]
155. 4 <=> calm(susan) [avatar definition]
168. 7 <=> ! [X1] : ~happy(X1) [avatar definition]
169. ~happy(X1) <- (7) [avatar component clause 168]
171. 7 | 4 [avatar split clause 87,155,168]
327. ~4 [avatar split clause 137,155]
330. $false <- (7) [resolution 169,135]
331. ~7 [avatar contradiction clause 330]
332. $false [avatar sat refutation 171,327,331]
% SZS output end Proof for 8862581761191990965594524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not rich then alice is generous or not wise.
If someone is either not calm or strong then susan is wise and vice versa.
Everyone who is not tall is either generous or creative.
Everyone who is not curious or not generous is both not kind and wise and vice versa.
If lucy is happy then someone is either wise or not strong.
Everyone who is creative is both not tall and humble and vice versa.
If paul is not calm or not humble then someone is not curious.
Everyone who is both patient and old is both not quiet and not rich.
Everyone who is not creative or not humble is both not tall and not old and vice versa.
Everyone who is either strong or generous is not wise or not generous.
If someone is not happy then lucy is either not rich or not calm and vice versa.
Everyone who is happy is either not humble or not creative and vice versa.
Everyone who is not funny is not humble or not curious.
If john is happy then someone is not funny or not strong.
Everyone who is both generous and tall is patient and vice versa.
Everyone who is quiet or old is either not generous or not kind and vice versa.
Someone is both curious and not tall.
Someone is rich or not creative.
Lucy is both not calm and not humble.
John is both not creative and strong.
Fred is both quiet and curious.
Mary is humble or not brave.
Someone is both not kind and not wise. | Lucy is not creative. | entailment | ((~rich(paul))=>((generous(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>strong(X))))<=>(wise(susan)))&
(![X]:(~tall(X)=>(generous(X)<~>creative(X))))&
(![X]:((~curious(X)|~generous(X))<=>(~kind(X)&wise(X))))&
((happy(lucy))=>(?[X]:((wise(X)<~>~strong(X)))))&
(![X]:(creative(X)<=>(~tall(X)&humble(X))))&
(((~calm(paul)|~humble(paul)))=>(?[X]:(~curious(X))))&
(![X]:((patient(X)&old(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>(~tall(X)&~old(X))))&
(![X]:((strong(X)<~>generous(X))=>(~wise(X)|~generous(X))))&
((?[X]:(~happy(X)))<=>((~rich(lucy)<~>~calm(lucy))))&
(![X]:(happy(X)<=>(~humble(X)<~>~creative(X))))&
(![X]:(~funny(X)=>(~humble(X)|~curious(X))))&
((happy(john))=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
(![X]:((quiet(X)|old(X))<=>(~generous(X)<~>~kind(X))))&
(?[X]:((curious(X)&~tall(X))))&
(?[X]:((rich(X)|~creative(X))))&
((~calm(lucy)&~humble(lucy)))&
((~creative(john)&strong(john)))&
((quiet(fred)&curious(fred)))&
((humble(mary)|~brave(mary)))&
(?[X]:((~kind(X)&~wise(X)))) | ~creative(lucy) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1874268795633592437371043
% SZS output start Proof for 1874268795633592437371043
6. ! [X0] : (creative(X0) <=> (humble(X0) & ~tall(X0))) [input p5]
19. ~humble(lucy) & ~calm(lucy) [input p18]
24. creative(lucy) [input hypothesis]
51. ! [X0] : ((creative(X0) | (~humble(X0) | tall(X0))) & ((humble(X0) & ~tall(X0)) | ~creative(X0))) [nnf transformation 6]
52. ! [X0] : ((creative(X0) | ~humble(X0) | tall(X0)) & ((humble(X0) & ~tall(X0)) | ~creative(X0))) [flattening 51]
88. ~creative(X0) | humble(X0) [cnf transformation 52]
122. ~humble(lucy) [cnf transformation 19]
129. creative(lucy) [cnf transformation 24]
250. humble(lucy) [resolution 88,129]
251. $false [subsumption resolution 250,122]
% SZS output end Proof for 1874268795633592437371043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is both not old and not tall.
If susan is not quiet then someone is brave or not humble.
If someone is both funny and not curious then mary is either patient or tall.
Everyone who is old is not patient or tall and vice versa.
Everyone who is happy is not generous and vice versa.
Everyone who is either not old or not rich is either not wise or wise.
Everyone who is rich is either not creative or not patient.
If someone is both tall and not patient then susan is either not tall or patient.
If someone is not kind or not happy then someone is humble.
If someone is not strong then susan is both not tall and not humble and vice versa.
Everyone who is both not quiet and quiet is both not quiet and not generous and vice versa.
If alice is either not generous or not wise then lucy is both not rich and funny.
Everyone who is not quiet or not old is not strong and vice versa.
Everyone who is not brave or not curious is brave or not humble.
If fred is either strong or not rich then someone is not strong or not creative.
Mary is either old or quiet.
Susan is both not creative and calm.
Fred is strong or not kind.
Alice is tall.
John is either calm or generous.
Someone is both wise and not old.
Lucy is either not wise or rich.
Fred is strong or not funny. | John is humble. | neutral | (![X]:((~happy(X)|~creative(X))=>(~old(X)&~tall(X))))&
((~quiet(susan))=>(?[X]:((brave(X)|~humble(X)))))&
((?[X]:((funny(X)&~curious(X))))=>((patient(mary)<~>tall(mary))))&
(![X]:(old(X)<=>(~patient(X)|tall(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:((~old(X)<~>~rich(X))=>(~wise(X)<~>wise(X))))&
(![X]:(rich(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((tall(X)&~patient(X))))=>((~tall(susan)<~>patient(susan))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>((~tall(susan)&~humble(susan))))&
(![X]:((~quiet(X)&quiet(X))<=>(~quiet(X)&~generous(X))))&
(((~generous(alice)<~>~wise(alice)))=>((~rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>~strong(X)))&
(![X]:((~brave(X)|~curious(X))=>(brave(X)|~humble(X))))&
(((strong(fred)<~>~rich(fred)))=>(?[X]:((~strong(X)|~creative(X)))))&
((old(mary)<~>quiet(mary)))&
((~creative(susan)&calm(susan)))&
((strong(fred)|~kind(fred)))&
(tall(alice))&
((calm(john)<~>generous(john)))&
(?[X]:((wise(X)&~old(X))))&
((~wise(lucy)<~>rich(lucy)))&
((strong(fred)|~funny(fred))) | humble(john) | [] | null | 0 |
Everyone who is not calm is kind or not wise and vice versa.
Everyone who is both not generous and not strong is quiet and vice versa.
If someone is either wise or kind then paul is both not brave and not patient.
Everyone who is either not curious or happy is either not humble or not rich.
Everyone who is creative or old is wise or quiet.
If mary is both curious and kind then someone is wise and vice versa.
Everyone who is generous is brave and vice versa.
If lucy is funny then paul is wise or not curious.
If someone is not wise then john is not wise and vice versa.
Everyone who is both not funny and not patient is either rich or wise.
Everyone who is not patient or not creative is not creative.
If mary is either not calm or wise then someone is either strong or not wise and vice versa.
If fred is either creative or not calm then paul is old.
Everyone who is wise or not happy is brave and vice versa.
Everyone who is quiet or not calm is either quiet or calm and vice versa.
Everyone who is not happy is both tall and kind.
Someone is both kind and not tall.
Paul is either kind or wise.
Paul is both old and not curious.
Fred is not tall or rich.
Someone is not humble or not wise. | Mary is strong. | contradiction | (![X]:(~calm(X)<=>(kind(X)|~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>quiet(X)))&
((?[X]:((wise(X)<~>kind(X))))=>((~brave(paul)&~patient(paul))))&
(![X]:((~curious(X)<~>happy(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((creative(X)|old(X))=>(wise(X)|quiet(X))))&
(((curious(mary)&kind(mary)))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>brave(X)))&
((funny(lucy))=>((wise(paul)|~curious(paul))))&
((?[X]:(~wise(X)))<=>(~wise(john)))&
(![X]:((~funny(X)&~patient(X))=>(rich(X)<~>wise(X))))&
(![X]:((~patient(X)|~creative(X))=>~creative(X)))&
(((~calm(mary)<~>wise(mary)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
(((creative(fred)<~>~calm(fred)))=>(old(paul)))&
(![X]:((wise(X)|~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|~calm(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
(?[X]:((kind(X)&~tall(X))))&
((kind(paul)<~>wise(paul)))&
((old(paul)&~curious(paul)))&
((~tall(fred)|rich(fred)))&
(?[X]:((~humble(X)|~wise(X)))) | strong(mary) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6250220614322725438581980
% SZS output start Proof for 6250220614322725438581980
2. ! [X0] : ((~strong(X0) & ~generous(X0)) <=> quiet(X0)) [input p1]
15. ! [X0] : ((~calm(X0) | quiet(X0)) <=> (quiet(X0) <~> calm(X0))) [input p14]
22. strong(mary) [input hypothesis]
36. ! [X0] : (((~strong(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) | generous(X0)))) [nnf transformation 2]
37. ! [X0] : (((~strong(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | strong(X0) | generous(X0))) [flattening 36]
58. ! [X0] : (((~calm(X0) | quiet(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (calm(X0) & ~quiet(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | quiet(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (calm(X0) & ~quiet(X0)))) [flattening 58]
70. ~quiet(X0) | ~strong(X0) [cnf transformation 37]
107. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 59]
108. ~calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 59]
111. ~calm(X0) | quiet(X0) | quiet(X0) | ~calm(X0) [cnf transformation 59]
122. strong(mary) [cnf transformation 22]
123. calm(X0) | quiet(X0) [duplicate literal removal 107]
124. ~calm(X0) | ~quiet(X0) [duplicate literal removal 108]
125. ~calm(X0) | quiet(X0) [duplicate literal removal 111]
234. ~calm(X0) [subsumption resolution 124,125]
235. quiet(X0) [subsumption resolution 123,234]
267. ~strong(X0) [resolution 70,235]
268. $false [resolution 267,122]
% SZS output end Proof for 6250220614322725438581980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and creative is both old and curious and vice versa.
Everyone who is not happy is not wise and vice versa.
Everyone who is either patient or humble is both not brave and not strong and vice versa.
Everyone who is wise or kind is either not kind or not curious and vice versa.
If someone is both not quiet and funny then someone is both not old and old and vice versa.
Everyone who is not strong is both quiet and not generous.
Everyone who is strong is humble.
If susan is both not funny and patient then someone is calm and vice versa.
If someone is both not humble and happy then someone is strong and vice versa.
Everyone who is both not quiet and humble is not patient and vice versa.
Everyone who is not quiet is both old and happy and vice versa.
If mary is both not wise and brave then someone is humble and vice versa.
Everyone who is tall is both patient and not generous.
Everyone who is both not generous and funny is curious and vice versa.
If mary is quiet then susan is either happy or not brave.
Everyone who is either kind or not generous is both quiet and calm and vice versa.
John is both not old and wise.
Paul is tall.
Paul is both not humble and not happy.
Someone is not humble.
Someone is either tall or not curious.
Someone is not funny or calm.
Alice is humble.
Someone is not wise or not quiet. | Mary is not kind. | neutral | (![X]:((rich(X)&creative(X))<=>(old(X)&curious(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
(![X]:((patient(X)<~>humble(X))<=>(~brave(X)&~strong(X))))&
(![X]:((wise(X)|kind(X))<=>(~kind(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((~old(X)&old(X)))))&
(![X]:(~strong(X)=>(quiet(X)&~generous(X))))&
(![X]:(strong(X)=>humble(X)))&
(((~funny(susan)&patient(susan)))<=>(?[X]:(calm(X))))&
((?[X]:((~humble(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(old(X)&happy(X))))&
(((~wise(mary)&brave(mary)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(patient(X)&~generous(X))))&
(![X]:((~generous(X)&funny(X))<=>curious(X)))&
((quiet(mary))=>((happy(susan)<~>~brave(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(quiet(X)&calm(X))))&
((~old(john)&wise(john)))&
(tall(paul))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice))&
(?[X]:((~wise(X)|~quiet(X)))) | ~kind(mary) | [] | null | 0 |
If alice is not old then someone is creative or not funny and vice versa. If someone is calm then someone is calm or not funny and vice versa. Everyone who is patient is tall or not old and vice versa. Everyone who is generous is both rich and not quiet and vice versa. Everyone who is not funny is either not old or patient and vice versa. If someone is not tall then someone is not brave or not generous and vice versa. Everyone who is either curious or not quiet is both not patient and not rich. If fred is either generous or not patient then fred is not brave. Everyone who is old is both creative and not funny and vice versa. Everyone who is both not quiet and not curious is wise or not funny and vice versa. Everyone who is both calm and not curious is not funny and vice versa. If mary is not strong or strong then someone is creative. If someone is humble then susan is not curious and vice versa. If someone is not happy then someone is not calm or rich and vice versa. Everyone who is creative is not strong or tall. Everyone who is tall or not quiet is both not tall and brave. Mary is both rich and not brave. Someone is not kind. John is both not tall and not calm. Someone is not brave. Someone is calm or tall. Fred is not curious. Paul is either tall or generous. Someone is both strong and not happy. | Fred is generous. | contradiction | ((~old(alice))<=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>~funny(X)))&
(((~strong(mary)|strong(mary)))=>(?[X]:(creative(X))))&
((?[X]:(humble(X)))<=>(~curious(susan)))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(creative(X)=>(~strong(X)|tall(X))))&
(![X]:((tall(X)|~quiet(X))=>(~tall(X)&brave(X))))&
((rich(mary)&~brave(mary)))&
(?[X]:(~kind(X)))&
((~tall(john)&~calm(john)))&
(?[X]:(~brave(X)))&
(?[X]:((calm(X)|tall(X))))&
(~curious(fred))&
((tall(paul)<~>generous(paul)))&
(?[X]:((strong(X)&~happy(X)))) | generous(fred) | [
"p2",
"p3",
"p4",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3960942764809653142450847
% SZS output start Proof for 3960942764809653142450847
3. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (~quiet(X0) & rich(X0))) [input p3]
5. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p4]
8. (generous(fred) <~> ~patient(fred)) => ~brave(fred) [input p7]
9. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p8]
16. ! [X0] : ((~quiet(X0) | tall(X0)) => (brave(X0) & ~tall(X0))) [input p15]
25. generous(fred) [input hypothesis]
31. ~brave(fred) | (generous(fred) <=> ~patient(fred)) [ennf transformation 8]
35. ! [X0] : ((brave(X0) & ~tall(X0)) | (quiet(X0) & ~tall(X0))) [ennf transformation 16]
45. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 3]
46. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 45]
47. ! [X0] : ((generous(X0) | (quiet(X0) | ~rich(X0))) & ((~quiet(X0) & rich(X0)) | ~generous(X0))) [nnf transformation 4]
48. ! [X0] : ((generous(X0) | quiet(X0) | ~rich(X0)) & ((~quiet(X0) & rich(X0)) | ~generous(X0))) [flattening 47]
49. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 5]
56. ~brave(fred) | ((generous(fred) | patient(fred)) & (~patient(fred) | ~generous(fred))) [nnf transformation 31]
57. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 9]
58. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 57]
87. ~patient(X0) | tall(X0) | ~old(X0) [cnf transformation 46]
89. patient(X0) | old(X0) [cnf transformation 46]
91. ~quiet(X0) | ~generous(X0) [cnf transformation 48]
93. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 49]
94. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 49]
104. ~brave(fred) | ~patient(fred) | ~generous(fred) [cnf transformation 56]
107. ~funny(X0) | ~old(X0) [cnf transformation 58]
125. ~tall(X0) | ~tall(X0) [cnf transformation 35]
128. brave(X0) | quiet(X0) [cnf transformation 35]
140. generous(fred) [cnf transformation 25]
141. ~tall(X0) [duplicate literal removal 125]
181. funny(X0) | old(X0) [subsumption resolution 94,89]
182. patient(X0) | funny(X0) [subsumption resolution 93,181]
208. 16 <=> patient(fred) [avatar definition]
209. ~patient(fred) <- (~16) [avatar component clause 208]
212. 17 <=> generous(fred) [avatar definition]
214. generous(fred) <- (17) [avatar component clause 212]
216. 18 <=> brave(fred) [avatar definition]
218. ~brave(fred) <- (~18) [avatar component clause 216]
220. ~17 | ~16 | ~18 [avatar split clause 104,216,208,212]
270. 17 [avatar split clause 140,212]
279. quiet(fred) <- (~18) [resolution 128,218]
288. ~generous(fred) <- (~18) [resolution 279,91]
289. $false <- (17, ~18) [subsumption resolution 288,214]
290. ~17 | 18 [avatar contradiction clause 289]
292. old(fred) <- (~16) [resolution 209,89]
293. tall(X0) | ~old(X0) | funny(X0) [resolution 87,182]
295. ~old(X0) | funny(X0) [subsumption resolution 293,141]
296. ~old(X0) [subsumption resolution 295,107]
316. $false <- (~16) [resolution 296,292]
317. 16 [avatar contradiction clause 316]
319. $false [avatar sat refutation 220,270,290,317]
% SZS output end Proof for 3960942764809653142450847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not tall is not calm or humble and vice versa. If susan is both not generous and kind then fred is either not brave or not kind. Everyone who is both not old and tall is creative or old and vice versa. Everyone who is both not humble and not patient is not brave or patient and vice versa. Everyone who is not creative or wise is not curious or humble. Everyone who is tall or not tall is either not brave or old. If mary is either quiet or humble then john is not tall. If susan is both curious and strong then someone is either kind or not creative and vice versa. If susan is patient then mary is both not wise and not funny. If someone is either brave or not patient then someone is not wise or humble. Everyone who is both patient and wise is strong and vice versa. If mary is either calm or funny then someone is either brave or not humble and vice versa. Everyone who is both patient and not quiet is both funny and calm. Everyone who is either old or curious is either not quiet or calm. Everyone who is quiet is either brave or creative and vice versa. John is not kind or curious. Someone is happy or not old. Fred is either generous or not creative. Mary is not tall or not rich. | Fred is brave. | contradiction | (![X]:((~humble(X)|~tall(X))<=>(~calm(X)|humble(X))))&
(((~generous(susan)&kind(susan)))=>((~brave(fred)<~>~kind(fred))))&
(![X]:((~old(X)&tall(X))<=>(creative(X)|old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~brave(X)|patient(X))))&
(![X]:((~creative(X)|wise(X))=>(~curious(X)|humble(X))))&
(![X]:((tall(X)|~tall(X))=>(~brave(X)<~>old(X))))&
(((quiet(mary)<~>humble(mary)))=>(~tall(john)))&
(((curious(susan)&strong(susan)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
((patient(susan))=>((~wise(mary)&~funny(mary))))&
((?[X]:((brave(X)<~>~patient(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((patient(X)&wise(X))<=>strong(X)))&
(((calm(mary)<~>funny(mary)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((patient(X)&~quiet(X))=>(funny(X)&calm(X))))&
(![X]:((old(X)<~>curious(X))=>(~quiet(X)<~>calm(X))))&
(![X]:(quiet(X)<=>(brave(X)<~>creative(X))))&
((~kind(john)|curious(john)))&
(?[X]:((happy(X)|~old(X))))&
((generous(fred)<~>~creative(fred)))&
((~tall(mary)|~rich(mary))) | brave(fred) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1438871686748903492449447
% SZS output start Proof for 1438871686748903492449447
3. ! [X0] : ((tall(X0) & ~old(X0)) <=> (old(X0) | creative(X0))) [input p2]
6. ! [X0] : ((~tall(X0) | tall(X0)) => (~brave(X0) <~> old(X0))) [input p5]
20. brave(fred) [input hypothesis]
28. ! [X0] : ((~brave(X0) <~> old(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 6]
38. ! [X0] : (((tall(X0) & ~old(X0)) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | (~tall(X0) | old(X0)))) [nnf transformation 3]
39. ! [X0] : (((tall(X0) & ~old(X0)) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | ~tall(X0) | old(X0))) [flattening 38]
42. ! [X0] : (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (tall(X0) & ~tall(X0))) [nnf transformation 28]
70. ~old(X0) | ~old(X0) [cnf transformation 39]
80. old(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 42]
81. old(X0) | ~brave(X0) | tall(X0) [cnf transformation 42]
120. brave(fred) [cnf transformation 20]
124. ~old(X0) [duplicate literal removal 70]
147. ~brave(X0) | tall(X0) [subsumption resolution 81,124]
148. ~brave(X0) | ~tall(X0) [subsumption resolution 80,124]
149. ~brave(X0) [subsumption resolution 148,147]
242. $false [subsumption resolution 120,149]
% SZS output end Proof for 1438871686748903492449447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both curious and strong.
Everyone who is not generous is either not brave or not happy.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is kind or not generous is either creative or not humble and vice versa.
If someone is not brave then someone is both curious and not creative.
If lucy is either quiet or happy then mary is calm or wise.
If someone is both tall and generous then someone is both not tall and funny and vice versa.
If lucy is funny then susan is not strong and vice versa.
Everyone who is both brave and creative is either not humble or not old and vice versa.
If someone is either tall or not strong then lucy is not creative and vice versa.
Everyone who is happy or patient is not humble.
If fred is either curious or calm then someone is both strong and creative and vice versa.
Everyone who is either tall or brave is tall or patient and vice versa.
Everyone who is not old or brave is happy and vice versa.
Everyone who is brave or not wise is humble.
Everyone who is either not old or kind is both generous and not kind.
Someone is creative.
Alice is both generous and humble.
Paul is generous.
Fred is quiet or happy.
Susan is either not quiet or not happy.
Mary is both not brave and humble. | Alice is happy. | contradiction | (![X]:(~humble(X)=>(curious(X)&strong(X))))&
(![X]:(~generous(X)=>(~brave(X)<~>~happy(X))))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:((curious(X)&~creative(X)))))&
(((quiet(lucy)<~>happy(lucy)))=>((calm(mary)|wise(mary))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~tall(X)&funny(X)))))&
((funny(lucy))<=>(~strong(susan)))&
(![X]:((brave(X)&creative(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~strong(X))))<=>(~creative(lucy)))&
(![X]:((happy(X)|patient(X))=>~humble(X)))&
(((curious(fred)<~>calm(fred)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(tall(X)|patient(X))))&
(![X]:((~old(X)|brave(X))<=>happy(X)))&
(![X]:((brave(X)|~wise(X))=>humble(X)))&
(![X]:((~old(X)<~>kind(X))=>(generous(X)&~kind(X))))&
(?[X]:(creative(X)))&
((generous(alice)&humble(alice)))&
(generous(paul))&
((quiet(fred)|happy(fred)))&
((~quiet(susan)<~>~happy(susan)))&
((~brave(mary)&humble(mary))) | happy(alice) | [
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3076420418942481498762553
% SZS output start Proof for 3076420418942481498762553
11. ! [X0] : ((patient(X0) | happy(X0)) => ~humble(X0)) [input p10]
18. humble(alice) & generous(alice) [input p17]
23. happy(alice) [input hypothesis]
31. ! [X0] : (~humble(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 11]
97. ~happy(X0) | ~humble(X0) [cnf transformation 31]
121. humble(alice) [cnf transformation 18]
128. happy(alice) [cnf transformation 23]
252. ~humble(alice) [resolution 97,128]
253. $false [subsumption resolution 252,121]
% SZS output end Proof for 3076420418942481498762553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not brave then someone is generous or not rich and vice versa.
Everyone who is both not funny and not happy is tall and vice versa.
Everyone who is both not creative and happy is both not quiet and calm and vice versa.
Everyone who is not creative or tall is both rich and old and vice versa.
Everyone who is not curious or not rich is both not quiet and patient and vice versa.
If someone is either not curious or old then mary is curious and vice versa.
If someone is not tall then someone is both not happy and not kind and vice versa.
Everyone who is not strong is not curious or happy.
If mary is both not rich and not humble then lucy is either wise or patient and vice versa.
Everyone who is tall or not humble is not generous.
Everyone who is either not generous or old is both not kind and patient.
Everyone who is both not patient and not quiet is funny or not strong and vice versa.
Everyone who is both patient and not quiet is tall or kind.
Everyone who is either not happy or wise is both wise and brave.
If lucy is either not strong or not curious then someone is not humble or not kind and vice versa.
If someone is generous then someone is either not kind or wise.
Someone is either not patient or not calm.
Someone is either tall or happy.
Fred is not old.
Mary is either humble or quiet.
Susan is either not generous or humble.
Lucy is wise or happy.
Mary is calm. | Mary is not generous. | entailment | ((?[X]:((strong(X)&~brave(X))))<=>(?[X]:((generous(X)|~rich(X)))))&
(![X]:((~funny(X)&~happy(X))<=>tall(X)))&
(![X]:((~creative(X)&happy(X))<=>(~quiet(X)&calm(X))))&
(![X]:((~creative(X)|tall(X))<=>(rich(X)&old(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~quiet(X)&patient(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>(curious(mary)))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(~strong(X)=>(~curious(X)|happy(X))))&
(((~rich(mary)&~humble(mary)))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((tall(X)|~humble(X))=>~generous(X)))&
(![X]:((~generous(X)<~>old(X))=>(~kind(X)&patient(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~quiet(X))=>(tall(X)|kind(X))))&
(![X]:((~happy(X)<~>wise(X))=>(wise(X)&brave(X))))&
(((~strong(lucy)<~>~curious(lucy)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((tall(X)<~>happy(X))))&
(~old(fred))&
((humble(mary)<~>quiet(mary)))&
((~generous(susan)<~>humble(susan)))&
((wise(lucy)|happy(lucy)))&
(calm(mary)) | ~generous(mary) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"p10",
"p12",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 371776661915414802641033
% SZS output start Proof for 371776661915414802641033
3. ! [X0] : ((happy(X0) & ~creative(X0)) <=> (calm(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (old(X0) & rich(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | ~curious(X0)) <=> (patient(X0) & ~quiet(X0))) [input p4]
6. ? [X0] : (~curious(X0) <~> old(X0)) <=> curious(mary) [input p5]
10. ! [X0] : ((~humble(X0) | tall(X0)) => ~generous(X0)) [input p9]
11. ! [X0] : ((~generous(X0) <~> old(X0)) => (patient(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((~quiet(X0) & patient(X0)) => (kind(X0) | tall(X0))) [input p12]
20. humble(mary) <~> quiet(mary) [input p19]
23. calm(mary) [input p22]
24. generous(mary) [input hypothesis]
30. ! [X0] : (~generous(X0) | (humble(X0) & ~tall(X0))) [ennf transformation 10]
31. ! [X0] : ((patient(X0) & ~kind(X0)) | (~generous(X0) <=> old(X0))) [ennf transformation 11]
32. ! [X0] : ((kind(X0) | tall(X0)) | (quiet(X0) | ~patient(X0))) [ennf transformation 13]
33. ! [X0] : (kind(X0) | tall(X0) | quiet(X0) | ~patient(X0)) [flattening 32]
43. ! [X0] : (((happy(X0) & ~creative(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (~happy(X0) | creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((happy(X0) & ~creative(X0)) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ~happy(X0) | creative(X0))) [flattening 43]
45. ! [X0] : (((tall(X0) | ~creative(X0)) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | (~tall(X0) & creative(X0)))) [nnf transformation 4]
46. ! [X0] : ((tall(X0) | ~creative(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | (~tall(X0) & creative(X0)))) [flattening 45]
47. ! [X0] : (((~rich(X0) | ~curious(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (rich(X0) & curious(X0)))) [nnf transformation 5]
48. ! [X0] : ((~rich(X0) | ~curious(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (rich(X0) & curious(X0)))) [flattening 47]
49. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~curious(mary)) & (curious(mary) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 6]
50. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~curious(mary)) & (curious(mary) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [rectify 49]
51. ? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) => ((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) [choice axiom]
52. (((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) | ~curious(mary)) & (curious(mary) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [skolemisation 50,51]
60. ! [X0] : ((patient(X0) & ~kind(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 31]
78. (~quiet(mary) | ~humble(mary)) & (quiet(mary) | humble(mary)) [nnf transformation 20]
90. ~calm(X0) | ~creative(X0) | quiet(X0) [cnf transformation 44]
92. creative(X0) | rich(X0) [cnf transformation 46]
94. old(X0) | creative(X0) [cnf transformation 46]
97. ~quiet(X0) | curious(X0) [cnf transformation 48]
99. patient(X0) | curious(X0) [cnf transformation 48]
101. ~patient(X0) | ~curious(X0) | ~rich(X0) | quiet(X0) [cnf transformation 48]
102. curious(mary) | old(X1) | curious(X1) [cnf transformation 52]
116. ~tall(X0) | ~generous(X0) [cnf transformation 30]
117. ~generous(X0) | humble(X0) [cnf transformation 30]
119. ~kind(X0) | ~generous(X0) | ~old(X0) [cnf transformation 60]
121. ~old(X0) | ~generous(X0) | patient(X0) [cnf transformation 60]
127. ~patient(X0) | tall(X0) | quiet(X0) | kind(X0) [cnf transformation 33]
146. ~quiet(mary) | ~humble(mary) [cnf transformation 78]
150. calm(mary) [cnf transformation 23]
151. generous(mary) [cnf transformation 24]
184. 8 <=> curious(mary) [avatar definition]
186. ~curious(mary) <- (~8) [avatar component clause 184]
202. 12 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
203. curious(X1) | old(X1) <- (12) [avatar component clause 202]
204. 12 | 8 [avatar split clause 102,184,202]
235. 20 <=> humble(mary) [avatar definition]
241. 21 <=> rich(mary) [avatar definition]
242. rich(mary) <- (21) [avatar component clause 241]
306. 34 <=> quiet(mary) [avatar definition]
308. ~quiet(mary) <- (~34) [avatar component clause 306]
309. ~20 | ~34 [avatar split clause 146,306,235]
331. humble(mary) [resolution 117,151]
396. ~creative(mary) | quiet(mary) [resolution 90,150]
418. ~generous(X0) | patient(X0) | creative(X0) [resolution 121,94]
484. tall(X2) | quiet(X2) | kind(X2) | curious(X2) [resolution 127,99]
490. kind(X2) | tall(X2) | curious(X2) [subsumption resolution 484,97]
540. 20 [avatar split clause 331,235]
552. 62 <=> creative(mary) [avatar definition]
554. ~creative(mary) <- (~62) [avatar component clause 552]
555. 34 | ~62 [avatar split clause 396,552,306]
634. rich(mary) <- (~62) [resolution 554,92]
637. 21 | 62 [avatar split clause 634,552,241]
752. patient(mary) | creative(mary) [resolution 418,151]
754. patient(mary) <- (~62) [subsumption resolution 752,554]
774. tall(X0) | curious(X0) | ~generous(X0) | ~old(X0) [resolution 490,119]
786. ~old(X0) | ~generous(X0) | curious(X0) [subsumption resolution 774,116]
816. ~curious(mary) | ~rich(mary) | quiet(mary) <- (~62) [resolution 754,101]
834. ~curious(mary) | quiet(mary) <- (21, ~62) [subsumption resolution 816,242]
835. ~curious(mary) <- (21, ~34, ~62) [subsumption resolution 834,308]
836. ~8 | ~21 | 34 | 62 [avatar split clause 835,552,306,241,184]
866. old(mary) <- (~8, 12) [resolution 203,186]
971. ~generous(mary) | curious(mary) <- (~8, 12) [resolution 786,866]
976. curious(mary) <- (~8, 12) [subsumption resolution 971,151]
977. $false <- (~8, 12) [subsumption resolution 976,186]
978. 8 | ~12 [avatar contradiction clause 977]
979. $false [avatar sat refutation 204,309,540,555,637,836,978]
% SZS output end Proof for 371776661915414802641033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not tall is either not quiet or not funny and vice versa.
If lucy is not patient then someone is both not patient and creative and vice versa.
Everyone who is kind or strong is quiet.
If someone is both not funny and not humble then mary is not kind and vice versa.
Everyone who is funny is not funny or wise and vice versa.
Everyone who is not strong or patient is not funny or brave and vice versa.
If paul is not happy then someone is either not tall or not old and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Someone is either not brave or not wise.
Someone is not humble.
Someone is both not creative and not rich.
Mary is either rich or not happy.
Someone is calm or brave.
Fred is either not brave or tall.
Alice is happy. | Fred is patient. | contradiction | (![X]:((quiet(X)<~>~tall(X))<=>(~quiet(X)<~>~funny(X))))&
((~patient(lucy))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:((kind(X)|strong(X))=>quiet(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>(~kind(mary)))&
(![X]:(funny(X)<=>(~funny(X)|wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~funny(X)|brave(X))))&
((~happy(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)&~rich(X))))&
((rich(mary)<~>~happy(mary)))&
(?[X]:((calm(X)|brave(X))))&
((~brave(fred)<~>tall(fred)))&
(happy(alice)) | patient(fred) | [
"p0",
"p4",
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 548963658771543052033187
% SZS output start Proof for 548963658771543052033187
1. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> (~quiet(X0) <~> ~funny(X0))) [input p0]
5. ! [X0] : (funny(X0) <=> (wise(X0) | ~funny(X0))) [input p4]
6. ! [X0] : ((patient(X0) | ~strong(X0)) <=> (brave(X0) | ~funny(X0))) [input p5]
21. ~brave(fred) <~> tall(fred) [input p20]
23. patient(fred) [input hypothesis]
34. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0)))) & (((funny(X0) | quiet(X0)) & (~funny(X0) | ~quiet(X0))) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 1]
43. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 5]
44. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~funny(X0))) [flattening 43]
45. ! [X0] : (((patient(X0) | ~strong(X0)) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | (~patient(X0) & strong(X0)))) [nnf transformation 6]
46. ! [X0] : ((patient(X0) | ~strong(X0) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | (~patient(X0) & strong(X0)))) [flattening 45]
79. (~tall(fred) | brave(fred)) & (tall(fred) | ~brave(fred)) [nnf transformation 21]
80. ~funny(X0) | ~quiet(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 34]
84. ~tall(X0) | quiet(X0) | ~funny(X0) | quiet(X0) [cnf transformation 34]
97. funny(X0) | funny(X0) [cnf transformation 44]
100. brave(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 46]
140. tall(fred) | ~brave(fred) [cnf transformation 79]
143. patient(fred) [cnf transformation 23]
147. funny(X0) [duplicate literal removal 97]
148. ~funny(X0) | ~quiet(X0) | ~tall(X0) [duplicate literal removal 80]
150. ~tall(X0) | quiet(X0) | ~funny(X0) [duplicate literal removal 84]
153. ~funny(X0) | ~tall(X0) [subsumption resolution 148,150]
191. ~patient(X0) | brave(X0) [subsumption resolution 100,147]
301. 32 <=> brave(fred) [avatar definition]
305. 33 <=> tall(fred) [avatar definition]
306. tall(fred) <- (33) [avatar component clause 305]
309. ~32 | 33 [avatar split clause 140,305,301]
319. ~tall(X1) [resolution 153,147]
320. brave(fred) [resolution 191,143]
323. 32 [avatar split clause 320,301]
324. $false <- (33) [subsumption resolution 306,319]
325. ~33 [avatar contradiction clause 324]
326. $false [avatar sat refutation 309,323,325]
% SZS output end Proof for 548963658771543052033187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not brave or not tall and vice versa.
If mary is patient or kind then someone is not strong.
Everyone who is not kind is not wise or not quiet and vice versa.
If lucy is not humble then someone is not curious.
Everyone who is both not happy and not creative is both not rich and not patient and vice versa.
Everyone who is both humble and generous is brave or tall and vice versa.
Everyone who is patient is generous and vice versa.
Everyone who is either not quiet or not rich is not curious or not strong and vice versa.
Everyone who is both rich and quiet is funny.
Everyone who is both old and not strong is not wise.
Everyone who is kind or not happy is not kind and vice versa.
If paul is wise or curious then paul is either not calm or funny.
If someone is both kind and strong then susan is either not strong or not happy.
If john is either funny or not funny then someone is funny and vice versa.
If alice is either generous or not humble then john is either not calm or quiet and vice versa.
If someone is either not happy or funny then susan is strong and vice versa.
Susan is either tall or quiet.
Someone is both creative and calm.
Someone is rich or humble.
Susan is kind or wise.
Paul is strong.
Fred is both patient and calm.
Alice is creative or not old. | Susan is not curious. | neutral | (![X]:(~creative(X)<=>(~brave(X)|~tall(X))))&
(((patient(mary)|kind(mary)))=>(?[X]:(~strong(X))))&
(![X]:(~kind(X)<=>(~wise(X)|~quiet(X))))&
((~humble(lucy))=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~creative(X))<=>(~rich(X)&~patient(X))))&
(![X]:((humble(X)&generous(X))<=>(brave(X)|tall(X))))&
(![X]:(patient(X)<=>generous(X)))&
(![X]:((~quiet(X)<~>~rich(X))<=>(~curious(X)|~strong(X))))&
(![X]:((rich(X)&quiet(X))=>funny(X)))&
(![X]:((old(X)&~strong(X))=>~wise(X)))&
(![X]:((kind(X)|~happy(X))<=>~kind(X)))&
(((wise(paul)|curious(paul)))=>((~calm(paul)<~>funny(paul))))&
((?[X]:((kind(X)&strong(X))))=>((~strong(susan)<~>~happy(susan))))&
(((funny(john)<~>~funny(john)))<=>(?[X]:(funny(X))))&
(((generous(alice)<~>~humble(alice)))<=>((~calm(john)<~>quiet(john))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(strong(susan)))&
((tall(susan)<~>quiet(susan)))&
(?[X]:((creative(X)&calm(X))))&
(?[X]:((rich(X)|humble(X))))&
((kind(susan)|wise(susan)))&
(strong(paul))&
((patient(fred)&calm(fred)))&
((creative(alice)|~old(alice))) | ~curious(susan) | [] | null | 0 |
Everyone who is quiet or not wise is strong.
Everyone who is not generous or not strong is both happy and wise and vice versa.
Everyone who is not happy is either not curious or not old.
Everyone who is both patient and not humble is either curious or not tall and vice versa.
Everyone who is old is both not strong and not rich.
If someone is wise or not humble then someone is either curious or not brave and vice versa.
Everyone who is both not quiet and brave is both humble and not strong.
Everyone who is not funny is both not strong and strong and vice versa.
Everyone who is either rich or not rich is rich or humble.
If someone is not calm or not rich then alice is not quiet or generous and vice versa.
Everyone who is wise is brave or happy and vice versa.
Everyone who is not quiet or not creative is either wise or humble and vice versa.
Everyone who is creative is either not funny or old and vice versa.
Everyone who is not brave is either humble or old and vice versa.
If alice is both old and happy then paul is creative.
If someone is patient then someone is either curious or not happy.
Mary is either tall or not funny.
Someone is curious.
Someone is both curious and not brave.
Someone is either not strong or curious.
Someone is creative or wise.
Someone is either not old or generous.
John is brave. | Mary is not creative. | entailment | (![X]:((quiet(X)|~wise(X))=>strong(X)))&
(![X]:((~generous(X)|~strong(X))<=>(happy(X)&wise(X))))&
(![X]:(~happy(X)=>(~curious(X)<~>~old(X))))&
(![X]:((patient(X)&~humble(X))<=>(curious(X)<~>~tall(X))))&
(![X]:(old(X)=>(~strong(X)&~rich(X))))&
((?[X]:((wise(X)|~humble(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~quiet(X)&brave(X))=>(humble(X)&~strong(X))))&
(![X]:(~funny(X)<=>(~strong(X)&strong(X))))&
(![X]:((rich(X)<~>~rich(X))=>(rich(X)|humble(X))))&
((?[X]:((~calm(X)|~rich(X))))<=>((~quiet(alice)|generous(alice))))&
(![X]:(wise(X)<=>(brave(X)|happy(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(wise(X)<~>humble(X))))&
(![X]:(creative(X)<=>(~funny(X)<~>old(X))))&
(![X]:(~brave(X)<=>(humble(X)<~>old(X))))&
(((old(alice)&happy(alice)))=>(creative(paul)))&
((?[X]:(patient(X)))=>(?[X]:((curious(X)<~>~happy(X)))))&
((tall(mary)<~>~funny(mary)))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((~old(X)<~>generous(X))))&
(brave(john)) | ~creative(mary) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8451105668962802674651238
% SZS output start Proof for 8451105668962802674651238
1. ! [X0] : ((~wise(X0) | quiet(X0)) => strong(X0)) [input p0]
5. ! [X0] : (old(X0) => (~rich(X0) & ~strong(X0))) [input p4]
7. ! [X0] : ((brave(X0) & ~quiet(X0)) => (~strong(X0) & humble(X0))) [input p6]
8. ! [X0] : (~funny(X0) <=> (strong(X0) & ~strong(X0))) [input p7]
9. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (humble(X0) | rich(X0))) [input p8]
12. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> (wise(X0) <~> humble(X0))) [input p11]
13. ! [X0] : (creative(X0) <=> (~funny(X0) <~> old(X0))) [input p12]
14. ! [X0] : (~brave(X0) <=> (humble(X0) <~> old(X0))) [input p13]
24. creative(mary) [input hypothesis]
27. ! [X0] : (strong(X0) | (wise(X0) & ~quiet(X0))) [ennf transformation 1]
29. ! [X0] : ((~rich(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 5]
30. ! [X0] : ((~strong(X0) & humble(X0)) | (~brave(X0) | quiet(X0))) [ennf transformation 7]
31. ! [X0] : ((~strong(X0) & humble(X0)) | ~brave(X0) | quiet(X0)) [flattening 30]
32. ! [X0] : ((humble(X0) | rich(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 9]
33. ! [X0] : (humble(X0) | rich(X0) | (rich(X0) <=> ~rich(X0))) [flattening 32]
47. ! [X0] : ((~funny(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | funny(X0))) [nnf transformation 8]
48. ! [X0] : ((~funny(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | funny(X0))) [flattening 47]
49. ! [X0] : (humble(X0) | rich(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 33]
57. ! [X0] : (((~creative(X0) | ~quiet(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (creative(X0) & quiet(X0)))) [nnf transformation 12]
58. ! [X0] : ((~creative(X0) | ~quiet(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (creative(X0) & quiet(X0)))) [flattening 57]
59. ! [X0] : ((creative(X0) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~creative(X0))) [nnf transformation 13]
60. ! [X0] : ((~brave(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) & (((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | brave(X0))) [nnf transformation 14]
78. ~quiet(X0) | strong(X0) [cnf transformation 27]
79. strong(X0) | wise(X0) [cnf transformation 27]
93. ~old(X0) | ~strong(X0) [cnf transformation 29]
94. ~rich(X0) | ~old(X0) [cnf transformation 29]
101. ~brave(X0) | humble(X0) | quiet(X0) [cnf transformation 31]
103. ~strong(X0) | funny(X0) [cnf transformation 48]
104. funny(X0) | strong(X0) [cnf transformation 48]
107. humble(X0) | rich(X0) | rich(X0) | rich(X0) [cnf transformation 49]
117. ~humble(X0) | ~wise(X0) | quiet(X0) [cnf transformation 58]
119. ~creative(X0) | ~quiet(X0) | humble(X0) | ~wise(X0) [cnf transformation 58]
121. old(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 59]
125. brave(X0) | humble(X0) | old(X0) [cnf transformation 60]
143. creative(mary) [cnf transformation 24]
145. rich(X0) | humble(X0) [duplicate literal removal 107]
180. funny(X0) [subsumption resolution 103,104]
208. ~creative(X0) | old(X0) [subsumption resolution 121,180]
275. ~old(X0) | humble(X0) [resolution 145,94]
276. old(mary) [resolution 208,143]
279. ~strong(mary) [resolution 276,93]
330. wise(mary) [resolution 279,79]
403. humble(X1) | old(X1) | humble(X1) | quiet(X1) [resolution 125,101]
405. humble(X1) | old(X1) | quiet(X1) [duplicate literal removal 403]
409. humble(X1) | quiet(X1) [subsumption resolution 405,275]
487. 52 <=> humble(mary) [avatar definition]
489. humble(mary) <- (52) [avatar component clause 487]
500. ~quiet(mary) | humble(mary) | ~wise(mary) [resolution 119,143]
504. ~quiet(mary) | humble(mary) [subsumption resolution 500,330]
505. humble(mary) [subsumption resolution 504,409]
506. 52 [avatar split clause 505,487]
517. ~wise(mary) | quiet(mary) <- (52) [resolution 489,117]
520. quiet(mary) <- (52) [subsumption resolution 517,330]
658. strong(mary) <- (52) [resolution 520,78]
659. $false <- (52) [subsumption resolution 658,279]
660. ~52 [avatar contradiction clause 659]
661. $false [avatar sat refutation 506,660]
% SZS output end Proof for 8451105668962802674651238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is creative or strong. If someone is either brave or humble then alice is both not curious and not generous. If someone is both calm and patient then john is both not generous and not funny and vice versa. Everyone who is both not creative and not humble is not brave or not wise and vice versa. Everyone who is not wise is both rich and not wise and vice versa. Everyone who is not generous or humble is both not calm and not brave and vice versa. If someone is generous or wise then someone is either not curious or not humble. If someone is both not strong and kind then fred is both happy and brave. If mary is not funny or not calm then someone is either not happy or not creative and vice versa. Everyone who is either not humble or kind is not curious or not wise and vice versa. If paul is both not kind and not brave then someone is not humble. Everyone who is both not creative and quiet is wise or not calm and vice versa. Everyone who is happy or brave is either generous or not curious and vice versa. Everyone who is not happy or not creative is either not patient or not rich. If someone is both not calm and rich then john is happy and vice versa. Everyone who is generous is both rich and curious. Someone is both not curious and not kind. Fred is not wise or quiet. Alice is both happy and kind. Paul is either not creative or funny. Mary is either not wise or not generous. Mary is calm. | Alice is patient. | contradiction | (![X]:(~creative(X)=>(creative(X)|strong(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((~curious(alice)&~generous(alice))))&
((?[X]:((calm(X)&patient(X))))<=>((~generous(john)&~funny(john))))&
(![X]:((~creative(X)&~humble(X))<=>(~brave(X)|~wise(X))))&
(![X]:(~wise(X)<=>(rich(X)&~wise(X))))&
(![X]:((~generous(X)|humble(X))<=>(~calm(X)&~brave(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((?[X]:((~strong(X)&kind(X))))=>((happy(fred)&brave(fred))))&
(((~funny(mary)|~calm(mary)))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(~curious(X)|~wise(X))))&
(((~kind(paul)&~brave(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~creative(X)&quiet(X))<=>(wise(X)|~calm(X))))&
(![X]:((happy(X)|brave(X))<=>(generous(X)<~>~curious(X))))&
(![X]:((~happy(X)|~creative(X))=>(~patient(X)<~>~rich(X))))&
((?[X]:((~calm(X)&rich(X))))<=>(happy(john)))&
(![X]:(generous(X)=>(rich(X)&curious(X))))&
(?[X]:((~curious(X)&~kind(X))))&
((~wise(fred)|quiet(fred)))&
((happy(alice)&kind(alice)))&
((~creative(paul)<~>funny(paul)))&
((~wise(mary)<~>~generous(mary)))&
(calm(mary)) | patient(alice) | [
"p3",
"p5",
"p9",
"p11",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4742874133911643207490414
% SZS output start Proof for 4742874133911643207490414
4. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> (~wise(X0) | ~brave(X0))) [input p3]
6. ! [X0] : ((humble(X0) | ~generous(X0)) <=> (~brave(X0) & ~calm(X0))) [input p5]
10. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~wise(X0) | ~curious(X0))) [input p9]
12. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> (~calm(X0) | wise(X0))) [input p11]
13. ! [X0] : ((brave(X0) | happy(X0)) <=> (generous(X0) <~> ~curious(X0))) [input p12]
14. ! [X0] : ((~creative(X0) | ~happy(X0)) => (~patient(X0) <~> ~rich(X0))) [input p13]
16. ! [X0] : (generous(X0) => (curious(X0) & rich(X0))) [input p15]
19. kind(alice) & happy(alice) [input p18]
23. patient(alice) [input hypothesis]
31. ! [X0] : ((~patient(X0) <~> ~rich(X0)) | (creative(X0) & happy(X0))) [ennf transformation 14]
32. ! [X0] : ((curious(X0) & rich(X0)) | ~generous(X0)) [ennf transformation 16]
39. ! [X0] : (((~humble(X0) & ~creative(X0)) | (wise(X0) & brave(X0))) & ((~wise(X0) | ~brave(X0)) | (humble(X0) | creative(X0)))) [nnf transformation 4]
40. ! [X0] : (((~humble(X0) & ~creative(X0)) | (wise(X0) & brave(X0))) & (~wise(X0) | ~brave(X0) | humble(X0) | creative(X0))) [flattening 39]
43. ! [X0] : (((humble(X0) | ~generous(X0)) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | (~humble(X0) & generous(X0)))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | ~generous(X0) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | (~humble(X0) & generous(X0)))) [flattening 43]
54. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (wise(X0) & curious(X0))) & ((~wise(X0) | ~curious(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (wise(X0) & curious(X0))) & (~wise(X0) | ~curious(X0) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 54]
58. ! [X0] : (((quiet(X0) & ~creative(X0)) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | (~quiet(X0) | creative(X0)))) [nnf transformation 12]
59. ! [X0] : (((quiet(X0) & ~creative(X0)) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | ~quiet(X0) | creative(X0))) [flattening 58]
60. ! [X0] : (((brave(X0) | happy(X0)) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0)))) & (((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (~brave(X0) & ~happy(X0)))) [nnf transformation 13]
61. ! [X0] : ((brave(X0) | happy(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0)))) & (((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (~brave(X0) & ~happy(X0)))) [flattening 60]
62. ! [X0] : (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (creative(X0) & happy(X0))) [nnf transformation 31]
81. ~creative(X0) | wise(X0) [cnf transformation 40]
82. ~humble(X0) | brave(X0) [cnf transformation 40]
90. ~humble(X0) | ~brave(X0) [cnf transformation 44]
106. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 55]
110. ~creative(X0) | ~wise(X0) [cnf transformation 59]
114. ~happy(X0) | generous(X0) | ~curious(X0) [cnf transformation 61]
121. ~rich(X0) | ~patient(X0) | creative(X0) [cnf transformation 62]
127. ~generous(X0) | rich(X0) [cnf transformation 32]
132. happy(alice) [cnf transformation 19]
133. kind(alice) [cnf transformation 19]
139. patient(alice) [cnf transformation 23]
141. 1 <=> ! [X0] : (brave(X0) | ~humble(X0)) [avatar definition]
142. brave(X0) | ~humble(X0) <- (1) [avatar component clause 141]
144. 2 <=> generous(alice) [avatar definition]
145. generous(alice) <- (2) [avatar component clause 144]
153. 4 <=> curious(alice) [avatar definition]
154. curious(alice) <- (4) [avatar component clause 153]
181. 1 [avatar split clause 82,141]
243. ~creative(X0) [subsumption resolution 110,81]
248. ~rich(X0) | ~patient(X0) [subsumption resolution 121,243]
280. ~humble(X0) <- (1) [subsumption resolution 142,90]
307. humble(alice) | curious(alice) [resolution 106,133]
308. curious(alice) <- (1) [subsumption resolution 307,280]
311. 4 | ~1 [avatar split clause 308,141,153]
313. generous(alice) | ~curious(alice) [resolution 114,132]
329. generous(alice) <- (4) [subsumption resolution 313,154]
330. 2 | ~4 [avatar split clause 329,153,144]
332. rich(alice) <- (2) [resolution 145,127]
339. ~patient(alice) <- (2) [resolution 332,248]
340. $false <- (2) [subsumption resolution 339,139]
341. ~2 [avatar contradiction clause 340]
342. $false [avatar sat refutation 181,311,330,341]
% SZS output end Proof for 4742874133911643207490414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and strong is not patient or humble and vice versa.
Everyone who is not generous or curious is either creative or kind and vice versa.
Everyone who is rich is not rich or old and vice versa.
If someone is either wise or tall then lucy is funny.
Everyone who is both not old and tall is humble or brave and vice versa.
If susan is curious or not happy then someone is either patient or not quiet.
Everyone who is either brave or patient is both not happy and brave.
Everyone who is not brave or calm is wise or not generous and vice versa.
If alice is both rich and strong then susan is not curious.
If paul is not kind or generous then someone is generous or quiet and vice versa.
If susan is either calm or strong then someone is both not humble and not quiet and vice versa.
Everyone who is either old or not strong is both generous and rich.
Everyone who is not happy or quiet is generous or not generous and vice versa.
If fred is strong or not happy then someone is not tall.
Everyone who is not curious or creative is either calm or rich and vice versa.
Someone is not funny.
Someone is either calm or not old.
Someone is either strong or tall.
John is calm or not humble.
Someone is both rich and not funny.
Alice is either humble or funny. | Susan is not funny. | neutral | (![X]:((~happy(X)&strong(X))<=>(~patient(X)|humble(X))))&
(![X]:((~generous(X)|curious(X))<=>(creative(X)<~>kind(X))))&
(![X]:(rich(X)<=>(~rich(X)|old(X))))&
((?[X]:((wise(X)<~>tall(X))))=>(funny(lucy)))&
(![X]:((~old(X)&tall(X))<=>(humble(X)|brave(X))))&
(((curious(susan)|~happy(susan)))=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((brave(X)<~>patient(X))=>(~happy(X)&brave(X))))&
(![X]:((~brave(X)|calm(X))<=>(wise(X)|~generous(X))))&
(((rich(alice)&strong(alice)))=>(~curious(susan)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
(((calm(susan)<~>strong(susan)))<=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:((old(X)<~>~strong(X))=>(generous(X)&rich(X))))&
(![X]:((~happy(X)|quiet(X))<=>(generous(X)|~generous(X))))&
(((strong(fred)|~happy(fred)))=>(?[X]:(~tall(X))))&
(![X]:((~curious(X)|creative(X))<=>(calm(X)<~>rich(X))))&
(?[X]:(~funny(X)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((strong(X)<~>tall(X))))&
((calm(john)|~humble(john)))&
(?[X]:((rich(X)&~funny(X))))&
((humble(alice)<~>funny(alice))) | ~funny(susan) | [] | null | 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa.
If lucy is not old or not tall then someone is funny or happy.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Someone is both rich and old.
Alice is not happy or old.
Someone is either generous or brave.
Someone is curious or quiet.
John is both humble and not patient.
Someone is not generous. | Susan is not quiet. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
(((~old(lucy)|~tall(lucy)))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(?[X]:((rich(X)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(?[X]:(~generous(X))) | ~quiet(susan) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2630508285126030834898
% SZS output start Proof for 2630508285126030834898
5. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p4]
14. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~generous(X0))) [input p13]
23. ~quiet(susan) [input hypothesis]
42. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 5]
43. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 42]
59. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ~quiet(X0))) [nnf transformation 14]
60. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ~quiet(X0))) [flattening 59]
89. quiet(X0) | ~generous(X0) | quiet(X0) [cnf transformation 43]
122. quiet(X0) | generous(X0) [cnf transformation 60]
144. ~quiet(susan) [cnf transformation 23]
154. quiet(X0) | ~generous(X0) [duplicate literal removal 89]
260. quiet(X0) [subsumption resolution 122,154]
290. $false [subsumption resolution 144,260]
% SZS output end Proof for 2630508285126030834898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and kind is either not old or brave.
Everyone who is not generous is calm and vice versa.
Everyone who is either not generous or not rich is not kind and vice versa.
If paul is either generous or patient then someone is not tall or not generous and vice versa.
If someone is strong then mary is either curious or not calm.
Everyone who is not brave is not happy or not funny.
Everyone who is not wise or brave is calm and vice versa.
If someone is not generous then susan is both kind and patient.
If someone is happy or generous then fred is creative.
If mary is either not wise or brave then someone is both not brave and not tall and vice versa.
Everyone who is not old or curious is either humble or generous.
Everyone who is both not calm and humble is either not wise or calm.
If fred is both strong and creative then fred is not curious or humble.
If lucy is either not tall or not humble then mary is both happy and not wise and vice versa.
Everyone who is either curious or quiet is either wise or calm.
If fred is not creative or calm then lucy is both not happy and not strong and vice versa.
Someone is both not brave and patient.
Someone is rich.
Someone is strong or not strong.
Someone is not funny.
Fred is not calm.
John is rich or not humble.
John is either kind or humble.
Someone is either not old or not wise. | Susan is kind. | entailment | (![X]:((wise(X)&kind(X))=>(~old(X)<~>brave(X))))&
(![X]:(~generous(X)<=>calm(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>~kind(X)))&
(((generous(paul)<~>patient(paul)))<=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:(strong(X)))=>((curious(mary)<~>~calm(mary))))&
(![X]:(~brave(X)=>(~happy(X)|~funny(X))))&
(![X]:((~wise(X)|brave(X))<=>calm(X)))&
((?[X]:(~generous(X)))=>((kind(susan)&patient(susan))))&
((?[X]:((happy(X)|generous(X))))=>(creative(fred)))&
(((~wise(mary)<~>brave(mary)))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((~old(X)|curious(X))=>(humble(X)<~>generous(X))))&
(![X]:((~calm(X)&humble(X))=>(~wise(X)<~>calm(X))))&
(((strong(fred)&creative(fred)))=>((~curious(fred)|humble(fred))))&
(((~tall(lucy)<~>~humble(lucy)))<=>((happy(mary)&~wise(mary))))&
(![X]:((curious(X)<~>quiet(X))=>(wise(X)<~>calm(X))))&
(((~creative(fred)|calm(fred)))<=>((~happy(lucy)&~strong(lucy))))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(~calm(fred))&
((rich(john)|~humble(john)))&
((kind(john)<~>humble(john)))&
(?[X]:((~old(X)<~>~wise(X)))) | kind(susan) | [
"p1",
"p3",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8675779520783065566988428
% SZS output start Proof for 8675779520783065566988428
2. ! [X0] : (~generous(X0) <=> calm(X0)) [input p1]
4. (generous(paul) <~> patient(paul)) <=> ? [X0] : (~generous(X0) | ~tall(X0)) [input p3]
7. ! [X0] : ((brave(X0) | ~wise(X0)) <=> calm(X0)) [input p6]
8. ? [X0] : ~generous(X0) => (patient(susan) & kind(susan)) [input p7]
10. (~wise(mary) <~> brave(mary)) <=> ? [X0] : (~tall(X0) & ~brave(X0)) [input p9]
12. ! [X0] : ((humble(X0) & ~calm(X0)) => (~wise(X0) <~> calm(X0))) [input p11]
14. (~tall(lucy) <~> ~humble(lucy)) <=> (~wise(mary) & happy(mary)) [input p13]
25. ~kind(susan) [input hypothesis]
31. (patient(susan) & kind(susan)) | ! [X0] : generous(X0) [ennf transformation 8]
34. ! [X0] : ((~wise(X0) <~> calm(X0)) | (~humble(X0) | calm(X0))) [ennf transformation 12]
35. ! [X0] : ((~wise(X0) <~> calm(X0)) | ~humble(X0) | calm(X0)) [flattening 34]
40. ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))) [nnf transformation 2]
42. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X0] : (~generous(X0) | ~tall(X0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [nnf transformation 4]
43. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X1] : (~generous(X1) | ~tall(X1)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [rectify 42]
44. ? [X1] : (~generous(X1) | ~tall(X1)) => (~generous(sK0) | ~tall(sK0)) [choice axiom]
45. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & ((~generous(sK0) | ~tall(sK0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [skolemisation 43,44]
47. ! [X0] : (((brave(X0) | ~wise(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 7]
48. ! [X0] : ((brave(X0) | ~wise(X0) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [flattening 47]
49. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X0] : (~tall(X0) & ~brave(X0)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [nnf transformation 10]
50. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X1] : (~tall(X1) & ~brave(X1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [rectify 49]
51. ? [X1] : (~tall(X1) & ~brave(X1)) => (~tall(sK1) & ~brave(sK1)) [choice axiom]
52. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & ((~tall(sK1) & ~brave(sK1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [skolemisation 50,51]
54. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~humble(X0) | calm(X0)) [nnf transformation 35]
55. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | (wise(mary) | ~happy(mary))) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [nnf transformation 14]
56. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | wise(mary) | ~happy(mary)) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [flattening 55]
73. ~calm(X0) | ~generous(X0) [cnf transformation 40]
78. ~generous(sK0) | ~tall(sK0) | patient(paul) | ~generous(paul) [cnf transformation 45]
82. ~patient(paul) | ~generous(paul) | tall(X0) [cnf transformation 45]
86. calm(X0) | wise(X0) [cnf transformation 48]
87. ~brave(X0) | calm(X0) [cnf transformation 48]
89. kind(susan) | generous(X0) [cnf transformation 31]
97. brave(mary) | ~wise(mary) | tall(X0) | brave(X0) [cnf transformation 52]
103. calm(X0) | ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 54]
109. ~wise(mary) | ~tall(lucy) | humble(lucy) [cnf transformation 56]
131. ~kind(susan) [cnf transformation 25]
132. calm(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 103]
134. 1 <=> ! [X0] : generous(X0) [avatar definition]
135. generous(X0) <- (1) [avatar component clause 134]
137. 2 <=> generous(paul) [avatar definition]
139. ~generous(paul) <- (~2) [avatar component clause 137]
141. 3 <=> patient(paul) [avatar definition]
146. 4 <=> ! [X0] : tall(X0) [avatar definition]
147. tall(X0) <- (4) [avatar component clause 146]
148. 4 | ~2 | ~3 [avatar split clause 82,141,137,146]
152. 5 <=> tall(sK0) [avatar definition]
154. ~tall(sK0) <- (~5) [avatar component clause 152]
156. 6 <=> generous(sK0) [avatar definition]
158. ~generous(sK0) <- (~6) [avatar component clause 156]
160. ~2 | 3 | ~5 | ~6 [avatar split clause 78,156,152,141,137]
169. 9 <=> calm(mary) [avatar definition]
170. ~calm(mary) <- (~9) [avatar component clause 169]
171. calm(mary) <- (9) [avatar component clause 169]
180. 11 <=> kind(susan) [avatar definition]
183. 1 | 11 [avatar split clause 89,180,134]
197. 15 <=> ! [X0] : (tall(X0) | brave(X0)) [avatar definition]
198. tall(X0) | brave(X0) <- (15) [avatar component clause 197]
200. 16 <=> wise(mary) [avatar definition]
201. ~wise(mary) <- (~16) [avatar component clause 200]
204. 17 <=> brave(mary) [avatar definition]
205. brave(mary) <- (17) [avatar component clause 204]
208. 15 | ~16 | 17 [avatar split clause 97,204,200,197]
221. ~humble(X0) | calm(X0) [subsumption resolution 132,86]
240. 24 <=> tall(lucy) [avatar definition]
241. ~tall(lucy) <- (~24) [avatar component clause 240]
244. 25 <=> humble(lucy) [avatar definition]
246. humble(lucy) <- (25) [avatar component clause 244]
249. 25 | ~24 | ~16 [avatar split clause 109,200,240,244]
296. ~11 [avatar split clause 131,180]
299. $false <- (1, ~2) [subsumption resolution 139,135]
300. ~1 | 2 [avatar contradiction clause 299]
301. $false <- (1, ~6) [subsumption resolution 158,135]
302. ~1 | 6 [avatar contradiction clause 301]
308. wise(mary) <- (~9) [resolution 86,170]
311. $false <- (~9, ~16) [subsumption resolution 308,201]
312. 9 | 16 [avatar contradiction clause 311]
314. ~generous(mary) <- (9) [resolution 171,73]
315. $false <- (1, 9) [subsumption resolution 314,135]
316. ~1 | ~9 [avatar contradiction clause 315]
326. calm(mary) <- (17) [resolution 205,87]
327. $false <- (~9, 17) [subsumption resolution 326,170]
328. 9 | ~17 [avatar contradiction clause 327]
329. brave(sK0) <- (~5, 15) [resolution 198,154]
332. calm(sK0) <- (~5, 15) [resolution 329,87]
347. ~generous(sK0) <- (~5, 15) [resolution 332,73]
348. $false <- (1, ~5, 15) [subsumption resolution 347,135]
349. ~1 | 5 | ~15 [avatar contradiction clause 348]
350. $false <- (4, ~24) [resolution 147,241]
351. ~4 | 24 [avatar contradiction clause 350]
352. calm(lucy) <- (25) [resolution 246,221]
356. ~generous(lucy) <- (25) [resolution 352,73]
358. $false <- (1, 25) [subsumption resolution 356,135]
359. ~1 | ~25 [avatar contradiction clause 358]
360. $false [avatar sat refutation 148,160,183,208,249,296,300,302,312,316,328,349,351,359]
% SZS output end Proof for 8675779520783065566988428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both curious and not patient. Everyone who is creative is either curious or not tall and vice versa. Everyone who is both old and not old is quiet and vice versa. If someone is patient or not strong then mary is either not brave or not wise and vice versa. If alice is either strong or creative then someone is not generous or curious and vice versa. Everyone who is happy or not generous is either not brave or kind and vice versa. If paul is both rich and not happy then someone is not calm or quiet. Everyone who is strong is not happy or brave. If someone is generous or not creative then john is either not rich or generous and vice versa. Everyone who is old is either creative or not wise. If someone is not happy or wise then lucy is not strong. Everyone who is both brave and not happy is not humble and vice versa. Everyone who is either not generous or happy is not tall and vice versa. If lucy is tall then someone is either not tall or kind and vice versa. If someone is not wise or not strong then someone is not rich or not happy. Someone is not kind or generous. Susan is both brave and calm. Someone is wise. Fred is either tall or not kind. Someone is tall or not brave. Someone is either not rich or not quiet. Lucy is not happy or funny. Someone is kind or old. | Mary is not quiet. | entailment | (![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(![X]:((old(X)&~old(X))<=>quiet(X)))&
((?[X]:((patient(X)|~strong(X))))<=>((~brave(mary)<~>~wise(mary))))&
(((strong(alice)<~>creative(alice)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((happy(X)|~generous(X))<=>(~brave(X)<~>kind(X))))&
(((rich(paul)&~happy(paul)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:(strong(X)=>(~happy(X)|brave(X))))&
((?[X]:((generous(X)|~creative(X))))<=>((~rich(john)<~>generous(john))))&
(![X]:(old(X)=>(creative(X)<~>~wise(X))))&
((?[X]:((~happy(X)|wise(X))))=>(~strong(lucy)))&
(![X]:((brave(X)&~happy(X))<=>~humble(X)))&
(![X]:((~generous(X)<~>happy(X))<=>~tall(X)))&
((tall(lucy))<=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:((~wise(X)|~strong(X))))=>(?[X]:((~rich(X)|~happy(X)))))&
(?[X]:((~kind(X)|generous(X))))&
((brave(susan)&calm(susan)))&
(?[X]:(wise(X)))&
((tall(fred)<~>~kind(fred)))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((~happy(lucy)|funny(lucy)))&
(?[X]:((kind(X)|old(X)))) | ~quiet(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8204867380219813169532643
% SZS output start Proof for 8204867380219813169532643
3. ! [X0] : ((~old(X0) & old(X0)) <=> quiet(X0)) [input p2]
24. quiet(mary) [input hypothesis]
39. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | ~old(X0)))) [nnf transformation 3]
40. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | ~old(X0))) [flattening 39]
85. old(X0) | ~quiet(X0) [cnf transformation 40]
86. ~old(X0) | ~quiet(X0) [cnf transformation 40]
138. quiet(mary) [cnf transformation 24]
139. ~quiet(X0) [subsumption resolution 85,86]
323. $false [subsumption resolution 138,139]
% SZS output end Proof for 8204867380219813169532643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and kind then someone is either not brave or kind.
If someone is not funny then fred is either old or not rich.
If paul is either not quiet or not creative then john is not happy or happy and vice versa.
Everyone who is creative or not calm is not kind or not curious and vice versa.
Everyone who is rich or not strong is not brave or not kind and vice versa.
Everyone who is not kind or patient is both not brave and not tall.
Everyone who is creative is rich and vice versa.
If alice is rich then mary is both patient and not happy and vice versa.
Everyone who is not kind is funny or creative.
If susan is not happy then someone is both not happy and not kind.
Everyone who is not generous or not calm is either funny or patient and vice versa.
Everyone who is both quiet and not tall is both generous and not wise and vice versa.
Everyone who is not curious or not generous is generous.
Everyone who is either creative or not happy is old or happy.
Everyone who is both not curious and not funny is not patient or happy and vice versa.
Everyone who is either not old or not funny is both kind and not strong and vice versa.
Someone is not calm or humble.
Someone is either not kind or brave.
Someone is not calm.
John is not old.
Someone is either not tall or kind.
Mary is both not curious and not creative.
Someone is either kind or not funny. | Mary is not happy. | contradiction | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
((?[X]:(~funny(X)))=>((old(fred)<~>~rich(fred))))&
(((~quiet(paul)<~>~creative(paul)))<=>((~happy(john)|happy(john))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(?[X]:((~calm(X)|humble(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(?[X]:(~calm(X)))&
(~old(john))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:((kind(X)<~>~funny(X)))) | ~happy(mary) | [
"p3",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2743691242080197367995378
% SZS output start Proof for 2743691242080197367995378
4. ! [X0] : ((~calm(X0) | creative(X0)) <=> (~curious(X0) | ~kind(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (funny(X0) <~> patient(X0))) [input p10]
15. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p14]
22. ~creative(mary) & ~curious(mary) [input p21]
24. ~happy(mary) [input hypothesis]
43. ! [X0] : (((~calm(X0) | creative(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 4]
44. ! [X0] : ((~calm(X0) | creative(X0) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | (calm(X0) & ~creative(X0)))) [flattening 43]
52. ! [X0] : (((~calm(X0) | ~generous(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [nnf transformation 11]
53. ! [X0] : ((~calm(X0) | ~generous(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [flattening 52]
57. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 15]
58. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 57]
85. ~calm(X0) | creative(X0) | curious(X0) [cnf transformation 44]
103. patient(X0) | funny(X0) | calm(X0) [cnf transformation 53]
105. ~patient(X0) | ~funny(X0) | calm(X0) [cnf transformation 53]
116. ~patient(X0) | happy(X0) | funny(X0) | curious(X0) [cnf transformation 58]
119. ~funny(X0) | patient(X0) [cnf transformation 58]
133. ~curious(mary) [cnf transformation 22]
134. ~creative(mary) [cnf transformation 22]
137. ~happy(mary) [cnf transformation 24]
183. 10 <=> patient(mary) [avatar definition]
184. patient(mary) <- (10) [avatar component clause 183]
185. ~patient(mary) <- (~10) [avatar component clause 183]
187. 11 <=> happy(mary) [avatar definition]
188. ~happy(mary) <- (~11) [avatar component clause 187]
239. ~11 [avatar split clause 137,187]
248. 23 <=> funny(mary) [avatar definition]
249. ~funny(mary) <- (~23) [avatar component clause 248]
250. funny(mary) <- (23) [avatar component clause 248]
262. funny(mary) | calm(mary) <- (~10) [resolution 103,185]
266. 26 <=> calm(mary) [avatar definition]
267. ~calm(mary) <- (~26) [avatar component clause 266]
268. calm(mary) <- (26) [avatar component clause 266]
269. 26 | 23 | 10 [avatar split clause 262,183,248,266]
270. creative(mary) | curious(mary) <- (26) [resolution 268,85]
272. curious(mary) <- (26) [subsumption resolution 270,134]
273. $false <- (26) [subsumption resolution 272,133]
274. ~26 [avatar contradiction clause 273]
283. ~funny(mary) | calm(mary) <- (10) [resolution 105,184]
285. ~funny(mary) <- (10, ~26) [subsumption resolution 283,267]
286. ~23 | ~10 | 26 [avatar split clause 285,266,183,248]
333. happy(mary) | funny(mary) | curious(mary) <- (10) [resolution 116,184]
336. funny(mary) | curious(mary) <- (10, ~11) [subsumption resolution 333,188]
337. curious(mary) <- (10, ~11, ~23) [subsumption resolution 336,249]
338. $false <- (10, ~11, ~23) [subsumption resolution 337,133]
339. ~10 | 11 | 23 [avatar contradiction clause 338]
342. patient(mary) <- (23) [resolution 250,119]
343. $false <- (~10, 23) [subsumption resolution 342,185]
344. 10 | ~23 [avatar contradiction clause 343]
345. $false [avatar sat refutation 239,269,274,286,339,344]
% SZS output end Proof for 2743691242080197367995378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not tall is tall.
Everyone who is both not calm and not humble is both not old and quiet and vice versa.
Everyone who is both not humble and tall is kind.
Everyone who is quiet is rich.
If someone is both old and quiet then someone is both not patient and happy and vice versa.
If someone is both kind and not brave then susan is not old or not wise and vice versa.
If susan is either not humble or happy then someone is either not humble or not patient.
Everyone who is both not old and not funny is brave.
Everyone who is both not wise and not kind is either strong or curious.
If someone is both not rich and not calm then lucy is either wise or happy and vice versa.
If lucy is both happy and not strong then susan is old or happy and vice versa.
Everyone who is both humble and not rich is curious.
Everyone who is either not rich or wise is not calm or not brave.
Everyone who is either brave or patient is either not calm or wise and vice versa.
Everyone who is both brave and patient is both humble and curious.
Everyone who is either not wise or generous is generous or not old and vice versa.
Someone is both not funny and not calm.
Someone is either brave or not happy.
Someone is both not happy and not patient.
Lucy is not funny or kind.
Someone is either wise or creative.
Lucy is both not funny and not patient.
Mary is both tall and not creative.
Someone is not funny. | Mary is not patient. | neutral | (![X]:((calm(X)<~>~tall(X))=>tall(X)))&
(![X]:((~calm(X)&~humble(X))<=>(~old(X)&quiet(X))))&
(![X]:((~humble(X)&tall(X))=>kind(X)))&
(![X]:(quiet(X)=>rich(X)))&
((?[X]:((old(X)&quiet(X))))<=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((kind(X)&~brave(X))))<=>((~old(susan)|~wise(susan))))&
(((~humble(susan)<~>happy(susan)))=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((~old(X)&~funny(X))=>brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(strong(X)<~>curious(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>((wise(lucy)<~>happy(lucy))))&
(((happy(lucy)&~strong(lucy)))<=>((old(susan)|happy(susan))))&
(![X]:((humble(X)&~rich(X))=>curious(X)))&
(![X]:((~rich(X)<~>wise(X))=>(~calm(X)|~brave(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~calm(X)<~>wise(X))))&
(![X]:((brave(X)&patient(X))=>(humble(X)&curious(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(generous(X)|~old(X))))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
(?[X]:((~happy(X)&~patient(X))))&
((~funny(lucy)|kind(lucy)))&
(?[X]:((wise(X)<~>creative(X))))&
((~funny(lucy)&~patient(lucy)))&
((tall(mary)&~creative(mary)))&
(?[X]:(~funny(X))) | ~patient(mary) | [] | null | 0 |
Everyone who is not patient or not creative is calm or not old.
If paul is quiet then someone is either strong or humble.
If someone is either not funny or happy then someone is either not generous or not kind.
Everyone who is not brave is both not funny and not calm.
If someone is both not generous and humble then john is both quiet and generous and vice versa.
Everyone who is both happy and funny is not brave and vice versa.
Everyone who is both wise and not wise is both not brave and not calm and vice versa.
If paul is either wise or curious then someone is not humble or not kind.
If someone is either not happy or not humble then someone is either not humble or not curious and vice versa.
Everyone who is not curious or not tall is kind and vice versa.
If lucy is both not happy and funny then alice is not kind and vice versa.
Everyone who is not strong is calm.
Everyone who is both rich and strong is either kind or not quiet.
Everyone who is either kind or happy is not wise.
Everyone who is both not curious and not brave is humble or not curious and vice versa.
Everyone who is strong is both brave and patient and vice versa.
Someone is quiet.
John is either not happy or not rich.
John is happy or old.
Fred is not calm.
Lucy is rich.
Mary is not rich or generous.
Someone is old or happy. | Paul is curious. | entailment | (![X]:((~patient(X)|~creative(X))=>(calm(X)|~old(X))))&
((quiet(paul))=>(?[X]:((strong(X)<~>humble(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)|~curious(X))))&
(![X]:(strong(X)<=>(brave(X)&patient(X))))&
(?[X]:(quiet(X)))&
((~happy(john)<~>~rich(john)))&
((happy(john)|old(john)))&
(~calm(fred))&
(rich(lucy))&
((~rich(mary)|generous(mary)))&
(?[X]:((old(X)|happy(X)))) | curious(paul) | [
"p3",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 475430250789601177619079
% SZS output start Proof for 475430250789601177619079
4. ! [X0] : (~brave(X0) => (~calm(X0) & ~funny(X0))) [input p3]
6. ! [X0] : ((funny(X0) & happy(X0)) <=> ~brave(X0)) [input p5]
15. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~curious(X0) | humble(X0))) [input p14]
24. ~curious(paul) [input hypothesis]
32. ! [X0] : ((~calm(X0) & ~funny(X0)) | brave(X0)) [ennf transformation 4]
50. ! [X0] : (((funny(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) | ~happy(X0)))) [nnf transformation 6]
51. ! [X0] : (((funny(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | ~funny(X0) | ~happy(X0))) [flattening 50]
68. ! [X0] : (((~brave(X0) & ~curious(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (brave(X0) | curious(X0)))) [nnf transformation 15]
69. ! [X0] : (((~brave(X0) & ~curious(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | brave(X0) | curious(X0))) [flattening 68]
84. ~funny(X0) | brave(X0) [cnf transformation 32]
92. funny(X0) | brave(X0) [cnf transformation 51]
122. ~brave(X0) | curious(X0) [cnf transformation 69]
134. ~curious(paul) [cnf transformation 24]
190. brave(X0) [subsumption resolution 92,84]
262. curious(X0) [subsumption resolution 122,190]
298. $false [subsumption resolution 134,262]
% SZS output end Proof for 475430250789601177619079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or curious then someone is both calm and not humble.
If john is both quiet and old then someone is creative or humble and vice versa.
Everyone who is both not kind and not quiet is not kind or tall.
Everyone who is not curious or patient is not rich and vice versa.
Everyone who is not generous or old is both not rich and strong.
If paul is brave then alice is both quiet and not wise and vice versa.
Everyone who is not strong or brave is not happy and vice versa.
If someone is both tall and old then susan is not curious.
Everyone who is creative is not strong or not curious and vice versa.
Everyone who is either not happy or brave is either not kind or funny and vice versa.
If john is either funny or not wise then fred is curious or not funny.
If someone is wise or not patient then someone is either not generous or tall and vice versa.
Everyone who is either not patient or old is not funny.
Everyone who is both wise and not quiet is not wise or not old.
If someone is both rich and creative then someone is both kind and tall and vice versa.
If someone is both funny and not creative then someone is not tall or happy and vice versa.
John is not tall.
Someone is both not rich and creative.
Lucy is quiet.
Paul is kind or not calm.
Someone is not brave or rich.
Lucy is either not rich or curious.
Lucy is curious.
Alice is not humble or not old. | Fred is not funny. | neutral | ((?[X]:((calm(X)<~>curious(X))))=>(?[X]:((calm(X)&~humble(X)))))&
(((quiet(john)&old(john)))<=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((~kind(X)&~quiet(X))=>(~kind(X)|tall(X))))&
(![X]:((~curious(X)|patient(X))<=>~rich(X)))&
(![X]:((~generous(X)|old(X))=>(~rich(X)&strong(X))))&
((brave(paul))<=>((quiet(alice)&~wise(alice))))&
(![X]:((~strong(X)|brave(X))<=>~happy(X)))&
((?[X]:((tall(X)&old(X))))=>(~curious(susan)))&
(![X]:(creative(X)<=>(~strong(X)|~curious(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~kind(X)<~>funny(X))))&
(((funny(john)<~>~wise(john)))=>((curious(fred)|~funny(fred))))&
((?[X]:((wise(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
(![X]:((~patient(X)<~>old(X))=>~funny(X)))&
(![X]:((wise(X)&~quiet(X))=>(~wise(X)|~old(X))))&
((?[X]:((rich(X)&creative(X))))<=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:((funny(X)&~creative(X))))<=>(?[X]:((~tall(X)|happy(X)))))&
(~tall(john))&
(?[X]:((~rich(X)&creative(X))))&
(quiet(lucy))&
((kind(paul)|~calm(paul)))&
(?[X]:((~brave(X)|rich(X))))&
((~rich(lucy)<~>curious(lucy)))&
(curious(lucy))&
((~humble(alice)|~old(alice))) | ~funny(fred) | [] | null | 0 |
If lucy is either not kind or curious then lucy is calm or curious.
If alice is not wise or tall then susan is creative or not kind.
If paul is rich then someone is not tall or not generous.
If someone is not wise or not creative then someone is either wise or not calm and vice versa.
Everyone who is either not strong or not creative is both creative and funny.
If lucy is both funny and old then someone is both not rich and not humble.
If paul is brave then mary is kind.
Everyone who is either not humble or tall is not quiet or wise and vice versa.
If fred is both not wise and brave then someone is either not generous or funny.
If paul is either not generous or not kind then someone is both creative and quiet and vice versa.
If someone is not kind or strong then someone is both old and not funny.
Everyone who is both kind and wise is both not old and not humble.
Everyone who is humble or brave is either quiet or not tall and vice versa.
If lucy is not generous or not curious then lucy is quiet or not wise.
If someone is both not tall and creative then lucy is rich or not strong.
Everyone who is either humble or not curious is strong or not quiet and vice versa.
Susan is not funny or not kind.
Someone is not humble or not creative.
Lucy is not patient or not tall.
Lucy is quiet.
Alice is either not tall or calm.
Someone is either not calm or creative.
Lucy is both brave and not kind.
Someone is both not brave and not tall. | Susan is creative. | neutral | (((~kind(lucy)<~>curious(lucy)))=>((calm(lucy)|curious(lucy))))&
(((~wise(alice)|tall(alice)))=>((creative(susan)|~kind(susan))))&
((rich(paul))=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((wise(X)<~>~calm(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(creative(X)&funny(X))))&
(((funny(lucy)&old(lucy)))=>(?[X]:((~rich(X)&~humble(X)))))&
((brave(paul))=>(kind(mary)))&
(![X]:((~humble(X)<~>tall(X))<=>(~quiet(X)|wise(X))))&
(((~wise(fred)&brave(fred)))=>(?[X]:((~generous(X)<~>funny(X)))))&
(((~generous(paul)<~>~kind(paul)))<=>(?[X]:((creative(X)&quiet(X)))))&
((?[X]:((~kind(X)|strong(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((kind(X)&wise(X))=>(~old(X)&~humble(X))))&
(![X]:((humble(X)|brave(X))<=>(quiet(X)<~>~tall(X))))&
(((~generous(lucy)|~curious(lucy)))=>((quiet(lucy)|~wise(lucy))))&
((?[X]:((~tall(X)&creative(X))))=>((rich(lucy)|~strong(lucy))))&
(![X]:((humble(X)<~>~curious(X))<=>(strong(X)|~quiet(X))))&
((~funny(susan)|~kind(susan)))&
(?[X]:((~humble(X)|~creative(X))))&
((~patient(lucy)|~tall(lucy)))&
(quiet(lucy))&
((~tall(alice)<~>calm(alice)))&
(?[X]:((~calm(X)<~>creative(X))))&
((brave(lucy)&~kind(lucy)))&
(?[X]:((~brave(X)&~tall(X)))) | creative(susan) | [] | null | 0 |
If someone is either happy or funny then fred is not quiet or not funny and vice versa. Everyone who is both not happy and not quiet is either wise or not happy and vice versa. Everyone who is either not wise or not brave is both curious and not strong. If fred is old then lucy is either wise or not creative and vice versa. Everyone who is either brave or tall is both wise and not brave. If susan is both generous and not generous then someone is strong or generous and vice versa. If alice is kind then someone is humble or old. Everyone who is not wise or generous is both not strong and quiet and vice versa. Everyone who is both kind and humble is either humble or not old and vice versa. If someone is either kind or old then mary is tall or not kind. Everyone who is not calm or not happy is both strong and not tall. Everyone who is calm is curious or strong. If alice is both not humble and brave then someone is both not happy and calm. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is funny or wise is happy. Everyone who is both patient and rich is not funny and vice versa. Someone is brave. Mary is creative or not patient. Fred is happy. Someone is happy or not happy. Someone is either not tall or humble. | Mary is strong. | contradiction | ((?[X]:((happy(X)<~>funny(X))))<=>((~quiet(fred)|~funny(fred))))&
(![X]:((~happy(X)&~quiet(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~brave(X))=>(curious(X)&~strong(X))))&
((old(fred))<=>((wise(lucy)<~>~creative(lucy))))&
(![X]:((brave(X)<~>tall(X))=>(wise(X)&~brave(X))))&
(((generous(susan)&~generous(susan)))<=>(?[X]:((strong(X)|generous(X)))))&
((kind(alice))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(?[X]:(brave(X)))&
((creative(mary)|~patient(mary)))&
(happy(fred))&
(?[X]:((happy(X)|~happy(X))))&
(?[X]:((~tall(X)<~>humble(X)))) | strong(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3868012108819343483676492
% SZS output start Proof for 3868012108819343483676492
6. (~generous(susan) & generous(susan)) <=> ? [X0] : (generous(X0) | strong(X0)) [input p5]
22. strong(mary) [input hypothesis]
46. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X0] : (generous(X0) | strong(X0)) | (generous(susan) | ~generous(susan))) [nnf transformation 6]
47. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X0] : (generous(X0) | strong(X0)) | generous(susan) | ~generous(susan)) [flattening 46]
48. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X1] : (generous(X1) | strong(X1)) | generous(susan) | ~generous(susan)) [rectify 47]
49. ? [X1] : (generous(X1) | strong(X1)) => (generous(sK1) | strong(sK1)) [choice axiom]
50. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & ((generous(sK1) | strong(sK1)) | generous(susan) | ~generous(susan)) [skolemisation 48,49]
93. generous(susan) | ~strong(X0) [cnf transformation 50]
95. ~generous(susan) | ~strong(X0) [cnf transformation 50]
129. strong(mary) [cnf transformation 22]
184. 11 <=> generous(susan) [avatar definition]
189. 12 <=> ! [X0] : ~strong(X0) [avatar definition]
190. ~strong(X0) <- (12) [avatar component clause 189]
191. 12 | ~11 [avatar split clause 95,184,189]
193. 12 | 11 [avatar split clause 93,184,189]
258. $false <- (12) [resolution 190,129]
259. ~12 [avatar contradiction clause 258]
260. $false [avatar sat refutation 191,193,259]
% SZS output end Proof for 3868012108819343483676492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or creative is either not tall or funny.
Everyone who is either not curious or brave is either funny or generous.
If someone is tall or kind then susan is humble.
If alice is either not happy or not calm then john is funny or calm.
Everyone who is not wise is both wise and generous and vice versa.
If paul is either wise or not brave then susan is either patient or creative and vice versa.
Everyone who is both not rich and happy is not creative or humble.
If john is both wise and strong then fred is either not old or not brave.
If someone is not quiet or quiet then alice is both not curious and funny and vice versa.
If someone is either not brave or not quiet then lucy is both not generous and creative and vice versa.
If someone is not quiet or not curious then someone is creative or not calm and vice versa.
If someone is either not calm or wise then fred is both humble and creative.
If mary is both brave and not happy then someone is both not funny and brave and vice versa.
If paul is strong then mary is not old and vice versa.
Everyone who is both quiet and not creative is old or curious.
If fred is funny or not creative then someone is wise and vice versa.
Someone is strong or patient.
Fred is not kind or wise.
John is happy or funny.
Someone is wise or not wise.
Lucy is either brave or not humble.
Paul is both happy and not patient.
Susan is not strong. | Susan is not humble. | contradiction | (![X]:((~kind(X)|creative(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~curious(X)<~>brave(X))=>(funny(X)<~>generous(X))))&
((?[X]:((tall(X)|kind(X))))=>(humble(susan)))&
(((~happy(alice)<~>~calm(alice)))=>((funny(john)|calm(john))))&
(![X]:(~wise(X)<=>(wise(X)&generous(X))))&
(((wise(paul)<~>~brave(paul)))<=>((patient(susan)<~>creative(susan))))&
(![X]:((~rich(X)&happy(X))=>(~creative(X)|humble(X))))&
(((wise(john)&strong(john)))=>((~old(fred)<~>~brave(fred))))&
((?[X]:((~quiet(X)|quiet(X))))<=>((~curious(alice)&funny(alice))))&
((?[X]:((~brave(X)<~>~quiet(X))))<=>((~generous(lucy)&creative(lucy))))&
((?[X]:((~quiet(X)|~curious(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
((?[X]:((~calm(X)<~>wise(X))))=>((humble(fred)&creative(fred))))&
(((brave(mary)&~happy(mary)))<=>(?[X]:((~funny(X)&brave(X)))))&
((strong(paul))<=>(~old(mary)))&
(![X]:((quiet(X)&~creative(X))=>(old(X)|curious(X))))&
(((funny(fred)|~creative(fred)))<=>(?[X]:(wise(X))))&
(?[X]:((strong(X)|patient(X))))&
((~kind(fred)|wise(fred)))&
((happy(john)|funny(john)))&
(?[X]:((wise(X)|~wise(X))))&
((brave(lucy)<~>~humble(lucy)))&
((happy(paul)&~patient(paul)))&
(~strong(susan)) | ~humble(susan) | [
"p0",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3655201228224273905465000
% SZS output start Proof for 3655201228224273905465000
1. ! [X0] : ((creative(X0) | ~kind(X0)) => (~tall(X0) <~> funny(X0))) [input p0]
3. ? [X0] : (kind(X0) | tall(X0)) => humble(susan) [input p2]
9. ? [X0] : (quiet(X0) | ~quiet(X0)) <=> (funny(alice) & ~curious(alice)) [input p8]
24. ~humble(susan) [input hypothesis]
27. ! [X0] : ((~tall(X0) <~> funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 1]
29. humble(susan) | ! [X0] : (~kind(X0) & ~tall(X0)) [ennf transformation 3]
37. ! [X0] : (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (~creative(X0) & kind(X0))) [nnf transformation 27]
44. (? [X0] : (quiet(X0) | ~quiet(X0)) | (~funny(alice) | curious(alice))) & ((funny(alice) & ~curious(alice)) | ! [X0] : (~quiet(X0) & quiet(X0))) [nnf transformation 9]
45. (? [X0] : (quiet(X0) | ~quiet(X0)) | ~funny(alice) | curious(alice)) & ((funny(alice) & ~curious(alice)) | ! [X0] : (~quiet(X0) & quiet(X0))) [flattening 44]
46. (? [X0] : (quiet(X0) | ~quiet(X0)) | ~funny(alice) | curious(alice)) & ((funny(alice) & ~curious(alice)) | ! [X1] : (~quiet(X1) & quiet(X1))) [rectify 45]
47. ? [X0] : (quiet(X0) | ~quiet(X0)) => (quiet(sK0) | ~quiet(sK0)) [choice axiom]
48. ((quiet(sK0) | ~quiet(sK0)) | ~funny(alice) | curious(alice)) & ((funny(alice) & ~curious(alice)) | ! [X1] : (~quiet(X1) & quiet(X1))) [skolemisation 46,47]
78. ~funny(X0) | tall(X0) | kind(X0) [cnf transformation 37]
84. humble(susan) | ~tall(X0) [cnf transformation 29]
85. humble(susan) | ~kind(X0) [cnf transformation 29]
103. funny(alice) | quiet(X1) [cnf transformation 48]
104. funny(alice) | ~quiet(X1) [cnf transformation 48]
139. ~humble(susan) [cnf transformation 24]
143. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
144. ~kind(X0) <- (1) [avatar component clause 143]
146. 2 <=> humble(susan) [avatar definition]
149. 1 | 2 [avatar split clause 85,146,143]
151. 3 <=> ! [X0] : ~tall(X0) [avatar definition]
152. ~tall(X0) <- (3) [avatar component clause 151]
153. 3 | 2 [avatar split clause 84,146,151]
209. 14 <=> ! [X1] : ~quiet(X1) [avatar definition]
210. ~quiet(X1) <- (14) [avatar component clause 209]
212. 15 <=> funny(alice) [avatar definition]
214. funny(alice) <- (15) [avatar component clause 212]
215. 14 | 15 [avatar split clause 104,212,209]
217. 16 <=> ! [X1] : quiet(X1) [avatar definition]
218. quiet(X1) <- (16) [avatar component clause 217]
219. 16 | 15 [avatar split clause 103,212,217]
361. ~2 [avatar split clause 139,146]
366. tall(alice) | kind(alice) <- (15) [resolution 78,214]
371. kind(alice) <- (3, 15) [subsumption resolution 366,152]
372. $false <- (1, 3, 15) [subsumption resolution 371,144]
373. ~1 | ~3 | ~15 [avatar contradiction clause 372]
377. $false <- (14, 16) [subsumption resolution 210,218]
378. ~14 | ~16 [avatar contradiction clause 377]
379. $false [avatar sat refutation 149,153,215,219,361,373,378]
% SZS output end Proof for 3655201228224273905465000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is either old or not kind.
If mary is funny then mary is not strong.
Everyone who is funny or quiet is both not brave and not patient and vice versa.
Everyone who is both not rich and happy is either not calm or tall.
If someone is either not rich or not happy then someone is either kind or calm.
Everyone who is both wise and not humble is not happy.
Everyone who is both brave and not patient is quiet.
If susan is both curious and wise then alice is both funny and strong.
Everyone who is quiet is curious and vice versa.
Everyone who is both quiet and rich is humble and vice versa.
Everyone who is either not old or rich is either rich or generous.
If someone is humble or brave then someone is kind.
If someone is both generous and not creative then paul is either quiet or not brave.
If someone is both not rich and rich then mary is rich and vice versa.
If susan is wise or not old then someone is either creative or not generous and vice versa.
Everyone who is not wise is not humble and vice versa.
Someone is both not calm and not patient.
Mary is both not happy and quiet.
Paul is not happy.
Someone is tall or generous.
John is either humble or funny.
Paul is tall.
Someone is either not brave or happy.
Someone is either patient or wise. | Mary is happy. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((old(X)<~>~kind(X)))))&
((funny(mary))=>(~strong(mary)))&
(![X]:((funny(X)|quiet(X))<=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)&happy(X))=>(~calm(X)<~>tall(X))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((wise(X)&~humble(X))=>~happy(X)))&
(![X]:((brave(X)&~patient(X))=>quiet(X)))&
(((curious(susan)&wise(susan)))=>((funny(alice)&strong(alice))))&
(![X]:(quiet(X)<=>curious(X)))&
(![X]:((quiet(X)&rich(X))<=>humble(X)))&
(![X]:((~old(X)<~>rich(X))=>(rich(X)<~>generous(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~creative(X))))=>((quiet(paul)<~>~brave(paul))))&
((?[X]:((~rich(X)&rich(X))))<=>(rich(mary)))&
(((wise(susan)|~old(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~wise(X)<=>~humble(X)))&
(?[X]:((~calm(X)&~patient(X))))&
((~happy(mary)&quiet(mary)))&
(~happy(paul))&
(?[X]:((tall(X)|generous(X))))&
((humble(john)<~>funny(john)))&
(tall(paul))&
(?[X]:((~brave(X)<~>happy(X))))&
(?[X]:((patient(X)<~>wise(X)))) | happy(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7862512114102797338609745
% SZS output start Proof for 7862512114102797338609745
18. quiet(mary) & ~happy(mary) [input p17]
25. happy(mary) [input hypothesis]
127. ~happy(mary) [cnf transformation 18]
138. happy(mary) [cnf transformation 25]
300. $false [subsumption resolution 138,127]
% SZS output end Proof for 7862512114102797338609745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or quiet is either wise or calm and vice versa.
If someone is not generous or not brave then lucy is either quiet or not quiet.
Everyone who is both not humble and not funny is both brave and not strong.
Everyone who is not funny is not kind and vice versa.
Everyone who is either happy or not rich is not tall or happy and vice versa.
If paul is calm then john is both funny and not patient.
Everyone who is either not funny or calm is tall and vice versa.
If mary is either kind or happy then someone is kind or not patient and vice versa.
If someone is both tall and funny then john is not rich or not brave.
Everyone who is either happy or patient is both happy and not tall and vice versa.
Everyone who is patient is wise and vice versa.
If john is both not strong and brave then someone is curious or not calm.
Everyone who is either curious or not tall is both not generous and not strong and vice versa.
Everyone who is old is patient and vice versa.
If someone is either not happy or not curious then someone is not old.
If someone is not old or not patient then susan is strong or not brave and vice versa.
Someone is curious or not tall.
Mary is not calm.
Someone is not tall.
Someone is either wise or not creative.
Someone is not curious.
Lucy is not funny.
Fred is brave. | Lucy is old. | neutral | (![X]:((strong(X)<~>quiet(X))<=>(wise(X)<~>calm(X))))&
((?[X]:((~generous(X)|~brave(X))))=>((quiet(lucy)<~>~quiet(lucy))))&
(![X]:((~humble(X)&~funny(X))=>(brave(X)&~strong(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(![X]:((happy(X)<~>~rich(X))<=>(~tall(X)|happy(X))))&
((calm(paul))=>((funny(john)&~patient(john))))&
(![X]:((~funny(X)<~>calm(X))<=>tall(X)))&
(((kind(mary)<~>happy(mary)))<=>(?[X]:((kind(X)|~patient(X)))))&
((?[X]:((tall(X)&funny(X))))=>((~rich(john)|~brave(john))))&
(![X]:((happy(X)<~>patient(X))<=>(happy(X)&~tall(X))))&
(![X]:(patient(X)<=>wise(X)))&
(((~strong(john)&brave(john)))=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:(~old(X))))&
((?[X]:((~old(X)|~patient(X))))<=>((strong(susan)|~brave(susan))))&
(?[X]:((curious(X)|~tall(X))))&
(~calm(mary))&
(?[X]:(~tall(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:(~curious(X)))&
(~funny(lucy))&
(brave(fred)) | old(lucy) | [] | null | 0 |
Everyone who is calm or creative is both not old and not curious.
If someone is old then mary is not creative or kind and vice versa.
Everyone who is not curious is not calm and vice versa.
If someone is happy or not kind then someone is not patient or not strong.
Everyone who is not funny or not old is both not quiet and generous and vice versa.
If paul is wise or not tall then john is curious or not tall and vice versa.
If alice is not brave then someone is not wise or not patient.
If paul is either not patient or not kind then susan is either old or not humble and vice versa.
Everyone who is either patient or not quiet is calm and vice versa.
Everyone who is both not humble and not wise is not calm or not rich and vice versa.
Everyone who is not brave is rich and vice versa.
If someone is not curious or not strong then someone is not creative or quiet and vice versa.
If someone is not happy or old then someone is not quiet or kind and vice versa.
If lucy is generous then someone is either not humble or funny.
Everyone who is not calm or calm is both old and funny.
If someone is not creative then paul is rich or not old.
Someone is funny or patient.
Someone is both not creative and not kind.
Paul is not wise.
Someone is both not happy and quiet.
Someone is generous or not happy.
Paul is both not calm and not humble. | Alice is not curious. | entailment | (![X]:((calm(X)|creative(X))=>(~old(X)&~curious(X))))&
((?[X]:(old(X)))<=>((~creative(mary)|kind(mary))))&
(![X]:(~curious(X)<=>~calm(X)))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~funny(X)|~old(X))<=>(~quiet(X)&generous(X))))&
(((wise(paul)|~tall(paul)))<=>((curious(john)|~tall(john))))&
((~brave(alice))=>(?[X]:((~wise(X)|~patient(X)))))&
(((~patient(paul)<~>~kind(paul)))<=>((old(susan)<~>~humble(susan))))&
(![X]:((patient(X)<~>~quiet(X))<=>calm(X)))&
(![X]:((~humble(X)&~wise(X))<=>(~calm(X)|~rich(X))))&
(![X]:(~brave(X)<=>rich(X)))&
((?[X]:((~curious(X)|~strong(X))))<=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:((~happy(X)|old(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
((generous(lucy))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|calm(X))=>(old(X)&funny(X))))&
((?[X]:(~creative(X)))=>((rich(paul)|~old(paul))))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(~wise(paul))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
((~calm(paul)&~humble(paul))) | ~curious(alice) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1536470798668992701705596
% SZS output start Proof for 1536470798668992701705596
1. ! [X0] : ((creative(X0) | calm(X0)) => (~curious(X0) & ~old(X0))) [input p0]
3. ! [X0] : (~curious(X0) <=> ~calm(X0)) [input p2]
23. curious(alice) [input hypothesis]
28. ! [X0] : ((~curious(X0) & ~old(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 1]
41. ! [X0] : ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))) [nnf transformation 3]
78. ~curious(X0) | ~calm(X0) [cnf transformation 28]
84. ~curious(X0) | calm(X0) [cnf transformation 41]
139. curious(alice) [cnf transformation 23]
158. ~curious(X0) [subsumption resolution 84,78]
307. $false [subsumption resolution 139,158]
% SZS output end Proof for 1536470798668992701705596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then fred is either rich or kind and vice versa.
If mary is not happy or humble then someone is not happy or not generous and vice versa.
If susan is calm or not creative then someone is not happy and vice versa.
If alice is not strong or not funny then someone is tall.
If someone is both funny and not strong then someone is rich and vice versa.
If someone is both strong and calm then fred is either strong or not tall and vice versa.
If someone is not patient then susan is either rich or not rich.
Everyone who is both not happy and not strong is happy and vice versa.
If john is either rich or tall then lucy is either tall or humble.
Everyone who is not happy or creative is both not creative and calm.
If alice is either not creative or not generous then john is rich.
Everyone who is not calm is both quiet and creative and vice versa.
Everyone who is both not generous and wise is humble.
If lucy is funny or curious then susan is both humble and funny and vice versa.
If lucy is both not brave and kind then paul is both not old and not generous.
If fred is either curious or brave then alice is not tall.
Someone is either not rich or wise.
Lucy is not kind or kind.
Mary is both not brave and calm.
Someone is not curious.
Someone is strong or not old.
Someone is both not patient and not kind. | Alice is not generous. | entailment | ((?[X]:(~generous(X)))<=>((rich(fred)<~>kind(fred))))&
(((~happy(mary)|humble(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(((calm(susan)|~creative(susan)))<=>(?[X]:(~happy(X))))&
(((~strong(alice)|~funny(alice)))=>(?[X]:(tall(X))))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:(rich(X))))&
((?[X]:((strong(X)&calm(X))))<=>((strong(fred)<~>~tall(fred))))&
((?[X]:(~patient(X)))=>((rich(susan)<~>~rich(susan))))&
(![X]:((~happy(X)&~strong(X))<=>happy(X)))&
(((rich(john)<~>tall(john)))=>((tall(lucy)<~>humble(lucy))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&calm(X))))&
(((~creative(alice)<~>~generous(alice)))=>(rich(john)))&
(![X]:(~calm(X)<=>(quiet(X)&creative(X))))&
(![X]:((~generous(X)&wise(X))=>humble(X)))&
(((funny(lucy)|curious(lucy)))<=>((humble(susan)&funny(susan))))&
(((~brave(lucy)&kind(lucy)))=>((~old(paul)&~generous(paul))))&
(((curious(fred)<~>brave(fred)))=>(~tall(alice)))&
(?[X]:((~rich(X)<~>wise(X))))&
((~kind(lucy)|kind(lucy)))&
((~brave(mary)&calm(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)|~old(X))))&
(?[X]:((~patient(X)&~kind(X)))) | ~generous(alice) | [
"p4",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8712863755083942114939572
% SZS output start Proof for 8712863755083942114939572
5. ? [X0] : (~strong(X0) & funny(X0)) <=> ? [X0] : rich(X0) [input p4]
8. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> happy(X0)) [input p7]
10. ! [X0] : ((creative(X0) | ~happy(X0)) => (calm(X0) & ~creative(X0))) [input p9]
11. (~creative(alice) <~> ~generous(alice)) => rich(john) [input p10]
23. generous(alice) [input hypothesis]
24. ? [X0] : (~strong(X0) & funny(X0)) <=> ? [X1] : rich(X1) [rectify 5]
30. ! [X0] : ((calm(X0) & ~creative(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 10]
31. rich(john) | (~creative(alice) <=> ~generous(alice)) [ennf transformation 11]
53. (? [X0] : (~strong(X0) & funny(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (strong(X0) | ~funny(X0))) [nnf transformation 24]
54. (? [X0] : (~strong(X0) & funny(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (strong(X3) | ~funny(X3))) [rectify 53]
55. ? [X0] : (~strong(X0) & funny(X0)) => (~strong(sK4) & funny(sK4)) [choice axiom]
56. ? [X2] : rich(X2) => rich(sK5) [choice axiom]
57. ((~strong(sK4) & funny(sK4)) | ! [X1] : ~rich(X1)) & (rich(sK5) | ! [X3] : (strong(X3) | ~funny(X3))) [skolemisation 54,56,55]
63. ! [X0] : (((~strong(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (strong(X0) | happy(X0)))) [nnf transformation 8]
64. ! [X0] : (((~strong(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | strong(X0) | happy(X0))) [flattening 63]
66. rich(john) | ((~creative(alice) | generous(alice)) & (~generous(alice) | creative(alice))) [nnf transformation 31]
94. ~strong(sK4) | ~rich(X1) [cnf transformation 57]
103. happy(X0) | strong(X0) | happy(X0) [cnf transformation 64]
104. ~happy(X0) | ~happy(X0) [cnf transformation 64]
111. ~creative(X0) | ~creative(X0) [cnf transformation 30]
114. rich(john) | ~generous(alice) | creative(alice) [cnf transformation 66]
136. generous(alice) [cnf transformation 23]
137. ~creative(X0) [duplicate literal removal 111]
138. happy(X0) | strong(X0) [duplicate literal removal 103]
139. ~happy(X0) [duplicate literal removal 104]
212. 16 <=> ! [X1] : ~rich(X1) [avatar definition]
213. ~rich(X1) <- (16) [avatar component clause 212]
215. 17 <=> strong(sK4) [avatar definition]
217. ~strong(sK4) <- (~17) [avatar component clause 215]
218. 16 | ~17 [avatar split clause 94,215,212]
257. strong(X0) [subsumption resolution 138,139]
263. 27 <=> rich(john) [avatar definition]
265. rich(john) <- (27) [avatar component clause 263]
279. rich(john) | ~generous(alice) [subsumption resolution 114,137]
281. 30 <=> generous(alice) [avatar definition]
284. ~30 | 27 [avatar split clause 279,263,281]
343. 30 [avatar split clause 136,281]
351. $false <- (16, 27) [resolution 265,213]
352. ~16 | ~27 [avatar contradiction clause 351]
353. $false <- (~17) [subsumption resolution 217,257]
354. 17 [avatar contradiction clause 353]
355. $false [avatar sat refutation 218,284,343,352,354]
% SZS output end Proof for 8712863755083942114939572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not curious is either old or humble and vice versa. If mary is both tall and not patient then someone is old or humble and vice versa. If fred is both calm and not calm then mary is either funny or not curious and vice versa. If susan is strong then mary is either not creative or strong and vice versa. If fred is both not rich and strong then someone is both not quiet and brave. If mary is both not happy and funny then lucy is both not generous and humble and vice versa. Everyone who is not curious is not tall or calm and vice versa. If mary is happy or calm then someone is either generous or strong and vice versa. Everyone who is both not creative and not old is both curious and patient and vice versa. If someone is curious or not calm then paul is not curious and vice versa. If someone is both strong and creative then someone is either old or not kind and vice versa. If alice is not happy then someone is both not old and wise and vice versa. Everyone who is not creative is both not funny and not curious and vice versa. If paul is rich then paul is either happy or not calm. Everyone who is humble is rich. If someone is both old and not funny then susan is not brave or brave. Someone is either not brave or not old. Someone is both not rich and quiet. Alice is both not rich and not strong. Someone is curious or happy. John is calm. Someone is both not quiet and not humble. Someone is either not kind or not humble. Mary is kind. | Susan is not generous. | neutral | (![X]:((curious(X)&~curious(X))<=>(old(X)<~>humble(X))))&
(((tall(mary)&~patient(mary)))<=>(?[X]:((old(X)|humble(X)))))&
(((calm(fred)&~calm(fred)))<=>((funny(mary)<~>~curious(mary))))&
((strong(susan))<=>((~creative(mary)<~>strong(mary))))&
(((~rich(fred)&strong(fred)))=>(?[X]:((~quiet(X)&brave(X)))))&
(((~happy(mary)&funny(mary)))<=>((~generous(lucy)&humble(lucy))))&
(![X]:(~curious(X)<=>(~tall(X)|calm(X))))&
(((happy(mary)|calm(mary)))<=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~creative(X)&~old(X))<=>(curious(X)&patient(X))))&
((?[X]:((curious(X)|~calm(X))))<=>(~curious(paul)))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:((old(X)<~>~kind(X)))))&
((~happy(alice))<=>(?[X]:((~old(X)&wise(X)))))&
(![X]:(~creative(X)<=>(~funny(X)&~curious(X))))&
((rich(paul))=>((happy(paul)<~>~calm(paul))))&
(![X]:(humble(X)=>rich(X)))&
((?[X]:((old(X)&~funny(X))))=>((~brave(susan)|brave(susan))))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((~rich(X)&quiet(X))))&
((~rich(alice)&~strong(alice)))&
(?[X]:((curious(X)|happy(X))))&
(calm(john))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:((~kind(X)<~>~humble(X))))&
(kind(mary)) | ~generous(susan) | [] | null | 0 |
Everyone who is both not tall and strong is funny and vice versa.
Everyone who is both curious and kind is not quiet or happy and vice versa.
Everyone who is not patient is not curious.
Everyone who is not patient or strong is either not quiet or humble.
Everyone who is not tall or not creative is humble and vice versa.
Everyone who is quiet is both not generous and rich and vice versa.
Everyone who is both not humble and creative is patient.
Everyone who is either not patient or not kind is generous and vice versa.
If fred is not tall then mary is not curious.
If someone is strong then mary is either humble or happy.
Everyone who is both not kind and wise is not funny and vice versa.
Everyone who is not old or not patient is both kind and rich.
If someone is both not patient and humble then paul is not curious.
If someone is either not rich or strong then someone is not curious and vice versa.
If someone is not calm or quiet then susan is not humble or not curious.
Everyone who is not calm or not patient is both generous and strong and vice versa.
Mary is quiet or not brave.
Susan is both not brave and not old.
Someone is either generous or funny.
Lucy is not wise.
Someone is both not wise and strong. | Susan is happy. | contradiction | (![X]:((~tall(X)&strong(X))<=>funny(X)))&
(![X]:((curious(X)&kind(X))<=>(~quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:((~patient(X)|strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~tall(X)|~creative(X))<=>humble(X)))&
(![X]:(quiet(X)<=>(~generous(X)&rich(X))))&
(![X]:((~humble(X)&creative(X))=>patient(X)))&
(![X]:((~patient(X)<~>~kind(X))<=>generous(X)))&
((~tall(fred))=>(~curious(mary)))&
((?[X]:(strong(X)))=>((humble(mary)<~>happy(mary))))&
(![X]:((~kind(X)&wise(X))<=>~funny(X)))&
(![X]:((~old(X)|~patient(X))=>(kind(X)&rich(X))))&
((?[X]:((~patient(X)&humble(X))))=>(~curious(paul)))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~calm(X)|quiet(X))))=>((~humble(susan)|~curious(susan))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)&strong(X))))&
((quiet(mary)|~brave(mary)))&
((~brave(susan)&~old(susan)))&
(?[X]:((generous(X)<~>funny(X))))&
(~wise(lucy))&
(?[X]:((~wise(X)&strong(X)))) | happy(susan) | [
"p0",
"p1",
"p4",
"p10",
"p11",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2406893616485877357460850
% SZS output start Proof for 2406893616485877357460850
1. ! [X0] : ((strong(X0) & ~tall(X0)) <=> funny(X0)) [input p0]
2. ! [X0] : ((kind(X0) & curious(X0)) <=> (happy(X0) | ~quiet(X0))) [input p1]
5. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> humble(X0)) [input p4]
11. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~funny(X0)) [input p10]
12. ! [X0] : ((~patient(X0) | ~old(X0)) => (rich(X0) & kind(X0))) [input p11]
14. ? [X0] : (~rich(X0) <~> strong(X0)) <=> ? [X0] : ~curious(X0) [input p13]
15. ? [X0] : (quiet(X0) | ~calm(X0)) => (~curious(susan) | ~humble(susan)) [input p14]
18. ~old(susan) & ~brave(susan) [input p17]
22. happy(susan) [input hypothesis]
23. ? [X0] : (~rich(X0) <~> strong(X0)) <=> ? [X1] : ~curious(X1) [rectify 14]
24. ~old(susan) [pure predicate removal 18]
32. ! [X0] : ((rich(X0) & kind(X0)) | (patient(X0) & old(X0))) [ennf transformation 12]
34. (~curious(susan) | ~humble(susan)) | ! [X0] : (~quiet(X0) & calm(X0)) [ennf transformation 15]
35. ~curious(susan) | ~humble(susan) | ! [X0] : (~quiet(X0) & calm(X0)) [flattening 34]
36. ! [X0] : (((strong(X0) & ~tall(X0)) | ~funny(X0)) & (funny(X0) | (~strong(X0) | tall(X0)))) [nnf transformation 1]
37. ! [X0] : (((strong(X0) & ~tall(X0)) | ~funny(X0)) & (funny(X0) | ~strong(X0) | tall(X0))) [flattening 36]
38. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~kind(X0) | ~curious(X0)))) [nnf transformation 2]
39. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~kind(X0) | ~curious(X0))) [flattening 38]
41. ! [X0] : (((~creative(X0) | ~tall(X0)) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [nnf transformation 5]
42. ! [X0] : ((~creative(X0) | ~tall(X0) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [flattening 41]
47. ! [X0] : (((wise(X0) & ~kind(X0)) | funny(X0)) & (~funny(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 11]
48. ! [X0] : (((wise(X0) & ~kind(X0)) | funny(X0)) & (~funny(X0) | ~wise(X0) | kind(X0))) [flattening 47]
49. (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) [nnf transformation 23]
50. (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : ((~rich(X3) | ~strong(X3)) & (strong(X3) | rich(X3)))) [rectify 49]
51. ? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) => ((~strong(sK0) | rich(sK0)) & (strong(sK0) | ~rich(sK0))) [choice axiom]
52. ? [X2] : ~curious(X2) => ~curious(sK1) [choice axiom]
53. (((~strong(sK0) | rich(sK0)) & (strong(sK0) | ~rich(sK0))) | ! [X1] : curious(X1)) & (~curious(sK1) | ! [X3] : ((~rich(X3) | ~strong(X3)) & (strong(X3) | rich(X3)))) [skolemisation 50,52,51]
62. ~funny(X0) | ~tall(X0) [cnf transformation 37]
63. ~funny(X0) | strong(X0) [cnf transformation 37]
65. quiet(X0) | curious(X0) [cnf transformation 39]
66. ~happy(X0) | curious(X0) [cnf transformation 39]
68. ~happy(X0) | kind(X0) [cnf transformation 39]
74. humble(X0) | tall(X0) [cnf transformation 42]
89. ~kind(X0) | funny(X0) [cnf transformation 48]
93. old(X0) | rich(X0) [cnf transformation 32]
97. ~curious(sK1) | ~rich(X3) | ~strong(X3) [cnf transformation 53]
101. ~curious(susan) | ~humble(susan) | ~quiet(X0) [cnf transformation 35]
107. ~old(susan) [cnf transformation 24]
113. happy(susan) [cnf transformation 22]
147. 8 <=> ! [X1] : curious(X1) [avatar definition]
148. curious(X1) <- (8) [avatar component clause 147]
160. 11 <=> ! [X3] : (~rich(X3) | ~strong(X3)) [avatar definition]
161. ~rich(X3) | ~strong(X3) <- (11) [avatar component clause 160]
163. 12 <=> curious(sK1) [avatar definition]
165. ~curious(sK1) <- (~12) [avatar component clause 163]
166. 11 | ~12 [avatar split clause 97,163,160]
172. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
173. ~quiet(X0) <- (14) [avatar component clause 172]
175. 15 <=> humble(susan) [avatar definition]
177. ~humble(susan) <- (~15) [avatar component clause 175]
179. 16 <=> curious(susan) [avatar definition]
182. 14 | ~15 | ~16 [avatar split clause 101,179,175,172]
199. curious(susan) [resolution 66,113]
200. 16 [avatar split clause 199,179]
201. kind(susan) [resolution 68,113]
203. tall(susan) <- (~15) [resolution 74,177]
209. funny(susan) [resolution 89,201]
222. rich(susan) [resolution 93,107]
224. strong(susan) [resolution 209,63]
225. ~tall(susan) [resolution 209,62]
226. $false <- (~15) [subsumption resolution 225,203]
227. 15 [avatar contradiction clause 226]
229. curious(X1) <- (14) [resolution 173,65]
230. 8 | ~14 [avatar split clause 229,172,147]
234. $false <- (8, ~12) [resolution 148,165]
235. ~8 | 12 [avatar contradiction clause 234]
242. ~strong(susan) <- (11) [resolution 161,222]
244. $false <- (11) [subsumption resolution 242,224]
245. ~11 [avatar contradiction clause 244]
246. $false [avatar sat refutation 166,182,200,227,230,235,245]
% SZS output end Proof for 2406893616485877357460850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not tall is not happy or calm.
If lucy is rich or humble then lucy is not rich or not patient.
Everyone who is not wise or not happy is not curious or rich.
Everyone who is not strong is funny or brave and vice versa.
Everyone who is not tall or old is not wise and vice versa.
If alice is both creative and tall then someone is funny or not generous and vice versa.
Everyone who is either not strong or happy is not happy and vice versa.
Everyone who is both curious and tall is rich and vice versa.
If someone is not funny or funny then alice is either not wise or not humble and vice versa.
If alice is both tall and not patient then someone is happy and vice versa.
Everyone who is either kind or patient is humble and vice versa.
Everyone who is not patient or not wise is both not kind and brave.
If someone is generous or wise then someone is not tall or generous.
Everyone who is either curious or wise is not rich and vice versa.
If someone is both patient and tall then susan is funny.
Everyone who is creative or kind is both strong and not generous.
Someone is either not generous or not calm.
Someone is not rich.
Fred is either not tall or not curious.
John is old or not patient.
Someone is happy or calm.
Alice is not patient.
Someone is not creative. | Fred is wise. | entailment | (![X]:((~kind(X)&~tall(X))=>(~happy(X)|calm(X))))&
(((rich(lucy)|humble(lucy)))=>((~rich(lucy)|~patient(lucy))))&
(![X]:((~wise(X)|~happy(X))=>(~curious(X)|rich(X))))&
(![X]:(~strong(X)<=>(funny(X)|brave(X))))&
(![X]:((~tall(X)|old(X))<=>~wise(X)))&
(((creative(alice)&tall(alice)))<=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((~strong(X)<~>happy(X))<=>~happy(X)))&
(![X]:((curious(X)&tall(X))<=>rich(X)))&
((?[X]:((~funny(X)|funny(X))))<=>((~wise(alice)<~>~humble(alice))))&
(((tall(alice)&~patient(alice)))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>humble(X)))&
(![X]:((~patient(X)|~wise(X))=>(~kind(X)&brave(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((curious(X)<~>wise(X))<=>~rich(X)))&
((?[X]:((patient(X)&tall(X))))=>(funny(susan)))&
(![X]:((creative(X)|kind(X))=>(strong(X)&~generous(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:(~rich(X)))&
((~tall(fred)<~>~curious(fred)))&
((old(john)|~patient(john)))&
(?[X]:((happy(X)|calm(X))))&
(~patient(alice))&
(?[X]:(~creative(X))) | wise(fred) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 660217672345802626022788
% SZS output start Proof for 660217672345802626022788
3. ! [X0] : ((~happy(X0) | ~wise(X0)) => (rich(X0) | ~curious(X0))) [input p2]
8. ! [X0] : ((tall(X0) & curious(X0)) <=> rich(X0)) [input p7]
14. ! [X0] : ((curious(X0) <~> wise(X0)) <=> ~rich(X0)) [input p13]
24. ~wise(fred) [input hypothesis]
30. ! [X0] : ((rich(X0) | ~curious(X0)) | (happy(X0) & wise(X0))) [ennf transformation 3]
31. ! [X0] : (rich(X0) | ~curious(X0) | (happy(X0) & wise(X0))) [flattening 30]
46. ! [X0] : (((tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (~tall(X0) | ~curious(X0)))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | ~tall(X0) | ~curious(X0))) [flattening 46]
61. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | rich(X0)) & (~rich(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 14]
75. rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
93. curious(X0) | ~rich(X0) [cnf transformation 47]
114. ~rich(X0) | wise(X0) | ~curious(X0) [cnf transformation 61]
116. wise(X0) | curious(X0) | rich(X0) [cnf transformation 61]
132. ~wise(fred) [cnf transformation 24]
224. wise(X0) | rich(X0) [subsumption resolution 116,75]
225. ~rich(X0) | wise(X0) [subsumption resolution 114,93]
226. wise(X0) [subsumption resolution 225,224]
276. $false [subsumption resolution 132,226]
% SZS output end Proof for 660217672345802626022788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or not tall is either creative or not quiet.
If john is both not patient and not creative then someone is calm or humble.
Everyone who is either not strong or wise is tall and vice versa.
Everyone who is both not rich and not patient is both not wise and not calm and vice versa.
If paul is both calm and creative then someone is happy or quiet and vice versa.
If fred is rich then someone is either generous or not happy.
Everyone who is curious is either not curious or strong.
If someone is not funny then someone is both rich and not brave and vice versa.
Everyone who is both calm and humble is creative or not strong and vice versa.
If someone is either rich or not kind then someone is either not generous or not humble.
Everyone who is wise is both not brave and creative.
If alice is not strong then alice is either generous or curious.
Everyone who is either not kind or brave is kind or rich.
If paul is either calm or not funny then someone is both rich and strong and vice versa.
Everyone who is strong or rich is patient or not kind and vice versa.
Everyone who is not curious or creative is both not happy and not rich.
Fred is both patient and brave.
Someone is curious or not strong.
Someone is rich.
Someone is either wise or not quiet.
Someone is not curious.
John is either not funny or generous.
Alice is either not curious or rich.
Lucy is not calm. | Fred is tall. | contradiction | (![X]:((~quiet(X)|~tall(X))=>(creative(X)<~>~quiet(X))))&
(((~patient(john)&~creative(john)))=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>tall(X)))&
(![X]:((~rich(X)&~patient(X))<=>(~wise(X)&~calm(X))))&
(((calm(paul)&creative(paul)))<=>(?[X]:((happy(X)|quiet(X)))))&
((rich(fred))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(curious(X)=>(~curious(X)<~>strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((calm(X)&humble(X))<=>(creative(X)|~strong(X))))&
((?[X]:((rich(X)<~>~kind(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:(wise(X)=>(~brave(X)&creative(X))))&
((~strong(alice))=>((generous(alice)<~>curious(alice))))&
(![X]:((~kind(X)<~>brave(X))=>(kind(X)|rich(X))))&
(((calm(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((strong(X)|rich(X))<=>(patient(X)|~kind(X))))&
(![X]:((~curious(X)|creative(X))=>(~happy(X)&~rich(X))))&
((patient(fred)&brave(fred)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>~quiet(X))))&
(?[X]:(~curious(X)))&
((~funny(john)<~>generous(john)))&
((~curious(alice)<~>rich(alice)))&
(~calm(lucy)) | tall(fred) | [
"p2",
"p6",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7919578214748866785133535
% SZS output start Proof for 7919578214748866785133535
3. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> tall(X0)) [input p2]
7. ! [X0] : (curious(X0) => (~curious(X0) <~> strong(X0))) [input p6]
11. ! [X0] : (wise(X0) => (creative(X0) & ~brave(X0))) [input p10]
15. ! [X0] : ((rich(X0) | strong(X0)) <=> (~kind(X0) | patient(X0))) [input p14]
16. ! [X0] : ((creative(X0) | ~curious(X0)) => (~rich(X0) & ~happy(X0))) [input p15]
17. brave(fred) & patient(fred) [input p16]
25. tall(fred) [input hypothesis]
28. ! [X0] : (tall(X0) => (~strong(X0) <~> wise(X0))) [unused predicate definition removal 3]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | ~tall(X0)) [ennf transformation 28]
34. ! [X0] : ((~curious(X0) <~> strong(X0)) | ~curious(X0)) [ennf transformation 7]
36. ! [X0] : ((creative(X0) & ~brave(X0)) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 16]
44. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~tall(X0)) [nnf transformation 32]
55. ! [X0] : (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ~curious(X0)) [nnf transformation 34]
73. ! [X0] : (((rich(X0) | strong(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 15]
74. ! [X0] : ((rich(X0) | strong(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | (~rich(X0) & ~strong(X0)))) [flattening 73]
91. ~strong(X0) | wise(X0) | ~tall(X0) [cnf transformation 44]
104. strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
118. ~brave(X0) | ~wise(X0) [cnf transformation 36]
132. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 74]
136. ~rich(X0) | curious(X0) [cnf transformation 40]
138. patient(fred) [cnf transformation 17]
139. brave(fred) [cnf transformation 17]
150. tall(fred) [cnf transformation 25]
152. ~curious(X0) | strong(X0) [duplicate literal removal 104]
199. 11 <=> rich(fred) [avatar definition]
200. rich(fred) <- (11) [avatar component clause 199]
328. ~wise(fred) [resolution 118,139]
445. strong(fred) | rich(fred) [resolution 132,138]
482. 57 <=> strong(fred) [avatar definition]
484. strong(fred) <- (57) [avatar component clause 482]
485. 11 | 57 [avatar split clause 445,482,199]
488. curious(fred) <- (11) [resolution 200,136]
546. strong(fred) <- (11) [resolution 488,152]
547. 57 | ~11 [avatar split clause 546,199,482]
549. wise(fred) | ~tall(fred) <- (57) [resolution 484,91]
552. ~tall(fred) <- (57) [subsumption resolution 549,328]
553. $false <- (57) [subsumption resolution 552,150]
554. ~57 [avatar contradiction clause 553]
555. $false [avatar sat refutation 485,547,554]
% SZS output end Proof for 7919578214748866785133535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not kind is either kind or not tall. If susan is both funny and rich then someone is both not funny and brave. Everyone who is not creative or not calm is both not patient and creative. Everyone who is both creative and not curious is patient or humble. Everyone who is both not funny and quiet is either not old or not kind and vice versa. Everyone who is quiet is both not curious and not patient. Everyone who is kind is wise. Everyone who is quiet or old is either strong or not quiet and vice versa. Everyone who is either not patient or not strong is both happy and strong and vice versa. Everyone who is happy or not curious is both rich and curious. Everyone who is not curious is not happy. Everyone who is not rich is both tall and generous. If john is both not happy and not rich then susan is either not quiet or wise. Everyone who is both not calm and not kind is not creative and vice versa. Everyone who is patient or curious is not patient or wise and vice versa. If someone is both not wise and rich then susan is either brave or not kind and vice versa. Mary is either happy or wise. Mary is not rich. Mary is humble. Lucy is funny. Alice is both rich and old. John is not happy. | John is brave. | neutral | (![X]:((creative(X)<~>~kind(X))=>(kind(X)<~>~tall(X))))&
(((funny(susan)&rich(susan)))=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:((~creative(X)|~calm(X))=>(~patient(X)&creative(X))))&
(![X]:((creative(X)&~curious(X))=>(patient(X)|humble(X))))&
(![X]:((~funny(X)&quiet(X))<=>(~old(X)<~>~kind(X))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:((quiet(X)|old(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>~strong(X))<=>(happy(X)&strong(X))))&
(![X]:((happy(X)|~curious(X))=>(rich(X)&curious(X))))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(((~happy(john)&~rich(john)))=>((~quiet(susan)<~>wise(susan))))&
(![X]:((~calm(X)&~kind(X))<=>~creative(X)))&
(![X]:((patient(X)|curious(X))<=>(~patient(X)|wise(X))))&
((?[X]:((~wise(X)&rich(X))))<=>((brave(susan)<~>~kind(susan))))&
((happy(mary)<~>wise(mary)))&
(~rich(mary))&
(humble(mary))&
(funny(lucy))&
((rich(alice)&old(alice)))&
(~happy(john)) | brave(john) | [] | null | 0 |
If john is patient then lucy is not quiet.
Everyone who is both brave and rich is calm or not patient.
Everyone who is both calm and curious is either not patient or rich.
Everyone who is both humble and not tall is quiet and vice versa.
If someone is not strong then someone is both quiet and not rich and vice versa.
Everyone who is old is not wise or patient.
If someone is both not happy and curious then someone is happy or not wise.
If mary is both rich and not old then susan is quiet or not patient.
Everyone who is either not patient or not funny is old.
Everyone who is both happy and funny is either generous or creative and vice versa.
If someone is either not strong or wise then someone is rich or not rich.
Everyone who is kind is both generous and not happy.
If someone is both quiet and brave then someone is not calm and vice versa.
Everyone who is either not kind or tall is calm.
Everyone who is not wise is either rich or not strong and vice versa.
Fred is both not kind and not funny.
Someone is either not old or happy.
Lucy is wise.
John is rich or not brave.
Mary is either patient or not rich.
Someone is both generous and not quiet.
Mary is funny or happy.
Someone is not generous. | Mary is not funny. | neutral | ((patient(john))=>(~quiet(lucy)))&
(![X]:((brave(X)&rich(X))=>(calm(X)|~patient(X))))&
(![X]:((calm(X)&curious(X))=>(~patient(X)<~>rich(X))))&
(![X]:((humble(X)&~tall(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:(old(X)=>(~wise(X)|patient(X))))&
((?[X]:((~happy(X)&curious(X))))=>(?[X]:((happy(X)|~wise(X)))))&
(((rich(mary)&~old(mary)))=>((quiet(susan)|~patient(susan))))&
(![X]:((~patient(X)<~>~funny(X))=>old(X)))&
(![X]:((happy(X)&funny(X))<=>(generous(X)<~>creative(X))))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(kind(X)=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)&brave(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)<~>tall(X))=>calm(X)))&
(![X]:(~wise(X)<=>(rich(X)<~>~strong(X))))&
((~kind(fred)&~funny(fred)))&
(?[X]:((~old(X)<~>happy(X))))&
(wise(lucy))&
((rich(john)|~brave(john)))&
((patient(mary)<~>~rich(mary)))&
(?[X]:((generous(X)&~quiet(X))))&
((funny(mary)|happy(mary)))&
(?[X]:(~generous(X))) | ~funny(mary) | [] | null | 0 |
If susan is either not tall or generous then someone is humble and vice versa.
Everyone who is either not old or not creative is strong or curious.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Everyone who is both not kind and curious is wise or rich and vice versa.
If someone is either tall or calm then john is calm and vice versa.
If paul is not creative or not kind then john is not wise or brave.
Everyone who is not quiet or not creative is kind or not creative and vice versa.
If alice is not generous or curious then paul is funny and vice versa.
If someone is both not tall and not rich then someone is not rich or funny and vice versa.
If someone is either not wise or not strong then someone is not generous or kind and vice versa.
Everyone who is not strong is old or wise.
Everyone who is curious or generous is not wise or calm and vice versa.
If someone is both rich and not strong then alice is both not calm and not wise.
Everyone who is both old and not rich is both curious and not brave.
John is both not creative and happy.
Someone is patient or not humble.
John is both wise and not brave.
Someone is either creative or quiet.
Fred is both not kind and not creative.
Someone is humble or calm.
Someone is calm.
Someone is either tall or not old. | Paul is kind. | entailment | (((~tall(susan)<~>generous(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~old(X)<~>~creative(X))=>(strong(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
(![X]:((~kind(X)&curious(X))<=>(wise(X)|rich(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(calm(john)))&
(((~creative(paul)|~kind(paul)))=>((~wise(john)|brave(john))))&
(![X]:((~quiet(X)|~creative(X))<=>(kind(X)|~creative(X))))&
(((~generous(alice)|curious(alice)))<=>(funny(paul)))&
((?[X]:((~tall(X)&~rich(X))))<=>(?[X]:((~rich(X)|funny(X)))))&
((?[X]:((~wise(X)<~>~strong(X))))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:(~strong(X)=>(old(X)|wise(X))))&
(![X]:((curious(X)|generous(X))<=>(~wise(X)|calm(X))))&
((?[X]:((rich(X)&~strong(X))))=>((~calm(alice)&~wise(alice))))&
(![X]:((old(X)&~rich(X))=>(curious(X)&~brave(X))))&
((~creative(john)&happy(john)))&
(?[X]:((patient(X)|~humble(X))))&
((wise(john)&~brave(john)))&
(?[X]:((creative(X)<~>quiet(X))))&
((~kind(fred)&~creative(fred)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((tall(X)<~>~old(X)))) | kind(paul) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2647581945761229607110516
% SZS output start Proof for 2647581945761229607110516
8. (~kind(paul) | ~creative(paul)) => (brave(john) | ~wise(john)) [input p7]
19. ~brave(john) & wise(john) [input p18]
25. ~kind(paul) [input hypothesis]
31. (brave(john) | ~wise(john)) | (kind(paul) & creative(paul)) [ennf transformation 8]
32. brave(john) | ~wise(john) | (kind(paul) & creative(paul)) [flattening 31]
114. brave(john) | ~wise(john) | kind(paul) [cnf transformation 32]
145. wise(john) [cnf transformation 19]
146. ~brave(john) [cnf transformation 19]
155. ~kind(paul) [cnf transformation 25]
227. 16 <=> kind(paul) [avatar definition]
231. 17 <=> wise(john) [avatar definition]
235. 18 <=> brave(john) [avatar definition]
238. 16 | ~17 | 18 [avatar split clause 114,235,231,227]
327. ~18 [avatar split clause 146,235]
328. 17 [avatar split clause 145,231]
358. ~16 [avatar split clause 155,227]
359. $false [avatar sat refutation 238,327,328,358]
% SZS output end Proof for 2647581945761229607110516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not quiet is either brave or calm and vice versa.
If someone is both calm and not wise then someone is patient or calm and vice versa.
If someone is either not happy or quiet then mary is both not patient and not calm and vice versa.
If paul is both creative and not rich then mary is not tall or creative.
Everyone who is not old or funny is either old or not patient.
If john is not wise then fred is not creative or not tall and vice versa.
Everyone who is not calm is creative or not wise and vice versa.
Everyone who is old is both wise and not calm and vice versa.
If mary is not generous then mary is not happy.
Everyone who is both kind and strong is not tall or funny and vice versa.
Everyone who is old or brave is old.
Everyone who is humble or not funny is not generous and vice versa.
Everyone who is either patient or funny is either not old or creative.
If someone is both kind and not brave then lucy is both curious and quiet and vice versa.
Everyone who is either old or generous is both humble and funny and vice versa.
Everyone who is not creative or generous is kind and vice versa.
Susan is not humble.
Someone is not kind.
Someone is strong.
Mary is both not funny and strong.
Someone is not patient.
Someone is not humble or happy.
Someone is either old or not generous. | Susan is funny. | contradiction | (![X]:((curious(X)&~quiet(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((calm(X)&~wise(X))))<=>(?[X]:((patient(X)|calm(X)))))&
((?[X]:((~happy(X)<~>quiet(X))))<=>((~patient(mary)&~calm(mary))))&
(((creative(paul)&~rich(paul)))=>((~tall(mary)|creative(mary))))&
(![X]:((~old(X)|funny(X))=>(old(X)<~>~patient(X))))&
((~wise(john))<=>((~creative(fred)|~tall(fred))))&
(![X]:(~calm(X)<=>(creative(X)|~wise(X))))&
(![X]:(old(X)<=>(wise(X)&~calm(X))))&
((~generous(mary))=>(~happy(mary)))&
(![X]:((kind(X)&strong(X))<=>(~tall(X)|funny(X))))&
(![X]:((old(X)|brave(X))=>old(X)))&
(![X]:((humble(X)|~funny(X))<=>~generous(X)))&
(![X]:((patient(X)<~>funny(X))=>(~old(X)<~>creative(X))))&
((?[X]:((kind(X)&~brave(X))))<=>((curious(lucy)&quiet(lucy))))&
(![X]:((old(X)<~>generous(X))<=>(humble(X)&funny(X))))&
(![X]:((~creative(X)|generous(X))<=>kind(X)))&
(~humble(susan))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
((~funny(mary)&strong(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((old(X)<~>~generous(X)))) | funny(susan) | [
"p1",
"p4",
"p6",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 387655058182514287663483
% SZS output start Proof for 387655058182514287663483
2. ? [X0] : (~wise(X0) & calm(X0)) <=> ? [X0] : (calm(X0) | patient(X0)) [input p1]
5. ! [X0] : ((funny(X0) | ~old(X0)) => (old(X0) <~> ~patient(X0))) [input p4]
7. ! [X0] : (~calm(X0) <=> (~wise(X0) | creative(X0))) [input p6]
12. ! [X0] : ((~funny(X0) | humble(X0)) <=> ~generous(X0)) [input p11]
15. ! [X0] : ((old(X0) <~> generous(X0)) <=> (funny(X0) & humble(X0))) [input p14]
17. ~humble(susan) [input p16]
24. funny(susan) [input hypothesis]
25. ? [X0] : (~wise(X0) & calm(X0)) <=> ? [X1] : (calm(X1) | patient(X1)) [rectify 2]
27. ! [X0] : ((old(X0) <~> ~patient(X0)) | (~funny(X0) & old(X0))) [ennf transformation 5]
33. (? [X0] : (~wise(X0) & calm(X0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & (? [X1] : (calm(X1) | patient(X1)) | ! [X0] : (wise(X0) | ~calm(X0))) [nnf transformation 25]
34. (? [X0] : (~wise(X0) & calm(X0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & (? [X2] : (calm(X2) | patient(X2)) | ! [X3] : (wise(X3) | ~calm(X3))) [rectify 33]
35. ? [X0] : (~wise(X0) & calm(X0)) => (~wise(sK0) & calm(sK0)) [choice axiom]
36. ? [X2] : (calm(X2) | patient(X2)) => (calm(sK1) | patient(sK1)) [choice axiom]
37. ((~wise(sK0) & calm(sK0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & ((calm(sK1) | patient(sK1)) | ! [X3] : (wise(X3) | ~calm(X3))) [skolemisation 34,36,35]
43. ! [X0] : (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~funny(X0) & old(X0))) [nnf transformation 27]
46. ! [X0] : ((~calm(X0) | (wise(X0) & ~creative(X0))) & ((~wise(X0) | creative(X0)) | calm(X0))) [nnf transformation 7]
47. ! [X0] : ((~calm(X0) | (wise(X0) & ~creative(X0))) & (~wise(X0) | creative(X0) | calm(X0))) [flattening 46]
52. ! [X0] : (((~funny(X0) | humble(X0)) | generous(X0)) & (~generous(X0) | (funny(X0) & ~humble(X0)))) [nnf transformation 12]
53. ! [X0] : ((~funny(X0) | humble(X0) | generous(X0)) & (~generous(X0) | (funny(X0) & ~humble(X0)))) [flattening 52]
60. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [flattening 60]
82. calm(sK0) | ~patient(X1) [cnf transformation 37]
84. ~wise(sK0) | ~patient(X1) [cnf transformation 37]
95. ~funny(X0) | ~old(X0) | patient(X0) [cnf transformation 43]
101. ~calm(X0) | wise(X0) [cnf transformation 47]
113. ~humble(X0) | ~generous(X0) [cnf transformation 53]
115. ~funny(X0) | humble(X0) | generous(X0) [cnf transformation 53]
125. humble(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
133. ~humble(susan) [cnf transformation 17]
142. funny(susan) [cnf transformation 24]
148. 2 <=> wise(sK0) [avatar definition]
153. 3 <=> ! [X1] : ~patient(X1) [avatar definition]
154. ~patient(X1) <- (3) [avatar component clause 153]
155. 3 | ~2 [avatar split clause 84,148,153]
157. 4 <=> calm(sK0) [avatar definition]
159. calm(sK0) <- (4) [avatar component clause 157]
161. 3 | 4 [avatar split clause 82,157,153]
163. 5 <=> ! [X3] : (wise(X3) | ~calm(X3)) [avatar definition]
164. ~calm(X3) | wise(X3) <- (5) [avatar component clause 163]
217. 5 [avatar split clause 101,163]
254. ~generous(X0) | old(X0) [subsumption resolution 125,113]
278. wise(sK0) <- (4, 5) [resolution 164,159]
281. 2 | ~4 | ~5 [avatar split clause 278,163,157,148]
285. ~old(susan) | patient(susan) [resolution 95,142]
286. ~old(susan) <- (3) [subsumption resolution 285,154]
295. humble(susan) | generous(susan) [resolution 115,142]
296. generous(susan) [subsumption resolution 295,133]
297. old(susan) [resolution 296,254]
300. $false <- (3) [subsumption resolution 297,286]
301. ~3 [avatar contradiction clause 300]
302. $false [avatar sat refutation 155,161,217,281,301]
% SZS output end Proof for 387655058182514287663483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is old and vice versa.
If john is both not curious and calm then lucy is tall.
Everyone who is either not patient or kind is both not rich and patient and vice versa.
Everyone who is not humble or not patient is either not happy or not brave and vice versa.
Everyone who is strong or curious is not happy and vice versa.
If mary is both not calm and humble then someone is generous or patient.
Everyone who is both brave and not curious is not patient or not brave and vice versa.
If paul is either humble or not happy then someone is both happy and kind.
Everyone who is curious or not kind is not kind and vice versa.
If someone is both old and humble then paul is either generous or not kind and vice versa.
If susan is not generous or old then someone is not brave or not curious.
Everyone who is calm is both not creative and funny and vice versa.
If someone is wise or not wise then someone is rich.
Everyone who is rich or old is both patient and not old.
Everyone who is not quiet is curious and vice versa.
Mary is brave.
Someone is creative or not rich.
John is either strong or humble.
Someone is either rich or not patient.
Someone is either brave or quiet.
Someone is both brave and humble.
Susan is both not humble and not happy. | Susan is creative. | neutral | (![X]:(wise(X)<=>old(X)))&
(((~curious(john)&calm(john)))=>(tall(lucy)))&
(![X]:((~patient(X)<~>kind(X))<=>(~rich(X)&patient(X))))&
(![X]:((~humble(X)|~patient(X))<=>(~happy(X)<~>~brave(X))))&
(![X]:((strong(X)|curious(X))<=>~happy(X)))&
(((~calm(mary)&humble(mary)))=>(?[X]:((generous(X)|patient(X)))))&
(![X]:((brave(X)&~curious(X))<=>(~patient(X)|~brave(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((curious(X)|~kind(X))<=>~kind(X)))&
((?[X]:((old(X)&humble(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~generous(susan)|old(susan)))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(calm(X)<=>(~creative(X)&funny(X))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|old(X))=>(patient(X)&~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
(brave(mary))&
(?[X]:((creative(X)|~rich(X))))&
((strong(john)<~>humble(john)))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((brave(X)&humble(X))))&
((~humble(susan)&~happy(susan))) | creative(susan) | [] | null | 0 |
If someone is either not rich or generous then fred is either calm or not old and vice versa. Everyone who is curious or brave is either happy or not patient and vice versa. Everyone who is both not quiet and not patient is brave or humble. Everyone who is both not funny and generous is wise or not tall. Everyone who is either brave or tall is happy or not quiet. If paul is both strong and not tall then someone is happy or curious. Everyone who is not kind or curious is humble. Everyone who is calm is either not old or not tall. If someone is either calm or creative then paul is both generous and not generous and vice versa. Everyone who is both calm and not kind is either not funny or not humble and vice versa. If lucy is not quiet or not funny then lucy is either rich or strong and vice versa. If john is not creative then someone is old or not kind. If someone is humble or not curious then someone is happy and vice versa. If paul is patient then susan is either not patient or funny and vice versa. Everyone who is curious is not curious. Susan is not creative. Someone is not brave or calm. Someone is creative. Someone is either creative or brave. Alice is not wise. Mary is strong or not tall. Fred is patient. Susan is both rich and generous. | Lucy is generous. | neutral | ((?[X]:((~rich(X)<~>generous(X))))<=>((calm(fred)<~>~old(fred))))&
(![X]:((curious(X)|brave(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~patient(X))=>(brave(X)|humble(X))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)|~tall(X))))&
(![X]:((brave(X)<~>tall(X))=>(happy(X)|~quiet(X))))&
(((strong(paul)&~tall(paul)))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:((~kind(X)|curious(X))=>humble(X)))&
(![X]:(calm(X)=>(~old(X)<~>~tall(X))))&
((?[X]:((calm(X)<~>creative(X))))<=>((generous(paul)&~generous(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>~humble(X))))&
(((~quiet(lucy)|~funny(lucy)))<=>((rich(lucy)<~>strong(lucy))))&
((~creative(john))=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:(happy(X))))&
((patient(paul))<=>((~patient(susan)<~>funny(susan))))&
(![X]:(curious(X)=>~curious(X)))&
(~creative(susan))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)<~>brave(X))))&
(~wise(alice))&
((strong(mary)|~tall(mary)))&
(patient(fred))&
((rich(susan)&generous(susan))) | generous(lucy) | [] | null | 0 |
If fred is either not calm or not curious then alice is strong or not funny and vice versa. Everyone who is not patient is not quiet or old. Everyone who is strong is happy or old. If lucy is not calm or not humble then john is both not happy and patient. If susan is not rich then someone is either quiet or not old and vice versa. If someone is either not humble or humble then paul is wise or quiet and vice versa. Everyone who is not kind or curious is both quiet and not curious. Everyone who is old or patient is both patient and strong. Everyone who is tall is not strong and vice versa. Everyone who is either not curious or not happy is both not patient and tall and vice versa. Everyone who is either humble or old is either not kind or old. If someone is not funny or not patient then someone is both wise and not brave. If lucy is not rich or funny then mary is not patient or generous and vice versa. If susan is not happy then alice is either not funny or not strong and vice versa. If someone is funny then someone is both not old and kind. If someone is either not old or funny then john is either calm or not creative. Alice is not generous or not wise. Someone is strong or not generous. Someone is rich or creative. Alice is both wise and strong. Susan is not rich. Lucy is not tall or not patient. Someone is rich. Paul is not tall. | Lucy is not curious. | entailment | (((~calm(fred)<~>~curious(fred)))<=>((strong(alice)|~funny(alice))))&
(![X]:(~patient(X)=>(~quiet(X)|old(X))))&
(![X]:(strong(X)=>(happy(X)|old(X))))&
(((~calm(lucy)|~humble(lucy)))=>((~happy(john)&patient(john))))&
((~rich(susan))<=>(?[X]:((quiet(X)<~>~old(X)))))&
((?[X]:((~humble(X)<~>humble(X))))<=>((wise(paul)|quiet(paul))))&
(![X]:((~kind(X)|curious(X))=>(quiet(X)&~curious(X))))&
(![X]:((old(X)|patient(X))=>(patient(X)&strong(X))))&
(![X]:(tall(X)<=>~strong(X)))&
(![X]:((~curious(X)<~>~happy(X))<=>(~patient(X)&tall(X))))&
(![X]:((humble(X)<~>old(X))=>(~kind(X)<~>old(X))))&
((?[X]:((~funny(X)|~patient(X))))=>(?[X]:((wise(X)&~brave(X)))))&
(((~rich(lucy)|funny(lucy)))<=>((~patient(mary)|generous(mary))))&
((~happy(susan))<=>((~funny(alice)<~>~strong(alice))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:((~old(X)<~>funny(X))))=>((calm(john)<~>~creative(john))))&
((~generous(alice)|~wise(alice)))&
(?[X]:((strong(X)|~generous(X))))&
(?[X]:((rich(X)|creative(X))))&
((wise(alice)&strong(alice)))&
(~rich(susan))&
((~tall(lucy)|~patient(lucy)))&
(?[X]:(rich(X)))&
(~tall(paul)) | ~curious(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6698631482843228193887456
% SZS output start Proof for 6698631482843228193887456
7. ! [X0] : ((curious(X0) | ~kind(X0)) => (~curious(X0) & quiet(X0))) [input p6]
25. curious(lucy) [input hypothesis]
34. ! [X0] : ((~curious(X0) & quiet(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 7]
96. ~curious(X0) | ~curious(X0) [cnf transformation 34]
138. curious(lucy) [cnf transformation 25]
141. ~curious(X0) [duplicate literal removal 96]
337. $false [subsumption resolution 138,141]
% SZS output end Proof for 6698631482843228193887456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is creative is not wise.
If someone is either not creative or tall then someone is old.
Everyone who is patient or not generous is both strong and generous and vice versa.
Everyone who is not tall or humble is either creative or quiet and vice versa.
Everyone who is not calm is both old and generous and vice versa.
Everyone who is strong or calm is both tall and funny and vice versa.
Everyone who is curious or not calm is not rich or happy.
If someone is patient then mary is both rich and not kind.
Everyone who is wise or rich is not generous and vice versa.
Everyone who is either generous or patient is either not tall or humble.
Everyone who is not strong is both happy and humble.
Everyone who is either calm or funny is either tall or not calm and vice versa.
If someone is either wise or rich then alice is not kind and vice versa.
Everyone who is either not old or calm is not tall.
Everyone who is both generous and tall is not brave.
Someone is either kind or not generous.
Someone is not happy or not creative.
Mary is not patient.
Someone is not funny or not wise.
Fred is either not brave or curious. | Alice is brave. | contradiction | (![X]:(creative(X)=>~wise(X)))&
((?[X]:((~creative(X)<~>tall(X))))=>(?[X]:(old(X))))&
(![X]:((patient(X)|~generous(X))<=>(strong(X)&generous(X))))&
(![X]:((~tall(X)|humble(X))<=>(creative(X)<~>quiet(X))))&
(![X]:(~calm(X)<=>(old(X)&generous(X))))&
(![X]:((strong(X)|calm(X))<=>(tall(X)&funny(X))))&
(![X]:((curious(X)|~calm(X))=>(~rich(X)|happy(X))))&
((?[X]:(patient(X)))=>((rich(mary)&~kind(mary))))&
(![X]:((wise(X)|rich(X))<=>~generous(X)))&
(![X]:((generous(X)<~>patient(X))=>(~tall(X)<~>humble(X))))&
(![X]:(~strong(X)=>(happy(X)&humble(X))))&
(![X]:((calm(X)<~>funny(X))<=>(tall(X)<~>~calm(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(~kind(alice)))&
(![X]:((~old(X)<~>calm(X))=>~tall(X)))&
(![X]:((generous(X)&tall(X))=>~brave(X)))&
(?[X]:((kind(X)<~>~generous(X))))&
(?[X]:((~happy(X)|~creative(X))))&
(~patient(mary))&
(?[X]:((~funny(X)|~wise(X))))&
((~brave(fred)<~>curious(fred))) | brave(alice) | [
"p2",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2796085521794747600285912
% SZS output start Proof for 2796085521794747600285912
3. ! [X0] : ((~generous(X0) | patient(X0)) <=> (generous(X0) & strong(X0))) [input p2]
6. ! [X0] : ((calm(X0) | strong(X0)) <=> (funny(X0) & tall(X0))) [input p5]
8. ? [X0] : patient(X0) => (~kind(mary) & rich(mary)) [input p7]
9. ! [X0] : ((rich(X0) | wise(X0)) <=> ~generous(X0)) [input p8]
10. ! [X0] : ((generous(X0) <~> patient(X0)) => (~tall(X0) <~> humble(X0))) [input p9]
11. ! [X0] : (~strong(X0) => (humble(X0) & happy(X0))) [input p10]
15. ! [X0] : ((tall(X0) & generous(X0)) => ~brave(X0)) [input p14]
21. brave(alice) [input hypothesis]
27. (~kind(mary) & rich(mary)) | ! [X0] : ~patient(X0) [ennf transformation 8]
28. ! [X0] : ((~tall(X0) <~> humble(X0)) | (generous(X0) <=> patient(X0))) [ennf transformation 10]
29. ! [X0] : ((humble(X0) & happy(X0)) | strong(X0)) [ennf transformation 11]
31. ! [X0] : (~brave(X0) | (~tall(X0) | ~generous(X0))) [ennf transformation 15]
32. ! [X0] : (~brave(X0) | ~tall(X0) | ~generous(X0)) [flattening 31]
37. ! [X0] : (((~generous(X0) | patient(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (generous(X0) & ~patient(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | patient(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (generous(X0) & ~patient(X0)))) [flattening 37]
43. ! [X0] : (((calm(X0) | strong(X0)) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 6]
44. ! [X0] : ((calm(X0) | strong(X0) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 43]
45. ! [X0] : (((rich(X0) | wise(X0)) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~wise(X0)))) [nnf transformation 9]
46. ! [X0] : ((rich(X0) | wise(X0) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~wise(X0)))) [flattening 45]
47. ! [X0] : (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) [nnf transformation 28]
68. generous(X0) | generous(X0) [cnf transformation 38]
79. ~strong(X0) | tall(X0) [cnf transformation 44]
86. rich(mary) | ~patient(X0) [cnf transformation 27]
89. ~generous(X0) | ~rich(X0) [cnf transformation 46]
93. ~humble(X0) | tall(X0) | patient(X0) | ~generous(X0) [cnf transformation 47]
96. humble(X0) | strong(X0) [cnf transformation 29]
111. ~brave(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 32]
119. brave(alice) [cnf transformation 21]
124. generous(X0) [duplicate literal removal 68]
140. 4 <=> ! [X0] : ~patient(X0) [avatar definition]
141. ~patient(X0) <- (4) [avatar component clause 140]
148. 6 <=> rich(mary) [avatar definition]
150. rich(mary) <- (6) [avatar component clause 148]
151. 4 | 6 [avatar split clause 86,148,140]
152. ~rich(X0) [subsumption resolution 89,124]
154. ~humble(X0) | tall(X0) | patient(X0) [subsumption resolution 93,124]
162. ~brave(X0) | ~tall(X0) [subsumption resolution 111,124]
188. ~tall(alice) [resolution 162,119]
193. tall(X0) | patient(X0) | strong(X0) [resolution 154,96]
194. tall(X0) | strong(X0) <- (4) [subsumption resolution 193,141]
195. tall(X0) <- (4) [subsumption resolution 194,79]
196. $false <- (4) [resolution 195,188]
197. ~4 [avatar contradiction clause 196]
200. $false <- (6) [subsumption resolution 150,152]
201. ~6 [avatar contradiction clause 200]
202. $false [avatar sat refutation 151,197,201]
% SZS output end Proof for 2796085521794747600285912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is curious or funny then lucy is either not tall or not strong and vice versa. If mary is not calm or quiet then someone is not humble and vice versa. Everyone who is not quiet is not rich. Everyone who is either quiet or not calm is both not strong and not quiet and vice versa. Everyone who is wise or calm is not funny and vice versa. If someone is both humble and not patient then john is both quiet and creative and vice versa. If someone is not brave or not patient then alice is rich or humble. If mary is both humble and not patient then lucy is old or not tall and vice versa. If lucy is both not quiet and not creative then paul is either calm or brave and vice versa. Everyone who is both curious and not strong is either not wise or curious. Everyone who is either not calm or not generous is not brave or not rich and vice versa. If lucy is not old then someone is not kind and vice versa. Everyone who is either happy or not humble is not happy and vice versa. Everyone who is humble or rich is either calm or brave and vice versa. Everyone who is not humble or tall is either not brave or quiet. If someone is both tall and patient then someone is not happy. Someone is not old. Fred is either generous or patient. Alice is not funny or not humble. Lucy is not brave. Susan is curious. Someone is both rich and quiet. Susan is not quiet. | Fred is not creative. | neutral | (((curious(alice)|funny(alice)))<=>((~tall(lucy)<~>~strong(lucy))))&
(((~calm(mary)|quiet(mary)))<=>(?[X]:(~humble(X))))&
(![X]:(~quiet(X)=>~rich(X)))&
(![X]:((quiet(X)<~>~calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((wise(X)|calm(X))<=>~funny(X)))&
((?[X]:((humble(X)&~patient(X))))<=>((quiet(john)&creative(john))))&
((?[X]:((~brave(X)|~patient(X))))=>((rich(alice)|humble(alice))))&
(((humble(mary)&~patient(mary)))<=>((old(lucy)|~tall(lucy))))&
(((~quiet(lucy)&~creative(lucy)))<=>((calm(paul)<~>brave(paul))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~happy(X)))&
(![X]:((humble(X)|rich(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~humble(X)|tall(X))=>(~brave(X)<~>quiet(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~happy(X))))&
(?[X]:(~old(X)))&
((generous(fred)<~>patient(fred)))&
((~funny(alice)|~humble(alice)))&
(~brave(lucy))&
(curious(susan))&
(?[X]:((rich(X)&quiet(X))))&
(~quiet(susan)) | ~creative(fred) | [] | null | 0 |
Everyone who is brave is both not tall and quiet.
If john is either not patient or not quiet then lucy is either kind or not wise.
Everyone who is creative or not humble is either not kind or not rich and vice versa.
Everyone who is either funny or curious is calm or not humble and vice versa.
Everyone who is kind or not happy is either curious or not humble and vice versa.
Everyone who is not tall or not old is either not generous or strong and vice versa.
Everyone who is not patient or not humble is either not humble or not curious and vice versa.
Everyone who is not wise is not calm.
Everyone who is both not rich and patient is either kind or not patient.
If someone is either not kind or not happy then someone is creative.
If someone is not kind or not tall then paul is calm and vice versa.
If lucy is both brave and not strong then someone is either not humble or patient and vice versa.
Everyone who is either not tall or not humble is either not quiet or not humble and vice versa.
If fred is wise then fred is both not rich and happy and vice versa.
If lucy is both not funny and wise then someone is both not creative and not brave.
Everyone who is either not happy or creative is curious or not calm.
Paul is tall.
Mary is not strong.
Someone is not quiet.
Fred is either tall or not old.
Someone is both not curious and old.
Someone is both curious and not generous. | Paul is not rich. | neutral | (![X]:(brave(X)=>(~tall(X)&quiet(X))))&
(((~patient(john)<~>~quiet(john)))=>((kind(lucy)<~>~wise(lucy))))&
(![X]:((creative(X)|~humble(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((funny(X)<~>curious(X))<=>(calm(X)|~humble(X))))&
(![X]:((kind(X)|~happy(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((~tall(X)|~old(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((~patient(X)|~humble(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(~wise(X)=>~calm(X)))&
(![X]:((~rich(X)&patient(X))=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:(creative(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(calm(paul)))&
(((brave(lucy)&~strong(lucy)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(~quiet(X)<~>~humble(X))))&
((wise(fred))<=>((~rich(fred)&happy(fred))))&
(((~funny(lucy)&wise(lucy)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(curious(X)|~calm(X))))&
(tall(paul))&
(~strong(mary))&
(?[X]:(~quiet(X)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((~curious(X)&old(X))))&
(?[X]:((curious(X)&~generous(X)))) | ~rich(paul) | [] | null | 0 |
If someone is not kind or not creative then lucy is not generous and vice versa.
Everyone who is not brave or not quiet is both creative and not kind.
Everyone who is both not patient and not wise is not wise.
If someone is not funny then lucy is either rich or strong and vice versa.
Everyone who is happy or not rich is not wise or kind.
Everyone who is curious is humble or not rich and vice versa.
If fred is old then someone is either not strong or not quiet.
Everyone who is both not quiet and funny is both quiet and not calm.
Everyone who is creative is old or not patient.
Everyone who is both strong and kind is not wise.
If mary is rich then fred is wise and vice versa.
If someone is not calm or funny then susan is either generous or not quiet.
If alice is both kind and not patient then someone is not generous or not rich.
Everyone who is both not happy and brave is either not humble or rich and vice versa.
Everyone who is both not curious and not rich is curious or not generous and vice versa.
If susan is not calm then john is both not curious and wise and vice versa.
Someone is not tall or patient.
Someone is brave or kind.
John is not tall.
Someone is curious or rich.
Fred is funny.
Someone is both not funny and not wise.
Alice is not patient or strong.
Someone is not generous or patient. | Alice is old. | entailment | ((?[X]:((~kind(X)|~creative(X))))<=>(~generous(lucy)))&
(![X]:((~brave(X)|~quiet(X))=>(creative(X)&~kind(X))))&
(![X]:((~patient(X)&~wise(X))=>~wise(X)))&
((?[X]:(~funny(X)))<=>((rich(lucy)<~>strong(lucy))))&
(![X]:((happy(X)|~rich(X))=>(~wise(X)|kind(X))))&
(![X]:(curious(X)<=>(humble(X)|~rich(X))))&
((old(fred))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)&funny(X))=>(quiet(X)&~calm(X))))&
(![X]:(creative(X)=>(old(X)|~patient(X))))&
(![X]:((strong(X)&kind(X))=>~wise(X)))&
((rich(mary))<=>(wise(fred)))&
((?[X]:((~calm(X)|funny(X))))=>((generous(susan)<~>~quiet(susan))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((brave(X)|kind(X))))&
(~tall(john))&
(?[X]:((curious(X)|rich(X))))&
(funny(fred))&
(?[X]:((~funny(X)&~wise(X))))&
((~patient(alice)|strong(alice)))&
(?[X]:((~generous(X)|patient(X)))) | old(alice) | [
"p0",
"p5",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2891707309499167137459749
% SZS output start Proof for 2891707309499167137459749
1. ? [X0] : (~creative(X0) | ~kind(X0)) <=> ~generous(lucy) [input p0]
6. ! [X0] : (curious(X0) <=> (~rich(X0) | humble(X0))) [input p5]
9. ! [X0] : (creative(X0) => (~patient(X0) | old(X0))) [input p8]
13. (~patient(alice) & kind(alice)) => ? [X0] : (~rich(X0) | ~generous(X0)) [input p12]
15. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~generous(X0) | curious(X0))) [input p14]
25. ~old(alice) [input hypothesis]
36. ! [X0] : ((~patient(X0) | old(X0)) | ~creative(X0)) [ennf transformation 9]
37. ! [X0] : (~patient(X0) | old(X0) | ~creative(X0)) [flattening 36]
41. ? [X0] : (~rich(X0) | ~generous(X0)) | (patient(alice) | ~kind(alice)) [ennf transformation 13]
42. ? [X0] : (~rich(X0) | ~generous(X0)) | patient(alice) | ~kind(alice) [flattening 41]
43. (? [X0] : (~creative(X0) | ~kind(X0)) | generous(lucy)) & (~generous(lucy) | ! [X0] : (creative(X0) & kind(X0))) [nnf transformation 1]
44. (? [X0] : (~creative(X0) | ~kind(X0)) | generous(lucy)) & (~generous(lucy) | ! [X1] : (creative(X1) & kind(X1))) [rectify 43]
45. ? [X0] : (~creative(X0) | ~kind(X0)) => (~creative(sK0) | ~kind(sK0)) [choice axiom]
46. ((~creative(sK0) | ~kind(sK0)) | generous(lucy)) & (~generous(lucy) | ! [X1] : (creative(X1) & kind(X1))) [skolemisation 44,45]
51. ! [X0] : ((curious(X0) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | ~curious(X0))) [nnf transformation 6]
52. ! [X0] : ((curious(X0) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | ~curious(X0))) [flattening 51]
58. ? [X0] : (~rich(X0) | ~generous(X0)) => (~rich(sK3) | ~generous(sK3)) [choice axiom]
59. (~rich(sK3) | ~generous(sK3)) | patient(alice) | ~kind(alice) [skolemisation 42,58]
62. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 15]
63. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 62]
74. ~generous(lucy) | kind(X1) [cnf transformation 46]
75. ~generous(lucy) | creative(X1) [cnf transformation 46]
90. curious(X0) | rich(X0) [cnf transformation 52]
95. ~patient(X0) | old(X0) | ~creative(X0) [cnf transformation 37]
103. ~rich(sK3) | ~generous(sK3) | patient(alice) | ~kind(alice) [cnf transformation 59]
111. ~curious(X0) | ~curious(X0) [cnf transformation 63]
114. ~rich(X0) | generous(X0) [cnf transformation 63]
125. ~old(alice) [cnf transformation 25]
127. ~curious(X0) [duplicate literal removal 111]
130. 1 <=> generous(lucy) [avatar definition]
131. ~generous(lucy) <- (~1) [avatar component clause 130]
143. 4 <=> ! [X1] : creative(X1) [avatar definition]
144. creative(X1) <- (4) [avatar component clause 143]
145. 4 | ~1 [avatar split clause 75,130,143]
147. 5 <=> ! [X1] : kind(X1) [avatar definition]
148. kind(X1) <- (5) [avatar component clause 147]
149. 5 | ~1 [avatar split clause 74,130,147]
212. 19 <=> kind(alice) [avatar definition]
214. ~kind(alice) <- (~19) [avatar component clause 212]
216. 20 <=> patient(alice) [avatar definition]
218. patient(alice) <- (20) [avatar component clause 216]
220. 21 <=> generous(sK3) [avatar definition]
222. ~generous(sK3) <- (~21) [avatar component clause 220]
224. 22 <=> rich(sK3) [avatar definition]
226. ~rich(sK3) <- (~22) [avatar component clause 224]
227. ~19 | 20 | ~21 | ~22 [avatar split clause 103,224,220,216,212]
255. rich(X0) [resolution 90,127]
262. generous(X0) [resolution 114,255]
263. $false <- (~1) [resolution 262,131]
265. $false <- (~21) [resolution 262,222]
268. 21 [avatar contradiction clause 265]
270. 1 [avatar contradiction clause 263]
271. $false <- (~22) [subsumption resolution 226,255]
272. 22 [avatar contradiction clause 271]
273. $false <- (5, ~19) [subsumption resolution 214,148]
274. ~5 | 19 [avatar contradiction clause 273]
283. old(alice) | ~creative(alice) <- (20) [resolution 95,218]
285. ~creative(alice) <- (20) [subsumption resolution 283,125]
286. $false <- (4, 20) [subsumption resolution 285,144]
287. ~4 | ~20 [avatar contradiction clause 286]
289. $false [avatar sat refutation 145,149,227,268,270,272,274,287]
% SZS output end Proof for 2891707309499167137459749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and quiet is either not quiet or patient and vice versa.
Everyone who is either funny or rich is not curious or not funny.
If someone is not humble then someone is both not kind and not quiet and vice versa.
If someone is not tall or not creative then paul is strong.
If lucy is both curious and creative then susan is either not curious or not patient and vice versa.
If someone is not funny then fred is either wise or not generous.
Everyone who is curious is not quiet or brave.
If someone is both not curious and not old then someone is strong.
Everyone who is both humble and tall is both funny and creative.
Everyone who is not humble is happy or not happy and vice versa.
Everyone who is either not creative or brave is kind.
Everyone who is both not rich and not funny is old.
If someone is not quiet or kind then fred is curious or not funny and vice versa.
Everyone who is not rich or rich is not old and vice versa.
If someone is not funny then someone is not tall or wise.
If someone is both not wise and generous then someone is wise.
Someone is either tall or curious.
John is kind or wise.
Someone is brave.
John is not generous or generous.
Susan is creative.
Someone is patient.
Paul is either not brave or creative.
Susan is funny or not strong. | Susan is not tall. | neutral | (![X]:((~humble(X)&quiet(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((funny(X)<~>rich(X))=>(~curious(X)|~funny(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:((~tall(X)|~creative(X))))=>(strong(paul)))&
(((curious(lucy)&creative(lucy)))<=>((~curious(susan)<~>~patient(susan))))&
((?[X]:(~funny(X)))=>((wise(fred)<~>~generous(fred))))&
(![X]:(curious(X)=>(~quiet(X)|brave(X))))&
((?[X]:((~curious(X)&~old(X))))=>(?[X]:(strong(X))))&
(![X]:((humble(X)&tall(X))=>(funny(X)&creative(X))))&
(![X]:(~humble(X)<=>(happy(X)|~happy(X))))&
(![X]:((~creative(X)<~>brave(X))=>kind(X)))&
(![X]:((~rich(X)&~funny(X))=>old(X)))&
((?[X]:((~quiet(X)|kind(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((~rich(X)|rich(X))<=>~old(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~tall(X)|wise(X)))))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:(wise(X))))&
(?[X]:((tall(X)<~>curious(X))))&
((kind(john)|wise(john)))&
(?[X]:(brave(X)))&
((~generous(john)|generous(john)))&
(creative(susan))&
(?[X]:(patient(X)))&
((~brave(paul)<~>creative(paul)))&
((funny(susan)|~strong(susan))) | ~tall(susan) | [] | null | 0 |
If paul is both not funny and funny then someone is either not strong or not old. Everyone who is not wise is either quiet or funny. If someone is brave or generous then fred is not curious and vice versa. Everyone who is kind or rich is wise or not calm and vice versa. Everyone who is either not brave or not wise is not rich and vice versa. If someone is patient then paul is not kind and vice versa. Everyone who is either curious or not creative is either not quiet or wise and vice versa. Everyone who is creative or generous is both not tall and wise. If mary is either not tall or not happy then alice is wise. Everyone who is either brave or not curious is generous. Everyone who is brave is humble or calm and vice versa. Everyone who is creative is both happy and not funny and vice versa. Everyone who is not wise is not funny or brave. If alice is not kind then mary is not strong. If someone is quiet or funny then paul is rich. If susan is either happy or not tall then john is both brave and generous. John is not creative or rich. Someone is either not tall or not quiet. Susan is either not creative or not generous. Fred is not old. Someone is kind or not funny. Alice is either funny or not quiet. Someone is either not old or not rich. Someone is not curious or strong. | Susan is not tall. | entailment | (((~funny(paul)&funny(paul)))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:(~wise(X)=>(quiet(X)<~>funny(X))))&
((?[X]:((brave(X)|generous(X))))<=>(~curious(fred)))&
(![X]:((kind(X)|rich(X))<=>(wise(X)|~calm(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>~rich(X)))&
((?[X]:(patient(X)))<=>(~kind(paul)))&
(![X]:((curious(X)<~>~creative(X))<=>(~quiet(X)<~>wise(X))))&
(![X]:((creative(X)|generous(X))=>(~tall(X)&wise(X))))&
(((~tall(mary)<~>~happy(mary)))=>(wise(alice)))&
(![X]:((brave(X)<~>~curious(X))=>generous(X)))&
(![X]:(brave(X)<=>(humble(X)|calm(X))))&
(![X]:(creative(X)<=>(happy(X)&~funny(X))))&
(![X]:(~wise(X)=>(~funny(X)|brave(X))))&
((~kind(alice))=>(~strong(mary)))&
((?[X]:((quiet(X)|funny(X))))=>(rich(paul)))&
(((happy(susan)<~>~tall(susan)))=>((brave(john)&generous(john))))&
((~creative(john)|rich(john)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((~creative(susan)<~>~generous(susan)))&
(~old(fred))&
(?[X]:((kind(X)|~funny(X))))&
((funny(alice)<~>~quiet(alice)))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~curious(X)|strong(X)))) | ~tall(susan) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1398572771762678930253986
% SZS output start Proof for 1398572771762678930253986
8. ! [X0] : ((generous(X0) | creative(X0)) => (wise(X0) & ~tall(X0))) [input p7]
19. ~creative(susan) <~> ~generous(susan) [input p18]
25. tall(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~tall(X0)) | (~generous(X0) & ~creative(X0))) [ennf transformation 8]
63. (generous(susan) | creative(susan)) & (~generous(susan) | ~creative(susan)) [nnf transformation 19]
97. ~tall(X0) | ~creative(X0) [cnf transformation 29]
98. ~tall(X0) | ~generous(X0) [cnf transformation 29]
123. generous(susan) | creative(susan) [cnf transformation 63]
131. tall(susan) [cnf transformation 25]
202. 17 <=> tall(susan) [avatar definition]
204. tall(susan) <- (17) [avatar component clause 202]
241. 25 <=> creative(susan) [avatar definition]
245. 26 <=> generous(susan) [avatar definition]
247. generous(susan) <- (26) [avatar component clause 245]
248. 25 | 26 [avatar split clause 123,245,241]
288. 17 [avatar split clause 131,202]
289. ~creative(susan) <- (17) [resolution 97,204]
293. ~25 | ~17 [avatar split clause 289,202,241]
294. ~generous(susan) <- (17) [resolution 98,204]
296. $false <- (17, 26) [subsumption resolution 294,247]
297. ~17 | ~26 [avatar contradiction clause 296]
298. $false [avatar sat refutation 248,288,293,297]
% SZS output end Proof for 1398572771762678930253986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and not creative then mary is not funny or not quiet.
Everyone who is both not kind and wise is calm or generous and vice versa.
If someone is generous or creative then someone is both not funny and funny.
Everyone who is not calm is not humble and vice versa.
If someone is patient or happy then someone is both strong and creative.
If someone is either not strong or generous then someone is old or calm and vice versa.
Everyone who is both not generous and not strong is not kind.
Everyone who is either tall or quiet is both patient and brave.
If someone is wise then john is not kind or calm.
Everyone who is humble or not creative is both calm and not funny and vice versa.
Everyone who is curious is not brave or old and vice versa.
Everyone who is either not quiet or not curious is either not creative or not wise and vice versa.
If someone is either not wise or rich then someone is not creative or not calm.
Everyone who is not creative is calm.
Everyone who is either humble or quiet is both old and generous and vice versa.
Someone is not creative.
Paul is humble.
Lucy is both not curious and quiet.
Paul is either not quiet or not rich. | John is happy. | contradiction | ((?[X]:((~quiet(X)&~creative(X))))=>((~funny(mary)|~quiet(mary))))&
(![X]:((~kind(X)&wise(X))<=>(calm(X)|generous(X))))&
((?[X]:((generous(X)|creative(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
((?[X]:((patient(X)|happy(X))))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
(![X]:((tall(X)<~>quiet(X))=>(patient(X)&brave(X))))&
((?[X]:(wise(X)))=>((~kind(john)|calm(john))))&
(![X]:((humble(X)|~creative(X))<=>(calm(X)&~funny(X))))&
(![X]:(curious(X)<=>(~brave(X)|old(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>rich(X))))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:(~creative(X)=>calm(X)))&
(![X]:((humble(X)<~>quiet(X))<=>(old(X)&generous(X))))&
(?[X]:(~creative(X)))&
(humble(paul))&
((~curious(lucy)&quiet(lucy)))&
((~quiet(paul)<~>~rich(paul))) | happy(john) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 246296887571554207812309
% SZS output start Proof for 246296887571554207812309
3. ? [X0] : (creative(X0) | generous(X0)) => ? [X0] : (funny(X0) & ~funny(X0)) [input p2]
5. ? [X0] : (happy(X0) | patient(X0)) => ? [X0] : (creative(X0) & strong(X0)) [input p4]
20. happy(john) [input hypothesis]
21. ? [X0] : (creative(X0) | generous(X0)) => ? [X1] : (funny(X1) & ~funny(X1)) [rectify 3]
22. ? [X0] : (happy(X0) | patient(X0)) => ? [X1] : (creative(X1) & strong(X1)) [rectify 5]
27. ? [X1] : (funny(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & ~generous(X0)) [ennf transformation 21]
28. ? [X1] : (creative(X1) & strong(X1)) | ! [X0] : (~happy(X0) & ~patient(X0)) [ennf transformation 22]
38. ? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & ~generous(X1)) [rectify 27]
39. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK0) & ~funny(sK0)) [choice axiom]
40. (funny(sK0) & ~funny(sK0)) | ! [X1] : (~creative(X1) & ~generous(X1)) [skolemisation 38,39]
42. ? [X0] : (creative(X0) & strong(X0)) | ! [X1] : (~happy(X1) & ~patient(X1)) [rectify 28]
43. ? [X0] : (creative(X0) & strong(X0)) => (creative(sK1) & strong(sK1)) [choice axiom]
44. (creative(sK1) & strong(sK1)) | ! [X1] : (~happy(X1) & ~patient(X1)) [skolemisation 42,43]
72. ~funny(sK0) | ~creative(X1) [cnf transformation 40]
74. funny(sK0) | ~creative(X1) [cnf transformation 40]
80. creative(sK1) | ~happy(X1) [cnf transformation 44]
124. happy(john) [cnf transformation 20]
138. 4 <=> ! [X1] : ~creative(X1) [avatar definition]
139. ~creative(X1) <- (4) [avatar component clause 138]
141. 5 <=> funny(sK0) [avatar definition]
144. 4 | 5 [avatar split clause 74,141,138]
149. 4 | ~5 [avatar split clause 72,141,138]
152. 7 <=> ! [X1] : ~happy(X1) [avatar definition]
153. ~happy(X1) <- (7) [avatar component clause 152]
155. 8 <=> creative(sK1) [avatar definition]
157. creative(sK1) <- (8) [avatar component clause 155]
158. 7 | 8 [avatar split clause 80,155,152]
239. $false <- (7) [resolution 153,124]
240. ~7 [avatar contradiction clause 239]
241. $false <- (4, 8) [subsumption resolution 157,139]
242. ~4 | ~8 [avatar contradiction clause 241]
243. $false [avatar sat refutation 144,149,158,240,242]
% SZS output end Proof for 246296887571554207812309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind is both rich and strong.
Everyone who is both not calm and calm is humble or creative and vice versa.
Everyone who is both not funny and not patient is not kind or not patient.
If lucy is both not happy and not patient then someone is quiet or not old and vice versa.
Everyone who is both not old and brave is not funny or happy and vice versa.
If lucy is both creative and not curious then someone is either not funny or humble.
Everyone who is not patient or funny is not funny.
If someone is both not quiet and not strong then fred is not funny or calm and vice versa.
If lucy is both brave and not tall then lucy is not patient or not creative.
Everyone who is either curious or tall is happy.
If fred is rich then someone is both not creative and not brave and vice versa.
Everyone who is not quiet or tall is not funny or happy.
Everyone who is both not brave and tall is wise or not humble.
If lucy is not humble then alice is both not curious and strong and vice versa.
If someone is not tall or not calm then lucy is humble.
Someone is both patient and curious.
Alice is not curious or wise.
Someone is not wise.
Alice is not rich.
Someone is either wise or not funny.
Someone is either not rich or strong.
Susan is quiet. | Alice is creative. | contradiction | (![X]:(~kind(X)=>(rich(X)&strong(X))))&
(![X]:((~calm(X)&calm(X))<=>(humble(X)|creative(X))))&
(![X]:((~funny(X)&~patient(X))=>(~kind(X)|~patient(X))))&
(((~happy(lucy)&~patient(lucy)))<=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((~old(X)&brave(X))<=>(~funny(X)|happy(X))))&
(((creative(lucy)&~curious(lucy)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:((~patient(X)|funny(X))=>~funny(X)))&
((?[X]:((~quiet(X)&~strong(X))))<=>((~funny(fred)|calm(fred))))&
(((brave(lucy)&~tall(lucy)))=>((~patient(lucy)|~creative(lucy))))&
(![X]:((curious(X)<~>tall(X))=>happy(X)))&
((rich(fred))<=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~quiet(X)|tall(X))=>(~funny(X)|happy(X))))&
(![X]:((~brave(X)&tall(X))=>(wise(X)|~humble(X))))&
((~humble(lucy))<=>((~curious(alice)&strong(alice))))&
((?[X]:((~tall(X)|~calm(X))))=>(humble(lucy)))&
(?[X]:((patient(X)&curious(X))))&
((~curious(alice)|wise(alice)))&
(?[X]:(~wise(X)))&
(~rich(alice))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(quiet(susan)) | creative(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6549315488418554419241320
% SZS output start Proof for 6549315488418554419241320
2. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (creative(X0) | humble(X0))) [input p1]
23. creative(alice) [input hypothesis]
38. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 2]
39. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | ~calm(X0) | calm(X0))) [flattening 38]
76. ~calm(X0) | ~creative(X0) [cnf transformation 39]
78. calm(X0) | ~creative(X0) [cnf transformation 39]
123. creative(alice) [cnf transformation 23]
125. ~creative(X0) [subsumption resolution 76,78]
201. $false [subsumption resolution 123,125]
% SZS output end Proof for 6549315488418554419241320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is not patient and vice versa.
If someone is old then mary is both humble and not quiet and vice versa.
If john is both strong and curious then paul is either not old or not rich and vice versa.
Everyone who is either generous or humble is either calm or not curious.
Everyone who is not generous or rich is kind and vice versa.
Everyone who is either not patient or creative is creative.
If someone is not rich then susan is brave.
Everyone who is humble or funny is not old and vice versa.
Everyone who is not kind is rich or not old and vice versa.
Everyone who is either not brave or not rich is either not calm or curious.
If someone is either humble or tall then someone is both rich and brave and vice versa.
Everyone who is either not creative or tall is generous.
If mary is both not happy and not creative then lucy is both brave and old and vice versa.
Everyone who is not humble or not curious is not calm and vice versa.
Everyone who is kind is patient.
Everyone who is kind or generous is creative.
Someone is tall or patient.
Fred is both not old and curious.
Mary is both not strong and tall.
Susan is either happy or quiet.
Paul is either not kind or tall.
Someone is not strong.
John is both humble and patient.
Someone is wise or calm. | Fred is not tall. | contradiction | (![X]:((~tall(X)<~>~creative(X))<=>~patient(X)))&
((?[X]:(old(X)))<=>((humble(mary)&~quiet(mary))))&
(((strong(john)&curious(john)))<=>((~old(paul)<~>~rich(paul))))&
(![X]:((generous(X)<~>humble(X))=>(calm(X)<~>~curious(X))))&
(![X]:((~generous(X)|rich(X))<=>kind(X)))&
(![X]:((~patient(X)<~>creative(X))=>creative(X)))&
((?[X]:(~rich(X)))=>(brave(susan)))&
(![X]:((humble(X)|funny(X))<=>~old(X)))&
(![X]:(~kind(X)<=>(rich(X)|~old(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(~calm(X)<~>curious(X))))&
((?[X]:((humble(X)<~>tall(X))))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~creative(X)<~>tall(X))=>generous(X)))&
(((~happy(mary)&~creative(mary)))<=>((brave(lucy)&old(lucy))))&
(![X]:((~humble(X)|~curious(X))<=>~calm(X)))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((kind(X)|generous(X))=>creative(X)))&
(?[X]:((tall(X)|patient(X))))&
((~old(fred)&curious(fred)))&
((~strong(mary)&tall(mary)))&
((happy(susan)<~>quiet(susan)))&
((~kind(paul)<~>tall(paul)))&
(?[X]:(~strong(X)))&
((humble(john)&patient(john)))&
(?[X]:((wise(X)|calm(X)))) | ~tall(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"p14",
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 613827486984717272802246
% SZS output start Proof for 613827486984717272802246
1. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> ~patient(X0)) [input p0]
2. ? [X0] : old(X0) <=> (~quiet(mary) & humble(mary)) [input p1]
4. ! [X0] : ((generous(X0) <~> humble(X0)) => (calm(X0) <~> ~curious(X0))) [input p3]
5. ! [X0] : ((rich(X0) | ~generous(X0)) <=> kind(X0)) [input p4]
6. ! [X0] : ((~patient(X0) <~> creative(X0)) => creative(X0)) [input p5]
9. ! [X0] : (~kind(X0) <=> (~old(X0) | rich(X0))) [input p8]
11. ? [X0] : (humble(X0) <~> tall(X0)) <=> ? [X0] : (brave(X0) & rich(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> tall(X0)) => generous(X0)) [input p11]
14. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> ~calm(X0)) [input p13]
15. ! [X0] : (kind(X0) => patient(X0)) [input p14]
16. ! [X0] : ((generous(X0) | kind(X0)) => creative(X0)) [input p15]
18. curious(fred) & ~old(fred) [input p17]
19. tall(mary) & ~strong(mary) [input p18]
25. ~tall(fred) [input hypothesis]
26. ? [X0] : (humble(X0) <~> tall(X0)) <=> ? [X1] : (brave(X1) & rich(X1)) [rectify 11]
28. ! [X0] : ((calm(X0) <~> ~curious(X0)) | (generous(X0) <=> humble(X0))) [ennf transformation 4]
29. ! [X0] : (creative(X0) | (~patient(X0) <=> creative(X0))) [ennf transformation 6]
32. ! [X0] : (generous(X0) | (~creative(X0) <=> tall(X0))) [ennf transformation 12]
33. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 15]
34. ! [X0] : (creative(X0) | (~generous(X0) & ~kind(X0))) [ennf transformation 16]
35. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | patient(X0)) & (~patient(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 1]
36. (? [X0] : old(X0) | (quiet(mary) | ~humble(mary))) & ((~quiet(mary) & humble(mary)) | ! [X0] : ~old(X0)) [nnf transformation 2]
37. (? [X0] : old(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X0] : ~old(X0)) [flattening 36]
38. (? [X0] : old(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : ~old(X1)) [rectify 37]
39. ? [X0] : old(X0) => old(sK0) [choice axiom]
40. (old(sK0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : ~old(X1)) [skolemisation 38,39]
43. ! [X0] : (((curious(X0) | ~calm(X0)) & (~curious(X0) | calm(X0))) | ((generous(X0) | ~humble(X0)) & (humble(X0) | ~generous(X0)))) [nnf transformation 28]
44. ! [X0] : (((rich(X0) | ~generous(X0)) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | ~generous(X0) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [flattening 44]
46. ! [X0] : (creative(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 29]
49. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | kind(X0))) [nnf transformation 9]
50. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | kind(X0))) [flattening 49]
52. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ! [X1] : (~brave(X1) | ~rich(X1))) & (? [X1] : (brave(X1) & rich(X1)) | ! [X0] : ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) [nnf transformation 26]
53. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ! [X1] : (~brave(X1) | ~rich(X1))) & (? [X2] : (brave(X2) & rich(X2)) | ! [X3] : ((humble(X3) | ~tall(X3)) & (tall(X3) | ~humble(X3)))) [rectify 52]
54. ? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) => ((~tall(sK1) | ~humble(sK1)) & (tall(sK1) | humble(sK1))) [choice axiom]
55. ? [X2] : (brave(X2) & rich(X2)) => (brave(sK2) & rich(sK2)) [choice axiom]
56. (((~tall(sK1) | ~humble(sK1)) & (tall(sK1) | humble(sK1))) | ! [X1] : (~brave(X1) | ~rich(X1))) & ((brave(sK2) & rich(sK2)) | ! [X3] : ((humble(X3) | ~tall(X3)) & (tall(X3) | ~humble(X3)))) [skolemisation 53,55,54]
57. ! [X0] : (generous(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) [nnf transformation 32]
60. ! [X0] : (((~curious(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & humble(X0)))) [nnf transformation 14]
61. ! [X0] : ((~curious(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & humble(X0)))) [flattening 60]
68. ~patient(X0) | ~creative(X0) | tall(X0) [cnf transformation 35]
69. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 35]
73. ~quiet(mary) | ~old(X1) [cnf transformation 40]
74. old(sK0) | quiet(mary) | ~humble(mary) [cnf transformation 40]
81. ~generous(X0) | calm(X0) | humble(X0) | ~curious(X0) [cnf transformation 43]
85. kind(X0) | generous(X0) [cnf transformation 45]
86. ~rich(X0) | kind(X0) [cnf transformation 45]
87. ~kind(X0) | ~generous(X0) | rich(X0) [cnf transformation 45]
88. creative(X0) | creative(X0) | patient(X0) [cnf transformation 46]
94. ~old(X0) | rich(X0) | kind(X0) [cnf transformation 50]
95. ~kind(X0) | ~rich(X0) [cnf transformation 50]
96. ~kind(X0) | old(X0) [cnf transformation 50]
101. rich(sK2) | tall(X3) | ~humble(X3) [cnf transformation 56]
102. rich(sK2) | humble(X3) | ~tall(X3) [cnf transformation 56]
107. generous(X0) | tall(X0) | creative(X0) [cnf transformation 57]
108. ~creative(X0) | generous(X0) | ~tall(X0) [cnf transformation 57]
113. ~calm(X0) | humble(X0) [cnf transformation 61]
116. ~kind(X0) | patient(X0) [cnf transformation 33]
118. ~generous(X0) | creative(X0) [cnf transformation 34]
121. curious(fred) [cnf transformation 18]
123. tall(mary) [cnf transformation 19]
131. ~tall(fred) [cnf transformation 25]
132. patient(X0) | creative(X0) [duplicate literal removal 88]
134. 1 <=> humble(mary) [avatar definition]
138. 2 <=> quiet(mary) [avatar definition]
142. 3 <=> old(sK0) [avatar definition]
144. old(sK0) <- (3) [avatar component clause 142]
145. ~1 | 2 | 3 [avatar split clause 74,142,138,134]
147. 4 <=> ! [X1] : ~old(X1) [avatar definition]
148. ~old(X1) <- (4) [avatar component clause 147]
149. 4 | ~2 [avatar split clause 73,138,147]
181. ~rich(X0) [subsumption resolution 95,86]
182. ~old(X0) | kind(X0) [subsumption resolution 94,181]
186. 11 <=> ! [X3] : (humble(X3) | ~tall(X3)) [avatar definition]
187. ~tall(X3) | humble(X3) <- (11) [avatar component clause 186]
194. 13 <=> ! [X3] : (tall(X3) | ~humble(X3)) [avatar definition]
195. ~humble(X3) | tall(X3) <- (13) [avatar component clause 194]
197. humble(X3) | ~tall(X3) [subsumption resolution 102,181]
198. 11 [avatar split clause 197,186]
199. tall(X3) | ~humble(X3) [subsumption resolution 101,181]
200. 13 [avatar split clause 199,194]
256. generous(X0) | old(X0) [resolution 96,85]
257. generous(X0) <- (4) [subsumption resolution 256,148]
262. humble(mary) <- (11) [resolution 187,123]
266. 1 | ~11 [avatar split clause 262,186,134]
278. ~tall(X0) | creative(X0) | creative(X0) [resolution 69,132]
279. ~tall(X0) | creative(X0) [duplicate literal removal 278]
298. tall(X0) | creative(X0) | creative(X0) [resolution 107,118]
299. creative(X0) | tall(X0) [duplicate literal removal 298]
309. 25 <=> humble(fred) [avatar definition]
310. humble(fred) <- (25) [avatar component clause 309]
337. calm(X1) | humble(X1) | ~curious(X1) <- (4) [resolution 81,257]
348. ~curious(X1) | humble(X1) <- (4) [subsumption resolution 337,113]
350. humble(fred) <- (4) [resolution 348,121]
353. 25 | ~4 [avatar split clause 350,147,309]
358. tall(fred) <- (13, 25) [resolution 310,195]
360. $false <- (13, 25) [subsumption resolution 358,131]
361. ~13 | ~25 [avatar contradiction clause 360]
366. creative(X0) [subsumption resolution 279,299]
368. kind(sK0) <- (3) [resolution 144,182]
374. ~tall(X0) | generous(X0) [resolution 366,108]
376. ~generous(sK0) | rich(sK0) <- (3) [resolution 368,87]
378. patient(sK0) <- (3) [resolution 368,116]
380. ~generous(sK0) <- (3) [subsumption resolution 376,181]
392. ~creative(sK0) | tall(sK0) <- (3) [resolution 378,68]
393. tall(sK0) <- (3) [subsumption resolution 392,366]
401. generous(sK0) <- (3) [resolution 393,374]
403. $false <- (3) [subsumption resolution 401,380]
404. ~3 [avatar contradiction clause 403]
405. $false [avatar sat refutation 145,149,198,200,266,353,361,404]
% SZS output end Proof for 613827486984717272802246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits