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
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|---|---|---|---|---|---|---|---|
If someone is humble then someone is either not generous or strong and vice versa. If john is both not generous and humble then someone is curious. If someone is either quiet or not happy then someone is either not brave or brave. If susan is not happy then lucy is either not calm or old. Everyone who is curious is either humble or happy and vice versa. Everyone who is kind is not calm or funny and vice versa. Everyone who is not funny or not wise is both not quiet and not funny. Everyone who is either wise or not funny is not old or not rich and vice versa. Everyone who is wise is either not wise or not curious and vice versa. Everyone who is either not wise or not humble is happy and vice versa. Everyone who is both calm and kind is both not rich and not curious and vice versa. If someone is either curious or not humble then someone is not wise and vice versa. Everyone who is either not tall or strong is both creative and not tall. If john is both not quiet and not generous then paul is both not happy and rich. Someone is strong or funny. Someone is old or brave. Someone is both patient and not calm. Someone is either kind or not brave. | Susan is calm. | neutral | ((?[X]:(humble(X)))<=>(?[X]:((~generous(X)<~>strong(X)))))&
(((~generous(john)&humble(john)))=>(?[X]:(curious(X))))&
((?[X]:((quiet(X)<~>~happy(X))))=>(?[X]:((~brave(X)<~>brave(X)))))&
((~happy(susan))=>((~calm(lucy)<~>old(lucy))))&
(![X]:(curious(X)<=>(humble(X)<~>happy(X))))&
(![X]:(kind(X)<=>(~calm(X)|funny(X))))&
(![X]:((~funny(X)|~wise(X))=>(~quiet(X)&~funny(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~old(X)|~rich(X))))&
(![X]:(wise(X)<=>(~wise(X)<~>~curious(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>happy(X)))&
(![X]:((calm(X)&kind(X))<=>(~rich(X)&~curious(X))))&
((?[X]:((curious(X)<~>~humble(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)<~>strong(X))=>(creative(X)&~tall(X))))&
(((~quiet(john)&~generous(john)))=>((~happy(paul)&rich(paul))))&
(?[X]:((strong(X)|funny(X))))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:((kind(X)<~>~brave(X)))) | calm(susan) | [] | null | 0 |
Everyone who is either not strong or not wise is happy or quiet. If someone is both happy and kind then someone is not old. Everyone who is not calm or tall is either patient or not wise. Everyone who is not strong or not kind is either not patient or not kind. Everyone who is not tall or old is not wise or rich and vice versa. Everyone who is curious or not patient is patient and vice versa. Everyone who is either tall or wise is not patient and vice versa. Everyone who is tall or not strong is either not wise or calm and vice versa. If someone is not rich then someone is either not strong or quiet. Everyone who is patient is both not quiet and rich and vice versa. If someone is happy or wise then someone is humble or not happy. If someone is generous or not curious then someone is not humble or strong and vice versa. If paul is quiet then someone is not tall. Everyone who is old is not rich or kind. If someone is both not patient and not creative then someone is patient or not strong. Everyone who is either not tall or not patient is either wise or tall and vice versa. Paul is not funny. Someone is both not happy and patient. Someone is not generous. Mary is either not calm or not happy. Someone is not patient or old. Someone is not kind or creative. | Mary is strong. | entailment | (![X]:((~strong(X)<~>~wise(X))=>(happy(X)|quiet(X))))&
((?[X]:((happy(X)&kind(X))))=>(?[X]:(~old(X))))&
(![X]:((~calm(X)|tall(X))=>(patient(X)<~>~wise(X))))&
(![X]:((~strong(X)|~kind(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~tall(X)|old(X))<=>(~wise(X)|rich(X))))&
(![X]:((curious(X)|~patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>wise(X))<=>~patient(X)))&
(![X]:((tall(X)|~strong(X))<=>(~wise(X)<~>calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:(patient(X)<=>(~quiet(X)&rich(X))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((humble(X)|~happy(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
((quiet(paul))=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~rich(X)|kind(X))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((~tall(X)<~>~patient(X))<=>(wise(X)<~>tall(X))))&
(~funny(paul))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:(~generous(X)))&
((~calm(mary)<~>~happy(mary)))&
(?[X]:((~patient(X)|old(X))))&
(?[X]:((~kind(X)|creative(X)))) | strong(mary) | [
"p3",
"p4",
"p5",
"p6",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3061091937321872621251653
% SZS output start Proof for 3061091937321872621251653
4. ! [X0] : ((~kind(X0) | ~strong(X0)) => (~patient(X0) <~> ~kind(X0))) [input p3]
5. ! [X0] : ((old(X0) | ~tall(X0)) <=> (rich(X0) | ~wise(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | curious(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((tall(X0) <~> wise(X0)) <=> ~patient(X0)) [input p6]
10. ! [X0] : (patient(X0) <=> (rich(X0) & ~quiet(X0))) [input p9]
14. ! [X0] : (old(X0) => (kind(X0) | ~rich(X0))) [input p13]
16. ! [X0] : ((~tall(X0) <~> ~patient(X0)) <=> (wise(X0) <~> tall(X0))) [input p15]
23. ~strong(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | (kind(X0) & strong(X0))) [ennf transformation 4]
40. ! [X0] : ((kind(X0) | ~rich(X0)) | ~old(X0)) [ennf transformation 14]
41. ! [X0] : (kind(X0) | ~rich(X0) | ~old(X0)) [flattening 40]
47. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (kind(X0) & strong(X0))) [nnf transformation 36]
48. ! [X0] : (((old(X0) | ~tall(X0)) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | (~old(X0) & tall(X0)))) [nnf transformation 5]
49. ! [X0] : ((old(X0) | ~tall(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | (~old(X0) & tall(X0)))) [flattening 48]
50. ! [X0] : (((~patient(X0) | curious(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~curious(X0)))) [nnf transformation 6]
51. ! [X0] : ((~patient(X0) | curious(X0) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~curious(X0)))) [flattening 50]
52. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | patient(X0)) & (~patient(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [nnf transformation 7]
59. ! [X0] : ((patient(X0) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | ~patient(X0))) [nnf transformation 10]
60. ! [X0] : ((patient(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | ~patient(X0))) [flattening 59]
71. ! [X0] : ((((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) & (((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))))) [nnf transformation 16]
86. ~patient(X0) | ~kind(X0) | strong(X0) [cnf transformation 47]
93. ~rich(X0) | ~tall(X0) | old(X0) [cnf transformation 49]
95. patient(X0) | patient(X0) [cnf transformation 51]
98. ~patient(X0) | tall(X0) | ~wise(X0) [cnf transformation 52]
110. rich(X0) | ~patient(X0) [cnf transformation 60]
119. ~rich(X0) | kind(X0) | ~old(X0) [cnf transformation 41]
120. tall(X0) | wise(X0) | ~patient(X0) | tall(X0) [cnf transformation 71]
134. ~strong(mary) [cnf transformation 23]
135. tall(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 120]
139. patient(X0) [duplicate literal removal 95]
150. ~wise(X0) | tall(X0) [subsumption resolution 98,139]
154. 3 <=> ! [X1] : rich(X1) [avatar definition]
155. rich(X1) <- (3) [avatar component clause 154]
166. rich(X0) [subsumption resolution 110,139]
167. 3 [avatar split clause 166,154]
217. tall(X0) | wise(X0) [subsumption resolution 135,139]
218. tall(X0) [subsumption resolution 217,150]
245. ~kind(X1) | strong(X1) [resolution 86,139]
253. ~tall(X0) | old(X0) <- (3) [resolution 93,155]
254. old(X0) <- (3) [subsumption resolution 253,218]
264. kind(X0) | ~old(X0) <- (3) [resolution 119,155]
265. kind(X0) <- (3) [subsumption resolution 264,254]
267. strong(X1) <- (3) [resolution 265,245]
269. $false <- (3) [resolution 267,134]
270. ~3 [avatar contradiction clause 269]
271. $false [avatar sat refutation 167,270]
% SZS output end Proof for 3061091937321872621251653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then john is happy.
Everyone who is not rich or strong is not curious or not calm.
If susan is strong then alice is both kind and not humble.
If someone is either calm or creative then someone is quiet and vice versa.
Everyone who is not creative is either not creative or not tall and vice versa.
Everyone who is either not rich or not humble is tall.
Everyone who is both not patient and not creative is curious.
If someone is quiet then someone is not curious.
If paul is both not humble and calm then john is old.
If someone is old then alice is not strong.
Everyone who is both calm and not happy is either not funny or calm.
Everyone who is either not tall or patient is not humble and vice versa.
If someone is not tall then someone is either not tall or old and vice versa.
Everyone who is either not strong or brave is not old.
If someone is both quiet and not quiet then someone is both strong and not humble.
Everyone who is both not curious and wise is happy or not old.
Someone is either tall or not tall.
John is both strong and not old.
Someone is tall.
Someone is either calm or happy.
Lucy is not rich or brave.
Someone is both strong and happy.
John is not rich. | Paul is not calm. | neutral | ((?[X]:(happy(X)))=>(happy(john)))&
(![X]:((~rich(X)|strong(X))=>(~curious(X)|~calm(X))))&
((strong(susan))=>((kind(alice)&~humble(alice))))&
((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>~humble(X))=>tall(X)))&
(![X]:((~patient(X)&~creative(X))=>curious(X)))&
((?[X]:(quiet(X)))=>(?[X]:(~curious(X))))&
(((~humble(paul)&calm(paul)))=>(old(john)))&
((?[X]:(old(X)))=>(~strong(alice)))&
(![X]:((calm(X)&~happy(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~tall(X)<~>patient(X))<=>~humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:((~strong(X)<~>brave(X))=>~old(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:((~curious(X)&wise(X))=>(happy(X)|~old(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((strong(john)&~old(john)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)<~>happy(X))))&
((~rich(lucy)|brave(lucy)))&
(?[X]:((strong(X)&happy(X))))&
(~rich(john)) | ~calm(paul) | [] | null | 0 |
If mary is either generous or not generous then someone is either curious or not brave and vice versa.
Everyone who is not tall is both rich and quiet.
Everyone who is happy is both old and creative and vice versa.
Everyone who is curious is strong or not quiet and vice versa.
Everyone who is strong is wise or funny.
Everyone who is both kind and not kind is either not old or not happy.
Everyone who is both happy and quiet is not curious or quiet.
Everyone who is both wise and patient is either funny or generous.
Everyone who is both not calm and not funny is both not wise and creative.
If alice is old or brave then lucy is both creative and old.
Everyone who is not rich or generous is both not calm and not tall.
If john is quiet or not humble then alice is both kind and not quiet and vice versa.
Everyone who is tall or not kind is either humble or brave and vice versa.
If mary is either not happy or rich then someone is old.
If someone is both rich and not happy then susan is either kind or humble.
Everyone who is either not quiet or not curious is both brave and wise.
Someone is not wise or not rich.
Someone is not strong or funny.
John is calm or brave.
Someone is both not generous and old. | Lucy is not creative. | contradiction | (((generous(mary)<~>~generous(mary)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~tall(X)=>(rich(X)&quiet(X))))&
(![X]:(happy(X)<=>(old(X)&creative(X))))&
(![X]:(curious(X)<=>(strong(X)|~quiet(X))))&
(![X]:(strong(X)=>(wise(X)|funny(X))))&
(![X]:((kind(X)&~kind(X))=>(~old(X)<~>~happy(X))))&
(![X]:((happy(X)&quiet(X))=>(~curious(X)|quiet(X))))&
(![X]:((wise(X)&patient(X))=>(funny(X)<~>generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~wise(X)&creative(X))))&
(((old(alice)|brave(alice)))=>((creative(lucy)&old(lucy))))&
(![X]:((~rich(X)|generous(X))=>(~calm(X)&~tall(X))))&
(((quiet(john)|~humble(john)))<=>((kind(alice)&~quiet(alice))))&
(![X]:((tall(X)|~kind(X))<=>(humble(X)<~>brave(X))))&
(((~happy(mary)<~>rich(mary)))=>(?[X]:(old(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(susan)<~>humble(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(brave(X)&wise(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((~strong(X)|funny(X))))&
((calm(john)|brave(john)))&
(?[X]:((~generous(X)&old(X)))) | ~creative(lucy) | [
"p1",
"p3",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8220899833618617747780080
% SZS output start Proof for 8220899833618617747780080
2. ! [X0] : (~tall(X0) => (quiet(X0) & rich(X0))) [input p1]
4. ! [X0] : (curious(X0) <=> (~quiet(X0) | strong(X0))) [input p3]
10. (brave(alice) | old(alice)) => (old(lucy) & creative(lucy)) [input p9]
12. (~humble(john) | quiet(john)) <=> (~quiet(alice) & kind(alice)) [input p11]
13. ! [X0] : ((~kind(X0) | tall(X0)) <=> (humble(X0) <~> brave(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) => (wise(X0) & brave(X0))) [input p15]
21. ~creative(lucy) [input hypothesis]
26. ! [X0] : ((quiet(X0) & rich(X0)) | tall(X0)) [ennf transformation 2]
31. (old(lucy) & creative(lucy)) | (~brave(alice) & ~old(alice)) [ennf transformation 10]
35. ! [X0] : ((wise(X0) & brave(X0)) | (~quiet(X0) <=> ~curious(X0))) [ennf transformation 16]
42. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~curious(X0))) [nnf transformation 4]
43. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~curious(X0))) [flattening 42]
45. ((~humble(john) | quiet(john)) | (quiet(alice) | ~kind(alice))) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [nnf transformation 12]
46. (~humble(john) | quiet(john) | quiet(alice) | ~kind(alice)) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [flattening 45]
47. ! [X0] : (((~kind(X0) | tall(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [nnf transformation 13]
48. ! [X0] : ((~kind(X0) | tall(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [flattening 47]
53. ! [X0] : ((wise(X0) & brave(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 35]
67. quiet(X0) | tall(X0) [cnf transformation 26]
73. quiet(X0) | curious(X0) [cnf transformation 43]
78. creative(lucy) | ~brave(alice) [cnf transformation 31]
87. ~quiet(alice) | ~quiet(john) [cnf transformation 46]
88. ~quiet(alice) | humble(john) [cnf transformation 46]
92. ~humble(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 48]
100. brave(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
108. ~creative(lucy) [cnf transformation 21]
130. 4 <=> brave(alice) [avatar definition]
132. ~brave(alice) <- (~4) [avatar component clause 130]
144. 7 <=> creative(lucy) [avatar definition]
147. ~4 | 7 [avatar split clause 78,144,130]
155. 9 <=> quiet(alice) [avatar definition]
156. ~quiet(alice) <- (~9) [avatar component clause 155]
159. 10 <=> quiet(john) [avatar definition]
160. ~quiet(john) <- (~10) [avatar component clause 159]
163. 11 <=> humble(john) [avatar definition]
164. humble(john) <- (11) [avatar component clause 163]
167. 11 | ~9 [avatar split clause 88,155,163]
168. ~10 | ~9 [avatar split clause 87,155,159]
199. quiet(X0) | brave(X0) [subsumption resolution 100,73]
206. 18 <=> brave(john) [avatar definition]
208. brave(john) <- (18) [avatar component clause 206]
210. ~7 [avatar split clause 108,144]
228. brave(alice) <- (~9) [resolution 199,156]
229. $false <- (~4, ~9) [subsumption resolution 228,132]
230. 4 | 9 [avatar contradiction clause 229]
231. brave(john) <- (~10) [resolution 160,199]
233. tall(john) <- (~10) [resolution 160,67]
234. 18 | 10 [avatar split clause 231,159,206]
249. ~brave(john) | ~tall(john) <- (11) [resolution 92,164]
251. ~tall(john) <- (11, 18) [subsumption resolution 249,208]
252. $false <- (~10, 11, 18) [subsumption resolution 251,233]
253. 10 | ~11 | ~18 [avatar contradiction clause 252]
254. $false [avatar sat refutation 147,167,168,210,230,234,253]
% SZS output end Proof for 8220899833618617747780080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or tall is not quiet or not brave. Everyone who is either not strong or not old is both not brave and calm and vice versa. Everyone who is not brave or not humble is not tall and vice versa. If paul is not quiet then someone is either kind or strong. If alice is rich or funny then mary is either not strong or calm. If lucy is both funny and not humble then someone is either humble or generous. If lucy is generous then someone is both calm and funny. Everyone who is not strong is strong. If someone is tall or not calm then susan is not patient or old and vice versa. Everyone who is not kind is rich and vice versa. If lucy is both not old and not strong then someone is both calm and strong. If fred is not wise then paul is not old and vice versa. If mary is not patient then someone is either creative or not strong. Everyone who is either not kind or strong is funny or not curious. Everyone who is both funny and quiet is rich or not kind and vice versa. If someone is kind then someone is not strong. John is both not brave and wise. Paul is generous. Someone is either not curious or strong. Someone is rich. Someone is patient or not funny. Susan is generous or not wise. Fred is quiet. Someone is either generous or not calm. | Fred is not tall. | entailment | (![X]:((~curious(X)|tall(X))=>(~quiet(X)|~brave(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(~brave(X)&calm(X))))&
(![X]:((~brave(X)|~humble(X))<=>~tall(X)))&
((~quiet(paul))=>(?[X]:((kind(X)<~>strong(X)))))&
(((rich(alice)|funny(alice)))=>((~strong(mary)<~>calm(mary))))&
(((funny(lucy)&~humble(lucy)))=>(?[X]:((humble(X)<~>generous(X)))))&
((generous(lucy))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((tall(X)|~calm(X))))<=>((~patient(susan)|old(susan))))&
(![X]:(~kind(X)<=>rich(X)))&
(((~old(lucy)&~strong(lucy)))=>(?[X]:((calm(X)&strong(X)))))&
((~wise(fred))<=>(~old(paul)))&
((~patient(mary))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~kind(X)<~>strong(X))=>(funny(X)|~curious(X))))&
(![X]:((funny(X)&quiet(X))<=>(rich(X)|~kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(~strong(X))))&
((~brave(john)&wise(john)))&
(generous(paul))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|~funny(X))))&
((generous(susan)|~wise(susan)))&
(quiet(fred))&
(?[X]:((generous(X)<~>~calm(X)))) | ~tall(fred) | [
"p0",
"p2",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5825345727327143919522720
% SZS output start Proof for 5825345727327143919522720
1. ! [X0] : ((tall(X0) | ~curious(X0)) => (~brave(X0) | ~quiet(X0))) [input p0]
3. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> ~tall(X0)) [input p2]
23. quiet(fred) [input p22]
25. tall(fred) [input hypothesis]
27. ! [X0] : ((~brave(X0) | ~quiet(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 1]
28. ! [X0] : (~brave(X0) | ~quiet(X0) | (~tall(X0) & curious(X0))) [flattening 27]
43. ! [X0] : (((~humble(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) & brave(X0)))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (humble(X0) & brave(X0)))) [flattening 43]
83. ~brave(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 28]
90. ~tall(X0) | brave(X0) [cnf transformation 44]
132. quiet(fred) [cnf transformation 23]
135. tall(fred) [cnf transformation 25]
287. brave(fred) [resolution 90,135]
313. ~quiet(fred) | ~tall(fred) [resolution 83,287]
314. ~tall(fred) [subsumption resolution 313,132]
315. $false [subsumption resolution 314,135]
% SZS output end Proof for 5825345727327143919522720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then someone is either tall or not generous. If someone is either brave or not strong then susan is not humble or not calm and vice versa. Everyone who is not wise is either wise or not funny and vice versa. If john is either not brave or strong then alice is quiet. Everyone who is both not humble and not funny is either not strong or old and vice versa. Everyone who is strong is not quiet or not old and vice versa. If someone is creative then paul is kind or patient. Everyone who is not curious or rich is both creative and not rich. Everyone who is both not brave and not rich is generous. Everyone who is patient or kind is either creative or not generous. Everyone who is not creative or tall is not kind or not old. Everyone who is both old and curious is both tall and not kind. If mary is both strong and not brave then someone is both not wise and not rich and vice versa. Everyone who is not tall is not patient. If lucy is not brave or quiet then lucy is not generous. Everyone who is humble is both funny and quiet. Fred is funny or not funny. John is both curious and calm. Someone is not quiet. Lucy is not kind or rich. Someone is both not happy and strong. Paul is wise or not kind. Someone is both not quiet and generous. Paul is either not patient or not generous. | Fred is strong. | entailment | ((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~generous(X)))))&
((?[X]:((brave(X)<~>~strong(X))))<=>((~humble(susan)|~calm(susan))))&
(![X]:(~wise(X)<=>(wise(X)<~>~funny(X))))&
(((~brave(john)<~>strong(john)))=>(quiet(alice)))&
(![X]:((~humble(X)&~funny(X))<=>(~strong(X)<~>old(X))))&
(![X]:(strong(X)<=>(~quiet(X)|~old(X))))&
((?[X]:(creative(X)))=>((kind(paul)|patient(paul))))&
(![X]:((~curious(X)|rich(X))=>(creative(X)&~rich(X))))&
(![X]:((~brave(X)&~rich(X))=>generous(X)))&
(![X]:((patient(X)|kind(X))=>(creative(X)<~>~generous(X))))&
(![X]:((~creative(X)|tall(X))=>(~kind(X)|~old(X))))&
(![X]:((old(X)&curious(X))=>(tall(X)&~kind(X))))&
(((strong(mary)&~brave(mary)))<=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:(~tall(X)=>~patient(X)))&
(((~brave(lucy)|quiet(lucy)))=>(~generous(lucy)))&
(![X]:(humble(X)=>(funny(X)&quiet(X))))&
((funny(fred)|~funny(fred)))&
((curious(john)&calm(john)))&
(?[X]:(~quiet(X)))&
((~kind(lucy)|rich(lucy)))&
(?[X]:((~happy(X)&strong(X))))&
((wise(paul)|~kind(paul)))&
(?[X]:((~quiet(X)&generous(X))))&
((~patient(paul)<~>~generous(paul))) | strong(fred) | [
"p2",
"p4",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8307999648207193605712428
% SZS output start Proof for 8307999648207193605712428
3. ! [X0] : (~wise(X0) <=> (wise(X0) <~> ~funny(X0))) [input p2]
5. ! [X0] : ((~funny(X0) & ~humble(X0)) <=> (~strong(X0) <~> old(X0))) [input p4]
6. ! [X0] : (strong(X0) <=> (~old(X0) | ~quiet(X0))) [input p5]
16. ! [X0] : (humble(X0) => (quiet(X0) & funny(X0))) [input p15]
25. ~strong(fred) [input hypothesis]
42. ! [X0] : ((quiet(X0) & funny(X0)) | ~humble(X0)) [ennf transformation 16]
52. ! [X0] : ((~wise(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | wise(X0))) [nnf transformation 3]
54. ! [X0] : (((~funny(X0) & ~humble(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (funny(X0) | humble(X0)))) [nnf transformation 5]
55. ! [X0] : (((~funny(X0) & ~humble(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | funny(X0) | humble(X0))) [flattening 54]
56. ! [X0] : ((strong(X0) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | ~strong(X0))) [nnf transformation 6]
57. ! [X0] : ((strong(X0) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | ~strong(X0))) [flattening 56]
79. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 52]
81. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 52]
86. ~old(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 55]
93. old(X0) | strong(X0) [cnf transformation 57]
115. funny(X0) | ~humble(X0) [cnf transformation 42]
128. ~strong(fred) [cnf transformation 25]
130. ~funny(X0) | wise(X0) [duplicate literal removal 79]
131. ~funny(X0) | ~wise(X0) [duplicate literal removal 81]
173. ~funny(X0) [subsumption resolution 130,131]
188. ~old(X0) | strong(X0) | humble(X0) [subsumption resolution 86,173]
233. ~humble(X0) [subsumption resolution 115,173]
274. strong(X0) | humble(X0) | strong(X0) [resolution 188,93]
275. strong(X0) | humble(X0) [duplicate literal removal 274]
276. strong(X0) [subsumption resolution 275,233]
303. $false [resolution 276,128]
% SZS output end Proof for 8307999648207193605712428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is strong or quiet then someone is either not strong or wise.
If alice is generous or not creative then someone is humble.
If someone is not generous or not rich then someone is not kind.
Everyone who is kind is not wise or not rich and vice versa.
If lucy is either not creative or not wise then someone is either not creative or not strong.
Everyone who is wise or not rich is not funny or wise and vice versa.
If someone is calm then alice is patient and vice versa.
If someone is either not humble or not tall then john is funny or not kind.
If someone is either not creative or humble then someone is both curious and not rich and vice versa.
If someone is both old and quiet then mary is either not humble or not rich.
Everyone who is rich is not tall and vice versa.
Everyone who is either not happy or not strong is both wise and not generous.
If someone is curious or not wise then susan is both not brave and not funny.
Everyone who is both not creative and not kind is both happy and not funny.
If someone is either not creative or old then someone is either not curious or not calm and vice versa.
Everyone who is either old or not calm is either generous or wise and vice versa.
Someone is both old and not rich.
Fred is both not wise and patient.
Paul is either rich or patient.
Someone is funny or not rich.
Alice is not tall.
Fred is funny.
Paul is either not brave or not rich.
Fred is both not brave and funny. | Fred is tall. | contradiction | (((strong(susan)|quiet(susan)))=>(?[X]:((~strong(X)<~>wise(X)))))&
(((generous(alice)|~creative(alice)))=>(?[X]:(humble(X))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(~kind(X))))&
(![X]:(kind(X)<=>(~wise(X)|~rich(X))))&
(((~creative(lucy)<~>~wise(lucy)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((wise(X)|~rich(X))<=>(~funny(X)|wise(X))))&
((?[X]:(calm(X)))<=>(patient(alice)))&
((?[X]:((~humble(X)<~>~tall(X))))=>((funny(john)|~kind(john))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
((?[X]:((old(X)&quiet(X))))=>((~humble(mary)<~>~rich(mary))))&
(![X]:(rich(X)<=>~tall(X)))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)&~generous(X))))&
((?[X]:((curious(X)|~wise(X))))=>((~brave(susan)&~funny(susan))))&
(![X]:((~creative(X)&~kind(X))=>(happy(X)&~funny(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((old(X)<~>~calm(X))<=>(generous(X)<~>wise(X))))&
(?[X]:((old(X)&~rich(X))))&
((~wise(fred)&patient(fred)))&
((rich(paul)<~>patient(paul)))&
(?[X]:((funny(X)|~rich(X))))&
(~tall(alice))&
(funny(fred))&
((~brave(paul)<~>~rich(paul)))&
((~brave(fred)&funny(fred))) | tall(fred) | [
"p5",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1011748298668064208921969
% SZS output start Proof for 1011748298668064208921969
6. ! [X0] : ((~rich(X0) | wise(X0)) <=> (wise(X0) | ~funny(X0))) [input p5]
11. ! [X0] : (rich(X0) <=> ~tall(X0)) [input p10]
18. patient(fred) & ~wise(fred) [input p17]
22. funny(fred) [input p21]
25. tall(fred) [input hypothesis]
54. ! [X0] : (((~rich(X0) | wise(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (rich(X0) & ~wise(X0)))) [nnf transformation 6]
55. ! [X0] : ((~rich(X0) | wise(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | (rich(X0) & ~wise(X0)))) [flattening 54]
66. ! [X0] : ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))) [nnf transformation 11]
94. ~funny(X0) | wise(X0) | rich(X0) [cnf transformation 55]
107. ~tall(X0) | ~rich(X0) [cnf transformation 66]
137. ~wise(fred) [cnf transformation 18]
143. funny(fred) [cnf transformation 22]
148. tall(fred) [cnf transformation 25]
352. ~rich(fred) [resolution 107,148]
363. wise(fred) | rich(fred) [resolution 94,143]
364. rich(fred) [subsumption resolution 363,137]
365. $false [subsumption resolution 364,352]
% SZS output end Proof for 1011748298668064208921969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not old is not tall or kind.
If john is both calm and not curious then someone is either generous or not patient.
Everyone who is not tall or old is old or not funny and vice versa.
If someone is both not curious and patient then paul is funny and vice versa.
If someone is either generous or not quiet then fred is either not patient or not brave.
Everyone who is humble is either old or not quiet and vice versa.
If someone is funny or not quiet then mary is either not kind or not happy.
Everyone who is either not generous or not tall is generous or not funny and vice versa.
Everyone who is either not creative or patient is either humble or quiet and vice versa.
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.
Everyone who is quiet is both humble and not wise and vice versa.
If fred is either creative or tall then paul is both patient and kind and vice versa.
Everyone who is humble is both tall and rich and vice versa.
If mary is both not rich and not happy then someone is strong.
If paul is curious or patient then susan is both quiet and not quiet.
Fred is old.
Fred is not creative.
Mary is both not strong and not quiet.
Someone is not brave or not quiet.
Someone is not creative.
Someone is not humble.
Lucy is either not funny or generous. | Paul is not old. | contradiction | (![X]:((strong(X)&~old(X))=>(~tall(X)|kind(X))))&
(((calm(john)&~curious(john)))=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:((~tall(X)|old(X))<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)&patient(X))))<=>(funny(paul)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((~patient(fred)<~>~brave(fred))))&
(![X]:(humble(X)<=>(old(X)<~>~quiet(X))))&
((?[X]:((funny(X)|~quiet(X))))=>((~kind(mary)<~>~happy(mary))))&
(![X]:((~generous(X)<~>~tall(X))<=>(generous(X)|~funny(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(humble(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)<=>(humble(X)&~wise(X))))&
(((creative(fred)<~>tall(fred)))<=>((patient(paul)&kind(paul))))&
(![X]:(humble(X)<=>(tall(X)&rich(X))))&
(((~rich(mary)&~happy(mary)))=>(?[X]:(strong(X))))&
(((curious(paul)|patient(paul)))=>((quiet(susan)&~quiet(susan))))&
(old(fred))&
(~creative(fred))&
((~strong(mary)&~quiet(mary)))&
(?[X]:((~brave(X)|~quiet(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~humble(X)))&
((~funny(lucy)<~>generous(lucy))) | ~old(paul) | [
"p2",
"p5",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8794565229459415598143927
% SZS output start Proof for 8794565229459415598143927
3. ! [X0] : ((old(X0) | ~tall(X0)) <=> (~funny(X0) | old(X0))) [input p2]
6. ! [X0] : (humble(X0) <=> (old(X0) <~> ~quiet(X0))) [input p5]
8. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (~funny(X0) | generous(X0))) [input p7]
12. ! [X0] : (quiet(X0) <=> (~wise(X0) & humble(X0))) [input p11]
14. ! [X0] : (humble(X0) <=> (rich(X0) & tall(X0))) [input p13]
24. ~old(paul) [input hypothesis]
39. ! [X0] : (((old(X0) | ~tall(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (~old(X0) & tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((old(X0) | ~tall(X0) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | (~old(X0) & tall(X0)))) [flattening 39]
46. ! [X0] : ((humble(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | ~humble(X0))) [nnf transformation 6]
48. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 8]
49. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [flattening 48]
56. ! [X0] : ((quiet(X0) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 12]
57. ! [X0] : ((quiet(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | ~quiet(X0))) [flattening 56]
60. ! [X0] : ((humble(X0) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | ~humble(X0))) [nnf transformation 14]
61. ! [X0] : ((humble(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | ~humble(X0))) [flattening 60]
74. ~funny(X0) | old(X0) | tall(X0) [cnf transformation 40]
77. ~tall(X0) | old(X0) | funny(X0) [cnf transformation 40]
88. humble(X0) | old(X0) | quiet(X0) [cnf transformation 46]
93. ~funny(X0) | generous(X0) | ~tall(X0) | generous(X0) [cnf transformation 49]
95. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 49]
114. ~quiet(X0) | humble(X0) [cnf transformation 57]
123. ~humble(X0) | tall(X0) [cnf transformation 61]
140. ~old(paul) [cnf transformation 24]
141. ~funny(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 93]
142. ~generous(X0) | ~tall(X0) [duplicate literal removal 95]
162. 5 <=> funny(paul) [avatar definition]
163. funny(paul) <- (5) [avatar component clause 162]
164. ~funny(paul) <- (~5) [avatar component clause 162]
215. ~funny(X0) | ~tall(X0) [subsumption resolution 141,142]
297. ~tall(paul) <- (5) [resolution 215,163]
301. old(paul) | tall(paul) <- (5) [resolution 74,163]
314. tall(paul) <- (5) [subsumption resolution 301,140]
315. $false <- (5) [subsumption resolution 314,297]
316. ~5 [avatar contradiction clause 315]
353. quiet(X3) | old(X3) | tall(X3) [resolution 88,123]
379. 39 <=> tall(paul) [avatar definition]
380. ~tall(paul) <- (~39) [avatar component clause 379]
381. tall(paul) <- (39) [avatar component clause 379]
390. old(paul) | funny(paul) <- (39) [resolution 381,77]
393. funny(paul) <- (39) [subsumption resolution 390,140]
394. $false <- (~5, 39) [subsumption resolution 393,164]
395. 5 | ~39 [avatar contradiction clause 394]
449. old(X1) | tall(X1) | humble(X1) [resolution 353,114]
451. tall(X1) | old(X1) [subsumption resolution 449,123]
457. old(paul) <- (~39) [resolution 451,380]
463. $false <- (~39) [subsumption resolution 457,140]
464. 39 [avatar contradiction clause 463]
465. $false [avatar sat refutation 316,395,464]
% SZS output end Proof for 8794565229459415598143927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and generous then someone is not rich and vice versa.
If paul is not curious then john is both not patient and calm and vice versa.
Everyone who is quiet is both not brave and not funny.
Everyone who is not happy is both generous and brave and vice versa.
If susan is not strong then john is either not old or not funny and vice versa.
If someone is not old or not wise then someone is old and vice versa.
If someone is both not patient and not brave then someone is either happy or not rich and vice versa.
Everyone who is either not brave or funny is either not happy or not calm and vice versa.
If mary is tall or curious then fred is not quiet or not humble and vice versa.
Everyone who is both not tall and not brave is either not patient or not quiet and vice versa.
Everyone who is wise is patient.
Everyone who is tall or curious is both not brave and calm and vice versa.
If mary is both humble and quiet then paul is not kind and vice versa.
Everyone who is not happy is both strong and not tall and vice versa.
Everyone who is wise is either humble or generous.
Everyone who is both not curious and not calm is either tall or brave.
John is both wise and funny.
Someone is both not calm and not wise.
Fred is old or not kind.
Fred is either not humble or creative.
Someone is either patient or humble.
Someone is both not creative and not happy.
Someone is either tall or not wise. | John is not calm. | contradiction | ((?[X]:((happy(X)&generous(X))))<=>(?[X]:(~rich(X))))&
((~curious(paul))<=>((~patient(john)&calm(john))))&
(![X]:(quiet(X)=>(~brave(X)&~funny(X))))&
(![X]:(~happy(X)<=>(generous(X)&brave(X))))&
((~strong(susan))<=>((~old(john)<~>~funny(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(old(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~brave(X)<~>funny(X))<=>(~happy(X)<~>~calm(X))))&
(((tall(mary)|curious(mary)))<=>((~quiet(fred)|~humble(fred))))&
(![X]:((~tall(X)&~brave(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(wise(X)=>patient(X)))&
(![X]:((tall(X)|curious(X))<=>(~brave(X)&calm(X))))&
(((humble(mary)&quiet(mary)))<=>(~kind(paul)))&
(![X]:(~happy(X)<=>(strong(X)&~tall(X))))&
(![X]:(wise(X)=>(humble(X)<~>generous(X))))&
(![X]:((~curious(X)&~calm(X))=>(tall(X)<~>brave(X))))&
((wise(john)&funny(john)))&
(?[X]:((~calm(X)&~wise(X))))&
((old(fred)|~kind(fred)))&
((~humble(fred)<~>creative(fred)))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((tall(X)<~>~wise(X)))) | ~calm(john) | [
"p2",
"p3",
"p7",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2511952598976951549319748
% SZS output start Proof for 2511952598976951549319748
3. ! [X0] : (quiet(X0) => (~funny(X0) & ~brave(X0))) [input p2]
4. ! [X0] : (~happy(X0) <=> (brave(X0) & generous(X0))) [input p3]
8. ! [X0] : ((~brave(X0) <~> funny(X0)) <=> (~happy(X0) <~> ~calm(X0))) [input p7]
10. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : (wise(X0) => patient(X0)) [input p10]
17. funny(john) & wise(john) [input p16]
24. ~calm(john) [input hypothesis]
28. ! [X0] : ((~funny(X0) & ~brave(X0)) | ~quiet(X0)) [ennf transformation 3]
29. ! [X0] : (patient(X0) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : ((~happy(X0) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | happy(X0))) [nnf transformation 4]
41. ! [X0] : ((~happy(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | happy(X0))) [flattening 40]
53. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0)))) & (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [nnf transformation 8]
56. ! [X0] : (((~brave(X0) & ~tall(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | (brave(X0) | tall(X0)))) [nnf transformation 10]
57. ! [X0] : (((~brave(X0) & ~tall(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | brave(X0) | tall(X0))) [flattening 56]
83. ~brave(X0) | ~quiet(X0) [cnf transformation 28]
86. brave(X0) | happy(X0) [cnf transformation 41]
108. ~funny(X0) | brave(X0) | ~happy(X0) | calm(X0) [cnf transformation 53]
118. ~brave(X0) | ~patient(X0) | quiet(X0) [cnf transformation 57]
119. ~wise(X0) | patient(X0) [cnf transformation 29]
135. wise(john) [cnf transformation 17]
136. funny(john) [cnf transformation 17]
148. ~calm(john) [cnf transformation 24]
171. 6 <=> patient(john) [avatar definition]
173. patient(john) <- (6) [avatar component clause 171]
175. 7 <=> calm(john) [avatar definition]
177. ~calm(john) <- (~7) [avatar component clause 175]
186. 9 <=> funny(john) [avatar definition]
188. funny(john) <- (9) [avatar component clause 186]
256. ~funny(X0) | brave(X0) | calm(X0) [subsumption resolution 108,86]
280. ~brave(X0) | ~patient(X0) [subsumption resolution 118,83]
298. 9 [avatar split clause 136,186]
334. ~7 [avatar split clause 148,175]
338. patient(john) [resolution 119,135]
339. 6 [avatar split clause 338,171]
370. brave(john) | calm(john) <- (9) [resolution 256,188]
371. brave(john) <- (~7, 9) [subsumption resolution 370,177]
373. ~patient(john) <- (~7, 9) [resolution 371,280]
377. $false <- (6, ~7, 9) [subsumption resolution 373,173]
378. ~6 | 7 | ~9 [avatar contradiction clause 377]
379. $false [avatar sat refutation 298,334,339,378]
% SZS output end Proof for 2511952598976951549319748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is rich or not happy then john is not humble or not creative. Everyone who is both not old and not wise is either not calm or not happy and vice versa. If someone is old then fred is brave. Everyone who is not generous or not old is both not brave and brave. Everyone who is not kind is either not tall or not funny and vice versa. Everyone who is both not wise and not old is both not humble and not kind. Everyone who is not brave or not funny is not calm. If someone is not generous or not kind then lucy is not funny and vice versa. If paul is not patient or humble then someone is patient or not funny and vice versa. Everyone who is both happy and not wise is both rich and happy. Everyone who is both not curious and not creative is generous. If paul is either brave or not quiet then susan is not rich or not strong and vice versa. Everyone who is either creative or not happy is not tall or wise and vice versa. If susan is not wise then someone is not strong or not patient. If someone is either not old or not quiet then someone is both funny and not curious and vice versa. If fred is both not wise and patient then alice is either strong or not wise and vice versa. Someone is either brave or not funny. Someone is both not humble and not funny. Someone is both rich and kind. Paul is old. John is not happy or not calm. Mary is either not tall or generous. Mary is brave. | Lucy is humble. | neutral | (((rich(susan)|~happy(susan)))=>((~humble(john)|~creative(john))))&
(![X]:((~old(X)&~wise(X))<=>(~calm(X)<~>~happy(X))))&
((?[X]:(old(X)))=>(brave(fred)))&
(![X]:((~generous(X)|~old(X))=>(~brave(X)&brave(X))))&
(![X]:(~kind(X)<=>(~tall(X)<~>~funny(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)|~funny(X))=>~calm(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>(~funny(lucy)))&
(((~patient(paul)|humble(paul)))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>generous(X)))&
(((brave(paul)<~>~quiet(paul)))<=>((~rich(susan)|~strong(susan))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)|wise(X))))&
((~wise(susan))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~wise(fred)&patient(fred)))<=>((strong(alice)<~>~wise(alice))))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((rich(X)&kind(X))))&
(old(paul))&
((~happy(john)|~calm(john)))&
((~tall(mary)<~>generous(mary)))&
(brave(mary)) | humble(lucy) | [] | null | 0 |
Everyone who is both creative and generous is rich or kind and vice versa.
Everyone who is both not strong and happy is patient or rich.
If lucy is not curious or not happy then susan is either patient or not kind.
If someone is either not tall or wise then alice is not happy or wise.
If someone is both not tall and creative then someone is both patient and wise and vice versa.
Everyone who is not humble or not rich is creative or strong and vice versa.
Everyone who is not rich is tall or not calm and vice versa.
Everyone who is not happy or not strong is both not funny and strong.
Everyone who is not curious is strong or quiet and vice versa.
Everyone who is not patient is either kind or creative and vice versa.
If paul is not generous or not tall then paul is not wise or humble and vice versa.
Everyone who is both kind and not wise is not wise or generous and vice versa.
Everyone who is both not rich and not calm is both not creative and humble.
If someone is old then someone is either not quiet or not tall.
If mary is either not rich or funny then someone is either generous or strong.
Everyone who is brave is not patient.
Lucy is not old.
Someone is strong or not happy.
Lucy is not generous.
Someone is humble.
Someone is not old.
Someone is strong or tall.
Alice is both not funny and happy. | Alice is generous. | contradiction | (![X]:((creative(X)&generous(X))<=>(rich(X)|kind(X))))&
(![X]:((~strong(X)&happy(X))=>(patient(X)|rich(X))))&
(((~curious(lucy)|~happy(lucy)))=>((patient(susan)<~>~kind(susan))))&
((?[X]:((~tall(X)<~>wise(X))))=>((~happy(alice)|wise(alice))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((patient(X)&wise(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)|strong(X))))&
(![X]:(~rich(X)<=>(tall(X)|~calm(X))))&
(![X]:((~happy(X)|~strong(X))=>(~funny(X)&strong(X))))&
(![X]:(~curious(X)<=>(strong(X)|quiet(X))))&
(![X]:(~patient(X)<=>(kind(X)<~>creative(X))))&
(((~generous(paul)|~tall(paul)))<=>((~wise(paul)|humble(paul))))&
(![X]:((kind(X)&~wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((~rich(X)&~calm(X))=>(~creative(X)&humble(X))))&
((?[X]:(old(X)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(((~rich(mary)<~>funny(mary)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(brave(X)=>~patient(X)))&
(~old(lucy))&
(?[X]:((strong(X)|~happy(X))))&
(~generous(lucy))&
(?[X]:(humble(X)))&
(?[X]:(~old(X)))&
(?[X]:((strong(X)|tall(X))))&
((~funny(alice)&happy(alice))) | generous(alice) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p10",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 858422629240815649626113
% SZS output start Proof for 858422629240815649626113
1. ! [X0] : ((generous(X0) & creative(X0)) <=> (kind(X0) | rich(X0))) [input p0]
4. ? [X0] : (~tall(X0) <~> wise(X0)) => (wise(alice) | ~happy(alice)) [input p3]
5. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X0] : (wise(X0) & patient(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (~calm(X0) | tall(X0))) [input p6]
10. ! [X0] : (~patient(X0) <=> (kind(X0) <~> creative(X0))) [input p9]
11. (~tall(paul) | ~generous(paul)) <=> (humble(paul) | ~wise(paul)) [input p10]
12. ! [X0] : ((~wise(X0) & kind(X0)) <=> (generous(X0) | ~wise(X0))) [input p11]
13. ! [X0] : ((~calm(X0) & ~rich(X0)) => (humble(X0) & ~creative(X0))) [input p12]
23. happy(alice) & ~funny(alice) [input p22]
24. generous(alice) [input hypothesis]
25. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X1] : (wise(X1) & patient(X1)) [rectify 5]
36. (wise(alice) | ~happy(alice)) | ! [X0] : (~tall(X0) <=> wise(X0)) [ennf transformation 4]
37. wise(alice) | ~happy(alice) | ! [X0] : (~tall(X0) <=> wise(X0)) [flattening 36]
40. ! [X0] : ((humble(X0) & ~creative(X0)) | (calm(X0) | rich(X0))) [ennf transformation 13]
41. ! [X0] : ((humble(X0) & ~creative(X0)) | calm(X0) | rich(X0)) [flattening 40]
43. ! [X0] : (((generous(X0) & creative(X0)) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | (~generous(X0) | ~creative(X0)))) [nnf transformation 1]
44. ! [X0] : (((generous(X0) & creative(X0)) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~generous(X0) | ~creative(X0))) [flattening 43]
46. wise(alice) | ~happy(alice) | ! [X0] : ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))) [nnf transformation 37]
47. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : (~wise(X1) | ~patient(X1))) & (? [X1] : (wise(X1) & patient(X1)) | ! [X0] : (~creative(X0) | tall(X0))) [nnf transformation 25]
48. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : (~wise(X1) | ~patient(X1))) & (? [X2] : (wise(X2) & patient(X2)) | ! [X3] : (~creative(X3) | tall(X3))) [rectify 47]
49. ? [X0] : (creative(X0) & ~tall(X0)) => (creative(sK0) & ~tall(sK0)) [choice axiom]
50. ? [X2] : (wise(X2) & patient(X2)) => (wise(sK1) & patient(sK1)) [choice axiom]
51. ((creative(sK0) & ~tall(sK0)) | ! [X1] : (~wise(X1) | ~patient(X1))) & ((wise(sK1) & patient(sK1)) | ! [X3] : (~creative(X3) | tall(X3))) [skolemisation 48,50,49]
54. ! [X0] : ((~rich(X0) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | rich(X0))) [nnf transformation 7]
55. ! [X0] : ((~rich(X0) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | rich(X0))) [flattening 54]
56. ! [X0] : ((~patient(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | patient(X0))) [nnf transformation 10]
57. ((~tall(paul) | ~generous(paul)) | (~humble(paul) & wise(paul))) & ((humble(paul) | ~wise(paul)) | (tall(paul) & generous(paul))) [nnf transformation 11]
58. (~tall(paul) | ~generous(paul) | (~humble(paul) & wise(paul))) & (humble(paul) | ~wise(paul) | (tall(paul) & generous(paul))) [flattening 57]
59. ! [X0] : (((~wise(X0) & kind(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (wise(X0) | ~kind(X0)))) [nnf transformation 12]
60. ! [X0] : (((~wise(X0) & kind(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | wise(X0) | ~kind(X0))) [flattening 59]
72. ~kind(X0) | creative(X0) [cnf transformation 44]
73. ~rich(X0) | generous(X0) [cnf transformation 44]
74. ~kind(X0) | generous(X0) [cnf transformation 44]
80. wise(alice) | ~happy(alice) | wise(X0) | tall(X0) [cnf transformation 46]
81. wise(alice) | ~happy(alice) | ~tall(X0) | ~wise(X0) [cnf transformation 46]
82. patient(sK1) | ~creative(X3) | tall(X3) [cnf transformation 51]
83. wise(sK1) | ~creative(X3) | tall(X3) [cnf transformation 51]
84. ~tall(sK0) | ~wise(X1) | ~patient(X1) [cnf transformation 51]
85. creative(sK0) | ~wise(X1) | ~patient(X1) [cnf transformation 51]
90. ~calm(X0) | tall(X0) | rich(X0) [cnf transformation 55]
92. ~rich(X0) | calm(X0) [cnf transformation 55]
98. creative(X0) | kind(X0) | patient(X0) [cnf transformation 56]
99. ~creative(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
104. ~tall(paul) | ~generous(paul) | wise(paul) [cnf transformation 58]
107. wise(X0) | kind(X0) [cnf transformation 60]
110. ~wise(X0) | ~generous(X0) [cnf transformation 60]
111. ~creative(X0) | calm(X0) | rich(X0) [cnf transformation 41]
122. happy(alice) [cnf transformation 23]
123. generous(alice) [cnf transformation 24]
146. 5 <=> ! [X0] : (~tall(X0) | ~wise(X0)) [avatar definition]
147. ~wise(X0) | ~tall(X0) <- (5) [avatar component clause 146]
149. 6 <=> happy(alice) [avatar definition]
153. 7 <=> wise(alice) [avatar definition]
155. wise(alice) <- (7) [avatar component clause 153]
156. 5 | ~6 | 7 [avatar split clause 81,153,149,146]
158. 8 <=> ! [X0] : (wise(X0) | tall(X0)) [avatar definition]
159. wise(X0) | tall(X0) <- (8) [avatar component clause 158]
160. 8 | ~6 | 7 [avatar split clause 80,153,149,158]
162. 9 <=> ! [X1] : (~wise(X1) | ~patient(X1)) [avatar definition]
163. ~wise(X1) | ~patient(X1) <- (9) [avatar component clause 162]
165. 10 <=> creative(sK0) [avatar definition]
167. creative(sK0) <- (10) [avatar component clause 165]
168. 9 | 10 [avatar split clause 85,165,162]
170. 11 <=> tall(sK0) [avatar definition]
172. ~tall(sK0) <- (~11) [avatar component clause 170]
173. 9 | ~11 [avatar split clause 84,170,162]
175. 12 <=> ! [X3] : (~creative(X3) | tall(X3)) [avatar definition]
176. ~creative(X3) | tall(X3) <- (12) [avatar component clause 175]
178. 13 <=> wise(sK1) [avatar definition]
180. wise(sK1) <- (13) [avatar component clause 178]
181. 12 | 13 [avatar split clause 83,178,175]
183. 14 <=> patient(sK1) [avatar definition]
185. patient(sK1) <- (14) [avatar component clause 183]
186. 12 | 14 [avatar split clause 82,183,175]
190. ~kind(X0) | patient(X0) [subsumption resolution 99,72]
191. patient(X0) | creative(X0) [subsumption resolution 98,190]
197. 16 <=> generous(paul) [avatar definition]
201. 17 <=> tall(paul) [avatar definition]
203. ~tall(paul) <- (~17) [avatar component clause 201]
206. 18 <=> wise(paul) [avatar definition]
207. ~wise(paul) <- (~18) [avatar component clause 206]
208. wise(paul) <- (18) [avatar component clause 206]
209. 18 | ~16 | ~17 [avatar split clause 104,201,197,206]
213. ~creative(X0) | calm(X0) [subsumption resolution 111,92]
230. 6 [avatar split clause 122,149]
231. kind(paul) <- (~18) [resolution 107,207]
233. generous(paul) <- (~18) [resolution 231,74]
237. 16 | 18 [avatar split clause 233,206,197]
239. ~generous(alice) <- (7) [resolution 110,155]
241. $false <- (7) [subsumption resolution 239,123]
242. ~7 [avatar contradiction clause 241]
247. tall(paul) <- (8, ~18) [resolution 159,207]
249. ~generous(X1) | tall(X1) <- (8) [resolution 159,110]
251. $false <- (8, ~17, ~18) [subsumption resolution 247,203]
252. ~8 | 17 | 18 [avatar contradiction clause 251]
254. ~tall(paul) <- (5, 18) [resolution 208,147]
261. ~17 | ~5 | ~18 [avatar split clause 254,206,146,201]
265. ~patient(paul) <- (9, 18) [resolution 163,208]
271. creative(paul) <- (9, 18) [resolution 191,265]
276. tall(paul) <- (9, 12, 18) [resolution 271,176]
277. $false <- (9, 12, ~17, 18) [subsumption resolution 276,203]
278. ~9 | ~12 | 17 | ~18 [avatar contradiction clause 277]
279. calm(sK0) <- (10) [resolution 167,213]
288. tall(sK0) | rich(sK0) <- (10) [resolution 90,279]
289. rich(sK0) <- (10, ~11) [subsumption resolution 288,172]
316. generous(sK0) <- (10, ~11) [resolution 289,73]
330. tall(sK0) <- (8, 10, ~11) [resolution 316,249]
333. $false <- (8, 10, ~11) [subsumption resolution 330,172]
334. ~8 | ~10 | 11 [avatar contradiction clause 333]
346. ~patient(sK1) <- (9, 13) [resolution 163,180]
347. $false <- (9, 13, 14) [subsumption resolution 346,185]
348. ~9 | ~13 | ~14 [avatar contradiction clause 347]
349. $false [avatar sat refutation 156,160,168,173,181,186,209,230,237,242,252,261,278,334,348]
% SZS output end Proof for 858422629240815649626113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not generous is either happy or not rich. If mary is either happy or not humble then someone is both not tall and not calm and vice versa. Everyone who is creative is not creative or tall. Everyone who is funny is either humble or not happy and vice versa. If someone is not quiet then someone is both not calm and wise and vice versa. If someone is quiet or wise then john is wise and vice versa. If john is not happy or not brave then someone is either not happy or not calm. If lucy is happy then alice is generous or not funny. Everyone who is either quiet or not generous is strong or not curious. If someone is quiet or not funny then someone is both tall and not kind. Everyone who is either funny or wise is kind. If susan is both funny and not curious then someone is both not tall and kind and vice versa. If someone is either not creative or old then john is both old and not happy and vice versa. If someone is tall then john is both quiet and creative and vice versa. Everyone who is either generous or patient is either not calm or kind and vice versa. Everyone who is either rich or tall is either not funny or not kind and vice versa. John is rich or not curious. John is both not patient and not quiet. Someone is both not curious and brave. John is either not happy or not creative. John is either patient or strong. Susan is both not creative and brave. Someone is not brave or not wise. Alice is not calm or kind. | Lucy is not funny. | contradiction | (![X]:((~tall(X)<~>~generous(X))=>(happy(X)<~>~rich(X))))&
(((happy(mary)<~>~humble(mary)))<=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:(creative(X)=>(~creative(X)|tall(X))))&
(![X]:(funny(X)<=>(humble(X)<~>~happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)&wise(X)))))&
((?[X]:((quiet(X)|wise(X))))<=>(wise(john)))&
(((~happy(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~calm(X)))))&
((happy(lucy))=>((generous(alice)|~funny(alice))))&
(![X]:((quiet(X)<~>~generous(X))=>(strong(X)|~curious(X))))&
((?[X]:((quiet(X)|~funny(X))))=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((funny(X)<~>wise(X))=>kind(X)))&
(((funny(susan)&~curious(susan)))<=>(?[X]:((~tall(X)&kind(X)))))&
((?[X]:((~creative(X)<~>old(X))))<=>((old(john)&~happy(john))))&
((?[X]:(tall(X)))<=>((quiet(john)&creative(john))))&
(![X]:((generous(X)<~>patient(X))<=>(~calm(X)<~>kind(X))))&
(![X]:((rich(X)<~>tall(X))<=>(~funny(X)<~>~kind(X))))&
((rich(john)|~curious(john)))&
((~patient(john)&~quiet(john)))&
(?[X]:((~curious(X)&brave(X))))&
((~happy(john)<~>~creative(john)))&
((patient(john)<~>strong(john)))&
((~creative(susan)&brave(susan)))&
(?[X]:((~brave(X)|~wise(X))))&
((~calm(alice)|kind(alice))) | ~funny(lucy) | [
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8574143273842834118965482
% SZS output start Proof for 8574143273842834118965482
10. ? [X0] : (~funny(X0) | quiet(X0)) => ? [X0] : (~kind(X0) & tall(X0)) [input p9]
14. ? [X0] : tall(X0) <=> (creative(john) & quiet(john)) [input p13]
18. ~quiet(john) & ~patient(john) [input p17]
25. ~funny(lucy) [input hypothesis]
27. ? [X0] : (~funny(X0) | quiet(X0)) => ? [X1] : (~kind(X1) & tall(X1)) [rectify 10]
36. ? [X1] : (~kind(X1) & tall(X1)) | ! [X0] : (funny(X0) & ~quiet(X0)) [ennf transformation 27]
57. ? [X0] : (~kind(X0) & tall(X0)) | ! [X1] : (funny(X1) & ~quiet(X1)) [rectify 36]
58. ? [X0] : (~kind(X0) & tall(X0)) => (~kind(sK5) & tall(sK5)) [choice axiom]
59. (~kind(sK5) & tall(sK5)) | ! [X1] : (funny(X1) & ~quiet(X1)) [skolemisation 57,58]
71. (? [X0] : tall(X0) | (~creative(john) | ~quiet(john))) & ((creative(john) & quiet(john)) | ! [X0] : ~tall(X0)) [nnf transformation 14]
72. (? [X0] : tall(X0) | ~creative(john) | ~quiet(john)) & ((creative(john) & quiet(john)) | ! [X0] : ~tall(X0)) [flattening 71]
73. (? [X0] : tall(X0) | ~creative(john) | ~quiet(john)) & ((creative(john) & quiet(john)) | ! [X1] : ~tall(X1)) [rectify 72]
74. ? [X0] : tall(X0) => tall(sK8) [choice axiom]
75. (tall(sK8) | ~creative(john) | ~quiet(john)) & ((creative(john) & quiet(john)) | ! [X1] : ~tall(X1)) [skolemisation 73,74]
113. tall(sK5) | funny(X1) [cnf transformation 59]
128. quiet(john) | ~tall(X1) [cnf transformation 75]
149. ~quiet(john) [cnf transformation 18]
160. ~funny(lucy) [cnf transformation 25]
263. 23 <=> ! [X1] : funny(X1) [avatar definition]
264. funny(X1) <- (23) [avatar component clause 263]
272. 25 <=> tall(sK5) [avatar definition]
274. tall(sK5) <- (25) [avatar component clause 272]
275. 23 | 25 [avatar split clause 113,272,263]
325. 36 <=> quiet(john) [avatar definition]
338. 39 <=> ! [X1] : ~tall(X1) [avatar definition]
339. ~tall(X1) <- (39) [avatar component clause 338]
341. 39 | 36 [avatar split clause 128,325,338]
351. ~36 [avatar split clause 149,325]
380. $false <- (23) [resolution 264,160]
381. ~23 [avatar contradiction clause 380]
382. $false <- (25, 39) [subsumption resolution 274,339]
383. ~25 | ~39 [avatar contradiction clause 382]
384. $false [avatar sat refutation 275,341,351,381,383]
% SZS output end Proof for 8574143273842834118965482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either rich or funny then paul is not generous.
Everyone who is both funny and not brave is both not calm and humble and vice versa.
If fred is rich or not generous then john is not wise or not strong.
If fred is either brave or not happy then paul is quiet.
Everyone who is either not humble or not brave is tall and vice versa.
Everyone who is creative or tall is funny or not tall.
If someone is funny or happy then someone is not funny or not generous and vice versa.
If susan is not kind or generous then someone is either curious or generous and vice versa.
Everyone who is both calm and not curious is funny and vice versa.
Everyone who is not old is both not humble and not tall and vice versa.
If someone is not creative or wise then someone is both not humble and quiet and vice versa.
If someone is both patient and not funny then paul is either not old or happy and vice versa.
If someone is not funny then john is happy or funny and vice versa.
If someone is either funny or not brave then someone is both strong and not strong.
Everyone who is either not strong or quiet is not tall.
If someone is not humble then someone is either humble or not humble.
Mary is either not brave or not quiet.
Someone is generous.
Someone is either not tall or not creative.
Someone is old or wise.
Alice is either not generous or humble.
Someone is either not patient or not tall. | Fred is not funny. | entailment | ((?[X]:((rich(X)<~>funny(X))))=>(~generous(paul)))&
(![X]:((funny(X)&~brave(X))<=>(~calm(X)&humble(X))))&
(((rich(fred)|~generous(fred)))=>((~wise(john)|~strong(john))))&
(((brave(fred)<~>~happy(fred)))=>(quiet(paul)))&
(![X]:((~humble(X)<~>~brave(X))<=>tall(X)))&
(![X]:((creative(X)|tall(X))=>(funny(X)|~tall(X))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:((calm(X)&~curious(X))<=>funny(X)))&
(![X]:(~old(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>((~old(paul)<~>happy(paul))))&
((?[X]:(~funny(X)))<=>((happy(john)|funny(john))))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~humble(X)))))&
((~brave(mary)<~>~quiet(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((old(X)|wise(X))))&
((~generous(alice)<~>humble(alice)))&
(?[X]:((~patient(X)<~>~tall(X)))) | ~funny(fred) | [
"p1",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 517492692129426495139838
% SZS output start Proof for 517492692129426495139838
2. ! [X0] : ((~brave(X0) & funny(X0)) <=> (humble(X0) & ~calm(X0))) [input p1]
9. ! [X0] : ((~curious(X0) & calm(X0)) <=> funny(X0)) [input p8]
14. ? [X0] : (funny(X0) <~> ~brave(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p13]
23. funny(fred) [input hypothesis]
26. ? [X0] : (funny(X0) <~> ~brave(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 14]
34. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (funny(X0) <=> ~brave(X0)) [ennf transformation 26]
38. ! [X0] : (((~brave(X0) & funny(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (brave(X0) | ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : (((~brave(X0) & funny(X0)) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | brave(X0) | ~funny(X0))) [flattening 38]
52. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~calm(X0)))) [nnf transformation 9]
53. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~calm(X0))) [flattening 52]
70. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))) [nnf transformation 34]
71. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1))) [rectify 70]
72. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK7) & strong(sK7)) [choice axiom]
73. (~strong(sK7) & strong(sK7)) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1))) [skolemisation 71,72]
93. ~calm(X0) | brave(X0) | ~funny(X0) [cnf transformation 39]
118. ~funny(X0) | calm(X0) [cnf transformation 53]
137. strong(sK7) | ~brave(X1) | ~funny(X1) [cnf transformation 73]
139. ~strong(sK7) | ~brave(X1) | ~funny(X1) [cnf transformation 73]
155. funny(fred) [cnf transformation 23]
192. 9 <=> brave(fred) [avatar definition]
193. ~brave(fred) <- (~9) [avatar component clause 192]
194. brave(fred) <- (9) [avatar component clause 192]
335. 41 <=> strong(sK7) [avatar definition]
340. 42 <=> ! [X1] : (~brave(X1) | ~funny(X1)) [avatar definition]
341. ~brave(X1) | ~funny(X1) <- (42) [avatar component clause 340]
342. 42 | ~41 [avatar split clause 139,335,340]
344. 42 | 41 [avatar split clause 137,335,340]
403. calm(fred) [resolution 118,155]
416. ~funny(fred) <- (9, 42) [resolution 341,194]
419. $false <- (9, 42) [subsumption resolution 416,155]
420. ~9 | ~42 [avatar contradiction clause 419]
424. brave(fred) | ~funny(fred) [resolution 93,403]
428. ~funny(fred) <- (~9) [subsumption resolution 424,193]
429. $false <- (~9) [subsumption resolution 428,155]
430. 9 [avatar contradiction clause 429]
434. $false [avatar sat refutation 342,344,420,430]
% SZS output end Proof for 517492692129426495139838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or calm is both not humble and generous.
Everyone who is funny or patient is either not strong or funny.
If someone is both not strong and strong then someone is not tall or not humble.
Everyone who is both wise and happy is both kind and not tall.
Everyone who is both creative and not kind is both not rich and generous and vice versa.
If someone is either not calm or tall then someone is quiet and vice versa.
Everyone who is both rich and not quiet is rich or not funny and vice versa.
If paul is not brave or strong then paul is not brave and vice versa.
If someone is not creative or not strong then someone is either humble or old.
Everyone who is both old and not old is brave and vice versa.
If someone is both funny and generous then lucy is not quiet and vice versa.
Everyone who is wise is patient or not funny and vice versa.
If paul is humble then someone is either not humble or funny and vice versa.
Everyone who is generous or quiet is not quiet or not humble.
If susan is either not tall or patient then lucy is not generous.
Everyone who is curious is either calm or happy and vice versa.
Lucy is either not strong or not tall.
Someone is either happy or rich.
Someone is both not calm and happy.
Someone is either humble or generous.
Someone is not wise.
Someone is old or calm.
Lucy is both strong and not curious.
Lucy is wise. | Susan is patient. | neutral | (![X]:((~wise(X)|calm(X))=>(~humble(X)&generous(X))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)<~>funny(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:((~tall(X)|~humble(X)))))&
(![X]:((wise(X)&happy(X))=>(kind(X)&~tall(X))))&
(![X]:((creative(X)&~kind(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)|~funny(X))))&
(((~brave(paul)|strong(paul)))<=>(~brave(paul)))&
((?[X]:((~creative(X)|~strong(X))))=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((old(X)&~old(X))<=>brave(X)))&
((?[X]:((funny(X)&generous(X))))<=>(~quiet(lucy)))&
(![X]:(wise(X)<=>(patient(X)|~funny(X))))&
((humble(paul))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)|~humble(X))))&
(((~tall(susan)<~>patient(susan)))=>(~generous(lucy)))&
(![X]:(curious(X)<=>(calm(X)<~>happy(X))))&
((~strong(lucy)<~>~tall(lucy)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)|calm(X))))&
((strong(lucy)&~curious(lucy)))&
(wise(lucy)) | patient(susan) | [] | null | 0 |
If someone is both not funny and old then someone is rich or curious and vice versa. Everyone who is both not generous and not funny is either not funny or funny. Everyone who is not brave is either not humble or rich. Everyone who is brave is both not patient and rich. If john is not generous then someone is not strong or rich and vice versa. If someone is not creative or calm then someone is happy or brave and vice versa. If someone is both calm and rich then susan is either not rich or not wise and vice versa. If paul is either generous or old then someone is wise and vice versa. Everyone who is quiet or not calm is both not strong and not rich and vice versa. Everyone who is either not patient or tall is not generous and vice versa. Everyone who is kind or not old is either not rich or not happy. Everyone who is either happy or not kind is both not kind and not humble. Everyone who is either quiet or generous is both curious and not quiet and vice versa. Everyone who is both quiet and creative is both patient and happy and vice versa. Everyone who is not wise or patient is either generous or not patient. Everyone who is both curious and strong is not kind and vice versa. Someone is both not quiet and kind. Fred is funny. Paul is both funny and curious. Mary is not quiet. Fred is strong. Someone is creative. Someone is either not strong or patient. | John is not generous. | entailment | ((?[X]:((~funny(X)&old(X))))<=>(?[X]:((rich(X)|curious(X)))))&
(![X]:((~generous(X)&~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:(~brave(X)=>(~humble(X)<~>rich(X))))&
(![X]:(brave(X)=>(~patient(X)&rich(X))))&
((~generous(john))<=>(?[X]:((~strong(X)|rich(X)))))&
((?[X]:((~creative(X)|calm(X))))<=>(?[X]:((happy(X)|brave(X)))))&
((?[X]:((calm(X)&rich(X))))<=>((~rich(susan)<~>~wise(susan))))&
(((generous(paul)<~>old(paul)))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|~calm(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~patient(X)<~>tall(X))<=>~generous(X)))&
(![X]:((kind(X)|~old(X))=>(~rich(X)<~>~happy(X))))&
(![X]:((happy(X)<~>~kind(X))=>(~kind(X)&~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(curious(X)&~quiet(X))))&
(![X]:((quiet(X)&creative(X))<=>(patient(X)&happy(X))))&
(![X]:((~wise(X)|patient(X))=>(generous(X)<~>~patient(X))))&
(![X]:((curious(X)&strong(X))<=>~kind(X)))&
(?[X]:((~quiet(X)&kind(X))))&
(funny(fred))&
((funny(paul)&curious(paul)))&
(~quiet(mary))&
(strong(fred))&
(?[X]:(creative(X)))&
(?[X]:((~strong(X)<~>patient(X)))) | ~generous(john) | [
"p4",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6668391524355858251178493
% SZS output start Proof for 6668391524355858251178493
5. ~generous(john) <=> ? [X0] : (rich(X0) | ~strong(X0)) [input p4]
11. ! [X0] : ((~old(X0) | kind(X0)) => (~rich(X0) <~> ~happy(X0))) [input p10]
12. ! [X0] : ((happy(X0) <~> ~kind(X0)) => (~humble(X0) & ~kind(X0))) [input p11]
17. ? [X0] : (kind(X0) & ~quiet(X0)) [input p16]
24. generous(john) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> ~happy(X0)) | (old(X0) & ~kind(X0))) [ennf transformation 11]
32. ! [X0] : ((~humble(X0) & ~kind(X0)) | (happy(X0) <=> ~kind(X0))) [ennf transformation 12]
41. (~generous(john) | ! [X0] : (~rich(X0) & strong(X0))) & (? [X0] : (rich(X0) | ~strong(X0)) | generous(john)) [nnf transformation 5]
42. (~generous(john) | ! [X0] : (~rich(X0) & strong(X0))) & (? [X1] : (rich(X1) | ~strong(X1)) | generous(john)) [rectify 41]
43. ? [X1] : (rich(X1) | ~strong(X1)) => (rich(sK2) | ~strong(sK2)) [choice axiom]
44. (~generous(john) | ! [X0] : (~rich(X0) & strong(X0))) & ((rich(sK2) | ~strong(sK2)) | generous(john)) [skolemisation 42,43]
61. ! [X0] : (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (old(X0) & ~kind(X0))) [nnf transformation 31]
62. ! [X0] : ((~humble(X0) & ~kind(X0)) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) [nnf transformation 32]
70. ? [X0] : (kind(X0) & ~quiet(X0)) => (kind(sK7) & ~quiet(sK7)) [choice axiom]
71. kind(sK7) & ~quiet(sK7) [skolemisation 17,70]
90. ~generous(john) | ~rich(X0) [cnf transformation 44]
116. ~kind(X0) | rich(X0) | happy(X0) [cnf transformation 61]
118. ~kind(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 62]
140. kind(sK7) [cnf transformation 71]
149. generous(john) [cnf transformation 24]
153. ~kind(X0) | ~happy(X0) [duplicate literal removal 118]
165. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
166. ~rich(X1) <- (3) [avatar component clause 165]
187. 8 <=> generous(john) [avatar definition]
190. 3 | ~8 [avatar split clause 90,187,165]
290. 8 [avatar split clause 149,187]
305. ~happy(sK7) [resolution 153,140]
343. rich(sK7) | happy(sK7) [resolution 116,140]
346. happy(sK7) <- (3) [subsumption resolution 343,166]
347. $false <- (3) [subsumption resolution 346,305]
348. ~3 [avatar contradiction clause 347]
351. $false [avatar sat refutation 190,290,348]
% SZS output end Proof for 6668391524355858251178493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and strong then someone is curious.
If someone is either humble or curious then lucy is both generous and old and vice versa.
If someone is happy or not calm then mary is not patient.
If someone is tall or calm then fred is either not calm or old.
If someone is either brave or curious then alice is not kind and vice versa.
Everyone who is funny is both quiet and not calm.
If alice is creative then paul is not creative or curious and vice versa.
If john is curious then someone is both not humble and not strong.
If fred is kind or funny then lucy is either not tall or rich and vice versa.
If mary is quiet or old then alice is not rich or not happy.
Everyone who is creative is not calm and vice versa.
Everyone who is tall or not patient is not funny.
Everyone who is not funny is curious.
If john is not calm then fred is both kind and generous and vice versa.
Everyone who is not old or not quiet is either calm or creative and vice versa.
If someone is both not quiet and not tall then someone is not curious and vice versa.
Susan is humble or not strong.
Alice is either not old or not tall.
Someone is both creative and not brave.
Alice is either not creative or not happy.
Someone is both not strong and patient.
Paul is calm.
Lucy is not strong.
Alice is both quiet and not old. | Mary is not curious. | contradiction | ((?[X]:((~wise(X)&strong(X))))=>(?[X]:(curious(X))))&
((?[X]:((humble(X)<~>curious(X))))<=>((generous(lucy)&old(lucy))))&
((?[X]:((happy(X)|~calm(X))))=>(~patient(mary)))&
((?[X]:((tall(X)|calm(X))))=>((~calm(fred)<~>old(fred))))&
((?[X]:((brave(X)<~>curious(X))))<=>(~kind(alice)))&
(![X]:(funny(X)=>(quiet(X)&~calm(X))))&
((creative(alice))<=>((~creative(paul)|curious(paul))))&
((curious(john))=>(?[X]:((~humble(X)&~strong(X)))))&
(((kind(fred)|funny(fred)))<=>((~tall(lucy)<~>rich(lucy))))&
(((quiet(mary)|old(mary)))=>((~rich(alice)|~happy(alice))))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:((tall(X)|~patient(X))=>~funny(X)))&
(![X]:(~funny(X)=>curious(X)))&
((~calm(john))<=>((kind(fred)&generous(fred))))&
(![X]:((~old(X)|~quiet(X))<=>(calm(X)<~>creative(X))))&
((?[X]:((~quiet(X)&~tall(X))))<=>(?[X]:(~curious(X))))&
((humble(susan)|~strong(susan)))&
((~old(alice)<~>~tall(alice)))&
(?[X]:((creative(X)&~brave(X))))&
((~creative(alice)<~>~happy(alice)))&
(?[X]:((~strong(X)&patient(X))))&
(calm(paul))&
(~strong(lucy))&
((quiet(alice)&~old(alice))) | ~curious(mary) | [
"p2",
"p10",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8315817688901791052705554
% SZS output start Proof for 8315817688901791052705554
3. ? [X0] : (~calm(X0) | happy(X0)) => ~patient(mary) [input p2]
11. ! [X0] : (creative(X0) <=> ~calm(X0)) [input p10]
12. ! [X0] : ((~patient(X0) | tall(X0)) => ~funny(X0)) [input p11]
13. ! [X0] : (~funny(X0) => curious(X0)) [input p12]
19. ? [X0] : (~brave(X0) & creative(X0)) [input p18]
25. ~curious(mary) [input hypothesis]
33. ~patient(mary) | ! [X0] : (calm(X0) & ~happy(X0)) [ennf transformation 3]
39. ! [X0] : (~funny(X0) | (patient(X0) & ~tall(X0))) [ennf transformation 12]
40. ! [X0] : (curious(X0) | funny(X0)) [ennf transformation 13]
57. ! [X0] : ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))) [nnf transformation 11]
68. ? [X0] : (~brave(X0) & creative(X0)) => (~brave(sK5) & creative(sK5)) [choice axiom]
69. ~brave(sK5) & creative(sK5) [skolemisation 19,68]
80. ~patient(mary) | calm(X0) [cnf transformation 33]
103. ~creative(X0) | ~calm(X0) [cnf transformation 57]
106. ~funny(X0) | patient(X0) [cnf transformation 39]
107. funny(X0) | curious(X0) [cnf transformation 40]
122. creative(sK5) [cnf transformation 69]
130. ~curious(mary) [cnf transformation 25]
160. 7 <=> ! [X0] : calm(X0) [avatar definition]
161. calm(X0) <- (7) [avatar component clause 160]
163. 8 <=> patient(mary) [avatar definition]
165. ~patient(mary) <- (~8) [avatar component clause 163]
166. 7 | ~8 [avatar split clause 80,163,160]
323. ~calm(sK5) [resolution 103,122]
327. patient(X0) | curious(X0) [resolution 107,106]
335. curious(mary) <- (~8) [resolution 327,165]
336. $false <- (~8) [subsumption resolution 335,130]
337. 8 [avatar contradiction clause 336]
341. $false <- (7) [resolution 161,323]
342. ~7 [avatar contradiction clause 341]
346. $false [avatar sat refutation 166,337,342]
% SZS output end Proof for 8315817688901791052705554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not curious then lucy is wise.
Everyone who is both not old and old is not generous or old and vice versa.
If mary is generous then susan is both quiet and happy.
Everyone who is not calm or not wise is kind or quiet and vice versa.
If susan is not creative then someone is patient or not funny and vice versa.
If someone is either not kind or curious then someone is both not wise and happy.
Everyone who is either old or rich is curious and vice versa.
Everyone who is not happy or curious is both generous and not happy.
If someone is either happy or not tall then someone is both generous and not calm.
Everyone who is either creative or rich is not tall and vice versa.
If someone is both patient and strong then someone is both not wise and strong and vice versa.
If someone is both not wise and old then lucy is not generous.
Everyone who is not brave or not generous is either happy or not kind.
If mary is calm or not quiet then someone is either not kind or old and vice versa.
Everyone who is both not humble and creative is either not funny or not patient and vice versa.
If someone is both not happy and not calm then mary is quiet or patient and vice versa.
Alice is not humble.
Someone is funny.
Paul is not patient or old.
Someone is either funny or strong.
John is not kind.
Susan is not humble or rich.
Someone is both not kind and not humble.
Someone is either not kind or happy. | Susan is not creative. | neutral | ((?[X]:((old(X)&~curious(X))))=>(wise(lucy)))&
(![X]:((~old(X)&old(X))<=>(~generous(X)|old(X))))&
((generous(mary))=>((quiet(susan)&happy(susan))))&
(![X]:((~calm(X)|~wise(X))<=>(kind(X)|quiet(X))))&
((~creative(susan))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((~kind(X)<~>curious(X))))=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((old(X)<~>rich(X))<=>curious(X)))&
(![X]:((~happy(X)|curious(X))=>(generous(X)&~happy(X))))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((generous(X)&~calm(X)))))&
(![X]:((creative(X)<~>rich(X))<=>~tall(X)))&
((?[X]:((patient(X)&strong(X))))<=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:((~wise(X)&old(X))))=>(~generous(lucy)))&
(![X]:((~brave(X)|~generous(X))=>(happy(X)<~>~kind(X))))&
(((calm(mary)|~quiet(mary)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
(~humble(alice))&
(?[X]:(funny(X)))&
((~patient(paul)|old(paul)))&
(?[X]:((funny(X)<~>strong(X))))&
(~kind(john))&
((~humble(susan)|rich(susan)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((~kind(X)<~>happy(X)))) | ~creative(susan) | [] | null | 0 |
Everyone who is wise is humble or creative and vice versa.
If lucy is brave then lucy is not tall or brave.
Everyone who is not wise or not funny is either quiet or not old.
Everyone who is strong or wise is either not happy or tall.
If john is both patient and not patient then someone is either not old or not tall and vice versa.
Everyone who is both not patient and not curious is either humble or rich and vice versa.
If someone is not strong or not calm then fred is not happy.
If john is either not strong or not tall then paul is either generous or not calm and vice versa.
Everyone who is either not humble or not funny is either not rich or not creative.
Everyone who is not creative is both not happy and patient and vice versa.
Everyone who is not creative or not strong is both not tall and not happy.
Everyone who is wise or tall is strong and vice versa.
Everyone who is creative or not wise is patient or not rich.
Everyone who is patient is either wise or rich.
If lucy is either not kind or curious then paul is both not brave and not humble.
Everyone who is not old or rich is not generous or not creative and vice versa.
Paul is either funny or not happy.
Someone is either rich or patient.
Susan is both not calm and not brave.
Fred is either not old or curious.
Someone is either not wise or old.
Someone is not creative or not quiet.
Mary is either not rich or patient. | Mary is not old. | neutral | (![X]:(wise(X)<=>(humble(X)|creative(X))))&
((brave(lucy))=>((~tall(lucy)|brave(lucy))))&
(![X]:((~wise(X)|~funny(X))=>(quiet(X)<~>~old(X))))&
(![X]:((strong(X)|wise(X))=>(~happy(X)<~>tall(X))))&
(((patient(john)&~patient(john)))<=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((~patient(X)&~curious(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~strong(X)|~calm(X))))=>(~happy(fred)))&
(((~strong(john)<~>~tall(john)))<=>((generous(paul)<~>~calm(paul))))&
(![X]:((~humble(X)<~>~funny(X))=>(~rich(X)<~>~creative(X))))&
(![X]:(~creative(X)<=>(~happy(X)&patient(X))))&
(![X]:((~creative(X)|~strong(X))=>(~tall(X)&~happy(X))))&
(![X]:((wise(X)|tall(X))<=>strong(X)))&
(![X]:((creative(X)|~wise(X))=>(patient(X)|~rich(X))))&
(![X]:(patient(X)=>(wise(X)<~>rich(X))))&
(((~kind(lucy)<~>curious(lucy)))=>((~brave(paul)&~humble(paul))))&
(![X]:((~old(X)|rich(X))<=>(~generous(X)|~creative(X))))&
((funny(paul)<~>~happy(paul)))&
(?[X]:((rich(X)<~>patient(X))))&
((~calm(susan)&~brave(susan)))&
((~old(fred)<~>curious(fred)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~creative(X)|~quiet(X))))&
((~rich(mary)<~>patient(mary))) | ~old(mary) | [] | null | 0 |
Everyone who is both kind and not curious is not quiet and vice versa.
If someone is not calm then someone is either not funny or calm and vice versa.
Everyone who is either quiet or rich is not wise and vice versa.
Everyone who is calm is not humble or not tall and vice versa.
If susan is not rich or not funny then fred is not calm.
Everyone who is brave is kind and vice versa.
If alice is both happy and not quiet then alice is not tall or not brave and vice versa.
Everyone who is not rich is not creative.
Everyone who is not quiet or kind is either not creative or kind and vice versa.
If someone is not funny or not old then susan is either calm or not kind.
Everyone who is either funny or not creative is both not rich and humble.
If someone is rich then someone is not strong and vice versa.
Everyone who is either not humble or creative is either calm or not wise and vice versa.
Everyone who is not creative or strong is not creative and vice versa.
Fred is humble or not humble.
Someone is either not wise or not kind.
Someone is creative.
John is either not old or not happy.
Susan is either curious or not funny. | John is happy. | neutral | (![X]:((kind(X)&~curious(X))<=>~quiet(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(~humble(X)|~tall(X))))&
(((~rich(susan)|~funny(susan)))=>(~calm(fred)))&
(![X]:(brave(X)<=>kind(X)))&
(((happy(alice)&~quiet(alice)))<=>((~tall(alice)|~brave(alice))))&
(![X]:(~rich(X)=>~creative(X)))&
(![X]:((~quiet(X)|kind(X))<=>(~creative(X)<~>kind(X))))&
((?[X]:((~funny(X)|~old(X))))=>((calm(susan)<~>~kind(susan))))&
(![X]:((funny(X)<~>~creative(X))=>(~rich(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(calm(X)<~>~wise(X))))&
(![X]:((~creative(X)|strong(X))<=>~creative(X)))&
((humble(fred)|~humble(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:(creative(X)))&
((~old(john)<~>~happy(john)))&
((curious(susan)<~>~funny(susan))) | happy(john) | [] | null | 0 |
If someone is both not old and not wise then someone is both not old and not curious and vice versa.
Everyone who is not brave or quiet is either not old or not rich and vice versa.
Everyone who is both tall and not rich is not old and vice versa.
If mary is either not creative or wise then someone is either humble or creative.
Everyone who is both not curious and happy is not tall and vice versa.
Everyone who is both creative and not funny is not quiet or not wise and vice versa.
If someone is both old and not wise then someone is either rich or not creative.
Everyone who is not rich or not kind is either not old or curious and vice versa.
Everyone who is both not tall and not curious is not kind or not calm.
Everyone who is not calm is either not patient or not strong.
If alice is patient or funny then someone is either not patient or strong.
If lucy is both patient and not generous then someone is funny or kind.
Everyone who is not brave or not wise is not old and vice versa.
If mary is both not kind and funny then paul is both not tall and generous.
If someone is strong then someone is humble and vice versa.
Everyone who is either quiet or not generous is not happy or kind.
Someone is both happy and creative.
Lucy is either wise or not happy.
Someone is not kind.
Mary is humble.
Someone is not humble.
Mary is not curious. | Alice is not strong. | neutral | ((?[X]:((~old(X)&~wise(X))))<=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((tall(X)&~rich(X))<=>~old(X)))&
(((~creative(mary)<~>wise(mary)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
(![X]:((creative(X)&~funny(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(~old(X)<~>curious(X))))&
(![X]:((~tall(X)&~curious(X))=>(~kind(X)|~calm(X))))&
(![X]:(~calm(X)=>(~patient(X)<~>~strong(X))))&
(((patient(alice)|funny(alice)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((patient(lucy)&~generous(lucy)))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~brave(X)|~wise(X))<=>~old(X)))&
(((~kind(mary)&funny(mary)))=>((~tall(paul)&generous(paul))))&
((?[X]:(strong(X)))<=>(?[X]:(humble(X))))&
(![X]:((quiet(X)<~>~generous(X))=>(~happy(X)|kind(X))))&
(?[X]:((happy(X)&creative(X))))&
((wise(lucy)<~>~happy(lucy)))&
(?[X]:(~kind(X)))&
(humble(mary))&
(?[X]:(~humble(X)))&
(~curious(mary)) | ~strong(alice) | [] | null | 0 |
If paul is both not quiet and not tall then someone is both humble and curious and vice versa.
If mary is happy or not happy then lucy is either not tall or not curious and vice versa.
Everyone who is either not calm or not old is not calm and vice versa.
If alice is not curious then john is both not kind and not rich and vice versa.
Everyone who is either not humble or not old is happy or not patient and vice versa.
Everyone who is happy or not generous is not calm or generous.
Everyone who is both humble and not patient is not curious.
Everyone who is not funny or old is both not curious and not kind and vice versa.
Everyone who is both not quiet and tall is either curious or rich and vice versa.
If someone is both not quiet and not old then fred is either not happy or calm and vice versa.
Everyone who is both curious and patient is either not creative or wise.
If someone is either happy or not calm then someone is both old and tall.
Everyone who is funny or kind is either patient or happy and vice versa.
Everyone who is either funny or curious is not calm or not brave.
If someone is either calm or not wise then someone is either tall or happy and vice versa.
Everyone who is both not wise and kind is patient or not funny and vice versa.
Someone is quiet.
John is not humble.
Alice is either not quiet or not patient.
Alice is both not brave and old. | Mary is calm. | neutral | (((~quiet(paul)&~tall(paul)))<=>(?[X]:((humble(X)&curious(X)))))&
(((happy(mary)|~happy(mary)))<=>((~tall(lucy)<~>~curious(lucy))))&
(![X]:((~calm(X)<~>~old(X))<=>~calm(X)))&
((~curious(alice))<=>((~kind(john)&~rich(john))))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~patient(X))))&
(![X]:((happy(X)|~generous(X))=>(~calm(X)|generous(X))))&
(![X]:((humble(X)&~patient(X))=>~curious(X)))&
(![X]:((~funny(X)|old(X))<=>(~curious(X)&~kind(X))))&
(![X]:((~quiet(X)&tall(X))<=>(curious(X)<~>rich(X))))&
((?[X]:((~quiet(X)&~old(X))))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((curious(X)&patient(X))=>(~creative(X)<~>wise(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((funny(X)|kind(X))<=>(patient(X)<~>happy(X))))&
(![X]:((funny(X)<~>curious(X))=>(~calm(X)|~brave(X))))&
((?[X]:((calm(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~wise(X)&kind(X))<=>(patient(X)|~funny(X))))&
(?[X]:(quiet(X)))&
(~humble(john))&
((~quiet(alice)<~>~patient(alice)))&
((~brave(alice)&old(alice))) | calm(mary) | [] | null | 0 |
Everyone who is either strong or not calm is not happy. If someone is both not wise and not happy then fred is not old and vice versa. If fred is not generous or not kind then someone is either brave or not creative and vice versa. If mary is creative then someone is either not creative or brave. If alice is both patient and calm then someone is tall or calm and vice versa. If someone is not old then someone is happy or not curious. Everyone who is either not patient or calm is not kind or calm. Everyone who is calm or not old is either not calm or humble. Everyone who is both strong and wise is not creative or quiet and vice versa. Everyone who is both tall and not strong is either funny or patient and vice versa. Everyone who is not curious is either patient or curious. If someone is either creative or wise then someone is either tall or creative. Everyone who is calm or not brave is either not quiet or old and vice versa. Everyone who is not curious or not kind is not humble or not calm. Everyone who is strong or curious is not strong and vice versa. Everyone who is not wise is both brave and not patient. Fred is either funny or tall. Someone is both not funny and curious. John is not tall. Someone is both not kind and not generous. | Mary is not strong. | entailment | (![X]:((strong(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>(~old(fred)))&
(((~generous(fred)|~kind(fred)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
((creative(mary))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((patient(alice)&calm(alice)))<=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(~kind(X)|calm(X))))&
(![X]:((calm(X)|~old(X))=>(~calm(X)<~>humble(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)|quiet(X))))&
(![X]:((tall(X)&~strong(X))<=>(funny(X)<~>patient(X))))&
(![X]:(~curious(X)=>(patient(X)<~>curious(X))))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((calm(X)|~brave(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~humble(X)|~calm(X))))&
(![X]:((strong(X)|curious(X))<=>~strong(X)))&
(![X]:(~wise(X)=>(brave(X)&~patient(X))))&
((funny(fred)<~>tall(fred)))&
(?[X]:((~funny(X)&curious(X))))&
(~tall(john))&
(?[X]:((~kind(X)&~generous(X)))) | ~strong(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4216404028475406949383354
% SZS output start Proof for 4216404028475406949383354
15. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p14]
21. strong(mary) [input hypothesis]
69. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [nnf transformation 15]
70. ! [X0] : ((curious(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [flattening 69]
126. ~strong(X0) | ~strong(X0) [cnf transformation 70]
138. strong(mary) [cnf transformation 21]
139. ~strong(X0) [duplicate literal removal 126]
277. $false [subsumption resolution 138,139]
% SZS output end Proof for 4216404028475406949383354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either kind or not patient then john is either not generous or not happy and vice versa.
If fred is brave then alice is both rich and strong and vice versa.
Everyone who is both not rich and happy is either funny or kind and vice versa.
Everyone who is either patient or not tall is not patient or wise and vice versa.
Everyone who is happy is quiet.
If someone is either quiet or not rich then susan is not old.
Everyone who is both brave and funny is curious or generous and vice versa.
Everyone who is both strong and funny is either humble or wise.
Everyone who is either not curious or happy is either kind or not old.
Everyone who is either not old or calm is quiet.
Everyone who is either not patient or old is both not wise and generous.
If paul is not calm or not patient then paul is both not brave and not kind and vice versa.
If someone is either not kind or generous then someone is not kind and vice versa.
Everyone who is not creative or humble is either generous or brave and vice versa.
Everyone who is either not kind or happy is generous.
If fred is creative then fred is either calm or not patient and vice versa.
Mary is either quiet or kind.
Mary is both not generous and not kind.
Susan is old.
Someone is either tall or not curious.
Someone is not creative or creative.
Paul is either not tall or brave.
Someone is either kind or calm.
Someone is either not brave or tall. | Paul is not funny. | contradiction | (((kind(mary)<~>~patient(mary)))<=>((~generous(john)<~>~happy(john))))&
((brave(fred))<=>((rich(alice)&strong(alice))))&
(![X]:((~rich(X)&happy(X))<=>(funny(X)<~>kind(X))))&
(![X]:((patient(X)<~>~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((quiet(X)<~>~rich(X))))=>(~old(susan)))&
(![X]:((brave(X)&funny(X))<=>(curious(X)|generous(X))))&
(![X]:((strong(X)&funny(X))=>(humble(X)<~>wise(X))))&
(![X]:((~curious(X)<~>happy(X))=>(kind(X)<~>~old(X))))&
(![X]:((~old(X)<~>calm(X))=>quiet(X)))&
(![X]:((~patient(X)<~>old(X))=>(~wise(X)&generous(X))))&
(((~calm(paul)|~patient(paul)))<=>((~brave(paul)&~kind(paul))))&
((?[X]:((~kind(X)<~>generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(generous(X)<~>brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>generous(X)))&
((creative(fred))<=>((calm(fred)<~>~patient(fred))))&
((quiet(mary)<~>kind(mary)))&
((~generous(mary)&~kind(mary)))&
(old(susan))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~creative(X)|creative(X))))&
((~tall(paul)<~>brave(paul)))&
(?[X]:((kind(X)<~>calm(X))))&
(?[X]:((~brave(X)<~>tall(X)))) | ~funny(paul) | [
"p2",
"p4",
"p5",
"p6",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 759933476394237815551720
% SZS output start Proof for 759933476394237815551720
3. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (funny(X0) <~> kind(X0))) [input p2]
5. ! [X0] : (happy(X0) => quiet(X0)) [input p4]
6. ? [X0] : (quiet(X0) <~> ~rich(X0)) => ~old(susan) [input p5]
7. ! [X0] : ((funny(X0) & brave(X0)) <=> (generous(X0) | curious(X0))) [input p6]
15. ! [X0] : ((~kind(X0) <~> happy(X0)) => generous(X0)) [input p14]
19. old(susan) [input p18]
25. ~funny(paul) [input hypothesis]
27. ! [X0] : (quiet(X0) | ~happy(X0)) [ennf transformation 5]
28. ~old(susan) | ! [X0] : (quiet(X0) <=> ~rich(X0)) [ennf transformation 6]
34. ! [X0] : (generous(X0) | (~kind(X0) <=> happy(X0))) [ennf transformation 15]
38. ! [X0] : (((happy(X0) & ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (~happy(X0) | rich(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) & (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | ~happy(X0) | rich(X0))) [flattening 38]
42. ~old(susan) | ! [X0] : ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))) [nnf transformation 28]
43. ! [X0] : (((funny(X0) & brave(X0)) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | (~funny(X0) | ~brave(X0)))) [nnf transformation 7]
44. ! [X0] : (((funny(X0) & brave(X0)) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ~funny(X0) | ~brave(X0))) [flattening 43]
58. ! [X0] : (generous(X0) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 34]
84. ~happy(X0) | funny(X0) | kind(X0) | rich(X0) [cnf transformation 39]
89. ~kind(X0) | funny(X0) | happy(X0) [cnf transformation 39]
96. ~happy(X0) | quiet(X0) [cnf transformation 27]
97. ~old(susan) | ~rich(X0) | ~quiet(X0) [cnf transformation 42]
103. ~generous(X0) | funny(X0) [cnf transformation 44]
131. happy(X0) | generous(X0) | kind(X0) [cnf transformation 58]
132. ~happy(X0) | ~kind(X0) | generous(X0) [cnf transformation 58]
141. old(susan) [cnf transformation 19]
151. ~funny(paul) [cnf transformation 25]
198. 9 <=> old(susan) [avatar definition]
203. 10 <=> ! [X0] : (~rich(X0) | ~quiet(X0)) [avatar definition]
204. ~quiet(X0) | ~rich(X0) <- (10) [avatar component clause 203]
205. 10 | ~9 [avatar split clause 97,198,203]
211. 12 <=> kind(paul) [avatar definition]
212. ~kind(paul) <- (~12) [avatar component clause 211]
213. kind(paul) <- (12) [avatar component clause 211]
279. 9 [avatar split clause 141,198]
368. 39 <=> quiet(paul) [avatar definition]
369. ~quiet(paul) <- (~39) [avatar component clause 368]
370. quiet(paul) <- (39) [avatar component clause 368]
434. quiet(X0) | kind(X0) | generous(X0) [resolution 131,96]
442. funny(X0) | kind(X0) | rich(X0) | generous(X0) | kind(X0) [resolution 84,131]
443. funny(X0) | kind(X0) | rich(X0) | generous(X0) [duplicate literal removal 442]
444. funny(X0) | kind(X0) | rich(X0) [subsumption resolution 443,103]
504. 57 <=> generous(paul) [avatar definition]
505. ~generous(paul) <- (~57) [avatar component clause 504]
506. generous(paul) <- (57) [avatar component clause 504]
536. 63 <=> happy(paul) [avatar definition]
538. happy(paul) <- (63) [avatar component clause 536]
569. kind(paul) | rich(paul) [resolution 444,151]
578. rich(paul) <- (~12) [subsumption resolution 569,212]
581. funny(paul) <- (57) [resolution 506,103]
583. $false <- (57) [subsumption resolution 581,151]
584. ~57 [avatar contradiction clause 583]
599. ~rich(paul) <- (10, 39) [resolution 370,204]
600. $false <- (10, ~12, 39) [subsumption resolution 599,578]
601. ~10 | 12 | ~39 [avatar contradiction clause 600]
609. kind(paul) | generous(paul) <- (~39) [resolution 369,434]
614. kind(paul) <- (~39, ~57) [subsumption resolution 609,505]
615. 12 | 39 | 57 [avatar split clause 614,504,368,211]
617. funny(paul) | happy(paul) <- (12) [resolution 213,89]
622. happy(paul) <- (12) [subsumption resolution 617,151]
625. 63 | ~12 [avatar split clause 622,211,536]
633. ~kind(paul) | generous(paul) <- (63) [resolution 538,132]
635. generous(paul) <- (12, 63) [subsumption resolution 633,213]
636. $false <- (12, ~57, 63) [subsumption resolution 635,505]
637. ~12 | 57 | ~63 [avatar contradiction clause 636]
638. $false [avatar sat refutation 205,279,584,601,615,625,637]
% SZS output end Proof for 759933476394237815551720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or patient is both not brave and not strong and vice versa.
Everyone who is either quiet or not patient is funny or wise.
If someone is rich then someone is quiet or not happy.
Everyone who is both creative and calm is either creative or not generous and vice versa.
Everyone who is tall is brave or generous.
Everyone who is not curious or not patient is happy.
Everyone who is either calm or curious is not wise or funny.
Everyone who is not rich or happy is both brave and not generous and vice versa.
If someone is not tall then someone is both not calm and not curious and vice versa.
If someone is either not calm or quiet then someone is not quiet and vice versa.
If john is not rich or brave then lucy is not curious and vice versa.
Everyone who is either not tall or not creative is curious or not humble.
Everyone who is either not calm or happy is not creative or strong and vice versa.
If mary is both not brave and calm then someone is rich.
If mary is not patient then lucy is creative or calm and vice versa.
If alice is both not humble and patient then someone is tall or kind.
Alice is happy or calm.
Someone is both calm and kind.
Someone is both not generous and funny.
Mary is not tall or old.
Alice is either not strong or not brave.
Lucy is not kind.
Someone is either not funny or not curious.
Someone is both not funny and not humble. | Mary is generous. | neutral | (![X]:((~kind(X)<~>patient(X))<=>(~brave(X)&~strong(X))))&
(![X]:((quiet(X)<~>~patient(X))=>(funny(X)|wise(X))))&
((?[X]:(rich(X)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((creative(X)&calm(X))<=>(creative(X)<~>~generous(X))))&
(![X]:(tall(X)=>(brave(X)|generous(X))))&
(![X]:((~curious(X)|~patient(X))=>happy(X)))&
(![X]:((calm(X)<~>curious(X))=>(~wise(X)|funny(X))))&
(![X]:((~rich(X)|happy(X))<=>(brave(X)&~generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~calm(X)&~curious(X)))))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:(~quiet(X))))&
(((~rich(john)|brave(john)))<=>(~curious(lucy)))&
(![X]:((~tall(X)<~>~creative(X))=>(curious(X)|~humble(X))))&
(![X]:((~calm(X)<~>happy(X))<=>(~creative(X)|strong(X))))&
(((~brave(mary)&calm(mary)))=>(?[X]:(rich(X))))&
((~patient(mary))<=>((creative(lucy)|calm(lucy))))&
(((~humble(alice)&patient(alice)))=>(?[X]:((tall(X)|kind(X)))))&
((happy(alice)|calm(alice)))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:((~generous(X)&funny(X))))&
((~tall(mary)|old(mary)))&
((~strong(alice)<~>~brave(alice)))&
(~kind(lucy))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~funny(X)&~humble(X)))) | generous(mary) | [] | null | 0 |
If fred is not happy or not generous then someone is both not humble and brave and vice versa.
Everyone who is either rich or not happy is both not patient and generous and vice versa.
Everyone who is either patient or funny is either not generous or rich and vice versa.
Everyone who is both not strong and not happy is both not quiet and tall.
Everyone who is rich is calm.
If someone is both not kind and curious then someone is strong or not old and vice versa.
Everyone who is either kind or not happy is not strong or patient and vice versa.
If fred is either happy or not kind then someone is both not quiet and not creative and vice versa.
If someone is both humble and funny then fred is not kind or not rich.
Everyone who is not calm or happy is not curious and vice versa.
Everyone who is either not tall or not generous is both not quiet and brave.
Everyone who is not funny is kind or strong and vice versa.
Everyone who is either creative or not curious is both wise and not calm.
Everyone who is both not happy and tall is old or not rich.
Everyone who is tall or not generous is generous and vice versa.
If someone is both not rich and not curious then someone is not tall.
Someone is rich.
Someone is not happy.
Someone is not generous or kind.
Susan is both old and not creative.
Alice is not generous or old.
Someone is not wise or not funny. | Alice is not calm. | contradiction | (((~happy(fred)|~generous(fred)))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((rich(X)<~>~happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((patient(X)<~>funny(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~strong(X)&~happy(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>calm(X)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(((happy(fred)<~>~kind(fred)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((humble(X)&funny(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~calm(X)|happy(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>~generous(X))=>(~quiet(X)&brave(X))))&
(![X]:(~funny(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)<~>~curious(X))=>(wise(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))=>(old(X)|~rich(X))))&
(![X]:((tall(X)|~generous(X))<=>generous(X)))&
((?[X]:((~rich(X)&~curious(X))))=>(?[X]:(~tall(X))))&
(?[X]:(rich(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)|kind(X))))&
((old(susan)&~creative(susan)))&
((~generous(alice)|old(alice)))&
(?[X]:((~wise(X)|~funny(X)))) | ~calm(alice) | [
"p4",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 334565716757684471612756
% SZS output start Proof for 334565716757684471612756
5. ! [X0] : (rich(X0) => calm(X0)) [input p4]
10. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~curious(X0)) [input p9]
15. ! [X0] : ((~generous(X0) | tall(X0)) <=> generous(X0)) [input p14]
16. ? [X0] : (~curious(X0) & ~rich(X0)) => ? [X0] : ~tall(X0) [input p15]
23. ~calm(alice) [input hypothesis]
25. ? [X0] : (~curious(X0) & ~rich(X0)) => ? [X1] : ~tall(X1) [rectify 16]
28. ! [X0] : (calm(X0) | ~rich(X0)) [ennf transformation 5]
35. ? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | rich(X0)) [ennf transformation 25]
55. ! [X0] : (((happy(X0) | ~calm(X0)) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 10]
56. ! [X0] : ((happy(X0) | ~calm(X0) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [flattening 55]
61. ! [X0] : (((~generous(X0) | tall(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 15]
62. ! [X0] : ((~generous(X0) | tall(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [flattening 61]
63. ? [X0] : ~tall(X0) | ! [X1] : (curious(X1) | rich(X1)) [rectify 35]
64. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
65. ~tall(sK4) | ! [X1] : (curious(X1) | rich(X1)) [skolemisation 63,64]
95. ~rich(X0) | calm(X0) [cnf transformation 28]
114. ~curious(X0) | calm(X0) [cnf transformation 56]
130. generous(X0) | generous(X0) [cnf transformation 62]
131. ~generous(X0) | tall(X0) | ~generous(X0) [cnf transformation 62]
132. ~tall(sK4) | curious(X1) | rich(X1) [cnf transformation 65]
140. ~calm(alice) [cnf transformation 23]
141. generous(X0) [duplicate literal removal 130]
142. ~generous(X0) | tall(X0) [duplicate literal removal 131]
228. 19 <=> ! [X1] : (curious(X1) | rich(X1)) [avatar definition]
229. curious(X1) | rich(X1) <- (19) [avatar component clause 228]
231. 20 <=> tall(sK4) [avatar definition]
233. ~tall(sK4) <- (~20) [avatar component clause 231]
234. 19 | ~20 [avatar split clause 132,231,228]
250. tall(X0) [resolution 142,141]
251. $false <- (~20) [resolution 250,233]
252. 20 [avatar contradiction clause 251]
254. rich(X1) | calm(X1) <- (19) [resolution 229,114]
255. calm(X1) <- (19) [subsumption resolution 254,95]
256. $false <- (19) [resolution 255,140]
257. ~19 [avatar contradiction clause 256]
258. $false [avatar sat refutation 234,252,257]
% SZS output end Proof for 334565716757684471612756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or generous is kind and vice versa. Everyone who is not curious or not tall is both wise and not calm and vice versa. Everyone who is either not wise or not creative is not kind. If lucy is either humble or not generous then someone is either not calm or not generous. Everyone who is tall or not wise is both not generous and funny and vice versa. Everyone who is not generous or wise is not tall or quiet. Everyone who is both not funny and funny is calm. Everyone who is either old or not creative is both humble and funny and vice versa. Everyone who is either humble or tall is both not strong and not kind and vice versa. If lucy is both not strong and old then lucy is happy and vice versa. Everyone who is not generous is creative or generous. Everyone who is both curious and generous is curious or quiet. If someone is strong or funny then mary is not patient and vice versa. If someone is either not wise or strong then paul is either not brave or brave. If lucy is either not brave or not humble then fred is curious or not kind and vice versa. Everyone who is quiet or brave is either not tall or not quiet and vice versa. Someone is either patient or not generous. Someone is wise or not brave. Fred is not strong. Lucy is both kind and not old. Someone is wise. | Lucy is not curious. | neutral | (![X]:((creative(X)|generous(X))<=>kind(X)))&
(![X]:((~curious(X)|~tall(X))<=>(wise(X)&~calm(X))))&
(![X]:((~wise(X)<~>~creative(X))=>~kind(X)))&
(((humble(lucy)<~>~generous(lucy)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((tall(X)|~wise(X))<=>(~generous(X)&funny(X))))&
(![X]:((~generous(X)|wise(X))=>(~tall(X)|quiet(X))))&
(![X]:((~funny(X)&funny(X))=>calm(X)))&
(![X]:((old(X)<~>~creative(X))<=>(humble(X)&funny(X))))&
(![X]:((humble(X)<~>tall(X))<=>(~strong(X)&~kind(X))))&
(((~strong(lucy)&old(lucy)))<=>(happy(lucy)))&
(![X]:(~generous(X)=>(creative(X)|generous(X))))&
(![X]:((curious(X)&generous(X))=>(curious(X)|quiet(X))))&
((?[X]:((strong(X)|funny(X))))<=>(~patient(mary)))&
((?[X]:((~wise(X)<~>strong(X))))=>((~brave(paul)<~>brave(paul))))&
(((~brave(lucy)<~>~humble(lucy)))<=>((curious(fred)|~kind(fred))))&
(![X]:((quiet(X)|brave(X))<=>(~tall(X)<~>~quiet(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((wise(X)|~brave(X))))&
(~strong(fred))&
((kind(lucy)&~old(lucy)))&
(?[X]:(wise(X))) | ~curious(lucy) | [] | null | 0 |
If paul is creative then someone is both strong and not patient.
If someone is both calm and generous then someone is both not humble and patient.
If paul is rich then someone is either strong or not happy and vice versa.
Everyone who is not curious or not generous is generous and vice versa.
Everyone who is both not kind and not strong is not creative or wise.
Everyone who is humble is quiet.
If lucy is calm or strong then someone is either curious or not wise.
Everyone who is not happy or not tall is both happy and rich.
Everyone who is not brave or generous is both patient and calm.
If paul is old or not rich then alice is both not patient and not quiet.
Everyone who is old is either not curious or rich.
Everyone who is not humble or creative is both not brave and not kind and vice versa.
If mary is both wise and not creative then mary is patient or not calm and vice versa.
If someone is both creative and not wise then fred is patient.
If someone is both quiet and not happy then alice is not old.
Lucy is not creative or not tall.
John is not curious or strong.
Someone is both humble and calm.
Alice is not generous or creative.
Susan is creative or brave.
Someone is patient.
Someone is both patient and not old. | Fred is not curious. | entailment | ((creative(paul))=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((rich(paul))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((~curious(X)|~generous(X))<=>generous(X)))&
(![X]:((~kind(X)&~strong(X))=>(~creative(X)|wise(X))))&
(![X]:(humble(X)=>quiet(X)))&
(((calm(lucy)|strong(lucy)))=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((~happy(X)|~tall(X))=>(happy(X)&rich(X))))&
(![X]:((~brave(X)|generous(X))=>(patient(X)&calm(X))))&
(((old(paul)|~rich(paul)))=>((~patient(alice)&~quiet(alice))))&
(![X]:(old(X)=>(~curious(X)<~>rich(X))))&
(![X]:((~humble(X)|creative(X))<=>(~brave(X)&~kind(X))))&
(((wise(mary)&~creative(mary)))<=>((patient(mary)|~calm(mary))))&
((?[X]:((creative(X)&~wise(X))))=>(patient(fred)))&
((?[X]:((quiet(X)&~happy(X))))=>(~old(alice)))&
((~creative(lucy)|~tall(lucy)))&
((~curious(john)|strong(john)))&
(?[X]:((humble(X)&calm(X))))&
((~generous(alice)|creative(alice)))&
((creative(susan)|brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)&~old(X)))) | ~curious(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1066043573376189264167944
% SZS output start Proof for 1066043573376189264167944
4. ! [X0] : ((~generous(X0) | ~curious(X0)) <=> generous(X0)) [input p3]
23. curious(fred) [input hypothesis]
48. ! [X0] : (((~generous(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & curious(X0)))) [nnf transformation 4]
49. ! [X0] : ((~generous(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & curious(X0)))) [flattening 48]
72. generous(X0) | generous(X0) [cnf transformation 49]
73. ~generous(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 49]
109. curious(fred) [cnf transformation 23]
111. generous(X0) [duplicate literal removal 72]
112. ~curious(X0) | ~generous(X0) [duplicate literal removal 73]
227. ~generous(fred) [resolution 112,109]
228. $false [subsumption resolution 227,111]
% SZS output end Proof for 1066043573376189264167944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is not old and vice versa.
If someone is either rich or wise then someone is not funny.
Everyone who is funny or curious is both tall and not strong and vice versa.
If someone is either not tall or not curious then someone is quiet and vice versa.
If someone is old or not funny then susan is not happy and vice versa.
If alice is rich then mary is either not curious or creative.
If someone is not creative then someone is creative and vice versa.
Everyone who is either rich or generous is both not funny and wise.
Everyone who is not curious or curious is not generous and vice versa.
Everyone who is either not wise or creative is either not happy or happy and vice versa.
Everyone who is either strong or creative is both not rich and not curious and vice versa.
Everyone who is either not kind or not funny is both not patient and not brave.
Everyone who is both not strong and not rich is either not brave or not patient and vice versa.
Everyone who is happy is not brave or not quiet.
Everyone who is creative is either strong or not old and vice versa.
Someone is both not calm and not kind.
Paul is both calm and not humble.
Fred is strong or happy.
Paul is not creative. | Susan is wise. | neutral | ((generous(john))<=>(?[X]:(~old(X))))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
(![X]:((funny(X)|curious(X))<=>(tall(X)&~strong(X))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((old(X)|~funny(X))))<=>(~happy(susan)))&
((rich(alice))=>((~curious(mary)<~>creative(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)<~>generous(X))=>(~funny(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>~generous(X)))&
(![X]:((~wise(X)<~>creative(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((strong(X)<~>creative(X))<=>(~rich(X)&~curious(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~patient(X)&~brave(X))))&
(![X]:((~strong(X)&~rich(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:(happy(X)=>(~brave(X)|~quiet(X))))&
(![X]:(creative(X)<=>(strong(X)<~>~old(X))))&
(?[X]:((~calm(X)&~kind(X))))&
((calm(paul)&~humble(paul)))&
((strong(fred)|happy(fred)))&
(~creative(paul)) | wise(susan) | [] | null | 0 |
Everyone who is either happy or patient is either not strong or not quiet. If someone is not creative then someone is either tall or funny. If someone is both funny and strong then alice is both quiet and not curious and vice versa. If someone is not old then someone is curious and vice versa. Everyone who is kind is not kind. If someone is either not curious or quiet then someone is tall or brave and vice versa. Everyone who is both not quiet and kind is humble or not curious and vice versa. If mary is either creative or tall then alice is not creative or rich and vice versa. If someone is not quiet or quiet then lucy is either not humble or creative. If someone is either not rich or tall then fred is curious or not happy. If someone is either not old or humble then someone is either kind or calm. Everyone who is humble is wise. If someone is not brave or not humble then alice is both tall and curious. If someone is not happy then someone is not tall or brave and vice versa. If someone is not humble then someone is either rich or quiet. Mary is either strong or not wise. Alice is either not happy or not patient. Someone is tall. Someone is both not funny and creative. Susan is either not quiet or strong. | Susan is not kind. | entailment | (![X]:((happy(X)<~>patient(X))=>(~strong(X)<~>~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((funny(X)&strong(X))))<=>((quiet(alice)&~curious(alice))))&
((?[X]:(~old(X)))<=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((curious(fred)|~happy(fred))))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(humble(X)=>wise(X)))&
((?[X]:((~brave(X)|~humble(X))))=>((tall(alice)&curious(alice))))&
((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)<~>quiet(X)))))&
((strong(mary)<~>~wise(mary)))&
((~happy(alice)<~>~patient(alice)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)&creative(X))))&
((~quiet(susan)<~>strong(susan))) | ~kind(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4008463665517463393596529
% SZS output start Proof for 4008463665517463393596529
5. ! [X0] : (kind(X0) => ~kind(X0)) [input p4]
21. kind(susan) [input hypothesis]
30. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 5]
96. ~kind(X0) | ~kind(X0) [cnf transformation 30]
143. kind(susan) [cnf transformation 21]
144. ~kind(X0) [duplicate literal removal 96]
340. $false [subsumption resolution 143,144]
% SZS output end Proof for 4008463665517463393596529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or kind then susan is not happy.
If alice is not kind or not creative then susan is not strong or wise and vice versa.
Everyone who is wise or not funny is either humble or not funny and vice versa.
If someone is both wise and not old then fred is both not old and humble and vice versa.
Everyone who is not funny is wise.
If someone is both not humble and not strong then someone is not tall or not strong.
If alice is generous or calm then someone is both rich and not calm and vice versa.
If john is not old or generous then fred is calm or not old.
Everyone who is humble or not wise is both strong and not happy and vice versa.
Everyone who is both curious and wise is both patient and not quiet.
If susan is both not creative and not happy then alice is either not wise or creative.
If someone is not quiet then someone is creative or not tall.
If someone is rich then someone is either not brave or funny and vice versa.
Everyone who is either brave or creative is not humble.
If paul is either not strong or old then someone is both humble and not kind and vice versa.
Everyone who is either kind or funny is kind and vice versa.
Someone is both not creative and rich.
Someone is not generous or generous.
John is either curious or not quiet.
Someone is both not kind and not patient.
Someone is either curious or not rich.
Fred is curious or not patient.
Someone is both not tall and not quiet. | Fred is humble. | contradiction | (((tall(john)<~>kind(john)))=>(~happy(susan)))&
(((~kind(alice)|~creative(alice)))<=>((~strong(susan)|wise(susan))))&
(![X]:((wise(X)|~funny(X))<=>(humble(X)<~>~funny(X))))&
((?[X]:((wise(X)&~old(X))))<=>((~old(fred)&humble(fred))))&
(![X]:(~funny(X)=>wise(X)))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((~tall(X)|~strong(X)))))&
(((generous(alice)|calm(alice)))<=>(?[X]:((rich(X)&~calm(X)))))&
(((~old(john)|generous(john)))=>((calm(fred)|~old(fred))))&
(![X]:((humble(X)|~wise(X))<=>(strong(X)&~happy(X))))&
(![X]:((curious(X)&wise(X))=>(patient(X)&~quiet(X))))&
(((~creative(susan)&~happy(susan)))=>((~wise(alice)<~>creative(alice))))&
((?[X]:(~quiet(X)))=>(?[X]:((creative(X)|~tall(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:((brave(X)<~>creative(X))=>~humble(X)))&
(((~strong(paul)<~>old(paul)))<=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((kind(X)<~>funny(X))<=>kind(X)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((~generous(X)|generous(X))))&
((curious(john)<~>~quiet(john)))&
(?[X]:((~kind(X)&~patient(X))))&
(?[X]:((curious(X)<~>~rich(X))))&
((curious(fred)|~patient(fred)))&
(?[X]:((~tall(X)&~quiet(X)))) | humble(fred) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1065225935573828693822520
% SZS output start Proof for 1065225935573828693822520
3. ! [X0] : ((~funny(X0) | wise(X0)) <=> (humble(X0) <~> ~funny(X0))) [input p2]
16. ! [X0] : ((kind(X0) <~> funny(X0)) <=> kind(X0)) [input p15]
24. humble(fred) [input hypothesis]
42. ! [X0] : (((~funny(X0) | wise(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (funny(X0) & ~wise(X0)))) [nnf transformation 3]
43. ! [X0] : ((~funny(X0) | wise(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (funny(X0) & ~wise(X0)))) [flattening 42]
73. ! [X0] : ((((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | ~kind(X0)) & (kind(X0) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0))))) [nnf transformation 16]
95. funny(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
134. kind(X0) | kind(X0) | ~funny(X0) [cnf transformation 73]
136. ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 73]
149. humble(fred) [cnf transformation 24]
150. kind(X0) | ~funny(X0) [duplicate literal removal 134]
151. ~funny(X0) | ~kind(X0) [duplicate literal removal 136]
152. ~humble(X0) | funny(X0) [duplicate literal removal 95]
193. 9 <=> humble(fred) [avatar definition]
194. humble(fred) <- (9) [avatar component clause 193]
333. ~funny(X0) [subsumption resolution 150,151]
363. 9 [avatar split clause 149,193]
371. funny(fred) <- (9) [resolution 152,194]
372. $false <- (9) [subsumption resolution 371,333]
373. ~9 [avatar contradiction clause 372]
374. $false [avatar sat refutation 363,373]
% SZS output end Proof for 1065225935573828693822520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not tall then someone is either tall or brave.
If mary is not tall or humble then alice is not wise or not kind.
If someone is calm then lucy is not kind or not generous and vice versa.
If someone is both not tall and curious then fred is old or humble.
If someone is both tall and not humble then fred is not generous.
If paul is wise or generous then paul is both not old and not funny and vice versa.
Everyone who is either generous or wise is funny or not generous and vice versa.
Everyone who is not strong is either not old or not calm and vice versa.
Everyone who is either not patient or patient is generous.
Everyone who is not calm or not happy is creative or humble.
Everyone who is happy is either calm or not patient and vice versa.
Everyone who is either not generous or not old is funny or quiet.
If someone is not happy then mary is not quiet or not old and vice versa.
Everyone who is not curious is both not tall and not patient and vice versa.
Everyone who is both not happy and funny is not curious.
Everyone who is either not brave or not kind is either wise or funny.
Someone is not happy.
Someone is not funny or not generous.
John is old.
Someone is both not patient and not tall.
Alice is either patient or not humble. | Lucy is humble. | neutral | ((?[X]:((quiet(X)|~tall(X))))=>(?[X]:((tall(X)<~>brave(X)))))&
(((~tall(mary)|humble(mary)))=>((~wise(alice)|~kind(alice))))&
((?[X]:(calm(X)))<=>((~kind(lucy)|~generous(lucy))))&
((?[X]:((~tall(X)&curious(X))))=>((old(fred)|humble(fred))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(![X]:((generous(X)<~>wise(X))<=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>patient(X))=>generous(X)))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|humble(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~old(X))=>(funny(X)|quiet(X))))&
((?[X]:(~happy(X)))<=>((~quiet(mary)|~old(mary))))&
(![X]:(~curious(X)<=>(~tall(X)&~patient(X))))&
(![X]:((~happy(X)&funny(X))=>~curious(X)))&
(![X]:((~brave(X)<~>~kind(X))=>(wise(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)|~generous(X))))&
(old(john))&
(?[X]:((~patient(X)&~tall(X))))&
((patient(alice)<~>~humble(alice))) | humble(lucy) | [] | null | 0 |
Everyone who is either tall or kind is not tall. If paul is both not strong and generous then someone is either curious or not patient and vice versa. If john is either calm or generous then someone is quiet or tall and vice versa. If someone is both not calm and patient then paul is not tall. Everyone who is both not funny and creative is happy or not happy. If someone is either generous or not quiet then someone is either happy or humble and vice versa. If john is either quiet or not quiet then someone is not calm or not brave. Everyone who is both not creative and not old is tall. Everyone who is either creative or not rich is both quiet and not wise. Everyone who is either not wise or strong is either creative or patient. Everyone who is not brave is curious or old. If someone is both old and wise then lucy is either creative or not brave. If someone is calm then someone is happy or not wise and vice versa. Everyone who is not patient or strong is both quiet and not funny and vice versa. If someone is not tall then john is both not brave and not creative. Everyone who is not wise or rich is both funny and not curious. Lucy is either not brave or not wise. Someone is both old and funny. Someone is not strong or not quiet. John is both not tall and not brave. Someone is either not creative or curious. Fred is not creative. Someone is either strong or not old. Someone is not brave. | Fred is not strong. | entailment | (![X]:((tall(X)<~>kind(X))=>~tall(X)))&
(((~strong(paul)&generous(paul)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(((calm(john)<~>generous(john)))<=>(?[X]:((quiet(X)|tall(X)))))&
((?[X]:((~calm(X)&patient(X))))=>(~tall(paul)))&
(![X]:((~funny(X)&creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(?[X]:((happy(X)<~>humble(X)))))&
(((quiet(john)<~>~quiet(john)))=>(?[X]:((~calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~old(X))=>tall(X)))&
(![X]:((creative(X)<~>~rich(X))=>(quiet(X)&~wise(X))))&
(![X]:((~wise(X)<~>strong(X))=>(creative(X)<~>patient(X))))&
(![X]:(~brave(X)=>(curious(X)|old(X))))&
((?[X]:((old(X)&wise(X))))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:((~patient(X)|strong(X))<=>(quiet(X)&~funny(X))))&
((?[X]:(~tall(X)))=>((~brave(john)&~creative(john))))&
(![X]:((~wise(X)|rich(X))=>(funny(X)&~curious(X))))&
((~brave(lucy)<~>~wise(lucy)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
((~tall(john)&~brave(john)))&
(?[X]:((~creative(X)<~>curious(X))))&
(~creative(fred))&
(?[X]:((strong(X)<~>~old(X))))&
(?[X]:(~brave(X))) | ~strong(fred) | [
"p8",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 471285393189264734212794
% SZS output start Proof for 471285393189264734212794
9. ! [X0] : ((creative(X0) <~> ~rich(X0)) => (~wise(X0) & quiet(X0))) [input p8]
14. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~funny(X0) & quiet(X0))) [input p13]
16. ! [X0] : ((rich(X0) | ~wise(X0)) => (~curious(X0) & funny(X0))) [input p15]
22. ~creative(fred) [input p21]
25. strong(fred) [input hypothesis]
35. ! [X0] : ((~wise(X0) & quiet(X0)) | (creative(X0) <=> ~rich(X0))) [ennf transformation 9]
41. ! [X0] : ((~curious(X0) & funny(X0)) | (~rich(X0) & wise(X0))) [ennf transformation 16]
60. ! [X0] : ((~wise(X0) & quiet(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 35]
68. ! [X0] : (((strong(X0) | ~patient(X0)) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 14]
69. ! [X0] : ((strong(X0) | ~patient(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | (~strong(X0) & patient(X0)))) [flattening 68]
113. ~wise(X0) | creative(X0) | rich(X0) [cnf transformation 60]
127. ~funny(X0) | ~strong(X0) [cnf transformation 69]
131. wise(X0) | funny(X0) [cnf transformation 41]
132. ~rich(X0) | funny(X0) [cnf transformation 41]
144. ~creative(fred) [cnf transformation 22]
148. strong(fred) [cnf transformation 25]
384. creative(X0) | rich(X0) | funny(X0) [resolution 113,131]
386. creative(X0) | funny(X0) [subsumption resolution 384,132]
430. funny(fred) [resolution 386,144]
455. ~strong(fred) [resolution 430,127]
457. $false [subsumption resolution 455,148]
% SZS output end Proof for 471285393189264734212794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is rich or patient and vice versa.
Everyone who is both creative and old is both strong and happy.
If someone is not creative or strong then someone is either not funny or tall and vice versa.
Everyone who is not strong or not old is strong or not old.
Everyone who is both quiet and tall is either happy or not rich and vice versa.
Everyone who is not tall or funny is either not happy or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
If susan is generous then someone is both old and not wise and vice versa.
Everyone who is both not funny and kind is both funny and not rich.
Everyone who is both strong and rich is either quiet or rich.
Everyone who is not funny is both humble and curious and vice versa.
Everyone who is either quiet or not tall is not old or not patient.
Someone is kind or creative.
Paul is either not old or not patient.
Susan is both wise and patient.
Someone is both not tall and not happy.
Someone is either rich or not tall.
Someone is not rich or not strong.
Someone is rich or funny.
John is either not old or not curious. | Paul is not wise. | neutral | (![X]:(~old(X)<=>(rich(X)|patient(X))))&
(![X]:((creative(X)&old(X))=>(strong(X)&happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((~strong(X)|~old(X))=>(strong(X)|~old(X))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)<~>~rich(X))))&
(![X]:((~tall(X)|funny(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((generous(susan))<=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((~funny(X)&kind(X))=>(funny(X)&~rich(X))))&
(![X]:((strong(X)&rich(X))=>(quiet(X)<~>rich(X))))&
(![X]:(~funny(X)<=>(humble(X)&curious(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(~old(X)|~patient(X))))&
(?[X]:((kind(X)|creative(X))))&
((~old(paul)<~>~patient(paul)))&
((wise(susan)&patient(susan)))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((rich(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~strong(X))))&
(?[X]:((rich(X)|funny(X))))&
((~old(john)<~>~curious(john))) | ~wise(paul) | [] | null | 0 |
Everyone who is either old or calm is quiet or not tall and vice versa.
If lucy is strong then susan is both curious and patient and vice versa.
Everyone who is either curious or not strong is either not funny or not calm and vice versa.
Everyone who is creative or wise is both brave and not generous and vice versa.
If mary is both curious and not quiet then someone is old or not strong.
If lucy is either not tall or tall then mary is either calm or strong and vice versa.
Everyone who is not old is kind.
If paul is both happy and not kind then someone is both creative and wise and vice versa.
Everyone who is quiet is not creative and vice versa.
Everyone who is strong is calm or not old and vice versa.
If someone is not kind then someone is patient and vice versa.
If someone is either calm or not kind then lucy is strong or not funny.
Everyone who is happy or not rich is either not kind or not patient and vice versa.
Everyone who is both funny and not calm is either kind or not old.
Everyone who is happy or rich is happy or tall.
Someone is not generous or not strong.
Someone is either brave or tall.
Someone is wise or not brave.
Someone is not patient or patient.
Fred is both not humble and not brave.
Susan is not old.
Someone is not strong. | Lucy is not generous. | neutral | (![X]:((old(X)<~>calm(X))<=>(quiet(X)|~tall(X))))&
((strong(lucy))<=>((curious(susan)&patient(susan))))&
(![X]:((curious(X)<~>~strong(X))<=>(~funny(X)<~>~calm(X))))&
(![X]:((creative(X)|wise(X))<=>(brave(X)&~generous(X))))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(((~tall(lucy)<~>tall(lucy)))<=>((calm(mary)<~>strong(mary))))&
(![X]:(~old(X)=>kind(X)))&
(((happy(paul)&~kind(paul)))<=>(?[X]:((creative(X)&wise(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(![X]:(strong(X)<=>(calm(X)|~old(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(patient(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((strong(lucy)|~funny(lucy))))&
(![X]:((happy(X)|~rich(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((funny(X)&~calm(X))=>(kind(X)<~>~old(X))))&
(![X]:((happy(X)|rich(X))=>(happy(X)|tall(X))))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((brave(X)<~>tall(X))))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((~patient(X)|patient(X))))&
((~humble(fred)&~brave(fred)))&
(~old(susan))&
(?[X]:(~strong(X))) | ~generous(lucy) | [] | null | 0 |
If lucy is kind or not generous then someone is both wise and not brave and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is both generous and kind is both not wise and not old and vice versa. If mary is either tall or quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Everyone who is funny or creative is not tall or not rich and vice versa. Someone is both calm and not brave. Paul is not tall or creative. Alice is both not calm and kind. Someone is either tall or not strong. Someone is either not creative or kind. Paul is not strong. | Fred is not curious. | entailment | (((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(![X]:((funny(X)|creative(X))<=>(~tall(X)|~rich(X))))&
(?[X]:((calm(X)&~brave(X))))&
((~tall(paul)|creative(paul)))&
((~calm(alice)&kind(alice)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~creative(X)<~>kind(X))))&
(~strong(paul)) | ~curious(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 232297399622113440262198
% SZS output start Proof for 232297399622113440262198
6. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p5]
23. curious(fred) [input hypothesis]
46. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 46]
100. ~curious(X0) | ~curious(X0) [cnf transformation 47]
149. curious(fred) [cnf transformation 23]
151. ~curious(X0) [duplicate literal removal 100]
309. $false [subsumption resolution 149,151]
% SZS output end Proof for 232297399622113440262198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not tall is not humble or not creative. Everyone who is either not wise or creative is rich or quiet. Everyone who is not brave or humble is either brave or not curious and vice versa. Everyone who is either not quiet or not humble is either funny or not creative and vice versa. If someone is either humble or not old then lucy is both brave and generous and vice versa. Everyone who is both not strong and quiet is not patient. Everyone who is either not old or not humble is not generous or not wise and vice versa. Everyone who is creative or not curious is creative. Everyone who is either not tall or calm is brave or happy and vice versa. If paul is not rich or not calm then someone is either kind or not rich and vice versa. Everyone who is both creative and not calm is either old or not old and vice versa. If someone is either calm or not curious then someone is not funny or not generous and vice versa. If someone is not tall or calm then susan is both not quiet and strong. Everyone who is either creative or not humble is both not kind and not strong and vice versa. Everyone who is not rich or patient is both humble and rich and vice versa. Someone is not kind. Someone is either not brave or kind. Alice is not tall or not rich. Paul is not kind or calm. John is either generous or not calm. John is either funny or curious. Fred is brave or not curious. | Susan is funny. | contradiction | (![X]:((~rich(X)|~tall(X))=>(~humble(X)|~creative(X))))&
(![X]:((~wise(X)<~>creative(X))=>(rich(X)|quiet(X))))&
(![X]:((~brave(X)|humble(X))<=>(brave(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((brave(lucy)&generous(lucy))))&
(![X]:((~strong(X)&quiet(X))=>~patient(X)))&
(![X]:((~old(X)<~>~humble(X))<=>(~generous(X)|~wise(X))))&
(![X]:((creative(X)|~curious(X))=>creative(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(brave(X)|happy(X))))&
(((~rich(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((creative(X)&~calm(X))<=>(old(X)<~>~old(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~tall(X)|calm(X))))=>((~quiet(susan)&strong(susan))))&
(![X]:((creative(X)<~>~humble(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~tall(alice)|~rich(alice)))&
((~kind(paul)|calm(paul)))&
((generous(john)<~>~calm(john)))&
((funny(john)<~>curious(john)))&
((brave(fred)|~curious(fred))) | funny(susan) | [
"p3",
"p10",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 208529042216129761230550
% SZS output start Proof for 208529042216129761230550
4. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) <=> (funny(X0) <~> ~creative(X0))) [input p3]
11. ! [X0] : ((~calm(X0) & creative(X0)) <=> (old(X0) <~> ~old(X0))) [input p10]
13. ? [X0] : (calm(X0) | ~tall(X0)) => (strong(susan) & ~quiet(susan)) [input p12]
14. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> (~strong(X0) & ~kind(X0))) [input p13]
15. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p14]
18. ~rich(alice) | ~tall(alice) [input p17]
23. funny(susan) [input hypothesis]
32. (strong(susan) & ~quiet(susan)) | ! [X0] : (~calm(X0) & tall(X0)) [ennf transformation 13]
36. ! [X0] : ((((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))))) [nnf transformation 4]
51. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (calm(X0) | ~creative(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | calm(X0) | ~creative(X0))) [flattening 51]
58. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 14]
59. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [flattening 58]
60. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 15]
61. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 60]
85. ~funny(X0) | quiet(X0) | ~creative(X0) | humble(X0) [cnf transformation 36]
116. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 52]
117. creative(X0) | old(X0) | old(X0) [cnf transformation 52]
126. ~quiet(susan) | tall(X0) [cnf transformation 32]
128. strong(susan) | tall(X0) [cnf transformation 32]
132. ~strong(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 59]
138. rich(X0) | rich(X0) [cnf transformation 61]
144. ~rich(alice) | ~tall(alice) [cnf transformation 18]
151. funny(susan) [cnf transformation 23]
152. rich(X0) [duplicate literal removal 138]
154. creative(X0) | ~old(X0) [duplicate literal removal 116]
155. old(X0) | creative(X0) [duplicate literal removal 117]
217. creative(X0) [subsumption resolution 154,155]
246. 19 <=> ! [X0] : tall(X0) [avatar definition]
247. tall(X0) <- (19) [avatar component clause 246]
249. 20 <=> strong(susan) [avatar definition]
251. strong(susan) <- (20) [avatar component clause 249]
252. 19 | 20 [avatar split clause 128,249,246]
254. 21 <=> quiet(susan) [avatar definition]
256. ~quiet(susan) <- (~21) [avatar component clause 254]
257. 19 | ~21 [avatar split clause 126,254,246]
259. ~strong(X0) | ~humble(X0) [subsumption resolution 132,217]
271. ~tall(alice) [subsumption resolution 144,152]
291. $false <- (19) [resolution 271,247]
292. ~19 [avatar contradiction clause 291]
298. ~humble(susan) <- (20) [resolution 259,251]
397. quiet(susan) | ~creative(susan) | humble(susan) [resolution 85,151]
399. ~creative(susan) | humble(susan) <- (~21) [subsumption resolution 397,256]
400. humble(susan) <- (~21) [subsumption resolution 399,217]
401. $false <- (20, ~21) [subsumption resolution 400,298]
402. ~20 | 21 [avatar contradiction clause 401]
406. $false [avatar sat refutation 252,257,292,402]
% SZS output end Proof for 208529042216129761230550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then paul is funny. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Everyone who is patient or kind is both kind and strong. Everyone who is either not curious or tall is either wise or curious. Everyone who is patient is curious or not rich. Everyone who is both happy and not humble is quiet or humble. If paul is not tall or kind then someone is either not old or not brave. Someone is old or curious. Someone is either not happy or not quiet. Someone is brave or old. Someone is not patient. | Mary is not wise. | entailment | ((brave(mary))=>(funny(paul)))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
(![X]:((patient(X)|kind(X))=>(kind(X)&strong(X))))&
(![X]:((~curious(X)<~>tall(X))=>(wise(X)<~>curious(X))))&
(![X]:(patient(X)=>(curious(X)|~rich(X))))&
(![X]:((happy(X)&~humble(X))=>(quiet(X)|humble(X))))&
(((~tall(paul)|kind(paul)))=>(?[X]:((~old(X)<~>~brave(X)))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:((brave(X)|old(X))))&
(?[X]:(~patient(X))) | ~wise(mary) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8833846706329433923876466
% SZS output start Proof for 8833846706329433923876466
4. ! [X0] : ((~generous(X0) | ~rich(X0)) => (generous(X0) & ~calm(X0))) [input p3]
7. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (~funny(X0) & ~wise(X0))) [input p6]
20. wise(mary) [input hypothesis]
28. ! [X0] : (~generous(X0) => (generous(X0) & ~calm(X0))) [pure predicate removal 4]
32. ! [X0] : ((generous(X0) & ~calm(X0)) | generous(X0)) [ennf transformation 28]
42. ! [X0] : (((generous(X0) | ~brave(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [nnf transformation 7]
43. ! [X0] : ((generous(X0) | ~brave(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [flattening 42]
70. generous(X0) | generous(X0) [cnf transformation 32]
74. ~wise(X0) | ~generous(X0) [cnf transformation 43]
99. wise(mary) [cnf transformation 20]
103. generous(X0) [duplicate literal removal 70]
117. ~wise(X0) [subsumption resolution 74,103]
176. $false [subsumption resolution 99,117]
% SZS output end Proof for 8833846706329433923876466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or rich then john is either old or patient and vice versa. If someone is either not strong or happy then paul is both funny and not brave. Everyone who is both not humble and not calm is either rich or humble. If someone is either not calm or not wise then someone is strong or wise and vice versa. Everyone who is not calm or happy is not humble and vice versa. Everyone who is either not funny or calm is both funny and not rich. Everyone who is both brave and not quiet is both generous and not calm and vice versa. If susan is not tall then someone is either not happy or not old and vice versa. Everyone who is not calm or not old is not happy. If someone is humble or old then someone is both happy and not calm and vice versa. Everyone who is either old or not funny is either quiet or calm. Everyone who is both quiet and curious is wise or kind and vice versa. If susan is either calm or brave then alice is both old and not kind. If someone is either not wise or not humble then lucy is rich or not funny. Everyone who is not funny is either calm or not rich. Everyone who is generous or kind is calm. Someone is both not strong and not patient. Someone is tall. Someone is both funny and quiet. Paul is not happy or not humble. Alice is not creative or quiet. | Lucy is strong. | neutral | ((?[X]:((humble(X)|rich(X))))<=>((old(john)<~>patient(john))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(((calm(susan)<~>brave(susan)))=>((old(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>~humble(X))))=>((rich(lucy)|~funny(lucy))))&
(![X]:(~funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((generous(X)|kind(X))=>calm(X)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:(tall(X)))&
(?[X]:((funny(X)&quiet(X))))&
((~happy(paul)|~humble(paul)))&
((~creative(alice)|quiet(alice))) | strong(lucy) | [] | null | 0 |
Everyone who is rich or not patient is strong or not generous.
Everyone who is both not kind and rich is not patient or not rich and vice versa.
Everyone who is not quiet is not funny and vice versa.
Everyone who is tall is not curious or not patient and vice versa.
Everyone who is not curious or brave is not curious or rich.
If someone is both not tall and calm then john is both creative and not happy and vice versa.
Everyone who is funny or not old is not patient or brave and vice versa.
If someone is not humble or curious then lucy is not creative.
Everyone who is both not humble and patient is not funny or not curious and vice versa.
If someone is either not creative or old then someone is wise or not patient and vice versa.
Everyone who is either quiet or not tall is wise and vice versa.
Everyone who is not generous or not quiet is not happy or funny and vice versa.
Everyone who is both kind and not quiet is not creative.
If fred is generous then someone is either wise or kind.
If someone is either kind or funny then alice is either not curious or curious.
Everyone who is either happy or creative is either not brave or wise.
Someone is not happy.
Someone is brave or not brave.
Someone is wise or not curious.
John is not creative or happy.
Lucy is happy or not brave.
Lucy is not tall or not wise.
Mary is wise.
Someone is both quiet and not kind. | Lucy is happy. | contradiction | (![X]:((rich(X)|~patient(X))=>(strong(X)|~generous(X))))&
(![X]:((~kind(X)&rich(X))<=>(~patient(X)|~rich(X))))&
(![X]:(~quiet(X)<=>~funny(X)))&
(![X]:(tall(X)<=>(~curious(X)|~patient(X))))&
(![X]:((~curious(X)|brave(X))=>(~curious(X)|rich(X))))&
((?[X]:((~tall(X)&calm(X))))<=>((creative(john)&~happy(john))))&
(![X]:((funny(X)|~old(X))<=>(~patient(X)|brave(X))))&
((?[X]:((~humble(X)|curious(X))))=>(~creative(lucy)))&
(![X]:((~humble(X)&patient(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>wise(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(~happy(X)|funny(X))))&
(![X]:((kind(X)&~quiet(X))=>~creative(X)))&
((generous(fred))=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:((kind(X)<~>funny(X))))=>((~curious(alice)<~>curious(alice))))&
(![X]:((happy(X)<~>creative(X))=>(~brave(X)<~>wise(X))))&
(?[X]:(~happy(X)))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((wise(X)|~curious(X))))&
((~creative(john)|happy(john)))&
((happy(lucy)|~brave(lucy)))&
((~tall(lucy)|~wise(lucy)))&
(wise(mary))&
(?[X]:((quiet(X)&~kind(X)))) | happy(lucy) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 794057865838752601921804
% SZS output start Proof for 794057865838752601921804
3. ! [X0] : (~quiet(X0) <=> ~funny(X0)) [input p2]
4. ! [X0] : (tall(X0) <=> (~patient(X0) | ~curious(X0))) [input p3]
7. ! [X0] : ((~old(X0) | funny(X0)) <=> (brave(X0) | ~patient(X0))) [input p6]
8. ? [X0] : (curious(X0) | ~humble(X0)) => ~creative(lucy) [input p7]
9. ! [X0] : ((patient(X0) & ~humble(X0)) <=> (~curious(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> wise(X0)) [input p10]
12. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (funny(X0) | ~happy(X0))) [input p11]
16. ! [X0] : ((happy(X0) <~> creative(X0)) => (~brave(X0) <~> wise(X0))) [input p15]
22. ~wise(lucy) | ~tall(lucy) [input p21]
25. happy(lucy) [input hypothesis]
30. ~creative(lucy) | ! [X0] : (~curious(X0) & humble(X0)) [ennf transformation 8]
35. ! [X0] : ((~brave(X0) <~> wise(X0)) | (happy(X0) <=> creative(X0))) [ennf transformation 16]
38. ! [X0] : ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0))) [nnf transformation 3]
39. ! [X0] : ((tall(X0) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 4]
40. ! [X0] : ((tall(X0) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | ~tall(X0))) [flattening 39]
46. ! [X0] : (((~old(X0) | funny(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 7]
47. ! [X0] : ((~old(X0) | funny(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | (old(X0) & ~funny(X0)))) [flattening 46]
48. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~patient(X0) | humble(X0)))) [nnf transformation 9]
49. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~patient(X0) | humble(X0))) [flattening 48]
55. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ~wise(X0)) & (wise(X0) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 11]
56. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (~funny(X0) & happy(X0))) & ((funny(X0) | ~happy(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 12]
57. ! [X0] : ((~quiet(X0) | ~generous(X0) | (~funny(X0) & happy(X0))) & (funny(X0) | ~happy(X0) | (quiet(X0) & generous(X0)))) [flattening 56]
62. ! [X0] : (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) [nnf transformation 35]
76. ~funny(X0) | quiet(X0) [cnf transformation 38]
77. ~quiet(X0) | funny(X0) [cnf transformation 38]
80. tall(X0) | patient(X0) [cnf transformation 40]
87. ~funny(X0) | ~patient(X0) | brave(X0) [cnf transformation 47]
91. ~creative(lucy) | humble(X0) [cnf transformation 30]
92. ~creative(lucy) | ~curious(X0) [cnf transformation 30]
95. ~humble(X0) | curious(X0) [cnf transformation 49]
104. ~tall(X0) | wise(X0) | ~quiet(X0) [cnf transformation 55]
107. ~wise(X0) | ~quiet(X0) | tall(X0) [cnf transformation 55]
109. funny(X0) | ~happy(X0) | quiet(X0) [cnf transformation 57]
119. ~happy(X0) | ~brave(X0) | creative(X0) | wise(X0) [cnf transformation 62]
128. ~wise(lucy) | ~tall(lucy) [cnf transformation 22]
132. happy(lucy) [cnf transformation 25]
160. 6 <=> ! [X0] : ~curious(X0) [avatar definition]
161. ~curious(X0) <- (6) [avatar component clause 160]
163. 7 <=> creative(lucy) [avatar definition]
166. 6 | ~7 [avatar split clause 92,163,160]
168. 8 <=> ! [X0] : humble(X0) [avatar definition]
169. humble(X0) <- (8) [avatar component clause 168]
170. 8 | ~7 [avatar split clause 91,163,168]
206. ~happy(X0) | funny(X0) [subsumption resolution 109,77]
232. 22 <=> happy(lucy) [avatar definition]
234. happy(lucy) <- (22) [avatar component clause 232]
236. 23 <=> brave(lucy) [avatar definition]
237. brave(lucy) <- (23) [avatar component clause 236]
241. 24 <=> tall(lucy) [avatar definition]
242. tall(lucy) <- (24) [avatar component clause 241]
243. ~tall(lucy) <- (~24) [avatar component clause 241]
245. 25 <=> wise(lucy) [avatar definition]
246. wise(lucy) <- (25) [avatar component clause 245]
247. ~wise(lucy) <- (~25) [avatar component clause 245]
248. ~24 | ~25 [avatar split clause 128,245,241]
249. 22 [avatar split clause 132,232]
253. patient(lucy) <- (~24) [resolution 80,243]
262. funny(lucy) <- (22) [resolution 206,234]
264. quiet(lucy) <- (22) [resolution 262,76]
269. ~patient(lucy) | brave(lucy) <- (22) [resolution 87,262]
279. brave(lucy) <- (22, ~24) [subsumption resolution 269,253]
280. 23 | ~22 | 24 [avatar split clause 279,241,232,236]
359. ~brave(lucy) | creative(lucy) | wise(lucy) <- (22) [resolution 119,234]
370. wise(lucy) | ~quiet(lucy) <- (24) [resolution 242,104]
371. ~quiet(lucy) <- (24, ~25) [subsumption resolution 370,247]
372. $false <- (22, 24, ~25) [subsumption resolution 371,264]
373. ~22 | ~24 | 25 [avatar contradiction clause 372]
378. ~quiet(lucy) | tall(lucy) <- (25) [resolution 246,107]
380. tall(lucy) <- (22, 25) [subsumption resolution 378,264]
381. $false <- (22, ~24, 25) [subsumption resolution 380,243]
382. ~22 | 24 | ~25 [avatar contradiction clause 381]
383. creative(lucy) | wise(lucy) <- (22, 23) [subsumption resolution 359,237]
384. 25 | 7 | ~22 | ~23 [avatar split clause 383,236,232,163,245]
391. curious(X0) <- (8) [resolution 169,95]
393. $false <- (6, 8) [subsumption resolution 391,161]
394. ~6 | ~8 [avatar contradiction clause 393]
395. $false [avatar sat refutation 166,170,248,249,280,373,382,384,394]
% SZS output end Proof for 794057865838752601921804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not calm then mary is either not patient or kind.
If fred is either strong or not rich then mary is both not rich and quiet and vice versa.
Everyone who is not calm is not generous and vice versa.
Everyone who is not kind is both not rich and not calm and vice versa.
Everyone who is quiet is both not old and rich.
If lucy is both not calm and generous then someone is both happy and not humble.
Everyone who is not quiet is both tall and not humble.
Everyone who is both not humble and happy is both patient and humble.
If fred is both not old and not patient then someone is not funny and vice versa.
If someone is not calm or not happy then fred is not patient or funny and vice versa.
If alice is both strong and not strong then someone is both calm and not generous.
Everyone who is both humble and creative is rich and vice versa.
If alice is both quiet and not tall then someone is not old.
Everyone who is either creative or calm is happy or not wise.
If susan is curious or creative then susan is not happy or wise.
If someone is not quiet or rich then someone is both old and calm and vice versa.
Someone is not generous or not tall.
Someone is not wise or old.
Someone is both not kind and brave.
Fred is not quiet or not brave.
Mary is curious.
Someone is not curious or rich.
Fred is both wise and not curious.
Fred is either not humble or brave. | Fred is not quiet. | entailment | ((?[X]:((patient(X)&~calm(X))))=>((~patient(mary)<~>kind(mary))))&
(((strong(fred)<~>~rich(fred)))<=>((~rich(mary)&quiet(mary))))&
(![X]:(~calm(X)<=>~generous(X)))&
(![X]:(~kind(X)<=>(~rich(X)&~calm(X))))&
(![X]:(quiet(X)=>(~old(X)&rich(X))))&
(((~calm(lucy)&generous(lucy)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:(~quiet(X)=>(tall(X)&~humble(X))))&
(![X]:((~humble(X)&happy(X))=>(patient(X)&humble(X))))&
(((~old(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~patient(fred)|funny(fred))))&
(((strong(alice)&~strong(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((humble(X)&creative(X))<=>rich(X)))&
(((quiet(alice)&~tall(alice)))=>(?[X]:(~old(X))))&
(![X]:((creative(X)<~>calm(X))=>(happy(X)|~wise(X))))&
(((curious(susan)|creative(susan)))=>((~happy(susan)|wise(susan))))&
((?[X]:((~quiet(X)|rich(X))))<=>(?[X]:((old(X)&calm(X)))))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~kind(X)&brave(X))))&
((~quiet(fred)|~brave(fred)))&
(curious(mary))&
(?[X]:((~curious(X)|rich(X))))&
((wise(fred)&~curious(fred)))&
((~humble(fred)<~>brave(fred))) | ~quiet(fred) | [
"p4",
"p11",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1718627277081901036387286
% SZS output start Proof for 1718627277081901036387286
5. ! [X0] : (quiet(X0) => (rich(X0) & ~old(X0))) [input p4]
12. ! [X0] : ((creative(X0) & humble(X0)) <=> rich(X0)) [input p11]
20. ~brave(fred) | ~quiet(fred) [input p19]
24. ~humble(fred) <~> brave(fred) [input p23]
25. quiet(fred) [input hypothesis]
28. ! [X0] : ((rich(X0) & ~old(X0)) | ~quiet(X0)) [ennf transformation 5]
62. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | (~creative(X0) | ~humble(X0)))) [nnf transformation 12]
63. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | ~creative(X0) | ~humble(X0))) [flattening 62]
80. (~brave(fred) | humble(fred)) & (brave(fred) | ~humble(fred)) [nnf transformation 24]
95. ~quiet(X0) | rich(X0) [cnf transformation 28]
112. ~rich(X0) | humble(X0) [cnf transformation 63]
128. ~brave(fred) | ~quiet(fred) [cnf transformation 20]
133. brave(fred) | ~humble(fred) [cnf transformation 80]
135. quiet(fred) [cnf transformation 25]
163. 7 <=> rich(fred) [avatar definition]
165. rich(fred) <- (7) [avatar component clause 163]
277. 31 <=> quiet(fred) [avatar definition]
278. quiet(fred) <- (31) [avatar component clause 277]
281. 32 <=> brave(fred) [avatar definition]
284. ~31 | ~32 [avatar split clause 128,281,277]
295. 35 <=> humble(fred) [avatar definition]
296. ~humble(fred) <- (~35) [avatar component clause 295]
299. ~35 | 32 [avatar split clause 133,281,295]
300. 31 [avatar split clause 135,277]
302. rich(fred) <- (31) [resolution 95,278]
307. 7 | ~31 [avatar split clause 302,277,163]
316. humble(fred) <- (7) [resolution 112,165]
317. $false <- (7, ~35) [subsumption resolution 316,296]
318. ~7 | 35 [avatar contradiction clause 317]
319. $false [avatar sat refutation 284,299,300,307,318]
% SZS output end Proof for 1718627277081901036387286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or generous is either not rich or happy.
If susan is either quiet or rich then someone is both strong and happy.
Everyone who is not kind or not patient is not old or not tall.
If someone is both not strong and not calm then alice is both not happy and happy and vice versa.
Everyone who is either curious or not funny is not creative.
If susan is not tall or curious then john is both humble and kind and vice versa.
Everyone who is creative is old or brave.
Everyone who is both generous and strong is humble and vice versa.
If lucy is not kind or old then alice is both not calm and strong.
Everyone who is either wise or not calm is either not creative or not wise and vice versa.
Everyone who is either rich or funny is generous or funny and vice versa.
If someone is either not strong or funny then someone is brave or not generous.
If someone is old then paul is both not happy and kind.
Everyone who is not creative is strong or not strong.
Everyone who is not curious is both humble and not tall.
Someone is old or rich.
Someone is both calm and not brave.
Fred is old or funny.
Someone is not happy or not quiet.
Lucy is both happy and brave.
Alice is not curious or funny.
Paul is rich. | John is not brave. | neutral | (![X]:((old(X)<~>generous(X))=>(~rich(X)<~>happy(X))))&
(((quiet(susan)<~>rich(susan)))=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((~kind(X)|~patient(X))=>(~old(X)|~tall(X))))&
((?[X]:((~strong(X)&~calm(X))))<=>((~happy(alice)&happy(alice))))&
(![X]:((curious(X)<~>~funny(X))=>~creative(X)))&
(((~tall(susan)|curious(susan)))<=>((humble(john)&kind(john))))&
(![X]:(creative(X)=>(old(X)|brave(X))))&
(![X]:((generous(X)&strong(X))<=>humble(X)))&
(((~kind(lucy)|old(lucy)))=>((~calm(alice)&strong(alice))))&
(![X]:((wise(X)<~>~calm(X))<=>(~creative(X)<~>~wise(X))))&
(![X]:((rich(X)<~>funny(X))<=>(generous(X)|funny(X))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((brave(X)|~generous(X)))))&
((?[X]:(old(X)))=>((~happy(paul)&kind(paul))))&
(![X]:(~creative(X)=>(strong(X)|~strong(X))))&
(![X]:(~curious(X)=>(humble(X)&~tall(X))))&
(?[X]:((old(X)|rich(X))))&
(?[X]:((calm(X)&~brave(X))))&
((old(fred)|funny(fred)))&
(?[X]:((~happy(X)|~quiet(X))))&
((happy(lucy)&brave(lucy)))&
((~curious(alice)|funny(alice)))&
(rich(paul)) | ~brave(john) | [] | null | 0 |
If someone is calm then someone is strong or humble and vice versa.
If someone is both calm and humble then someone is either rich or not quiet.
If someone is both kind and not patient then someone is both tall and not old.
If someone is not generous or generous then fred is either rich or not patient and vice versa.
Everyone who is both not old and not strong is not rich or strong and vice versa.
If someone is wise then john is not tall or not strong and vice versa.
Everyone who is not humble is both not old and wise and vice versa.
Everyone who is either not rich or creative is both calm and kind and vice versa.
If susan is both calm and not humble then fred is either not old or tall and vice versa.
Everyone who is not funny or happy is both funny and humble.
Everyone who is curious is either not old or old.
Everyone who is not brave is both not calm and not brave.
Everyone who is calm or not humble is either not brave or not calm.
Everyone who is both rich and not rich is either curious or happy and vice versa.
If someone is not calm or calm then someone is both brave and not patient.
If fred is both curious and not happy then someone is either not wise or not tall and vice versa.
Someone is either quiet or not strong.
Mary is either funny or quiet.
Someone is quiet or not old. | Fred is not old. | entailment | ((?[X]:(calm(X)))<=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((~generous(X)|generous(X))))<=>((rich(fred)<~>~patient(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~rich(X)|strong(X))))&
((?[X]:(wise(X)))<=>((~tall(john)|~strong(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(calm(X)&kind(X))))&
(((calm(susan)&~humble(susan)))<=>((~old(fred)<~>tall(fred))))&
(![X]:((~funny(X)|happy(X))=>(funny(X)&humble(X))))&
(![X]:(curious(X)=>(~old(X)<~>old(X))))&
(![X]:(~brave(X)=>(~calm(X)&~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)&~rich(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(((curious(fred)&~happy(fred)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(?[X]:((quiet(X)<~>~strong(X))))&
((funny(mary)<~>quiet(mary)))&
(?[X]:((quiet(X)|~old(X)))) | ~old(fred) | [
"p0",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 602338909329355642923164
% SZS output start Proof for 602338909329355642923164
1. ? [X0] : calm(X0) <=> ? [X0] : (humble(X0) | strong(X0)) [input p0]
7. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p6]
12. ! [X0] : (~brave(X0) => (~brave(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((~humble(X0) | calm(X0)) => (~brave(X0) <~> ~calm(X0))) [input p12]
20. old(fred) [input hypothesis]
21. ? [X0] : calm(X0) <=> ? [X1] : (humble(X1) | strong(X1)) [rectify 1]
29. ! [X0] : ((~brave(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 12]
30. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 13]
32. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X1] : (humble(X1) | strong(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 21]
33. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X2] : (humble(X2) | strong(X2)) | ! [X3] : ~calm(X3)) [rectify 32]
34. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
35. ? [X2] : (humble(X2) | strong(X2)) => (humble(sK1) | strong(sK1)) [choice axiom]
36. (calm(sK0) | ! [X1] : (~humble(X1) & ~strong(X1))) & ((humble(sK1) | strong(sK1)) | ! [X3] : ~calm(X3)) [skolemisation 33,35,34]
55. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 7]
56. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 55]
62. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (humble(X0) & ~calm(X0))) [nnf transformation 30]
81. calm(sK0) | ~humble(X1) [cnf transformation 36]
100. ~old(X0) | humble(X0) [cnf transformation 56]
121. ~calm(X0) | brave(X0) [cnf transformation 29]
123. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 62]
148. old(fred) [cnf transformation 20]
149. ~calm(X0) | ~brave(X0) [duplicate literal removal 123]
154. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
155. ~humble(X1) <- (1) [avatar component clause 154]
157. 2 <=> calm(sK0) [avatar definition]
159. calm(sK0) <- (2) [avatar component clause 157]
160. 1 | 2 [avatar split clause 81,157,154]
166. 4 <=> ! [X3] : ~calm(X3) [avatar definition]
167. ~calm(X3) <- (4) [avatar component clause 166]
245. 22 <=> old(fred) [avatar definition]
246. old(fred) <- (22) [avatar component clause 245]
264. ~calm(X0) [subsumption resolution 149,121]
265. 4 [avatar split clause 264,166]
321. 22 [avatar split clause 148,245]
326. $false <- (2, 4) [resolution 167,159]
327. ~2 | ~4 [avatar contradiction clause 326]
333. humble(fred) <- (22) [resolution 100,246]
334. $false <- (1, 22) [subsumption resolution 333,155]
335. ~1 | ~22 [avatar contradiction clause 334]
336. $false [avatar sat refutation 160,265,321,327,335]
% SZS output end Proof for 602338909329355642923164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa. If john is rich then someone is not creative or not brave and vice versa. Everyone who is both not calm and wise is both not strong and curious and vice versa. If alice is both strong and old then susan is calm. Everyone who is both generous and not calm is not brave. Everyone who is either not kind or tall is either not strong or tall and vice versa. If someone is either tall or calm then john is either not creative or wise. If lucy is both not kind and not humble then fred is both not generous and not curious. Everyone who is either patient or tall is strong or not tall and vice versa. Everyone who is not quiet is not wise or not calm. Everyone who is either not wise or tall is both not rich and not quiet. If mary is calm or not curious then mary is not old. Everyone who is either calm or wise is both not patient and not strong. If fred is both not quiet and not patient then someone is both tall and not happy. Everyone who is not calm or humble is either not curious or not tall and vice versa. If mary is not patient or not old then someone is not humble and vice versa. Someone is not patient or tall. Someone is either brave or calm. Paul is brave. Someone is generous or wise. Someone is either kind or not rich. Someone is kind or not wise. Someone is not patient or funny. Alice is both not rich and not wise. | Susan is not kind. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
((rich(john))<=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((~calm(X)&wise(X))<=>(~strong(X)&curious(X))))&
(((strong(alice)&old(alice)))=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice))) | ~kind(susan) | [
"p0",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6625594589858815591592104
% SZS output start Proof for 6625594589858815591592104
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
6. ! [X0] : ((~kind(X0) <~> tall(X0)) <=> (~strong(X0) <~> tall(X0))) [input p5]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
13. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p12]
25. ~kind(susan) [input hypothesis]
39. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 13]
42. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
43. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 42]
50. ! [X0] : ((((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 52]
55. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 39]
78. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
80. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 43]
81. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 43]
92. tall(X0) | ~strong(X0) | tall(X0) | kind(X0) [cnf transformation 50]
99. ~tall(X0) | kind(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 50]
107. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 53]
109. tall(X0) | patient(X0) | tall(X0) [cnf transformation 53]
120. ~patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 55]
143. ~kind(susan) [cnf transformation 25]
144. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 107]
145. tall(X0) | patient(X0) [duplicate literal removal 109]
146. tall(X0) | ~strong(X0) | kind(X0) [duplicate literal removal 92]
149. ~tall(X0) | kind(X0) | ~strong(X0) [duplicate literal removal 99]
150. ~patient(X0) | wise(X0) [duplicate literal removal 78]
151. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 81]
182. 8 <=> calm(susan) [avatar definition]
184. calm(susan) <- (8) [avatar component clause 182]
187. ~strong(X0) | kind(X0) [subsumption resolution 146,149]
224. strong(X0) | patient(X0) [subsumption resolution 144,145]
239. ~patient(X0) | calm(X0) [subsumption resolution 120,80]
307. kind(X0) | patient(X0) [resolution 224,187]
313. patient(susan) [resolution 307,143]
317. calm(susan) [resolution 313,239]
318. wise(susan) [resolution 313,150]
320. 34 <=> wise(susan) [avatar definition]
322. wise(susan) <- (34) [avatar component clause 320]
324. 8 [avatar split clause 317,182]
325. 34 [avatar split clause 318,320]
477. ~patient(susan) | ~wise(susan) <- (8) [resolution 151,184]
478. ~wise(susan) <- (8) [subsumption resolution 477,313]
479. $false <- (8, 34) [subsumption resolution 478,322]
480. ~8 | ~34 [avatar contradiction clause 479]
481. $false [avatar sat refutation 324,325,480]
% SZS output end Proof for 6625594589858815591592104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and wise is both tall and rich. If paul is not patient then fred is both not kind and not patient. If someone is funny or strong then someone is both creative and not creative and vice versa. Everyone who is not curious is not tall and vice versa. Everyone who is patient is not rich or not kind. If paul is rich then someone is either creative or tall. Everyone who is not quiet or not old is happy. If someone is creative or humble then someone is old and vice versa. Everyone who is both generous and not quiet is rich or not patient. Everyone who is not tall is either calm or humble and vice versa. Everyone who is both not wise and tall is both rich and not funny and vice versa. Everyone who is not tall is kind or strong. If lucy is not curious or not calm then lucy is generous and vice versa. If someone is strong then someone is either generous or not wise. Everyone who is either not funny or tall is both not calm and creative and vice versa. If paul is either wise or humble then alice is strong or rich and vice versa. Alice is quiet. John is brave or not quiet. Lucy is not old or curious. Someone is both not quiet and happy. Someone is either not creative or not tall. Someone is old. | Lucy is not patient. | neutral | (![X]:((rich(X)&wise(X))=>(tall(X)&rich(X))))&
((~patient(paul))=>((~kind(fred)&~patient(fred))))&
((?[X]:((funny(X)|strong(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:(~curious(X)<=>~tall(X)))&
(![X]:(patient(X)=>(~rich(X)|~kind(X))))&
((rich(paul))=>(?[X]:((creative(X)<~>tall(X)))))&
(![X]:((~quiet(X)|~old(X))=>happy(X)))&
((?[X]:((creative(X)|humble(X))))<=>(?[X]:(old(X))))&
(![X]:((generous(X)&~quiet(X))=>(rich(X)|~patient(X))))&
(![X]:(~tall(X)<=>(calm(X)<~>humble(X))))&
(![X]:((~wise(X)&tall(X))<=>(rich(X)&~funny(X))))&
(![X]:(~tall(X)=>(kind(X)|strong(X))))&
(((~curious(lucy)|~calm(lucy)))<=>(generous(lucy)))&
((?[X]:(strong(X)))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((~funny(X)<~>tall(X))<=>(~calm(X)&creative(X))))&
(((wise(paul)<~>humble(paul)))<=>((strong(alice)|rich(alice))))&
(quiet(alice))&
((brave(john)|~quiet(john)))&
((~old(lucy)|curious(lucy)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:(old(X))) | ~patient(lucy) | [] | null | 0 |
Everyone who is not quiet or kind is creative and vice versa.
If john is both wise and humble then susan is both wise and not quiet.
Everyone who is not patient or funny is funny or tall.
Everyone who is both calm and not creative is either curious or not quiet.
Everyone who is happy is not quiet or tall.
If someone is old or calm then lucy is both brave and not calm.
If someone is calm or quiet then mary is old or strong and vice versa.
Everyone who is both old and not happy is both quiet and not brave.
If someone is strong or not strong then alice is creative and vice versa.
If paul is both old and not patient then someone is either generous or creative.
Everyone who is not brave is both not calm and generous and vice versa.
Everyone who is either strong or patient is both not calm and not funny.
Everyone who is either funny or patient is happy and vice versa.
If fred is either curious or not kind then john is both quiet and not old.
If mary is both not tall and humble then someone is not strong.
Everyone who is both not curious and kind is brave.
Someone is not happy.
Lucy is both not calm and strong.
Someone is quiet or humble.
Mary is both curious and not quiet.
Someone is both quiet and not brave.
Alice is either not creative or generous.
Someone is both not rich and humble.
Someone is either not wise or strong. | Mary is happy. | neutral | (![X]:((~quiet(X)|kind(X))<=>creative(X)))&
(((wise(john)&humble(john)))=>((wise(susan)&~quiet(susan))))&
(![X]:((~patient(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&~creative(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>((brave(lucy)&~calm(lucy))))&
((?[X]:((calm(X)|quiet(X))))<=>((old(mary)|strong(mary))))&
(![X]:((old(X)&~happy(X))=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(creative(alice)))&
(((old(paul)&~patient(paul)))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~brave(X)<=>(~calm(X)&generous(X))))&
(![X]:((strong(X)<~>patient(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)<~>patient(X))<=>happy(X)))&
(((curious(fred)<~>~kind(fred)))=>((quiet(john)&~old(john))))&
(((~tall(mary)&humble(mary)))=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&kind(X))=>brave(X)))&
(?[X]:(~happy(X)))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
((curious(mary)&~quiet(mary)))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice)))&
(?[X]:((~rich(X)&humble(X))))&
(?[X]:((~wise(X)<~>strong(X)))) | happy(mary) | [] | null | 0 |
Everyone who is wise is not calm and vice versa. If john is curious or brave then fred is patient or not calm and vice versa. If john is not calm or old then susan is either generous or not funny. If paul is not funny or tall then someone is both quiet and not generous. Everyone who is either not funny or old is brave. Everyone who is not brave or not old is either not creative or old. Everyone who is not creative or not curious is both rich and strong. Everyone who is both not wise and not quiet is happy or not creative. If alice is kind then fred is either not wise or patient and vice versa. Everyone who is not patient or not kind is both generous and not rich and vice versa. If someone is old then fred is either not strong or not creative. Everyone who is both not calm and funny is patient. Everyone who is both strong and not humble is not brave or not generous and vice versa. Everyone who is both not creative and calm is both brave and happy. If alice is both not happy and not generous then someone is generous. If someone is either not strong or rich then john is not happy or not rich. Lucy is both not quiet and not brave. Someone is either brave or quiet. Someone is both not creative and kind. Mary is not tall or rich. Someone is not funny. Someone is calm or not old. Someone is funny or kind. Fred is not wise or not old. | Lucy is not quiet. | entailment | (![X]:(wise(X)<=>~calm(X)))&
(((curious(john)|brave(john)))<=>((patient(fred)|~calm(fred))))&
(((~calm(john)|old(john)))=>((generous(susan)<~>~funny(susan))))&
(((~funny(paul)|tall(paul)))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:((~funny(X)<~>old(X))=>brave(X)))&
(![X]:((~brave(X)|~old(X))=>(~creative(X)<~>old(X))))&
(![X]:((~creative(X)|~curious(X))=>(rich(X)&strong(X))))&
(![X]:((~wise(X)&~quiet(X))=>(happy(X)|~creative(X))))&
((kind(alice))<=>((~wise(fred)<~>patient(fred))))&
(![X]:((~patient(X)|~kind(X))<=>(generous(X)&~rich(X))))&
((?[X]:(old(X)))=>((~strong(fred)<~>~creative(fred))))&
(![X]:((~calm(X)&funny(X))=>patient(X)))&
(![X]:((strong(X)&~humble(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~creative(X)&calm(X))=>(brave(X)&happy(X))))&
(((~happy(alice)&~generous(alice)))=>(?[X]:(generous(X))))&
((?[X]:((~strong(X)<~>rich(X))))=>((~happy(john)|~rich(john))))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((~creative(X)&kind(X))))&
((~tall(mary)|rich(mary)))&
(?[X]:(~funny(X)))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:((funny(X)|kind(X))))&
((~wise(fred)|~old(fred))) | ~quiet(lucy) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4429847108231960621659711
% SZS output start Proof for 4429847108231960621659711
17. ~brave(lucy) & ~quiet(lucy) [input p16]
25. quiet(lucy) [input hypothesis]
117. ~quiet(lucy) [cnf transformation 17]
127. quiet(lucy) [cnf transformation 25]
269. $false [subsumption resolution 127,117]
% SZS output end Proof for 4429847108231960621659711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not calm then someone is funny or not strong and vice versa.
Everyone who is both rich and wise is not humble and vice versa.
Everyone who is curious is both patient and creative and vice versa.
If john is tall or not curious then someone is both not patient and quiet.
If someone is either not patient or calm then alice is either not funny or not happy and vice versa.
Everyone who is rich or humble is old and vice versa.
Everyone who is either not old or calm is both not brave and not tall.
If someone is either happy or calm then someone is either not generous or tall and vice versa.
If lucy is not happy then someone is either kind or curious.
Everyone who is wise or generous is both not happy and creative.
Everyone who is rich or not patient is wise.
Everyone who is happy or not humble is not patient and vice versa.
Everyone who is either not rich or funny is quiet.
If mary is not curious then someone is kind or curious and vice versa.
If someone is strong then someone is either patient or not kind and vice versa.
Everyone who is tall is patient or quiet.
Someone is either patient or not patient.
Someone is not funny.
Someone is generous or not curious.
Someone is either not curious or patient.
John is either not tall or creative.
Someone is not strong or not curious. | John is not strong. | neutral | ((~calm(fred))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((rich(X)&wise(X))<=>~humble(X)))&
(![X]:(curious(X)<=>(patient(X)&creative(X))))&
(((tall(john)|~curious(john)))=>(?[X]:((~patient(X)&quiet(X)))))&
((?[X]:((~patient(X)<~>calm(X))))<=>((~funny(alice)<~>~happy(alice))))&
(![X]:((rich(X)|humble(X))<=>old(X)))&
(![X]:((~old(X)<~>calm(X))=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((~happy(lucy))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)&creative(X))))&
(![X]:((rich(X)|~patient(X))=>wise(X)))&
(![X]:((happy(X)|~humble(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>funny(X))=>quiet(X)))&
((~curious(mary))<=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~kind(X)))))&
(![X]:(tall(X)=>(patient(X)|quiet(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((~tall(john)<~>creative(john)))&
(?[X]:((~strong(X)|~curious(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is either not patient or kind is strong and vice versa. Everyone who is not patient or not happy is both calm and rich and vice versa. Everyone who is both not rich and not curious is either tall or not kind. Everyone who is not rich is either patient or happy. Everyone who is both humble and quiet is both not creative and not tall. Everyone who is both creative and not rich is either not old or not brave. If someone is calm then alice is not wise and vice versa. Everyone who is either not happy or strong is both not rich and not humble. If someone is not rich then fred is quiet and vice versa. Everyone who is both not creative and not strong is curious and vice versa. Everyone who is not happy or not quiet is both not quiet and funny. Everyone who is not curious is either creative or tall. Everyone who is generous or brave is both old and not funny and vice versa. Everyone who is wise or not wise is not happy or creative. If john is not generous then paul is both not wise and wise and vice versa. If lucy is not curious or not creative then alice is either brave or curious and vice versa. Fred is either not brave or calm. Lucy is not tall or not curious. Someone is not kind or not old. Someone is not strong. Mary is not calm. Paul is not happy or not tall. | Mary is humble. | neutral | (![X]:((~patient(X)<~>kind(X))<=>strong(X)))&
(![X]:((~patient(X)|~happy(X))<=>(calm(X)&rich(X))))&
(![X]:((~rich(X)&~curious(X))=>(tall(X)<~>~kind(X))))&
(![X]:(~rich(X)=>(patient(X)<~>happy(X))))&
(![X]:((humble(X)&quiet(X))=>(~creative(X)&~tall(X))))&
(![X]:((creative(X)&~rich(X))=>(~old(X)<~>~brave(X))))&
((?[X]:(calm(X)))<=>(~wise(alice)))&
(![X]:((~happy(X)<~>strong(X))=>(~rich(X)&~humble(X))))&
((?[X]:(~rich(X)))<=>(quiet(fred)))&
(![X]:((~creative(X)&~strong(X))<=>curious(X)))&
(![X]:((~happy(X)|~quiet(X))=>(~quiet(X)&funny(X))))&
(![X]:(~curious(X)=>(creative(X)<~>tall(X))))&
(![X]:((generous(X)|brave(X))<=>(old(X)&~funny(X))))&
(![X]:((wise(X)|~wise(X))=>(~happy(X)|creative(X))))&
((~generous(john))<=>((~wise(paul)&wise(paul))))&
(((~curious(lucy)|~creative(lucy)))<=>((brave(alice)<~>curious(alice))))&
((~brave(fred)<~>calm(fred)))&
((~tall(lucy)|~curious(lucy)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:(~strong(X)))&
(~calm(mary))&
((~happy(paul)|~tall(paul))) | humble(mary) | [] | null | 0 |
Everyone who is funny is both strong and tall and vice versa.
Everyone who is both quiet and not funny is curious or not funny.
Everyone who is calm is both not humble and generous.
Everyone who is not brave or tall is either not brave or calm.
If someone is not tall or wise then lucy is both curious and not curious and vice versa.
Everyone who is either not old or calm is both not curious and humble and vice versa.
If paul is creative or not kind then someone is either rich or not tall and vice versa.
Everyone who is patient is both not funny and not quiet and vice versa.
Everyone who is humble is wise or tall and vice versa.
Everyone who is both curious and not kind is either not creative or not tall and vice versa.
Everyone who is both brave and not strong is either happy or generous and vice versa.
Everyone who is funny or humble is either humble or not kind.
If susan is either not happy or not strong then susan is old or curious.
If paul is either quiet or patient then fred is either not strong or not creative and vice versa.
Everyone who is not happy or not brave is not wise and vice versa.
Everyone who is both not calm and wise is either brave or curious.
Paul is either tall or not kind.
Susan is not funny or not strong.
John is kind or quiet.
Mary is both not happy and not generous.
Someone is both tall and happy.
Susan is rich or not old. | Susan is not strong. | entailment | (![X]:(funny(X)<=>(strong(X)&tall(X))))&
(![X]:((quiet(X)&~funny(X))=>(curious(X)|~funny(X))))&
(![X]:(calm(X)=>(~humble(X)&generous(X))))&
(![X]:((~brave(X)|tall(X))=>(~brave(X)<~>calm(X))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&humble(X))))&
(((creative(paul)|~kind(paul)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(patient(X)<=>(~funny(X)&~quiet(X))))&
(![X]:(humble(X)<=>(wise(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((brave(X)&~strong(X))<=>(happy(X)<~>generous(X))))&
(![X]:((funny(X)|humble(X))=>(humble(X)<~>~kind(X))))&
(((~happy(susan)<~>~strong(susan)))=>((old(susan)|curious(susan))))&
(((quiet(paul)<~>patient(paul)))<=>((~strong(fred)<~>~creative(fred))))&
(![X]:((~happy(X)|~brave(X))<=>~wise(X)))&
(![X]:((~calm(X)&wise(X))=>(brave(X)<~>curious(X))))&
((tall(paul)<~>~kind(paul)))&
((~funny(susan)|~strong(susan)))&
((kind(john)|quiet(john)))&
((~happy(mary)&~generous(mary)))&
(?[X]:((tall(X)&happy(X))))&
((rich(susan)|~old(susan))) | ~strong(susan) | [
"p0",
"p4",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 323580463034473795728976
% SZS output start Proof for 323580463034473795728976
1. ! [X0] : (funny(X0) <=> (tall(X0) & strong(X0))) [input p0]
5. ? [X0] : (wise(X0) | ~tall(X0)) <=> (~curious(lucy) & curious(lucy)) [input p4]
18. ~strong(susan) | ~funny(susan) [input p17]
23. strong(susan) [input hypothesis]
33. ! [X0] : ((funny(X0) | (~tall(X0) | ~strong(X0))) & ((tall(X0) & strong(X0)) | ~funny(X0))) [nnf transformation 1]
34. ! [X0] : ((funny(X0) | ~tall(X0) | ~strong(X0)) & ((tall(X0) & strong(X0)) | ~funny(X0))) [flattening 33]
36. (? [X0] : (wise(X0) | ~tall(X0)) | (curious(lucy) | ~curious(lucy))) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [nnf transformation 5]
37. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [flattening 36]
38. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [rectify 37]
39. ? [X0] : (wise(X0) | ~tall(X0)) => (wise(sK0) | ~tall(sK0)) [choice axiom]
40. ((wise(sK0) | ~tall(sK0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [skolemisation 38,39]
65. ~funny(X0) | strong(X0) [cnf transformation 34]
67. ~tall(X0) | funny(X0) | ~strong(X0) [cnf transformation 34]
75. curious(lucy) | tall(X1) [cnf transformation 40]
77. ~curious(lucy) | tall(X1) [cnf transformation 40]
131. ~strong(susan) | ~funny(susan) [cnf transformation 18]
138. strong(susan) [cnf transformation 23]
145. 2 <=> curious(lucy) [avatar definition]
150. 3 <=> ! [X1] : tall(X1) [avatar definition]
151. tall(X1) <- (3) [avatar component clause 150]
152. 3 | ~2 [avatar split clause 77,145,150]
154. 3 | 2 [avatar split clause 75,145,150]
186. 10 <=> strong(susan) [avatar definition]
188. strong(susan) <- (10) [avatar component clause 186]
236. ~funny(susan) [subsumption resolution 131,65]
251. 10 [avatar split clause 138,186]
266. ~strong(X0) | funny(X0) <- (3) [resolution 67,151]
276. funny(susan) <- (3, 10) [resolution 266,188]
277. $false <- (3, 10) [subsumption resolution 276,236]
278. ~3 | ~10 [avatar contradiction clause 277]
279. $false [avatar sat refutation 152,154,251,278]
% SZS output end Proof for 323580463034473795728976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not calm is either calm or quiet and vice versa.
If paul is not rich then someone is not brave or not calm.
Everyone who is not rich or not generous is both humble and calm.
If alice is either not funny or calm then someone is either brave or creative and vice versa.
If someone is quiet then someone is quiet or not strong.
Everyone who is either not happy or tall is not calm or patient and vice versa.
Everyone who is both not rich and not calm is not happy and vice versa.
Everyone who is either not tall or wise is either not rich or calm and vice versa.
If alice is not quiet or curious then someone is either not calm or kind and vice versa.
If paul is not old then someone is not funny and vice versa.
Everyone who is either patient or calm is either calm or funny and vice versa.
If someone is both not patient and not strong then john is both not curious and wise and vice versa.
If someone is either not quiet or wise then someone is either strong or rich.
If someone is not kind or not funny then someone is both funny and creative and vice versa.
If someone is either not strong or not wise then susan is generous or not creative and vice versa.
Everyone who is rich or strong is both rich and quiet and vice versa.
Alice is creative.
Someone is not rich or not patient.
Fred is not patient.
Lucy is not quiet.
Lucy is both not strong and not funny.
Someone is old.
Someone is either not creative or generous.
Mary is tall or not creative. | John is curious. | contradiction | (![X]:((~brave(X)|~calm(X))<=>(calm(X)<~>quiet(X))))&
((~rich(paul))=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~rich(X)|~generous(X))=>(humble(X)&calm(X))))&
(((~funny(alice)<~>calm(alice)))<=>(?[X]:((brave(X)<~>creative(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(~calm(X)|patient(X))))&
(![X]:((~rich(X)&~calm(X))<=>~happy(X)))&
(![X]:((~tall(X)<~>wise(X))<=>(~rich(X)<~>calm(X))))&
(((~quiet(alice)|curious(alice)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
((~old(paul))<=>(?[X]:(~funny(X))))&
(![X]:((patient(X)<~>calm(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>((~curious(john)&wise(john))))&
((?[X]:((~quiet(X)<~>wise(X))))=>(?[X]:((strong(X)<~>rich(X)))))&
((?[X]:((~kind(X)|~funny(X))))<=>(?[X]:((funny(X)&creative(X)))))&
((?[X]:((~strong(X)<~>~wise(X))))<=>((generous(susan)|~creative(susan))))&
(![X]:((rich(X)|strong(X))<=>(rich(X)&quiet(X))))&
(creative(alice))&
(?[X]:((~rich(X)|~patient(X))))&
(~patient(fred))&
(~quiet(lucy))&
((~strong(lucy)&~funny(lucy)))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)<~>generous(X))))&
((tall(mary)|~creative(mary))) | curious(john) | [
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5333020816133258667129113
% SZS output start Proof for 5333020816133258667129113
11. ! [X0] : ((patient(X0) <~> calm(X0)) <=> (calm(X0) <~> funny(X0))) [input p10]
12. ? [X0] : (~strong(X0) & ~patient(X0)) <=> (wise(john) & ~curious(john)) [input p11]
21. ~funny(lucy) & ~strong(lucy) [input p20]
25. curious(john) [input hypothesis]
59. ! [X0] : ((((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0))))) [nnf transformation 11]
60. (? [X0] : (~strong(X0) & ~patient(X0)) | (~wise(john) | curious(john))) & ((wise(john) & ~curious(john)) | ! [X0] : (strong(X0) | patient(X0))) [nnf transformation 12]
61. (? [X0] : (~strong(X0) & ~patient(X0)) | ~wise(john) | curious(john)) & ((wise(john) & ~curious(john)) | ! [X0] : (strong(X0) | patient(X0))) [flattening 60]
62. (? [X0] : (~strong(X0) & ~patient(X0)) | ~wise(john) | curious(john)) & ((wise(john) & ~curious(john)) | ! [X1] : (strong(X1) | patient(X1))) [rectify 61]
63. ? [X0] : (~strong(X0) & ~patient(X0)) => (~strong(sK5) & ~patient(sK5)) [choice axiom]
64. ((~strong(sK5) & ~patient(sK5)) | ~wise(john) | curious(john)) & ((wise(john) & ~curious(john)) | ! [X1] : (strong(X1) | patient(X1))) [skolemisation 62,63]
131. funny(X0) | calm(X0) | calm(X0) | ~patient(X0) [cnf transformation 59]
137. ~calm(X0) | ~patient(X0) | funny(X0) | ~calm(X0) [cnf transformation 59]
139. ~curious(john) | strong(X1) | patient(X1) [cnf transformation 64]
167. ~strong(lucy) [cnf transformation 21]
168. ~funny(lucy) [cnf transformation 21]
173. curious(john) [cnf transformation 25]
174. funny(X0) | calm(X0) | ~patient(X0) [duplicate literal removal 131]
177. ~patient(X0) | ~calm(X0) | funny(X0) [duplicate literal removal 137]
281. ~patient(X0) | funny(X0) [subsumption resolution 174,177]
283. 22 <=> curious(john) [avatar definition]
301. 26 <=> ! [X1] : (strong(X1) | patient(X1)) [avatar definition]
302. patient(X1) | strong(X1) <- (26) [avatar component clause 301]
304. 26 | ~22 [avatar split clause 139,283,301]
406. 22 [avatar split clause 173,283]
446. strong(X0) | funny(X0) <- (26) [resolution 302,281]
580. funny(lucy) <- (26) [resolution 446,167]
583. $false <- (26) [subsumption resolution 580,168]
584. ~26 [avatar contradiction clause 583]
585. $false [avatar sat refutation 304,406,584]
% SZS output end Proof for 5333020816133258667129113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and funny is not calm or not generous and vice versa. Everyone who is both not old and not strong is either not happy or not old and vice versa. If someone is both not quiet and not wise then someone is both rich and not curious and vice versa. If someone is humble or curious then fred is either curious or not curious and vice versa. Everyone who is old is both rich and not humble and vice versa. Everyone who is wise or creative is both not quiet and not patient. If someone is both happy and not happy then someone is either not tall or strong and vice versa. Everyone who is either patient or humble is not wise and vice versa. If someone is funny then someone is wise or generous. If someone is not curious or old then fred is either not curious or tall. If lucy is tall then someone is either not rich or not generous. Everyone who is not humble or not calm is both old and not rich. If someone is either not generous or not humble then someone is not funny or not rich. If lucy is either not tall or not calm then paul is humble or not curious and vice versa. If someone is both not creative and funny then someone is not rich or not curious. If mary is patient then alice is both patient and not generous and vice versa. Someone is not humble or not strong. Someone is either creative or kind. John is either calm or quiet. Lucy is either not strong or not tall. Someone is either not kind or not calm. Someone is not wise or kind. Alice is either not creative or creative. | Alice is not patient. | entailment | (![X]:((curious(X)&funny(X))<=>(~calm(X)|~generous(X))))&
(![X]:((~old(X)&~strong(X))<=>(~happy(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((rich(X)&~curious(X)))))&
((?[X]:((humble(X)|curious(X))))<=>((curious(fred)<~>~curious(fred))))&
(![X]:(old(X)<=>(rich(X)&~humble(X))))&
(![X]:((wise(X)|creative(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((patient(X)<~>humble(X))<=>~wise(X)))&
((?[X]:(funny(X)))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((~curious(X)|old(X))))=>((~curious(fred)<~>tall(fred))))&
((tall(lucy))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~humble(X)|~calm(X))=>(old(X)&~rich(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
(((~tall(lucy)<~>~calm(lucy)))<=>((humble(paul)|~curious(paul))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((patient(mary))<=>((patient(alice)&~generous(alice))))&
(?[X]:((~humble(X)|~strong(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((calm(john)<~>quiet(john)))&
((~strong(lucy)<~>~tall(lucy)))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((~wise(X)|kind(X))))&
((~creative(alice)<~>creative(alice))) | ~patient(alice) | [
"p4",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4237962967735270868349803
% SZS output start Proof for 4237962967735270868349803
5. ! [X0] : (old(X0) <=> (~humble(X0) & rich(X0))) [input p4]
6. ! [X0] : ((creative(X0) | wise(X0)) => (~patient(X0) & ~quiet(X0))) [input p5]
8. ! [X0] : ((patient(X0) <~> humble(X0)) <=> ~wise(X0)) [input p7]
12. ! [X0] : ((~calm(X0) | ~humble(X0)) => (~rich(X0) & old(X0))) [input p11]
24. patient(alice) [input hypothesis]
30. ! [X0] : ((~patient(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0))) [ennf transformation 6]
34. ! [X0] : ((~rich(X0) & old(X0)) | (calm(X0) & humble(X0))) [ennf transformation 12]
50. ! [X0] : ((old(X0) | (humble(X0) | ~rich(X0))) & ((~humble(X0) & rich(X0)) | ~old(X0))) [nnf transformation 5]
51. ! [X0] : ((old(X0) | humble(X0) | ~rich(X0)) & ((~humble(X0) & rich(X0)) | ~old(X0))) [flattening 50]
57. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | wise(X0)) & (~wise(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 8]
110. ~old(X0) | rich(X0) [cnf transformation 51]
115. ~patient(X0) | ~wise(X0) [cnf transformation 30]
126. ~humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 57]
134. humble(X0) | old(X0) [cnf transformation 34]
136. ~rich(X0) | humble(X0) [cnf transformation 34]
162. patient(alice) [cnf transformation 24]
222. ~patient(X0) | ~humble(X0) [subsumption resolution 126,115]
311. 32 <=> patient(alice) [avatar definition]
312. patient(alice) <- (32) [avatar component clause 311]
379. 32 [avatar split clause 162,311]
426. ~humble(alice) <- (32) [resolution 222,312]
431. old(alice) <- (32) [resolution 426,134]
476. rich(alice) <- (32) [resolution 431,110]
494. humble(alice) <- (32) [resolution 476,136]
495. $false <- (32) [subsumption resolution 494,426]
496. ~32 [avatar contradiction clause 495]
497. $false [avatar sat refutation 379,496]
% SZS output end Proof for 4237962967735270868349803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or strong is not happy or not calm and vice versa.
Everyone who is either not strong or not tall is not rich and vice versa.
Everyone who is rich is humble and vice versa.
Everyone who is quiet is not calm or patient.
Everyone who is both calm and generous is both not humble and brave.
Everyone who is not wise or curious is not strong or quiet and vice versa.
Everyone who is both not quiet and not tall is either not rich or wise and vice versa.
Everyone who is either humble or brave is brave.
Everyone who is creative or rich is either quiet or strong.
If susan is creative then someone is either tall or strong.
If someone is either kind or happy then fred is both not strong and creative and vice versa.
If alice is not calm or funny then someone is both tall and not brave.
If someone is creative then someone is not curious.
Everyone who is either not rich or curious is both creative and wise and vice versa.
If lucy is generous or old then someone is both humble and not patient.
If fred is not humble then someone is either strong or not patient and vice versa.
Someone is tall.
Susan is not strong.
Paul is either not generous or strong.
Lucy is rich.
Someone is not rich or not patient.
Alice is rich or generous.
Someone is not rich or happy. | Lucy is not patient. | contradiction | (![X]:((curious(X)|strong(X))<=>(~happy(X)|~calm(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>~rich(X)))&
(![X]:(rich(X)<=>humble(X)))&
(![X]:(quiet(X)=>(~calm(X)|patient(X))))&
(![X]:((calm(X)&generous(X))=>(~humble(X)&brave(X))))&
(![X]:((~wise(X)|curious(X))<=>(~strong(X)|quiet(X))))&
(![X]:((~quiet(X)&~tall(X))<=>(~rich(X)<~>wise(X))))&
(![X]:((humble(X)<~>brave(X))=>brave(X)))&
(![X]:((creative(X)|rich(X))=>(quiet(X)<~>strong(X))))&
((creative(susan))=>(?[X]:((tall(X)<~>strong(X)))))&
((?[X]:((kind(X)<~>happy(X))))<=>((~strong(fred)&creative(fred))))&
(((~calm(alice)|funny(alice)))=>(?[X]:((tall(X)&~brave(X)))))&
((?[X]:(creative(X)))=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(creative(X)&wise(X))))&
(((generous(lucy)|old(lucy)))=>(?[X]:((humble(X)&~patient(X)))))&
((~humble(fred))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(?[X]:(tall(X)))&
(~strong(susan))&
((~generous(paul)<~>strong(paul)))&
(rich(lucy))&
(?[X]:((~rich(X)|~patient(X))))&
((rich(alice)|generous(alice)))&
(?[X]:((~rich(X)|happy(X)))) | ~patient(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p6",
"p8",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7309638799933113357719664
% SZS output start Proof for 7309638799933113357719664
1. ! [X0] : ((strong(X0) | curious(X0)) <=> (~calm(X0) | ~happy(X0))) [input p0]
2. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~rich(X0)) [input p1]
4. ! [X0] : (quiet(X0) => (patient(X0) | ~calm(X0))) [input p3]
6. ! [X0] : ((curious(X0) | ~wise(X0)) <=> (quiet(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((~tall(X0) & ~quiet(X0)) <=> (~rich(X0) <~> wise(X0))) [input p6]
9. ! [X0] : ((rich(X0) | creative(X0)) => (quiet(X0) <~> strong(X0))) [input p8]
14. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> (wise(X0) & creative(X0))) [input p13]
20. rich(lucy) [input p19]
24. ~patient(lucy) [input hypothesis]
28. ! [X0] : ((patient(X0) | ~calm(X0)) | ~quiet(X0)) [ennf transformation 4]
29. ! [X0] : (patient(X0) | ~calm(X0) | ~quiet(X0)) [flattening 28]
33. ! [X0] : ((quiet(X0) <~> strong(X0)) | (~rich(X0) & ~creative(X0))) [ennf transformation 9]
38. ! [X0] : (((strong(X0) | curious(X0)) | (calm(X0) & happy(X0))) & ((~calm(X0) | ~happy(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 1]
39. ! [X0] : ((strong(X0) | curious(X0) | (calm(X0) & happy(X0))) & (~calm(X0) | ~happy(X0) | (~strong(X0) & ~curious(X0)))) [flattening 38]
40. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | rich(X0)) & (~rich(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 2]
42. ! [X0] : (((curious(X0) | ~wise(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (~curious(X0) & wise(X0)))) [nnf transformation 6]
43. ! [X0] : ((curious(X0) | ~wise(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | (~curious(X0) & wise(X0)))) [flattening 42]
44. ! [X0] : (((~tall(X0) & ~quiet(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0)))) & (((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (tall(X0) | quiet(X0)))) [nnf transformation 7]
45. ! [X0] : (((~tall(X0) & ~quiet(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0)))) & (((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | tall(X0) | quiet(X0))) [flattening 44]
47. ! [X0] : (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | (~rich(X0) & ~creative(X0))) [nnf transformation 33]
61. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [flattening 61]
79. calm(X0) | curious(X0) | strong(X0) [cnf transformation 39]
81. ~rich(X0) | ~strong(X0) | tall(X0) [cnf transformation 40]
86. ~quiet(X0) | ~calm(X0) | patient(X0) [cnf transformation 29]
89. ~strong(X0) | quiet(X0) | wise(X0) [cnf transformation 43]
96. ~wise(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 45]
98. ~wise(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 45]
102. ~rich(X0) | quiet(X0) | strong(X0) [cnf transformation 47]
104. ~quiet(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 47]
119. ~rich(X0) | wise(X0) | ~curious(X0) [cnf transformation 62]
132. rich(lucy) [cnf transformation 20]
136. ~patient(lucy) [cnf transformation 24]
319. 36 <=> strong(lucy) [avatar definition]
320. ~strong(lucy) <- (~36) [avatar component clause 319]
321. strong(lucy) <- (36) [avatar component clause 319]
323. 37 <=> tall(lucy) [avatar definition]
324. tall(lucy) <- (37) [avatar component clause 323]
332. ~strong(lucy) | tall(lucy) [resolution 81,132]
416. quiet(lucy) | strong(lucy) [resolution 102,132]
420. quiet(lucy) <- (~36) [subsumption resolution 416,320]
456. ~calm(lucy) | patient(lucy) <- (~36) [resolution 420,86]
457. ~calm(lucy) <- (~36) [subsumption resolution 456,136]
464. 52 <=> curious(lucy) [avatar definition]
466. ~curious(lucy) <- (~52) [avatar component clause 464]
496. wise(lucy) | ~curious(lucy) [resolution 119,132]
644. curious(lucy) | strong(lucy) <- (~36) [resolution 457,79]
645. strong(lucy) <- (~36, ~52) [subsumption resolution 644,466]
646. $false <- (~36, ~52) [subsumption resolution 645,320]
647. 36 | 52 [avatar contradiction clause 646]
649. 66 <=> quiet(lucy) [avatar definition]
651. quiet(lucy) <- (66) [avatar component clause 649]
653. 67 <=> wise(lucy) [avatar definition]
655. wise(lucy) <- (67) [avatar component clause 653]
657. 36 | 66 [avatar split clause 416,649,319]
658. 37 | ~36 [avatar split clause 332,319,323]
660. quiet(lucy) | wise(lucy) <- (36) [resolution 321,89]
661. 67 | 66 | ~36 [avatar split clause 660,319,649,653]
664. ~strong(lucy) | ~rich(lucy) <- (66) [resolution 651,104]
667. ~rich(lucy) <- (36, 66) [subsumption resolution 664,321]
668. $false <- (36, 66) [subsumption resolution 667,132]
669. ~36 | ~66 [avatar contradiction clause 668]
673. ~rich(lucy) | ~tall(lucy) <- (67) [resolution 655,98]
677. ~tall(lucy) <- (67) [subsumption resolution 673,132]
678. $false <- (37, 67) [subsumption resolution 677,324]
679. ~37 | ~67 [avatar contradiction clause 678]
680. ~52 | 67 [avatar split clause 496,653,464]
691. ~rich(lucy) | ~quiet(lucy) <- (67) [resolution 655,96]
694. ~quiet(lucy) <- (67) [subsumption resolution 691,132]
695. $false <- (66, 67) [subsumption resolution 694,651]
696. ~66 | ~67 [avatar contradiction clause 695]
697. $false [avatar sat refutation 647,657,658,661,669,679,680,696]
% SZS output end Proof for 7309638799933113357719664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not old is both not creative and not happy and vice versa.
Everyone who is both not happy and tall is either calm or quiet and vice versa.
Everyone who is either happy or calm is either not old or not happy and vice versa.
If someone is both funny and creative then fred is either not patient or not happy.
Everyone who is not curious or not brave is either wise or not rich.
If someone is curious then someone is happy or calm.
Everyone who is not calm or happy is both wise and not rich.
Everyone who is not old is kind and vice versa.
Everyone who is both not old and not strong is quiet and vice versa.
Everyone who is funny is quiet or not strong and vice versa.
Everyone who is both creative and not wise is calm or not happy and vice versa.
If susan is calm then someone is not old or not generous and vice versa.
If someone is rich or generous then someone is both not old and wise.
Everyone who is either not quiet or kind is either not funny or happy and vice versa.
If someone is old then someone is either wise or not brave.
Lucy is not quiet.
John is not brave.
Someone is curious or not calm. | Lucy is not happy. | entailment | (![X]:((~strong(X)|~old(X))<=>(~creative(X)&~happy(X))))&
(![X]:((~happy(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((funny(X)&creative(X))))=>((~patient(fred)<~>~happy(fred))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)<~>~rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~calm(X)|happy(X))=>(wise(X)&~rich(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~old(X)&~strong(X))<=>quiet(X)))&
(![X]:(funny(X)<=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)&~wise(X))<=>(calm(X)|~happy(X))))&
((calm(susan))<=>(?[X]:((~old(X)|~generous(X)))))&
((?[X]:((rich(X)|generous(X))))=>(?[X]:((~old(X)&wise(X)))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(old(X)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(~quiet(lucy))&
(~brave(john))&
(?[X]:((curious(X)|~calm(X)))) | ~happy(lucy) | [
"p0",
"p2",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2339408190714989319413402
% SZS output start Proof for 2339408190714989319413402
1. ! [X0] : ((~old(X0) | ~strong(X0)) <=> (~happy(X0) & ~creative(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p2]
7. ! [X0] : ((happy(X0) | ~calm(X0)) => (~rich(X0) & wise(X0))) [input p6]
11. ! [X0] : ((~wise(X0) & creative(X0)) <=> (~happy(X0) | calm(X0))) [input p10]
19. happy(lucy) [input hypothesis]
26. ! [X0] : ((~rich(X0) & wise(X0)) | (~happy(X0) & calm(X0))) [ennf transformation 7]
29. ! [X0] : (((~old(X0) | ~strong(X0)) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | (old(X0) & strong(X0)))) [nnf transformation 1]
30. ! [X0] : ((~old(X0) | ~strong(X0) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | (old(X0) & strong(X0)))) [flattening 29]
33. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 3]
44. ! [X0] : (((~wise(X0) & creative(X0)) | (happy(X0) & ~calm(X0))) & ((~happy(X0) | calm(X0)) | (wise(X0) | ~creative(X0)))) [nnf transformation 11]
45. ! [X0] : (((~wise(X0) & creative(X0)) | (happy(X0) & ~calm(X0))) & (~happy(X0) | calm(X0) | wise(X0) | ~creative(X0))) [flattening 44]
63. ~happy(X0) | old(X0) [cnf transformation 30]
71. ~happy(X0) | ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 33]
76. calm(X0) | happy(X0) | ~old(X0) | happy(X0) [cnf transformation 33]
87. ~happy(X0) | wise(X0) [cnf transformation 26]
101. ~wise(X0) | ~calm(X0) [cnf transformation 45]
123. happy(lucy) [cnf transformation 19]
124. ~happy(X0) | ~old(X0) | calm(X0) [duplicate literal removal 71]
126. calm(X0) | happy(X0) | ~old(X0) [duplicate literal removal 76]
129. ~old(X0) | calm(X0) [subsumption resolution 124,126]
222. old(lucy) [resolution 63,123]
224. wise(lucy) [resolution 87,123]
241. ~calm(lucy) [resolution 101,224]
249. calm(lucy) [resolution 129,222]
251. $false [subsumption resolution 249,241]
% SZS output end Proof for 2339408190714989319413402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.047 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or calm is either wise or not tall and vice versa. If someone is either not funny or not patient then someone is not quiet and vice versa. If someone is not old or calm then someone is either rich or patient and vice versa. If alice is both not creative and not humble then someone is both not tall and strong. If someone is both not calm and not rich then mary is creative or calm and vice versa. If someone is happy then alice is both creative and calm. If john is both wise and not wise then lucy is not curious or not quiet and vice versa. If someone is not happy then alice is either not old or funny. Everyone who is either funny or old is patient. If susan is both creative and not rich then someone is funny or strong. Everyone who is both patient and not kind is not rich. If alice is not strong or brave then someone is not rich. If someone is not humble or happy then someone is wise or strong. Everyone who is either strong or not quiet is both calm and tall and vice versa. Everyone who is not generous or quiet is not old or humble and vice versa. If someone is humble or not rich then lucy is either kind or generous. John is either tall or brave. John is both rich and quiet. Susan is either quiet or curious. Someone is both not kind and not old. Someone is happy or not patient. Susan is creative or patient. Fred is both curious and rich. Someone is not brave or not humble. | Lucy is quiet. | entailment | (![X]:((~creative(X)|calm(X))<=>(wise(X)<~>~tall(X))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((rich(X)<~>patient(X)))))&
(((~creative(alice)&~humble(alice)))=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((~calm(X)&~rich(X))))<=>((creative(mary)|calm(mary))))&
((?[X]:(happy(X)))=>((creative(alice)&calm(alice))))&
(((wise(john)&~wise(john)))<=>((~curious(lucy)|~quiet(lucy))))&
((?[X]:(~happy(X)))=>((~old(alice)<~>funny(alice))))&
(![X]:((funny(X)<~>old(X))=>patient(X)))&
(((creative(susan)&~rich(susan)))=>(?[X]:((funny(X)|strong(X)))))&
(![X]:((patient(X)&~kind(X))=>~rich(X)))&
(((~strong(alice)|brave(alice)))=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:((strong(X)<~>~quiet(X))<=>(calm(X)&tall(X))))&
(![X]:((~generous(X)|quiet(X))<=>(~old(X)|humble(X))))&
((?[X]:((humble(X)|~rich(X))))=>((kind(lucy)<~>generous(lucy))))&
((tall(john)<~>brave(john)))&
((rich(john)&quiet(john)))&
((quiet(susan)<~>curious(susan)))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:((happy(X)|~patient(X))))&
((creative(susan)|patient(susan)))&
((curious(fred)&rich(fred)))&
(?[X]:((~brave(X)|~humble(X)))) | quiet(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3737534822465469366887927
% SZS output start Proof for 3737534822465469366887927
7. (~wise(john) & wise(john)) <=> (~quiet(lucy) | ~curious(lucy)) [input p6]
25. ~quiet(lucy) [input hypothesis]
60. ((~wise(john) & wise(john)) | (quiet(lucy) & curious(lucy))) & ((~quiet(lucy) | ~curious(lucy)) | (wise(john) | ~wise(john))) [nnf transformation 7]
61. ((~wise(john) & wise(john)) | (quiet(lucy) & curious(lucy))) & (~quiet(lucy) | ~curious(lucy) | wise(john) | ~wise(john)) [flattening 60]
111. wise(john) | quiet(lucy) [cnf transformation 61]
113. ~wise(john) | quiet(lucy) [cnf transformation 61]
151. ~quiet(lucy) [cnf transformation 25]
263. 26 <=> quiet(lucy) [avatar definition]
267. 27 <=> wise(john) [avatar definition]
270. 26 | ~27 [avatar split clause 113,267,263]
276. 26 | 27 [avatar split clause 111,267,263]
396. ~26 [avatar split clause 151,263]
397. $false [avatar sat refutation 270,276,396]
% SZS output end Proof for 3737534822465469366887927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not strong is generous and vice versa.
Everyone who is not brave or funny is not humble and vice versa.
Everyone who is wise or not kind is either patient or not funny.
If someone is wise then mary is either strong or not happy.
If someone is not patient then mary is tall.
If lucy is not humble then someone is calm or not patient.
Everyone who is either not funny or not happy is either not brave or not funny and vice versa.
Everyone who is old is not kind and vice versa.
Everyone who is quiet or funny is creative or brave and vice versa.
Everyone who is either kind or not happy is both not tall and not funny and vice versa.
Everyone who is creative is either not wise or not strong and vice versa.
Everyone who is both funny and not old is both not old and humble.
Everyone who is creative or not humble is not quiet or quiet and vice versa.
If someone is rich or quiet then someone is both not quiet and strong and vice versa.
Everyone who is old is either not wise or not strong and vice versa.
If someone is both creative and strong then someone is not brave.
Someone is both wise and not humble.
Someone is either not calm or creative.
Someone is either not wise or tall.
Paul is both not quiet and not wise.
Lucy is not tall or not brave.
Susan is either brave or not humble. | Paul is tall. | entailment | (![X]:((~generous(X)|~strong(X))<=>generous(X)))&
(![X]:((~brave(X)|funny(X))<=>~humble(X)))&
(![X]:((wise(X)|~kind(X))=>(patient(X)<~>~funny(X))))&
((?[X]:(wise(X)))=>((strong(mary)<~>~happy(mary))))&
((?[X]:(~patient(X)))=>(tall(mary)))&
((~humble(lucy))=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:(old(X)<=>~kind(X)))&
(![X]:((quiet(X)|funny(X))<=>(creative(X)|brave(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~tall(X)&~funny(X))))&
(![X]:(creative(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((funny(X)&~old(X))=>(~old(X)&humble(X))))&
(![X]:((creative(X)|~humble(X))<=>(~quiet(X)|quiet(X))))&
((?[X]:((rich(X)|quiet(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~strong(X))))&
((?[X]:((creative(X)&strong(X))))=>(?[X]:(~brave(X))))&
(?[X]:((wise(X)&~humble(X))))&
(?[X]:((~calm(X)<~>creative(X))))&
(?[X]:((~wise(X)<~>tall(X))))&
((~quiet(paul)&~wise(paul)))&
((~tall(lucy)|~brave(lucy)))&
((brave(susan)<~>~humble(susan))) | tall(paul) | [
"p0",
"p1",
"p6",
"p7",
"p8",
"p9",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5101962602549644871651459
% SZS output start Proof for 5101962602549644871651459
1. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : ((funny(X0) | ~brave(X0)) <=> ~humble(X0)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~happy(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p6]
8. ! [X0] : (old(X0) <=> ~kind(X0)) [input p7]
9. ! [X0] : ((funny(X0) | quiet(X0)) <=> (brave(X0) | creative(X0))) [input p8]
10. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (~funny(X0) & ~tall(X0))) [input p9]
12. ! [X0] : ((~old(X0) & funny(X0)) => (humble(X0) & ~old(X0))) [input p11]
15. ! [X0] : (old(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p14]
20. ~wise(paul) & ~quiet(paul) [input p19]
23. ~tall(paul) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~old(X0)) | (old(X0) | ~funny(X0))) [ennf transformation 12]
31. ! [X0] : ((humble(X0) & ~old(X0)) | old(X0) | ~funny(X0)) [flattening 30]
33. ! [X0] : (((~strong(X0) | ~generous(X0)) | ~generous(X0)) & (generous(X0) | (strong(X0) & generous(X0)))) [nnf transformation 1]
34. ! [X0] : ((~strong(X0) | ~generous(X0) | ~generous(X0)) & (generous(X0) | (strong(X0) & generous(X0)))) [flattening 33]
35. ! [X0] : (((funny(X0) | ~brave(X0)) | humble(X0)) & (~humble(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 2]
36. ! [X0] : ((funny(X0) | ~brave(X0) | humble(X0)) & (~humble(X0) | (~funny(X0) & brave(X0)))) [flattening 35]
41. ! [X0] : ((((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0))))) [nnf transformation 7]
42. ! [X0] : ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))) [nnf transformation 8]
43. ! [X0] : (((funny(X0) | quiet(X0)) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 9]
44. ! [X0] : ((funny(X0) | quiet(X0) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | (~funny(X0) & ~quiet(X0)))) [flattening 43]
45. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 10]
46. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 45]
55. ! [X0] : ((old(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~old(X0))) [nnf transformation 15]
68. generous(X0) | generous(X0) [cnf transformation 34]
70. ~strong(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 34]
72. ~humble(X0) | ~funny(X0) [cnf transformation 36]
84. funny(X0) | brave(X0) | ~happy(X0) | funny(X0) [cnf transformation 41]
86. ~happy(X0) | ~funny(X0) | ~funny(X0) | brave(X0) [cnf transformation 41]
91. old(X0) | kind(X0) [cnf transformation 42]
95. ~brave(X0) | quiet(X0) | funny(X0) [cnf transformation 44]
101. ~kind(X0) | happy(X0) | funny(X0) | tall(X0) [cnf transformation 46]
107. humble(X0) | old(X0) | ~funny(X0) [cnf transformation 31]
118. ~old(X0) | wise(X0) | strong(X0) [cnf transformation 55]
128. ~quiet(paul) [cnf transformation 20]
129. ~wise(paul) [cnf transformation 20]
133. ~tall(paul) [cnf transformation 23]
135. funny(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 84]
136. ~happy(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 86]
138. generous(X0) [duplicate literal removal 68]
139. ~strong(X0) | ~generous(X0) [duplicate literal removal 70]
174. ~happy(X0) | brave(X0) [subsumption resolution 135,136]
176. ~funny(X0) | old(X0) [subsumption resolution 107,72]
297. kind(X0) | strong(X0) | wise(X0) [resolution 118,91]
338. tall(X0) | wise(X0) | happy(X0) | funny(X0) | strong(X0) [resolution 297,101]
339. wise(paul) | happy(paul) | funny(paul) | strong(paul) [resolution 338,133]
344. happy(paul) | funny(paul) | strong(paul) [subsumption resolution 339,129]
346. 32 <=> strong(paul) [avatar definition]
347. ~strong(paul) <- (~32) [avatar component clause 346]
348. strong(paul) <- (32) [avatar component clause 346]
350. 33 <=> funny(paul) [avatar definition]
351. ~funny(paul) <- (~33) [avatar component clause 350]
352. funny(paul) <- (33) [avatar component clause 350]
354. 34 <=> happy(paul) [avatar definition]
356. happy(paul) <- (34) [avatar component clause 354]
357. 32 | 33 | 34 [avatar split clause 344,354,350,346]
417. ~generous(paul) <- (32) [resolution 348,139]
422. $false <- (32) [subsumption resolution 417,138]
423. ~32 [avatar contradiction clause 422]
428. old(paul) <- (33) [resolution 352,176]
435. 43 <=> brave(paul) [avatar definition]
437. brave(paul) <- (43) [avatar component clause 435]
493. wise(paul) | strong(paul) <- (33) [resolution 428,118]
496. strong(paul) <- (33) [subsumption resolution 493,129]
497. $false <- (~32, 33) [subsumption resolution 496,347]
498. 32 | ~33 [avatar contradiction clause 497]
504. brave(paul) <- (34) [resolution 356,174]
507. quiet(paul) | funny(paul) <- (43) [resolution 437,95]
510. funny(paul) <- (43) [subsumption resolution 507,128]
511. $false <- (~33, 43) [subsumption resolution 510,351]
512. 33 | ~43 [avatar contradiction clause 511]
514. 43 | ~34 [avatar split clause 504,354,435]
515. $false [avatar sat refutation 357,423,498,512,514]
% SZS output end Proof for 5101962602549644871651459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and strong is calm and vice versa. If fred is either not rich or not patient then fred is both quiet and not brave. If someone is not happy or funny then mary is either not brave or curious. Everyone who is both calm and wise is either rich or wise and vice versa. If paul is not humble then someone is both not curious and brave. Everyone who is not brave or patient is both patient and not kind and vice versa. If paul is calm or not old then alice is humble. If mary is rich then susan is either not calm or brave and vice versa. If someone is not wise or brave then someone is both kind and not rich and vice versa. If paul is brave or happy then someone is either tall or not humble and vice versa. Everyone who is either not old or strong is both not kind and not creative and vice versa. Everyone who is both tall and not happy is both creative and not wise and vice versa. Everyone who is either not wise or wise is wise. Everyone who is not patient is both not happy and humble. Everyone who is old or not generous is either happy or not rich. Someone is either not patient or rich. John is either not quiet or not old. Someone is either wise or not tall. Someone is not brave or not old. Someone is not creative or not humble. Susan is not tall. Mary is creative. Fred is either not wise or humble. | Mary is not kind. | entailment | (![X]:((~strong(X)&strong(X))<=>calm(X)))&
(((~rich(fred)<~>~patient(fred)))=>((quiet(fred)&~brave(fred))))&
((?[X]:((~happy(X)|funny(X))))=>((~brave(mary)<~>curious(mary))))&
(![X]:((calm(X)&wise(X))<=>(rich(X)<~>wise(X))))&
((~humble(paul))=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:((~brave(X)|patient(X))<=>(patient(X)&~kind(X))))&
(((calm(paul)|~old(paul)))=>(humble(alice)))&
((rich(mary))<=>((~calm(susan)<~>brave(susan))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:((kind(X)&~rich(X)))))&
(((brave(paul)|happy(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((~old(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
(![X]:((tall(X)&~happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((~wise(X)<~>wise(X))=>wise(X)))&
(![X]:(~patient(X)=>(~happy(X)&humble(X))))&
(![X]:((old(X)|~generous(X))=>(happy(X)<~>~rich(X))))&
(?[X]:((~patient(X)<~>rich(X))))&
((~quiet(john)<~>~old(john)))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(~tall(susan))&
(creative(mary))&
((~wise(fred)<~>humble(fred))) | ~kind(mary) | [
"p0",
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 756337859553481986522420
% SZS output start Proof for 756337859553481986522420
1. ! [X0] : ((strong(X0) & ~strong(X0)) <=> calm(X0)) [input p0]
4. ! [X0] : ((wise(X0) & calm(X0)) <=> (rich(X0) <~> wise(X0))) [input p3]
6. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (~kind(X0) & patient(X0))) [input p5]
9. ? [X0] : (brave(X0) | ~wise(X0)) <=> ? [X0] : (~rich(X0) & kind(X0)) [input p8]
13. ! [X0] : ((~wise(X0) <~> wise(X0)) => wise(X0)) [input p12]
24. kind(mary) [input hypothesis]
25. ? [X0] : (brave(X0) | ~wise(X0)) <=> ? [X1] : (~rich(X1) & kind(X1)) [rectify 9]
32. ! [X0] : (wise(X0) | (~wise(X0) <=> wise(X0))) [ennf transformation 13]
35. ! [X0] : (((strong(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | (~strong(X0) | strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((strong(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | ~strong(X0) | strong(X0))) [flattening 35]
39. ! [X0] : (((wise(X0) & calm(X0)) | ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0)))) & (((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (~wise(X0) | ~calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((wise(X0) & calm(X0)) | ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0)))) & (((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | ~wise(X0) | ~calm(X0))) [flattening 39]
43. ! [X0] : (((patient(X0) | ~brave(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~patient(X0) & brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((patient(X0) | ~brave(X0) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | (~patient(X0) & brave(X0)))) [flattening 43]
46. (? [X0] : (brave(X0) | ~wise(X0)) | ! [X1] : (rich(X1) | ~kind(X1))) & (? [X1] : (~rich(X1) & kind(X1)) | ! [X0] : (~brave(X0) & wise(X0))) [nnf transformation 25]
47. (? [X0] : (brave(X0) | ~wise(X0)) | ! [X1] : (rich(X1) | ~kind(X1))) & (? [X2] : (~rich(X2) & kind(X2)) | ! [X3] : (~brave(X3) & wise(X3))) [rectify 46]
48. ? [X0] : (brave(X0) | ~wise(X0)) => (brave(sK1) | ~wise(sK1)) [choice axiom]
49. ? [X2] : (~rich(X2) & kind(X2)) => (~rich(sK2) & kind(sK2)) [choice axiom]
50. ((brave(sK1) | ~wise(sK1)) | ! [X1] : (rich(X1) | ~kind(X1))) & ((~rich(sK2) & kind(sK2)) | ! [X3] : (~brave(X3) & wise(X3))) [skolemisation 47,49,48]
60. ! [X0] : (wise(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 32]
75. ~strong(X0) | ~calm(X0) [cnf transformation 36]
76. ~calm(X0) | strong(X0) [cnf transformation 36]
86. calm(X0) | rich(X0) | ~wise(X0) [cnf transformation 40]
93. ~kind(X0) | brave(X0) [cnf transformation 44]
105. ~rich(sK2) | ~brave(X3) [cnf transformation 50]
123. wise(X0) | wise(X0) | wise(X0) [cnf transformation 60]
141. kind(mary) [cnf transformation 24]
142. wise(X0) [duplicate literal removal 123]
146. ~calm(X0) [subsumption resolution 75,76]
171. 6 <=> brave(mary) [avatar definition]
173. brave(mary) <- (6) [avatar component clause 171]
180. ~wise(X0) | rich(X0) [subsumption resolution 86,146]
229. 18 <=> ! [X3] : ~brave(X3) [avatar definition]
230. ~brave(X3) <- (18) [avatar component clause 229]
232. 19 <=> rich(sK2) [avatar definition]
234. ~rich(sK2) <- (~19) [avatar component clause 232]
235. 18 | ~19 [avatar split clause 105,232,229]
237. 20 <=> ! [X3] : wise(X3) [avatar definition]
238. wise(X3) <- (20) [avatar component clause 237]
274. 20 [avatar split clause 142,237]
346. brave(mary) [resolution 93,141]
350. 6 [avatar split clause 346,171]
357. rich(X0) <- (20) [resolution 180,238]
389. $false <- (6, 18) [resolution 230,173]
390. ~6 | ~18 [avatar contradiction clause 389]
399. $false <- (~19, 20) [resolution 357,234]
402. 19 | ~20 [avatar contradiction clause 399]
404. $false [avatar sat refutation 235,274,350,390,402]
% SZS output end Proof for 756337859553481986522420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either not generous or strong and vice versa.
If someone is not calm then lucy is both not wise and not creative.
Everyone who is old or not kind is both not curious and not generous.
Everyone who is both kind and tall is either brave or old.
Everyone who is both not creative and not humble is both not strong and not rich and vice versa.
Everyone who is either humble or tall is quiet and vice versa.
If fred is both patient and not curious then lucy is either old or not happy.
Everyone who is both not funny and not tall is creative or not generous.
Everyone who is either not strong or generous is generous or not kind and vice versa.
Everyone who is brave or not brave is not brave and vice versa.
Everyone who is not quiet or not happy is both wise and strong.
Everyone who is not tall or creative is creative or not patient and vice versa.
Everyone who is both not rich and quiet is either not brave or not humble.
Everyone who is not patient is both quiet and not rich.
Everyone who is quiet is both tall and funny.
Everyone who is not patient is funny or generous.
John is both quiet and not generous.
Alice is either not curious or patient.
John is patient.
Lucy is either not rich or wise.
Someone is not funny or wise.
Paul is either not tall or not kind.
Someone is either not tall or humble. | Paul is not calm. | contradiction | (![X]:(~brave(X)<=>(~generous(X)<~>strong(X))))&
((?[X]:(~calm(X)))=>((~wise(lucy)&~creative(lucy))))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&~generous(X))))&
(![X]:((kind(X)&tall(X))=>(brave(X)<~>old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~strong(X)&~rich(X))))&
(![X]:((humble(X)<~>tall(X))<=>quiet(X)))&
(((patient(fred)&~curious(fred)))=>((old(lucy)<~>~happy(lucy))))&
(![X]:((~funny(X)&~tall(X))=>(creative(X)|~generous(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))=>(wise(X)&strong(X))))&
(![X]:((~tall(X)|creative(X))<=>(creative(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:(~patient(X)=>(quiet(X)&~rich(X))))&
(![X]:(quiet(X)=>(tall(X)&funny(X))))&
(![X]:(~patient(X)=>(funny(X)|generous(X))))&
((quiet(john)&~generous(john)))&
((~curious(alice)<~>patient(alice)))&
(patient(john))&
((~rich(lucy)<~>wise(lucy)))&
(?[X]:((~funny(X)|wise(X))))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:((~tall(X)<~>humble(X)))) | ~calm(paul) | [
"p1",
"p5",
"p9",
"p10",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 32058764238386452369099
% SZS output start Proof for 32058764238386452369099
2. ? [X0] : ~calm(X0) => (~creative(lucy) & ~wise(lucy)) [input p1]
6. ! [X0] : ((humble(X0) <~> tall(X0)) <=> quiet(X0)) [input p5]
10. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (strong(X0) & wise(X0))) [input p10]
13. ! [X0] : ((quiet(X0) & ~rich(X0)) => (~brave(X0) <~> ~humble(X0))) [input p12]
15. ! [X0] : (quiet(X0) => (funny(X0) & tall(X0))) [input p14]
20. ~rich(lucy) <~> wise(lucy) [input p19]
24. ~calm(paul) [input hypothesis]
25. (~creative(lucy) & ~wise(lucy)) | ! [X0] : calm(X0) [ennf transformation 2]
33. ! [X0] : ((strong(X0) & wise(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 11]
34. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | (~quiet(X0) | rich(X0))) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | ~quiet(X0) | rich(X0)) [flattening 34]
37. ! [X0] : ((funny(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 15]
44. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~quiet(X0)) & (quiet(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 6]
48. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 10]
49. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 48]
52. ! [X0] : (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | ~quiet(X0) | rich(X0)) [nnf transformation 35]
54. (~wise(lucy) | rich(lucy)) & (wise(lucy) | ~rich(lucy)) [nnf transformation 20]
65. ~wise(lucy) | calm(X0) [cnf transformation 25]
80. ~quiet(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 44]
90. ~brave(X0) | ~brave(X0) [cnf transformation 49]
93. quiet(X0) | wise(X0) [cnf transformation 33]
102. humble(X0) | brave(X0) | ~quiet(X0) | rich(X0) [cnf transformation 52]
105. ~quiet(X0) | tall(X0) [cnf transformation 37]
113. wise(lucy) | ~rich(lucy) [cnf transformation 54]
120. ~calm(paul) [cnf transformation 24]
121. ~brave(X0) [duplicate literal removal 90]
126. 1 <=> ! [X0] : calm(X0) [avatar definition]
127. calm(X0) <- (1) [avatar component clause 126]
134. 3 <=> wise(lucy) [avatar definition]
136. ~wise(lucy) <- (~3) [avatar component clause 134]
137. 1 | ~3 [avatar split clause 65,134,126]
158. ~quiet(X0) | humble(X0) | rich(X0) [subsumption resolution 102,121]
170. 10 <=> rich(lucy) [avatar definition]
171. ~rich(lucy) <- (~10) [avatar component clause 170]
174. ~10 | 3 [avatar split clause 113,134,170]
208. tall(X1) | wise(X1) [resolution 105,93]
264. ~humble(X1) | ~tall(X1) | wise(X1) [resolution 80,93]
269. ~humble(X1) | wise(X1) [subsumption resolution 264,208]
319. humble(X1) | rich(X1) | wise(X1) [resolution 158,93]
324. rich(X1) | wise(X1) [subsumption resolution 319,269]
404. $false <- (1) [resolution 127,120]
405. ~1 [avatar contradiction clause 404]
426. wise(lucy) <- (~10) [resolution 324,171]
427. $false <- (~3, ~10) [subsumption resolution 426,136]
428. 3 | 10 [avatar contradiction clause 427]
429. $false [avatar sat refutation 137,174,405,428]
% SZS output end Proof for 32058764238386452369099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa. Everyone who is old is either happy or not creative. Everyone who is both old and not happy is generous or not rich and vice versa. If someone is not patient then someone is both wise and creative and vice versa. If john is not funny then someone is kind or happy and vice versa. If someone is happy or funny then someone is not funny or happy. If susan is not brave then mary is not creative. Everyone who is either not kind or not strong is curious or calm. Everyone who is either not brave or not quiet is humble. If someone is not old then john is not wise or strong. Everyone who is quiet is both brave and quiet and vice versa. If mary is either not creative or kind then someone is both calm and generous and vice versa. If susan is old then someone is not happy or not wise. Everyone who is curious is both tall and calm and vice versa. Everyone who is patient or not calm is curious and vice versa. Everyone who is either rich or not humble is humble. Paul is either creative or curious. Fred is tall. Susan is both funny and not tall. Mary is creative. Someone is both humble and not generous. Alice is not brave or not old. Paul is either happy or not quiet. | Susan is not calm. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&~happy(X))<=>(generous(X)|~rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)&creative(X)))))&
((~funny(john))<=>(?[X]:((kind(X)|happy(X)))))&
((?[X]:((happy(X)|funny(X))))=>(?[X]:((~funny(X)|happy(X)))))&
((~brave(susan))=>(~creative(mary)))&
(![X]:((~kind(X)<~>~strong(X))=>(curious(X)|calm(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>humble(X)))&
((?[X]:(~old(X)))=>((~wise(john)|strong(john))))&
(![X]:(quiet(X)<=>(brave(X)&quiet(X))))&
(((~creative(mary)<~>kind(mary)))<=>(?[X]:((calm(X)&generous(X)))))&
((old(susan))=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:(curious(X)<=>(tall(X)&calm(X))))&
(![X]:((patient(X)|~calm(X))<=>curious(X)))&
(![X]:((rich(X)<~>~humble(X))=>humble(X)))&
((creative(paul)<~>curious(paul)))&
(tall(fred))&
((funny(susan)&~tall(susan)))&
(creative(mary))&
(?[X]:((humble(X)&~generous(X))))&
((~brave(alice)|~old(alice)))&
((happy(paul)<~>~quiet(paul))) | ~calm(susan) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 393616950475481733974826
% SZS output start Proof for 393616950475481733974826
14. ! [X0] : (curious(X0) <=> (calm(X0) & tall(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | patient(X0)) <=> curious(X0)) [input p14]
24. ~calm(susan) [input hypothesis]
63. ! [X0] : ((curious(X0) | (~calm(X0) | ~tall(X0))) & ((calm(X0) & tall(X0)) | ~curious(X0))) [nnf transformation 14]
64. ! [X0] : ((curious(X0) | ~calm(X0) | ~tall(X0)) & ((calm(X0) & tall(X0)) | ~curious(X0))) [flattening 63]
65. ! [X0] : (((~calm(X0) | patient(X0)) | ~curious(X0)) & (curious(X0) | (calm(X0) & ~patient(X0)))) [nnf transformation 15]
66. ! [X0] : ((~calm(X0) | patient(X0) | ~curious(X0)) & (curious(X0) | (calm(X0) & ~patient(X0)))) [flattening 65]
108. calm(X0) | ~curious(X0) [cnf transformation 64]
111. curious(X0) | calm(X0) [cnf transformation 66]
126. ~calm(susan) [cnf transformation 24]
239. calm(X0) [subsumption resolution 111,108]
270. $false [subsumption resolution 126,239]
% SZS output end Proof for 393616950475481733974826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both humble and funny then john is either not generous or not humble. If someone is not brave then lucy is both not curious and not kind and vice versa. Everyone who is both rich and not creative is quiet and vice versa. If mary is either not creative or patient then someone is both not rich and not humble and vice versa. If someone is not wise or calm then paul is both tall and generous and vice versa. If mary is curious then someone is both rich and not humble and vice versa. If someone is either not creative or not curious then susan is both not tall and old and vice versa. If someone is either not calm or old then alice is both patient and kind and vice versa. If mary is both kind and wise then fred is either not tall or not creative and vice versa. If someone is both not happy and funny then someone is both not tall and not old. Everyone who is both not generous and quiet is either not quiet or calm and vice versa. If john is either not strong or not funny then someone is both not rich and curious. Everyone who is both curious and not patient is not creative or kind and vice versa. If someone is humble then someone is either not funny or not creative. If john is either rich or not tall then john is curious or not quiet. Everyone who is not brave is old or not strong and vice versa. Paul is either not tall or old. Lucy is either humble or not old. Someone is not creative. John is not happy. Someone is either wise or humble. Someone is both rich and generous. John is funny or not happy. Susan is both curious and old. | Paul is brave. | contradiction | (((humble(john)&funny(john)))=>((~generous(john)<~>~humble(john))))&
((?[X]:(~brave(X)))<=>((~curious(lucy)&~kind(lucy))))&
(![X]:((rich(X)&~creative(X))<=>quiet(X)))&
(((~creative(mary)<~>patient(mary)))<=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:((~wise(X)|calm(X))))<=>((tall(paul)&generous(paul))))&
((curious(mary))<=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((~creative(X)<~>~curious(X))))<=>((~tall(susan)&old(susan))))&
((?[X]:((~calm(X)<~>old(X))))<=>((patient(alice)&kind(alice))))&
(((kind(mary)&wise(mary)))<=>((~tall(fred)<~>~creative(fred))))&
((?[X]:((~happy(X)&funny(X))))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((~generous(X)&quiet(X))<=>(~quiet(X)<~>calm(X))))&
(((~strong(john)<~>~funny(john)))=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((curious(X)&~patient(X))<=>(~creative(X)|kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(((rich(john)<~>~tall(john)))=>((curious(john)|~quiet(john))))&
(![X]:(~brave(X)<=>(old(X)|~strong(X))))&
((~tall(paul)<~>old(paul)))&
((humble(lucy)<~>~old(lucy)))&
(?[X]:(~creative(X)))&
(~happy(john))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((rich(X)&generous(X))))&
((funny(john)|~happy(john)))&
((curious(susan)&old(susan))) | brave(paul) | [
"p4",
"p7",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8937480522938954399136302
% SZS output start Proof for 8937480522938954399136302
5. ? [X0] : (calm(X0) | ~wise(X0)) <=> (generous(paul) & tall(paul)) [input p4]
8. ? [X0] : (~calm(X0) <~> old(X0)) <=> (kind(alice) & patient(alice)) [input p7]
13. ! [X0] : ((~patient(X0) & curious(X0)) <=> (kind(X0) | ~creative(X0))) [input p12]
16. ! [X0] : (~brave(X0) <=> (~strong(X0) | old(X0))) [input p15]
17. ~tall(paul) <~> old(paul) [input p16]
25. brave(paul) [input hypothesis]
47. (? [X0] : (calm(X0) | ~wise(X0)) | (~generous(paul) | ~tall(paul))) & ((generous(paul) & tall(paul)) | ! [X0] : (~calm(X0) & wise(X0))) [nnf transformation 5]
48. (? [X0] : (calm(X0) | ~wise(X0)) | ~generous(paul) | ~tall(paul)) & ((generous(paul) & tall(paul)) | ! [X0] : (~calm(X0) & wise(X0))) [flattening 47]
49. (? [X0] : (calm(X0) | ~wise(X0)) | ~generous(paul) | ~tall(paul)) & ((generous(paul) & tall(paul)) | ! [X1] : (~calm(X1) & wise(X1))) [rectify 48]
50. ? [X0] : (calm(X0) | ~wise(X0)) => (calm(sK2) | ~wise(sK2)) [choice axiom]
51. ((calm(sK2) | ~wise(sK2)) | ~generous(paul) | ~tall(paul)) & ((generous(paul) & tall(paul)) | ! [X1] : (~calm(X1) & wise(X1))) [skolemisation 49,50]
61. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (~kind(alice) | ~patient(alice))) & ((kind(alice) & patient(alice)) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [nnf transformation 8]
62. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | ~kind(alice) | ~patient(alice)) & ((kind(alice) & patient(alice)) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [flattening 61]
63. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | ~kind(alice) | ~patient(alice)) & ((kind(alice) & patient(alice)) | ! [X1] : ((~calm(X1) | ~old(X1)) & (old(X1) | calm(X1)))) [rectify 62]
64. ? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) => ((~old(sK5) | calm(sK5)) & (old(sK5) | ~calm(sK5))) [choice axiom]
65. (((~old(sK5) | calm(sK5)) & (old(sK5) | ~calm(sK5))) | ~kind(alice) | ~patient(alice)) & ((kind(alice) & patient(alice)) | ! [X1] : ((~calm(X1) | ~old(X1)) & (old(X1) | calm(X1)))) [skolemisation 63,64]
76. ! [X0] : (((~patient(X0) & curious(X0)) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | (patient(X0) | ~curious(X0)))) [nnf transformation 13]
77. ! [X0] : (((~patient(X0) & curious(X0)) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | patient(X0) | ~curious(X0))) [flattening 76]
83. ! [X0] : ((~brave(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | brave(X0))) [nnf transformation 16]
84. ! [X0] : ((~brave(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | brave(X0))) [flattening 83]
85. (~old(paul) | tall(paul)) & (old(paul) | ~tall(paul)) [nnf transformation 17]
109. tall(paul) | ~calm(X1) [cnf transformation 51]
122. patient(alice) | old(X1) | calm(X1) [cnf transformation 65]
124. kind(alice) | old(X1) | calm(X1) [cnf transformation 65]
150. ~patient(X0) | ~kind(X0) [cnf transformation 77]
156. ~old(X0) | ~brave(X0) [cnf transformation 84]
158. old(paul) | ~tall(paul) [cnf transformation 85]
171. brave(paul) [cnf transformation 25]
232. 13 <=> tall(paul) [avatar definition]
249. 17 <=> ! [X1] : ~calm(X1) [avatar definition]
250. ~calm(X1) <- (17) [avatar component clause 249]
256. 17 | 13 [avatar split clause 109,232,249]
305. 29 <=> patient(alice) [avatar definition]
306. patient(alice) <- (29) [avatar component clause 305]
309. 30 <=> kind(alice) [avatar definition]
327. 34 <=> ! [X1] : (old(X1) | calm(X1)) [avatar definition]
328. old(X1) | calm(X1) <- (34) [avatar component clause 327]
329. 34 | 30 [avatar split clause 124,309,327]
331. 34 | 29 [avatar split clause 122,305,327]
412. 51 <=> old(paul) [avatar definition]
413. old(paul) <- (51) [avatar component clause 412]
414. ~old(paul) <- (~51) [avatar component clause 412]
416. ~13 | 51 [avatar split clause 158,412,232]
448. ~kind(alice) <- (29) [resolution 150,306]
451. ~30 | ~29 [avatar split clause 448,305,309]
452. old(X1) <- (17, 34) [subsumption resolution 328,250]
454. $false <- (17, 34, ~51) [resolution 452,414]
459. ~17 | ~34 | 51 [avatar contradiction clause 454]
464. ~brave(paul) <- (51) [resolution 156,413]
465. $false <- (51) [subsumption resolution 464,171]
466. ~51 [avatar contradiction clause 465]
467. $false [avatar sat refutation 256,329,331,416,451,459,466]
% SZS output end Proof for 8937480522938954399136302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not happy is patient or not quiet.
Everyone who is not tall is patient or tall.
Everyone who is either quiet or generous is both not rich and not funny.
Everyone who is either not strong or patient is humble or wise and vice versa.
If lucy is both quiet and not quiet then susan is curious and vice versa.
Everyone who is either not quiet or not tall is either not brave or not creative and vice versa.
If someone is either kind or not brave then someone is patient or kind and vice versa.
If someone is both quiet and not tall then alice is both tall and happy and vice versa.
If susan is either not patient or brave then john is old or strong and vice versa.
Everyone who is not old or not strong is both funny and kind and vice versa.
Everyone who is either not curious or happy is not calm.
Everyone who is not generous is brave or kind and vice versa.
Everyone who is strong or calm is quiet and vice versa.
Everyone who is not generous is humble.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is not calm is not rich and vice versa.
Someone is not wise.
Susan is not strong or generous.
Alice is brave or patient.
John is either wise or not brave.
John is either not patient or not quiet.
Someone is funny or not creative.
John is not brave.
Lucy is not tall. | Alice is patient. | neutral | (![X]:((~patient(X)<~>~happy(X))=>(patient(X)|~quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|tall(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)&~funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|wise(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>(curious(susan)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((quiet(X)&~tall(X))))<=>((tall(alice)&happy(alice))))&
(((~patient(susan)<~>brave(susan)))<=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(?[X]:(~wise(X)))&
((~strong(susan)|generous(susan)))&
((brave(alice)|patient(alice)))&
((wise(john)<~>~brave(john)))&
((~patient(john)<~>~quiet(john)))&
(?[X]:((funny(X)|~creative(X))))&
(~brave(john))&
(~tall(lucy)) | patient(alice) | [] | null | 0 |
If alice is both tall and funny then someone is not funny and vice versa.
If lucy is generous then lucy is old or happy.
If someone is happy then lucy is both not rich and kind.
Everyone who is not rich is either patient or not strong and vice versa.
Everyone who is not happy or humble is quiet or not funny.
Everyone who is patient or not kind is old and vice versa.
Everyone who is happy is patient or not creative.
Everyone who is both funny and not funny is both funny and not strong.
Everyone who is not strong is either not brave or not quiet and vice versa.
Everyone who is either not funny or not brave is either not quiet or wise.
If someone is brave then susan is either creative or not funny and vice versa.
If someone is both kind and old then lucy is old.
If alice is not kind or not curious then someone is not happy or not brave and vice versa.
Everyone who is not patient or not brave is either kind or not funny and vice versa.
If fred is both not strong and not humble then someone is either not generous or calm and vice versa.
If someone is not patient or brave then someone is not tall or not humble and vice versa.
Mary is both calm and not strong.
Paul is not kind.
Susan is not brave or not quiet.
Alice is both strong and old.
Lucy is both generous and happy.
Someone is not wise or not calm.
Someone is either creative or funny. | Alice is not rich. | entailment | (((tall(alice)&funny(alice)))<=>(?[X]:(~funny(X))))&
((generous(lucy))=>((old(lucy)|happy(lucy))))&
((?[X]:(happy(X)))=>((~rich(lucy)&kind(lucy))))&
(![X]:(~rich(X)<=>(patient(X)<~>~strong(X))))&
(![X]:((~happy(X)|humble(X))=>(quiet(X)|~funny(X))))&
(![X]:((patient(X)|~kind(X))<=>old(X)))&
(![X]:(happy(X)=>(patient(X)|~creative(X))))&
(![X]:((funny(X)&~funny(X))=>(funny(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~brave(X)<~>~quiet(X))))&
(![X]:((~funny(X)<~>~brave(X))=>(~quiet(X)<~>wise(X))))&
((?[X]:(brave(X)))<=>((creative(susan)<~>~funny(susan))))&
((?[X]:((kind(X)&old(X))))=>(old(lucy)))&
(((~kind(alice)|~curious(alice)))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((~patient(X)|~brave(X))<=>(kind(X)<~>~funny(X))))&
(((~strong(fred)&~humble(fred)))<=>(?[X]:((~generous(X)<~>calm(X)))))&
((?[X]:((~patient(X)|brave(X))))<=>(?[X]:((~tall(X)|~humble(X)))))&
((calm(mary)&~strong(mary)))&
(~kind(paul))&
((~brave(susan)|~quiet(susan)))&
((strong(alice)&old(alice)))&
((generous(lucy)&happy(lucy)))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((creative(X)<~>funny(X)))) | ~rich(alice) | [
"p0",
"p3",
"p5",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 158700121900681033485602
% SZS output start Proof for 158700121900681033485602
1. (funny(alice) & tall(alice)) <=> ? [X0] : ~funny(X0) [input p0]
4. ! [X0] : (~rich(X0) <=> (patient(X0) <~> ~strong(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | patient(X0)) <=> old(X0)) [input p5]
14. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> (kind(X0) <~> ~funny(X0))) [input p13]
20. old(alice) & strong(alice) [input p19]
24. rich(alice) [input hypothesis]
37. ((funny(alice) & tall(alice)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | (~funny(alice) | ~tall(alice))) [nnf transformation 1]
38. ((funny(alice) & tall(alice)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | ~funny(alice) | ~tall(alice)) [flattening 37]
39. ((funny(alice) & tall(alice)) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | ~funny(alice) | ~tall(alice)) [rectify 38]
40. ? [X1] : ~funny(X1) => ~funny(sK0) [choice axiom]
41. ((funny(alice) & tall(alice)) | ! [X0] : funny(X0)) & (~funny(sK0) | ~funny(alice) | ~tall(alice)) [skolemisation 39,40]
42. ! [X0] : ((~rich(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | rich(X0))) [nnf transformation 4]
43. ! [X0] : (((~kind(X0) | patient(X0)) | ~old(X0)) & (old(X0) | (kind(X0) & ~patient(X0)))) [nnf transformation 6]
44. ! [X0] : ((~kind(X0) | patient(X0) | ~old(X0)) & (old(X0) | (kind(X0) & ~patient(X0)))) [flattening 43]
56. ! [X0] : (((~brave(X0) | ~patient(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (brave(X0) & patient(X0)))) [nnf transformation 14]
57. ! [X0] : ((~brave(X0) | ~patient(X0) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (brave(X0) & patient(X0)))) [flattening 56]
75. funny(alice) | funny(X0) [cnf transformation 41]
81. ~strong(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 42]
87. ~kind(X0) | patient(X0) | ~old(X0) [cnf transformation 44]
108. ~funny(X0) | kind(X0) | patient(X0) [cnf transformation 57]
128. strong(alice) [cnf transformation 20]
129. old(alice) [cnf transformation 20]
135. rich(alice) [cnf transformation 24]
138. 1 <=> ! [X0] : funny(X0) [avatar definition]
139. funny(X0) <- (1) [avatar component clause 138]
141. 2 <=> funny(alice) [avatar definition]
142. ~funny(alice) <- (~2) [avatar component clause 141]
143. funny(alice) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 75,141,138]
208. 17 <=> kind(alice) [avatar definition]
209. kind(alice) <- (17) [avatar component clause 208]
322. ~rich(alice) | ~patient(alice) [resolution 81,128]
323. ~patient(alice) [subsumption resolution 322,135]
388. kind(alice) | patient(alice) <- (2) [resolution 108,143]
392. kind(alice) <- (2) [subsumption resolution 388,323]
393. 17 | ~2 [avatar split clause 392,141,208]
394. patient(alice) | ~old(alice) <- (17) [resolution 209,87]
395. ~old(alice) <- (17) [subsumption resolution 394,323]
396. $false <- (17) [subsumption resolution 395,129]
397. ~17 [avatar contradiction clause 396]
406. $false <- (1, ~2) [resolution 142,139]
407. ~1 | 2 [avatar contradiction clause 406]
408. $false [avatar sat refutation 144,393,397,407]
% SZS output end Proof for 158700121900681033485602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is happy then someone is old or not rich and vice versa. If someone is not brave then susan is not quiet. Everyone who is not rich is either not humble or not patient. If fred is both generous and happy then fred is generous and vice versa. Everyone who is old is not tall. If someone is both not curious and not quiet then someone is both calm and humble. Everyone who is either not generous or not kind is either humble or not patient. If alice is both strong and not wise then susan is either not curious or quiet and vice versa. Everyone who is either not humble or quiet is not funny or not wise and vice versa. Everyone who is both not humble and tall is both not humble and happy. Everyone who is either not rich or not calm is either not kind or not strong. If susan is old or humble then susan is not calm or calm. Everyone who is humble or not kind is brave and vice versa. Everyone who is both creative and not patient is not humble or not happy and vice versa. Everyone who is either happy or not patient is either creative or old. If alice is either creative or quiet then fred is patient and vice versa. Alice is both not kind and generous. Someone is both not happy and not kind. John is both strong and patient. Susan is not happy or wise. Someone is creative. Someone is not old. Susan is both not funny and not happy. Someone is both creative and humble. | Alice is not old. | entailment | ((happy(susan))<=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:(~brave(X)))=>(~quiet(susan)))&
(![X]:(~rich(X)=>(~humble(X)<~>~patient(X))))&
(((generous(fred)&happy(fred)))<=>(generous(fred)))&
(![X]:(old(X)=>~tall(X)))&
((?[X]:((~curious(X)&~quiet(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~generous(X)<~>~kind(X))=>(humble(X)<~>~patient(X))))&
(((strong(alice)&~wise(alice)))<=>((~curious(susan)<~>quiet(susan))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~funny(X)|~wise(X))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)&happy(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~kind(X)<~>~strong(X))))&
(((old(susan)|humble(susan)))=>((~calm(susan)|calm(susan))))&
(![X]:((humble(X)|~kind(X))<=>brave(X)))&
(![X]:((creative(X)&~patient(X))<=>(~humble(X)|~happy(X))))&
(![X]:((happy(X)<~>~patient(X))=>(creative(X)<~>old(X))))&
(((creative(alice)<~>quiet(alice)))<=>(patient(fred)))&
((~kind(alice)&generous(alice)))&
(?[X]:((~happy(X)&~kind(X))))&
((strong(john)&patient(john)))&
((~happy(susan)|wise(susan)))&
(?[X]:(creative(X)))&
(?[X]:(~old(X)))&
((~funny(susan)&~happy(susan)))&
(?[X]:((creative(X)&humble(X)))) | ~old(alice) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2740339626633555189587168
% SZS output start Proof for 2740339626633555189587168
1. happy(susan) <=> ? [X0] : (~rich(X0) | old(X0)) [input p0]
23. ~happy(susan) & ~funny(susan) [input p22]
25. old(alice) [input hypothesis]
40. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & (? [X0] : (~rich(X0) | old(X0)) | ~happy(susan)) [nnf transformation 1]
41. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & (? [X1] : (~rich(X1) | old(X1)) | ~happy(susan)) [rectify 40]
42. ? [X1] : (~rich(X1) | old(X1)) => (~rich(sK0) | old(sK0)) [choice axiom]
43. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & ((~rich(sK0) | old(sK0)) | ~happy(susan)) [skolemisation 41,42]
69. happy(susan) | ~old(X0) [cnf transformation 43]
125. ~happy(susan) [cnf transformation 23]
128. old(alice) [cnf transformation 25]
133. 2 <=> happy(susan) [avatar definition]
138. 3 <=> ! [X0] : ~old(X0) [avatar definition]
139. ~old(X0) <- (3) [avatar component clause 138]
140. 3 | 2 [avatar split clause 69,133,138]
223. ~2 [avatar split clause 125,133]
224. $false <- (3) [resolution 139,128]
225. ~3 [avatar contradiction clause 224]
226. $false [avatar sat refutation 140,223,225]
% SZS output end Proof for 2740339626633555189587168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not creative then john is tall. Everyone who is either patient or not old is either old or not calm and vice versa. Everyone who is not kind or calm is both kind and not curious and vice versa. Everyone who is both generous and not curious is not tall or calm. If susan is both kind and not funny then paul is not curious or rich and vice versa. Everyone who is both curious and funny is not calm or not kind. Everyone who is both tall and not rich is either not creative or quiet and vice versa. If mary is either not creative or not generous then someone is funny or rich and vice versa. If someone is either not curious or not brave then someone is both not generous and curious. Everyone who is brave or funny is both happy and not strong and vice versa. Everyone who is either tall or wise is not rich and vice versa. Everyone who is both not generous and not patient is quiet. Everyone who is humble is either curious or wise and vice versa. If someone is both not kind and not calm then paul is quiet and vice versa. If someone is old then someone is not curious and vice versa. If someone is both not calm and wise then susan is wise or not curious and vice versa. Fred is either brave or not rich. Mary is patient or brave. Someone is either not wise or quiet. Paul is either strong or calm. Someone is not wise or not happy. Someone is not happy. Someone is both not quiet and creative. Someone is both curious and not rich. | Paul is quiet. | contradiction | (((kind(alice)|~creative(alice)))=>(tall(john)))&
(![X]:((patient(X)<~>~old(X))<=>(old(X)<~>~calm(X))))&
(![X]:((~kind(X)|calm(X))<=>(kind(X)&~curious(X))))&
(![X]:((generous(X)&~curious(X))=>(~tall(X)|calm(X))))&
(((kind(susan)&~funny(susan)))<=>((~curious(paul)|rich(paul))))&
(![X]:((curious(X)&funny(X))=>(~calm(X)|~kind(X))))&
(![X]:((tall(X)&~rich(X))<=>(~creative(X)<~>quiet(X))))&
(((~creative(mary)<~>~generous(mary)))<=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((~generous(X)&curious(X)))))&
(![X]:((brave(X)|funny(X))<=>(happy(X)&~strong(X))))&
(![X]:((tall(X)<~>wise(X))<=>~rich(X)))&
(![X]:((~generous(X)&~patient(X))=>quiet(X)))&
(![X]:(humble(X)<=>(curious(X)<~>wise(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(quiet(paul)))&
((?[X]:(old(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~calm(X)&wise(X))))<=>((wise(susan)|~curious(susan))))&
((brave(fred)<~>~rich(fred)))&
((patient(mary)|brave(mary)))&
(?[X]:((~wise(X)<~>quiet(X))))&
((strong(paul)<~>calm(paul)))&
(?[X]:((~wise(X)|~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((curious(X)&~rich(X)))) | quiet(paul) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 425467429980526112244875
% SZS output start Proof for 425467429980526112244875
3. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (~curious(X0) & kind(X0))) [input p2]
14. ? [X0] : (~calm(X0) & ~kind(X0)) <=> quiet(paul) [input p13]
25. quiet(paul) [input hypothesis]
37. ! [X0] : (((calm(X0) | ~kind(X0)) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 3]
38. ! [X0] : ((calm(X0) | ~kind(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | (~calm(X0) & kind(X0)))) [flattening 37]
54. (? [X0] : (~calm(X0) & ~kind(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X0] : (calm(X0) | kind(X0))) [nnf transformation 14]
55. (? [X0] : (~calm(X0) & ~kind(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (calm(X1) | kind(X1))) [rectify 54]
56. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
57. ((~calm(sK2) & ~kind(sK2)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (calm(X1) | kind(X1))) [skolemisation 55,56]
91. kind(X0) | kind(X0) [cnf transformation 38]
130. ~kind(sK2) | ~quiet(paul) [cnf transformation 57]
152. quiet(paul) [cnf transformation 25]
153. kind(X0) [duplicate literal removal 91]
238. 17 <=> quiet(paul) [avatar definition]
246. ~quiet(paul) [subsumption resolution 130,153]
247. ~17 [avatar split clause 246,238]
336. 17 [avatar split clause 152,238]
337. $false [avatar sat refutation 247,336]
% SZS output end Proof for 425467429980526112244875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not quiet or kind then someone is kind or not humble.
Everyone who is either funny or not humble is rich or brave and vice versa.
If someone is not old then john is not humble or generous and vice versa.
If someone is calm or not strong then someone is curious.
Everyone who is not quiet or generous is either not creative or not wise.
Everyone who is not strong or old is not brave or curious.
If paul is humble then john is both not patient and generous.
Everyone who is patient or wise is both strong and not tall.
If john is not humble or patient then lucy is curious or patient.
Everyone who is both not tall and wise is not happy or not creative.
Everyone who is both not rich and happy is not tall and vice versa.
Everyone who is curious or calm is curious or happy and vice versa.
If someone is either tall or curious then someone is either creative or not funny and vice versa.
If someone is both not old and not rich then paul is either not old or old and vice versa.
Everyone who is old or not rich is both funny and not wise.
Everyone who is creative or not happy is not kind or quiet and vice versa.
Someone is not tall.
Someone is either not rich or not patient.
Someone is both not funny and generous.
Someone is both not quiet and not calm.
Someone is not funny or not wise.
Paul is both generous and not funny.
Someone is generous or not kind. | Paul is not calm. | neutral | (((~quiet(alice)<~>kind(alice)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
((?[X]:(~old(X)))<=>((~humble(john)|generous(john))))&
((?[X]:((calm(X)|~strong(X))))=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|generous(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~strong(X)|old(X))=>(~brave(X)|curious(X))))&
((humble(paul))=>((~patient(john)&generous(john))))&
(![X]:((patient(X)|wise(X))=>(strong(X)&~tall(X))))&
(((~humble(john)|patient(john)))=>((curious(lucy)|patient(lucy))))&
(![X]:((~tall(X)&wise(X))=>(~happy(X)|~creative(X))))&
(![X]:((~rich(X)&happy(X))<=>~tall(X)))&
(![X]:((curious(X)|calm(X))<=>(curious(X)|happy(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>(?[X]:((creative(X)<~>~funny(X)))))&
((?[X]:((~old(X)&~rich(X))))<=>((~old(paul)<~>old(paul))))&
(![X]:((old(X)|~rich(X))=>(funny(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(~kind(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>~patient(X))))&
(?[X]:((~funny(X)&generous(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((generous(paul)&~funny(paul)))&
(?[X]:((generous(X)|~kind(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is creative or brave is either not tall or old and vice versa. If someone is not strong or old then someone is not strong. If someone is not patient then someone is either not generous or happy. If someone is calm or not funny then mary is not calm. If lucy is either not happy or not wise then someone is not strong or not quiet. Everyone who is both curious and generous is funny or not strong and vice versa. Everyone who is either not tall or strong is both not curious and funny. If john is not rich or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. Someone is both curious and not generous. Someone is happy. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. | Mary is quiet. | neutral | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((~strong(X)|old(X))))=>(?[X]:(~strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~generous(X)<~>happy(X)))))&
((?[X]:((calm(X)|~funny(X))))=>(~calm(mary)))&
(((~happy(lucy)<~>~wise(lucy)))=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
(?[X]:((curious(X)&~generous(X))))&
(?[X]:(happy(X)))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X)))) | quiet(mary) | [] | null | 0 |
If someone is not curious then paul is not patient or happy and vice versa.
If someone is either not strong or not wise then john is both not patient and funny.
Everyone who is both calm and creative is strong and vice versa.
Everyone who is not calm or patient is not kind and vice versa.
Everyone who is both not rich and not funny is not tall.
If john is either not funny or calm then paul is calm or creative and vice versa.
Everyone who is humble or not funny is both not calm and curious.
If alice is not happy then fred is both not generous and not happy.
If susan is not brave then someone is either rich or not strong and vice versa.
If someone is creative then paul is either not quiet or not funny.
Everyone who is not old is strong or not patient and vice versa.
If someone is generous then someone is either calm or rich.
If mary is both humble and funny then someone is both humble and quiet and vice versa.
Everyone who is either wise or not strong is humble or wise and vice versa.
If john is either not strong or creative then someone is both not strong and quiet and vice versa.
Everyone who is kind is not brave and vice versa.
Lucy is either not wise or creative.
Alice is either patient or rich.
Paul is kind or happy.
Alice is either patient or strong.
Alice is either not strong or not funny.
Someone is both not kind and not generous.
Someone is creative or quiet. | Susan is not kind. | contradiction | ((?[X]:(~curious(X)))<=>((~patient(paul)|happy(paul))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~patient(john)&funny(john))))&
(![X]:((calm(X)&creative(X))<=>strong(X)))&
(![X]:((~calm(X)|patient(X))<=>~kind(X)))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(((~funny(john)<~>calm(john)))<=>((calm(paul)|creative(paul))))&
(![X]:((humble(X)|~funny(X))=>(~calm(X)&curious(X))))&
((~happy(alice))=>((~generous(fred)&~happy(fred))))&
((~brave(susan))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(creative(X)))=>((~quiet(paul)<~>~funny(paul))))&
(![X]:(~old(X)<=>(strong(X)|~patient(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(((humble(mary)&funny(mary)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|wise(X))))&
(((~strong(john)<~>creative(john)))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:(kind(X)<=>~brave(X)))&
((~wise(lucy)<~>creative(lucy)))&
((patient(alice)<~>rich(alice)))&
((kind(paul)|happy(paul)))&
((patient(alice)<~>strong(alice)))&
((~strong(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((creative(X)|quiet(X)))) | ~kind(susan) | [
"p2",
"p6",
"p8",
"p15",
"p17",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8539533994086765710340766
% SZS output start Proof for 8539533994086765710340766
3. ! [X0] : ((creative(X0) & calm(X0)) <=> strong(X0)) [input p2]
7. ! [X0] : ((~funny(X0) | humble(X0)) => (curious(X0) & ~calm(X0))) [input p6]
9. ~brave(susan) <=> ? [X0] : (rich(X0) <~> ~strong(X0)) [input p8]
16. ! [X0] : (kind(X0) <=> ~brave(X0)) [input p15]
18. patient(alice) <~> rich(alice) [input p17]
20. patient(alice) <~> strong(alice) [input p19]
21. ~strong(alice) <~> ~funny(alice) [input p20]
24. ~kind(susan) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~calm(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 7]
40. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | ~calm(X0)))) [nnf transformation 3]
41. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | ~calm(X0))) [flattening 40]
46. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X0] : ((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | brave(susan)) [nnf transformation 9]
47. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) | brave(susan)) [rectify 46]
48. ? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) => ((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) [choice axiom]
49. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) | brave(susan)) [skolemisation 47,48]
62. ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))) [nnf transformation 16]
64. (~rich(alice) | ~patient(alice)) & (rich(alice) | patient(alice)) [nnf transformation 18]
65. (~strong(alice) | ~patient(alice)) & (strong(alice) | patient(alice)) [nnf transformation 20]
66. (funny(alice) | strong(alice)) & (~funny(alice) | ~strong(alice)) [nnf transformation 21]
79. ~strong(X0) | calm(X0) [cnf transformation 41]
91. ~calm(X0) | funny(X0) [cnf transformation 31]
98. ~brave(susan) | rich(X0) | strong(X0) [cnf transformation 49]
118. brave(X0) | kind(X0) [cnf transformation 62]
122. ~rich(alice) | ~patient(alice) [cnf transformation 64]
124. strong(alice) | patient(alice) [cnf transformation 65]
126. ~funny(alice) | ~strong(alice) [cnf transformation 66]
127. funny(alice) | strong(alice) [cnf transformation 66]
130. ~kind(susan) [cnf transformation 24]
197. 14 <=> ! [X0] : (rich(X0) | strong(X0)) [avatar definition]
198. rich(X0) | strong(X0) <- (14) [avatar component clause 197]
200. 15 <=> brave(susan) [avatar definition]
202. ~brave(susan) <- (~15) [avatar component clause 200]
203. 14 | ~15 [avatar split clause 98,200,197]
294. 34 <=> patient(alice) [avatar definition]
298. 35 <=> rich(alice) [avatar definition]
300. ~rich(alice) <- (~35) [avatar component clause 298]
301. ~34 | ~35 [avatar split clause 122,298,294]
309. 37 <=> strong(alice) [avatar definition]
310. strong(alice) <- (37) [avatar component clause 309]
311. ~strong(alice) <- (~37) [avatar component clause 309]
313. 34 | 37 [avatar split clause 124,309,294]
315. 38 <=> funny(alice) [avatar definition]
316. ~funny(alice) <- (~38) [avatar component clause 315]
318. 37 | 38 [avatar split clause 127,315,309]
319. ~37 | ~38 [avatar split clause 126,315,309]
331. calm(alice) <- (37) [resolution 79,310]
338. funny(alice) <- (37) [resolution 91,331]
340. $false <- (37, ~38) [subsumption resolution 338,316]
341. ~37 | 38 [avatar contradiction clause 340]
347. kind(susan) <- (~15) [resolution 118,202]
349. $false <- (~15) [subsumption resolution 347,130]
350. 15 [avatar contradiction clause 349]
353. strong(alice) <- (14, ~35) [resolution 198,300]
356. $false <- (14, ~35, ~37) [subsumption resolution 353,311]
357. ~14 | 35 | 37 [avatar contradiction clause 356]
358. $false [avatar sat refutation 203,301,313,318,319,341,350,357]
% SZS output end Proof for 8539533994086765710340766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either not calm or curious.
If fred is humble then someone is strong or humble.
Everyone who is either not calm or not rich is both not curious and quiet.
Everyone who is not patient is either quiet or curious and vice versa.
If someone is both not kind and happy then someone is quiet and vice versa.
Everyone who is both rich and curious is both not kind and not generous.
Everyone who is not rich or calm is either quiet or funny and vice versa.
Everyone who is wise is not strong and vice versa.
If someone is both tall and not strong then someone is not creative or quiet and vice versa.
If alice is either rich or strong then alice is both not tall and not funny and vice versa.
Everyone who is curious or kind is wise.
Everyone who is not wise or kind is not old or not quiet and vice versa.
If alice is both not happy and not patient then alice is either happy or humble and vice versa.
If mary is both not curious and not brave then alice is both funny and generous.
If alice is not funny or wise then john is wise or not generous.
Someone is humble or not funny.
Someone is old or not kind.
Fred is curious or humble.
Someone is quiet or not old.
Someone is either not curious or curious.
Lucy is both not strong and brave.
Mary is not humble or tall.
Susan is not old. | Lucy is not wise. | contradiction | (![X]:(old(X)=>(~calm(X)<~>curious(X))))&
((humble(fred))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~calm(X)<~>~rich(X))=>(~curious(X)&quiet(X))))&
(![X]:(~patient(X)<=>(quiet(X)<~>curious(X))))&
((?[X]:((~kind(X)&happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((rich(X)&curious(X))=>(~kind(X)&~generous(X))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
((?[X]:((tall(X)&~strong(X))))<=>(?[X]:((~creative(X)|quiet(X)))))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(![X]:((~wise(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(((~happy(alice)&~patient(alice)))<=>((happy(alice)<~>humble(alice))))&
(((~curious(mary)&~brave(mary)))=>((funny(alice)&generous(alice))))&
(((~funny(alice)|wise(alice)))=>((wise(john)|~generous(john))))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((old(X)|~kind(X))))&
((curious(fred)|humble(fred)))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
((~strong(lucy)&brave(lucy)))&
((~humble(mary)|tall(mary)))&
(~old(susan)) | ~wise(lucy) | [
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4322137577716365119482877
% SZS output start Proof for 4322137577716365119482877
8. ! [X0] : (wise(X0) <=> ~strong(X0)) [input p7]
21. brave(lucy) & ~strong(lucy) [input p20]
24. ~wise(lucy) [input hypothesis]
27. ~strong(lucy) [pure predicate removal 21]
49. ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 8]
92. wise(X0) | strong(X0) [cnf transformation 49]
122. ~strong(lucy) [cnf transformation 27]
125. ~wise(lucy) [cnf transformation 24]
271. strong(lucy) [resolution 92,125]
273. $false [subsumption resolution 271,122]
% SZS output end Proof for 4322137577716365119482877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not brave then alice is both old and not strong and vice versa.
If someone is patient then john is rich.
If mary is funny then someone is not wise or not strong.
Everyone who is curious or not old is brave or not wise.
Everyone who is tall is not generous and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Paul is both not humble and not generous.
Someone is either not funny or not wise.
Someone is either not brave or not funny.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise. | Paul is curious. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~brave(alice)))<=>((old(alice)&~strong(alice))))&
((?[X]:(patient(X)))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | curious(paul) | [
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3342937417163126743324515
% SZS output start Proof for 3342937417163126743324515
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
23. ~curious(paul) [input hypothesis]
43. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
44. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 44]
46. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 46]
57. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
58. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 57]
86. ~brave(X0) | patient(X0) [cnf transformation 43]
87. ~patient(X0) | brave(X0) [cnf transformation 43]
91. brave(X0) | patient(X0) | strong(X0) [cnf transformation 45]
93. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 45]
96. ~strong(X0) | calm(X0) [cnf transformation 47]
114. ~calm(X0) | curious(X0) [cnf transformation 58]
133. ~curious(paul) [cnf transformation 23]
185. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 93,86]
186. patient(X0) | strong(X0) [subsumption resolution 91,86]
247. strong(X0) | brave(X0) [resolution 186,87]
248. brave(X0) | calm(X0) [resolution 247,96]
368. strong(X0) | calm(X0) | calm(X0) [resolution 185,248]
370. strong(X0) | calm(X0) [duplicate literal removal 368]
371. calm(X0) [subsumption resolution 370,96]
374. curious(X1) [resolution 371,114]
411. $false [resolution 374,133]
% SZS output end Proof for 3342937417163126743324515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or quiet then alice is either not happy or not calm and vice versa. If someone is brave or not humble then someone is calm and vice versa. If paul is both humble and calm then paul is not humble or rich. Everyone who is kind is either humble or rich. Everyone who is both tall and not humble is not patient or patient and vice versa. Everyone who is either not humble or humble is both curious and calm and vice versa. If fred is not happy or not curious then alice is generous or calm and vice versa. If someone is either generous or rich then someone is not humble or old and vice versa. Everyone who is old is generous. Everyone who is both not calm and kind is both humble and not old. If someone is funny then lucy is curious or not strong and vice versa. If someone is either not patient or quiet then someone is both curious and creative and vice versa. Everyone who is not funny is creative or not generous and vice versa. If mary is both brave and not generous then someone is both not humble and not happy and vice versa. Everyone who is both not wise and not patient is not creative and vice versa. If someone is not calm or not curious then someone is not quiet and vice versa. Paul is curious. Someone is either humble or kind. Someone is either not brave or not old. Someone is either kind or not wise. Alice is either brave or tall. Alice is not humble or creative. John is not patient or not happy. | Mary is old. | contradiction | ((?[X]:((~old(X)<~>quiet(X))))<=>((~happy(alice)<~>~calm(alice))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(((humble(paul)&calm(paul)))=>((~humble(paul)|rich(paul))))&
(![X]:(kind(X)=>(humble(X)<~>rich(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(curious(X)&calm(X))))&
(((~happy(fred)|~curious(fred)))<=>((generous(alice)|calm(alice))))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:(~funny(X)<=>(creative(X)|~generous(X))))&
(((brave(mary)&~generous(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~wise(X)&~patient(X))<=>~creative(X)))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(curious(paul))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
((brave(alice)<~>tall(alice)))&
((~humble(alice)|creative(alice)))&
((~patient(john)|~happy(john))) | old(mary) | [
"p0",
"p4",
"p5",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 899540678407162682291311
% SZS output start Proof for 899540678407162682291311
1. ? [X0] : (~old(X0) <~> quiet(X0)) <=> (~happy(alice) <~> ~calm(alice)) [input p0]
5. ! [X0] : ((~humble(X0) & tall(X0)) <=> (patient(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (calm(X0) & curious(X0))) [input p5]
9. ! [X0] : (old(X0) => generous(X0)) [input p8]
14. (~generous(mary) & brave(mary)) <=> ? [X0] : (~happy(X0) & ~humble(X0)) [input p13]
16. ? [X0] : (~curious(X0) | ~calm(X0)) <=> ? [X0] : ~quiet(X0) [input p15]
24. old(mary) [input hypothesis]
28. ? [X0] : (~curious(X0) | ~calm(X0)) <=> ? [X1] : ~quiet(X1) [rectify 16]
32. ! [X0] : (generous(X0) | ~old(X0)) [ennf transformation 9]
35. (? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X0] : ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) [nnf transformation 1]
36. (? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X1] : ((~old(X1) | ~quiet(X1)) & (quiet(X1) | old(X1)))) [rectify 35]
37. ? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) => ((~quiet(sK0) | old(sK0)) & (quiet(sK0) | ~old(sK0))) [choice axiom]
38. (((~quiet(sK0) | old(sK0)) & (quiet(sK0) | ~old(sK0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X1] : ((~old(X1) | ~quiet(X1)) & (quiet(X1) | old(X1)))) [skolemisation 36,37]
45. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0))) [flattening 45]
47. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 6]
48. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 47]
68. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X0] : (~happy(X0) & ~humble(X0)) | (generous(mary) | ~brave(mary))) [nnf transformation 14]
69. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X0] : (~happy(X0) & ~humble(X0)) | generous(mary) | ~brave(mary)) [flattening 68]
70. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X1] : (~happy(X1) & ~humble(X1)) | generous(mary) | ~brave(mary)) [rectify 69]
71. ? [X1] : (~happy(X1) & ~humble(X1)) => (~happy(sK8) & ~humble(sK8)) [choice axiom]
72. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & ((~happy(sK8) & ~humble(sK8)) | generous(mary) | ~brave(mary)) [skolemisation 70,71]
75. (? [X0] : (~curious(X0) | ~calm(X0)) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : (curious(X0) & calm(X0))) [nnf transformation 28]
76. (? [X0] : (~curious(X0) | ~calm(X0)) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : (curious(X3) & calm(X3))) [rectify 75]
77. ? [X0] : (~curious(X0) | ~calm(X0)) => (~curious(sK9) | ~calm(sK9)) [choice axiom]
78. ? [X2] : ~quiet(X2) => ~quiet(sK10) [choice axiom]
79. ((~curious(sK9) | ~calm(sK9)) | ! [X1] : quiet(X1)) & (~quiet(sK10) | ! [X3] : (curious(X3) & calm(X3))) [skolemisation 76,78,77]
91. ~calm(alice) | ~happy(alice) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
107. ~humble(X0) | patient(X0) [cnf transformation 46]
108. ~patient(X0) | ~humble(X0) [cnf transformation 46]
109. curious(X0) | humble(X0) | humble(X0) [cnf transformation 48]
111. calm(X0) | humble(X0) | humble(X0) [cnf transformation 48]
125. ~old(X0) | generous(X0) [cnf transformation 32]
143. ~generous(mary) | happy(X0) | humble(X0) [cnf transformation 72]
149. ~curious(sK9) | ~calm(sK9) | quiet(X1) [cnf transformation 79]
161. old(mary) [cnf transformation 24]
162. curious(X0) | humble(X0) [duplicate literal removal 109]
164. calm(X0) | humble(X0) [duplicate literal removal 111]
168. 1 <=> calm(alice) [avatar definition]
169. ~calm(alice) <- (~1) [avatar component clause 168]
172. 2 <=> happy(alice) [avatar definition]
174. ~happy(alice) <- (~2) [avatar component clause 172]
188. 5 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
189. ~old(X1) | ~quiet(X1) <- (5) [avatar component clause 188]
195. 5 | ~2 | ~1 [avatar split clause 91,168,172,188]
234. ~humble(X0) [subsumption resolution 107,108]
236. calm(X0) [subsumption resolution 164,234]
237. curious(X0) [subsumption resolution 162,234]
241. 16 <=> ! [X1] : ~old(X1) [avatar definition]
242. ~old(X1) <- (16) [avatar component clause 241]
295. ~generous(mary) | happy(X0) [subsumption resolution 143,234]
297. 27 <=> ! [X0] : happy(X0) [avatar definition]
298. happy(X0) <- (27) [avatar component clause 297]
300. 28 <=> generous(mary) [avatar definition]
302. ~generous(mary) <- (~28) [avatar component clause 300]
303. 27 | ~28 [avatar split clause 295,300,297]
315. ~calm(sK9) | quiet(X1) [subsumption resolution 149,237]
316. quiet(X1) [subsumption resolution 315,236]
354. $false <- (~1) [subsumption resolution 169,236]
355. 1 [avatar contradiction clause 354]
356. ~old(X1) <- (5) [subsumption resolution 189,316]
357. 16 | ~5 [avatar split clause 356,188,241]
358. $false <- (16) [resolution 242,161]
359. ~16 [avatar contradiction clause 358]
360. $false <- (~2, 27) [subsumption resolution 174,298]
361. 2 | ~27 [avatar contradiction clause 360]
366. generous(mary) [resolution 125,161]
368. $false <- (~28) [subsumption resolution 366,302]
369. 28 [avatar contradiction clause 368]
370. $false [avatar sat refutation 195,303,355,357,359,361,369]
% SZS output end Proof for 899540678407162682291311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not kind is either not old or not wise and vice versa.
Everyone who is not creative is either calm or not funny.
Everyone who is not tall is not curious or not strong and vice versa.
If alice is funny then mary is strong or patient.
Everyone who is either old or not creative is either strong or not wise.
Everyone who is both funny and not quiet is humble or creative and vice versa.
Everyone who is either humble or wise is not old.
If someone is not generous or not kind then susan is not rich or not calm and vice versa.
Everyone who is not strong or not creative is both not generous and not tall and vice versa.
If john is not brave then susan is either not quiet or not funny.
Everyone who is both tall and old is not humble and vice versa.
Everyone who is both not happy and not humble is either not kind or not quiet.
Everyone who is both not quiet and not brave is both not kind and not creative.
Everyone who is either rich or not old is brave.
Everyone who is strong or not curious is either calm or rich and vice versa.
Everyone who is both not kind and humble is generous or not strong.
Alice is kind or brave.
Someone is old.
Someone is calm or not generous.
Mary is strong or creative.
Alice is not old.
Someone is either not generous or not strong.
Someone is either not generous or not kind. | John is not quiet. | entailment | (![X]:((~humble(X)&~kind(X))<=>(~old(X)<~>~wise(X))))&
(![X]:(~creative(X)=>(calm(X)<~>~funny(X))))&
(![X]:(~tall(X)<=>(~curious(X)|~strong(X))))&
((funny(alice))=>((strong(mary)|patient(mary))))&
(![X]:((old(X)<~>~creative(X))=>(strong(X)<~>~wise(X))))&
(![X]:((funny(X)&~quiet(X))<=>(humble(X)|creative(X))))&
(![X]:((humble(X)<~>wise(X))=>~old(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>((~rich(susan)|~calm(susan))))&
(![X]:((~strong(X)|~creative(X))<=>(~generous(X)&~tall(X))))&
((~brave(john))=>((~quiet(susan)<~>~funny(susan))))&
(![X]:((tall(X)&old(X))<=>~humble(X)))&
(![X]:((~happy(X)&~humble(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~brave(X))=>(~kind(X)&~creative(X))))&
(![X]:((rich(X)<~>~old(X))=>brave(X)))&
(![X]:((strong(X)|~curious(X))<=>(calm(X)<~>rich(X))))&
(![X]:((~kind(X)&humble(X))=>(generous(X)|~strong(X))))&
((kind(alice)|brave(alice)))&
(?[X]:(old(X)))&
(?[X]:((calm(X)|~generous(X))))&
((strong(mary)|creative(mary)))&
(~old(alice))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:((~generous(X)<~>~kind(X)))) | ~quiet(john) | [
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6436852257564472859506737
% SZS output start Proof for 6436852257564472859506737
6. ! [X0] : ((~quiet(X0) & funny(X0)) <=> (creative(X0) | humble(X0))) [input p5]
9. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (~tall(X0) & ~generous(X0))) [input p8]
11. ! [X0] : ((old(X0) & tall(X0)) <=> ~humble(X0)) [input p10]
24. quiet(john) [input hypothesis]
42. ! [X0] : (((~quiet(X0) & funny(X0)) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | (quiet(X0) | ~funny(X0)))) [nnf transformation 6]
43. ! [X0] : (((~quiet(X0) & funny(X0)) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | quiet(X0) | ~funny(X0))) [flattening 42]
50. ! [X0] : (((~creative(X0) | ~strong(X0)) | (tall(X0) | generous(X0))) & ((~tall(X0) & ~generous(X0)) | (creative(X0) & strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((~creative(X0) | ~strong(X0) | tall(X0) | generous(X0)) & ((~tall(X0) & ~generous(X0)) | (creative(X0) & strong(X0)))) [flattening 50]
52. ! [X0] : (((old(X0) & tall(X0)) | humble(X0)) & (~humble(X0) | (~old(X0) | ~tall(X0)))) [nnf transformation 11]
53. ! [X0] : (((old(X0) & tall(X0)) | humble(X0)) & (~humble(X0) | ~old(X0) | ~tall(X0))) [flattening 52]
84. ~quiet(X0) | ~humble(X0) [cnf transformation 43]
85. ~quiet(X0) | ~creative(X0) [cnf transformation 43]
95. ~tall(X0) | creative(X0) [cnf transformation 51]
98. tall(X0) | humble(X0) [cnf transformation 53]
115. quiet(john) [cnf transformation 24]
172. ~humble(john) [resolution 84,115]
173. ~creative(john) [resolution 85,115]
177. creative(X0) | humble(X0) [resolution 98,95]
213. humble(john) [resolution 177,173]
215. $false [subsumption resolution 213,172]
% SZS output end Proof for 6436852257564472859506737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong or strong then lucy is both not brave and not tall and vice versa.
Everyone who is not patient or brave is quiet and vice versa.
Everyone who is both humble and rich is both not generous and not calm and vice versa.
Everyone who is either brave or not calm is brave.
Everyone who is either not humble or not calm is both wise and humble.
Everyone who is either not humble or not old is kind or calm and vice versa.
Everyone who is not rich or not happy is quiet and vice versa.
If someone is either not old or not brave then someone is both rich and not curious.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | Alice is not quiet. | contradiction | (((~strong(mary)|strong(mary)))<=>((~brave(lucy)&~tall(lucy))))&
(![X]:((~patient(X)|brave(X))<=>quiet(X)))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&~calm(X))))&
(![X]:((brave(X)<~>~calm(X))=>brave(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(kind(X)|calm(X))))&
(![X]:((~rich(X)|~happy(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | ~quiet(alice) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1804116521431938760186588
% SZS output start Proof for 1804116521431938760186588
2. ! [X0] : ((brave(X0) | ~patient(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : ((rich(X0) & humble(X0)) <=> (~calm(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((brave(X0) <~> ~calm(X0)) => brave(X0)) [input p3]
5. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => (humble(X0) & wise(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> quiet(X0)) [input p6]
25. ~quiet(alice) [input hypothesis]
29. ! [X0] : (brave(X0) | (brave(X0) <=> ~calm(X0))) [ennf transformation 4]
30. ! [X0] : ((humble(X0) & wise(X0)) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 5]
38. ! [X0] : (((brave(X0) | ~patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~patient(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [flattening 38]
40. ! [X0] : (((rich(X0) & humble(X0)) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((rich(X0) & humble(X0)) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~rich(X0) | ~humble(X0))) [flattening 40]
42. ! [X0] : (brave(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) [nnf transformation 29]
43. ! [X0] : ((humble(X0) & wise(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 30]
46. ! [X0] : (((~happy(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [nnf transformation 7]
47. ! [X0] : ((~happy(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [flattening 46]
85. ~brave(X0) | quiet(X0) [cnf transformation 39]
88. ~calm(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 41]
92. brave(X0) | brave(X0) | calm(X0) [cnf transformation 42]
95. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 43]
103. rich(X0) | quiet(X0) [cnf transformation 47]
143. ~quiet(alice) [cnf transformation 25]
144. ~calm(X0) | humble(X0) [duplicate literal removal 95]
145. calm(X0) | brave(X0) [duplicate literal removal 92]
314. humble(X0) | brave(X0) [resolution 145,144]
334. ~rich(X0) | ~humble(X0) | brave(X0) [resolution 88,145]
336. ~rich(X0) | brave(X0) [subsumption resolution 334,314]
342. brave(X0) | quiet(X0) [resolution 336,103]
343. quiet(X0) [subsumption resolution 342,85]
346. $false [resolution 343,143]
% SZS output end Proof for 1804116521431938760186588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not tall is either not kind or wise. Everyone who is both not humble and not quiet is kind and vice versa. If someone is either wise or brave then lucy is calm or not calm. Everyone who is either funny or not happy is not kind and vice versa. Everyone who is wise or not rich is curious. Everyone who is either creative or patient is both curious and not tall and vice versa. Everyone who is generous or not strong is rich. Everyone who is both not rich and not quiet is not tall or patient. If someone is both not kind and generous then mary is both not happy and not generous and vice versa. If lucy is not generous then mary is calm and vice versa. Everyone who is funny is rich or not calm and vice versa. If mary is not rich or not strong then alice is both not wise and brave. Everyone who is not kind or not strong is either funny or quiet and vice versa. If fred is both not generous and not tall then paul is not strong. Everyone who is both old and rich is both not old and not curious. Everyone who is both calm and kind is old or not rich and vice versa. Mary is both funny and not happy. Alice is not quiet or wise. Someone is both not kind and strong. Someone is both not rich and tall. John is both not quiet and not funny. Mary is not creative or not patient. Someone is curious. | John is not calm. | contradiction | (![X]:((~generous(X)|~tall(X))=>(~kind(X)<~>wise(X))))&
(![X]:((~humble(X)&~quiet(X))<=>kind(X)))&
((?[X]:((wise(X)<~>brave(X))))=>((calm(lucy)|~calm(lucy))))&
(![X]:((funny(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((wise(X)|~rich(X))=>curious(X)))&
(![X]:((creative(X)<~>patient(X))<=>(curious(X)&~tall(X))))&
(![X]:((generous(X)|~strong(X))=>rich(X)))&
(![X]:((~rich(X)&~quiet(X))=>(~tall(X)|patient(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((~happy(mary)&~generous(mary))))&
((~generous(lucy))<=>(calm(mary)))&
(![X]:(funny(X)<=>(rich(X)|~calm(X))))&
(((~rich(mary)|~strong(mary)))=>((~wise(alice)&brave(alice))))&
(![X]:((~kind(X)|~strong(X))<=>(funny(X)<~>quiet(X))))&
(((~generous(fred)&~tall(fred)))=>(~strong(paul)))&
(![X]:((old(X)&rich(X))=>(~old(X)&~curious(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)|~rich(X))))&
((funny(mary)&~happy(mary)))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((~rich(X)&tall(X))))&
((~quiet(john)&~funny(john)))&
((~creative(mary)|~patient(mary)))&
(?[X]:(curious(X))) | ~calm(john) | [
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4368688804301686916894527
% SZS output start Proof for 4368688804301686916894527
11. ! [X0] : (funny(X0) <=> (~calm(X0) | rich(X0))) [input p10]
21. ~funny(john) & ~quiet(john) [input p20]
24. ~calm(john) [input hypothesis]
50. ! [X0] : ((funny(X0) | (calm(X0) & ~rich(X0))) & ((~calm(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 11]
51. ! [X0] : ((funny(X0) | (calm(X0) & ~rich(X0))) & (~calm(X0) | rich(X0) | ~funny(X0))) [flattening 50]
94. funny(X0) | calm(X0) [cnf transformation 51]
121. ~funny(john) [cnf transformation 21]
124. ~calm(john) [cnf transformation 24]
214. calm(john) [resolution 94,121]
215. $false [subsumption resolution 214,124]
% SZS output end Proof for 4368688804301686916894527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either not kind or not humble.
Everyone who is rich or not rich is not kind.
If susan is either not creative or old then someone is generous or calm and vice versa.
Everyone who is both not funny and not happy is curious or kind.
Everyone who is not generous is not quiet or old and vice versa.
If someone is not old then paul is not curious or old and vice versa.
Everyone who is either wise or not tall is both not wise and not happy and vice versa.
If someone is not old or not generous then someone is both not curious and not happy and vice versa.
Everyone who is not calm or tall is both not humble and kind.
Everyone who is rich or wise is creative and vice versa.
Everyone who is generous is either humble or quiet and vice versa.
Everyone who is not strong or curious is not wise and vice versa.
If john is either not funny or not quiet then mary is happy and vice versa.
Everyone who is patient or not calm is creative and vice versa.
If someone is either kind or not old then mary is either not humble or happy.
If fred is creative then mary is curious or not curious.
Mary is not generous.
Someone is funny or creative.
Someone is either not wise or creative.
Lucy is not quiet or not happy.
Someone is either brave or tall.
Lucy is wise.
Someone is not brave or not old. | Lucy is not rich. | neutral | (![X]:(generous(X)=>(~kind(X)<~>~humble(X))))&
(![X]:((rich(X)|~rich(X))=>~kind(X)))&
(((~creative(susan)<~>old(susan)))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~funny(X)&~happy(X))=>(curious(X)|kind(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|old(X))))&
((?[X]:(~old(X)))<=>((~curious(paul)|old(paul))))&
(![X]:((wise(X)<~>~tall(X))<=>(~wise(X)&~happy(X))))&
((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((~calm(X)|tall(X))=>(~humble(X)&kind(X))))&
(![X]:((rich(X)|wise(X))<=>creative(X)))&
(![X]:(generous(X)<=>(humble(X)<~>quiet(X))))&
(![X]:((~strong(X)|curious(X))<=>~wise(X)))&
(((~funny(john)<~>~quiet(john)))<=>(happy(mary)))&
(![X]:((patient(X)|~calm(X))<=>creative(X)))&
((?[X]:((kind(X)<~>~old(X))))=>((~humble(mary)<~>happy(mary))))&
((creative(fred))=>((curious(mary)|~curious(mary))))&
(~generous(mary))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
((~quiet(lucy)|~happy(lucy)))&
(?[X]:((brave(X)<~>tall(X))))&
(wise(lucy))&
(?[X]:((~brave(X)|~old(X)))) | ~rich(lucy) | [] | null | 0 |
Everyone who is either generous or quiet is either not rich or tall.
Everyone who is happy or tall is either wise or tall.
If someone is either rich or not curious then lucy is either humble or not kind and vice versa.
Everyone who is kind or not humble is curious.
Everyone who is both not patient and not tall is calm or not old and vice versa.
If someone is both strong and generous then someone is either generous or happy.
If alice is creative or old then someone is not calm and vice versa.
Everyone who is not tall or tall is not tall or rich.
Everyone who is both kind and brave is not patient or not wise.
If someone is not patient then fred is quiet and vice versa.
If someone is wise or not strong then someone is either not strong or brave.
Everyone who is generous is funny or not calm and vice versa.
Everyone who is old is wise and vice versa.
If someone is brave or generous then mary is either not creative or generous and vice versa.
Everyone who is both quiet and not quiet is both not funny and not patient and vice versa.
Everyone who is either not brave or brave is strong and vice versa.
Susan is kind.
Mary is not rich.
Alice is funny or brave.
Someone is not curious or humble.
Someone is not tall.
Someone is both not rich and wise.
Someone is patient.
Paul is either not old or not patient. | Mary is tall. | contradiction | (![X]:((generous(X)<~>quiet(X))=>(~rich(X)<~>tall(X))))&
(![X]:((happy(X)|tall(X))=>(wise(X)<~>tall(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((humble(lucy)<~>~kind(lucy))))&
(![X]:((kind(X)|~humble(X))=>curious(X)))&
(![X]:((~patient(X)&~tall(X))<=>(calm(X)|~old(X))))&
((?[X]:((strong(X)&generous(X))))=>(?[X]:((generous(X)<~>happy(X)))))&
(((creative(alice)|old(alice)))<=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)|rich(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)|~wise(X))))&
((?[X]:(~patient(X)))<=>(quiet(fred)))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(generous(X)<=>(funny(X)|~calm(X))))&
(![X]:(old(X)<=>wise(X)))&
((?[X]:((brave(X)|generous(X))))<=>((~creative(mary)<~>generous(mary))))&
(![X]:((quiet(X)&~quiet(X))<=>(~funny(X)&~patient(X))))&
(![X]:((~brave(X)<~>brave(X))<=>strong(X)))&
(kind(susan))&
(~rich(mary))&
((funny(alice)|brave(alice)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)&wise(X))))&
(?[X]:(patient(X)))&
((~old(paul)<~>~patient(paul))) | tall(mary) | [
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1789309235795389344135309
% SZS output start Proof for 1789309235795389344135309
8. ! [X0] : ((tall(X0) | ~tall(X0)) => (rich(X0) | ~tall(X0))) [input p7]
18. ~rich(mary) [input p17]
25. tall(mary) [input hypothesis]
32. ! [X0] : ((rich(X0) | ~tall(X0)) | (~tall(X0) & tall(X0))) [ennf transformation 8]
33. ! [X0] : (rich(X0) | ~tall(X0) | (~tall(X0) & tall(X0))) [flattening 32]
110. rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 33]
138. ~rich(mary) [cnf transformation 18]
147. tall(mary) [cnf transformation 25]
150. ~tall(X0) | rich(X0) [duplicate literal removal 110]
309. rich(mary) [resolution 150,147]
310. $false [subsumption resolution 309,138]
% SZS output end Proof for 1789309235795389344135309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or kind is not generous or not wise.
Everyone who is patient is both rich and funny.
Everyone who is both not tall and funny is either curious or not patient and vice versa.
Everyone who is tall is both brave and not wise.
If someone is both not tall and not kind then fred is both calm and generous and vice versa.
If susan is both not kind and patient then someone is not patient and vice versa.
Everyone who is kind is either kind or not curious.
Everyone who is happy is not funny and vice versa.
Everyone who is not old is both not kind and quiet.
If someone is not creative or not strong then fred is either not brave or tall and vice versa.
If someone is both not wise and quiet then mary is not generous and vice versa.
If paul is both humble and not kind then john is calm.
Everyone who is either creative or patient is curious or calm.
Everyone who is wise is tall or rich and vice versa.
Someone is either not curious or brave.
Someone is wise or calm.
Someone is both not wise and creative.
John is kind or not happy.
Alice is creative or calm.
Alice is both wise and generous.
Someone is not kind.
Mary is not generous. | Alice is not tall. | entailment | (![X]:((wise(X)<~>kind(X))=>(~generous(X)|~wise(X))))&
(![X]:(patient(X)=>(rich(X)&funny(X))))&
(![X]:((~tall(X)&funny(X))<=>(curious(X)<~>~patient(X))))&
(![X]:(tall(X)=>(brave(X)&~wise(X))))&
((?[X]:((~tall(X)&~kind(X))))<=>((calm(fred)&generous(fred))))&
(((~kind(susan)&patient(susan)))<=>(?[X]:(~patient(X))))&
(![X]:(kind(X)=>(kind(X)<~>~curious(X))))&
(![X]:(happy(X)<=>~funny(X)))&
(![X]:(~old(X)=>(~kind(X)&quiet(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((~brave(fred)<~>tall(fred))))&
((?[X]:((~wise(X)&quiet(X))))<=>(~generous(mary)))&
(((humble(paul)&~kind(paul)))=>(calm(john)))&
(![X]:((creative(X)<~>patient(X))=>(curious(X)|calm(X))))&
(![X]:(wise(X)<=>(tall(X)|rich(X))))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:((~wise(X)&creative(X))))&
((kind(john)|~happy(john)))&
((creative(alice)|calm(alice)))&
((wise(alice)&generous(alice)))&
(?[X]:(~kind(X)))&
(~generous(mary)) | ~tall(alice) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5690681471140116867687095
% SZS output start Proof for 5690681471140116867687095
4. ! [X0] : (tall(X0) => (~wise(X0) & brave(X0))) [input p3]
14. ! [X0] : (wise(X0) <=> (rich(X0) | tall(X0))) [input p13]
23. tall(alice) [input hypothesis]
30. ! [X0] : ((~wise(X0) & brave(X0)) | ~tall(X0)) [ennf transformation 4]
58. ! [X0] : ((wise(X0) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | ~wise(X0))) [nnf transformation 14]
59. ! [X0] : ((wise(X0) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ~wise(X0))) [flattening 58]
80. ~wise(X0) | ~tall(X0) [cnf transformation 30]
103. wise(X0) | ~tall(X0) [cnf transformation 59]
116. tall(alice) [cnf transformation 23]
208. ~tall(X0) [subsumption resolution 103,80]
248. $false [subsumption resolution 116,208]
% SZS output end Proof for 5690681471140116867687095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not kind is tall.
If paul is rich or not humble then alice is patient or not creative.
If lucy is both quiet and brave then someone is patient or quiet and vice versa.
Everyone who is strong is both not old and wise and vice versa.
Everyone who is not strong or brave is either not wise or kind.
Everyone who is both not happy and curious is either old or not curious.
If someone is both not wise and tall then lucy is either not humble or wise.
Everyone who is wise or tall is both not happy and wise and vice versa.
Everyone who is funny or not generous is not curious or not brave.
If someone is either not funny or calm then lucy is both not humble and not curious.
Everyone who is both not rich and brave is not wise.
If someone is calm or wise then fred is either not tall or not strong and vice versa.
Everyone who is either not quiet or old is both rich and not old.
If someone is both patient and old then lucy is either creative or patient.
If someone is either calm or funny then someone is not quiet.
If someone is both rich and not curious then alice is either generous or not tall.
John is not humble.
Alice is both creative and kind.
Susan is either kind or not humble.
Someone is either not rich or kind.
Mary is not quiet or not creative.
Someone is not brave or strong.
Someone is both not quiet and tall. | Alice is creative. | entailment | (![X]:((humble(X)|~kind(X))=>tall(X)))&
(((rich(paul)|~humble(paul)))=>((patient(alice)|~creative(alice))))&
(((quiet(lucy)&brave(lucy)))<=>(?[X]:((patient(X)|quiet(X)))))&
(![X]:(strong(X)<=>(~old(X)&wise(X))))&
(![X]:((~strong(X)|brave(X))=>(~wise(X)<~>kind(X))))&
(![X]:((~happy(X)&curious(X))=>(old(X)<~>~curious(X))))&
((?[X]:((~wise(X)&tall(X))))=>((~humble(lucy)<~>wise(lucy))))&
(![X]:((wise(X)|tall(X))<=>(~happy(X)&wise(X))))&
(![X]:((funny(X)|~generous(X))=>(~curious(X)|~brave(X))))&
((?[X]:((~funny(X)<~>calm(X))))=>((~humble(lucy)&~curious(lucy))))&
(![X]:((~rich(X)&brave(X))=>~wise(X)))&
((?[X]:((calm(X)|wise(X))))<=>((~tall(fred)<~>~strong(fred))))&
(![X]:((~quiet(X)<~>old(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)&old(X))))=>((creative(lucy)<~>patient(lucy))))&
((?[X]:((calm(X)<~>funny(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)&~curious(X))))=>((generous(alice)<~>~tall(alice))))&
(~humble(john))&
((creative(alice)&kind(alice)))&
((kind(susan)<~>~humble(susan)))&
(?[X]:((~rich(X)<~>kind(X))))&
((~quiet(mary)|~creative(mary)))&
(?[X]:((~brave(X)|strong(X))))&
(?[X]:((~quiet(X)&tall(X)))) | creative(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 700696750926862092905343
% SZS output start Proof for 700696750926862092905343
18. kind(alice) & creative(alice) [input p17]
24. ~creative(alice) [input hypothesis]
123. creative(alice) [cnf transformation 18]
133. ~creative(alice) [cnf transformation 24]
145. 3 <=> creative(alice) [avatar definition]
276. 3 [avatar split clause 123,145]
315. ~3 [avatar split clause 133,145]
316. $false [avatar sat refutation 276,315]
% SZS output end Proof for 700696750926862092905343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or funny then alice is both calm and not humble. If fred is creative or not wise then john is not patient. Everyone who is not quiet or tall is either brave or rich and vice versa. If fred is both not strong and not creative then someone is either not old or tall. Everyone who is patient is both not quiet and happy. If someone is curious then someone is calm. Everyone who is patient or not kind is happy or funny and vice versa. Everyone who is both not tall and strong is old. If someone is patient then someone is either calm or rich. Everyone who is tall or not funny is both happy and wise. Everyone who is not patient or patient is funny and vice versa. Everyone who is either not rich or patient is both not funny and kind and vice versa. If mary is curious then someone is not curious or generous and vice versa. Everyone who is not kind is either strong or not quiet and vice versa. Everyone who is not quiet or generous is both strong and generous and vice versa. Everyone who is either not generous or kind is strong or brave. Alice is patient or humble. Someone is either not funny or tall. Susan is both not calm and not quiet. Someone is curious. Paul is not strong or patient. Someone is not curious. Someone is not brave or curious. | Alice is not brave. | contradiction | ((?[X]:((~brave(X)<~>funny(X))))=>((calm(alice)&~humble(alice))))&
(((creative(fred)|~wise(fred)))=>(~patient(john)))&
(![X]:((~quiet(X)|tall(X))<=>(brave(X)<~>rich(X))))&
(((~strong(fred)&~creative(fred)))=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:(patient(X)=>(~quiet(X)&happy(X))))&
((?[X]:(curious(X)))=>(?[X]:(calm(X))))&
(![X]:((patient(X)|~kind(X))<=>(happy(X)|funny(X))))&
(![X]:((~tall(X)&strong(X))=>old(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)|patient(X))<=>funny(X)))&
(![X]:((~rich(X)<~>patient(X))<=>(~funny(X)&kind(X))))&
((curious(mary))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~kind(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|generous(X))<=>(strong(X)&generous(X))))&
(![X]:((~generous(X)<~>kind(X))=>(strong(X)|brave(X))))&
((patient(alice)|humble(alice)))&
(?[X]:((~funny(X)<~>tall(X))))&
((~calm(susan)&~quiet(susan)))&
(?[X]:(curious(X)))&
((~strong(paul)|patient(paul)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)|curious(X)))) | ~brave(alice) | [
"p0",
"p2",
"p4",
"p6",
"p10",
"p11",
"p13",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8030296497043391836697642
% SZS output start Proof for 8030296497043391836697642
1. ? [X0] : (~brave(X0) <~> funny(X0)) => (~humble(alice) & calm(alice)) [input p0]
3. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> (brave(X0) <~> rich(X0))) [input p2]
5. ! [X0] : (patient(X0) => (happy(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | patient(X0)) <=> (funny(X0) | happy(X0))) [input p6]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> funny(X0)) [input p10]
12. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (kind(X0) & ~funny(X0))) [input p11]
14. ! [X0] : (~kind(X0) <=> (strong(X0) <~> ~quiet(X0))) [input p13]
15. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (generous(X0) & strong(X0))) [input p14]
17. humble(alice) | patient(alice) [input p16]
21. patient(paul) | ~strong(paul) [input p20]
24. ~brave(alice) [input hypothesis]
29. (~humble(alice) & calm(alice)) | ! [X0] : (~brave(X0) <=> funny(X0)) [ennf transformation 1]
33. ! [X0] : ((happy(X0) & ~quiet(X0)) | ~patient(X0)) [ennf transformation 5]
41. (~humble(alice) & calm(alice)) | ! [X0] : ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))) [nnf transformation 29]
42. ! [X0] : (((tall(X0) | ~quiet(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (~tall(X0) & quiet(X0)))) [nnf transformation 3]
43. ! [X0] : ((tall(X0) | ~quiet(X0) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (~tall(X0) & quiet(X0)))) [flattening 42]
50. ! [X0] : (((~kind(X0) | patient(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (kind(X0) & ~patient(X0)))) [nnf transformation 7]
51. ! [X0] : ((~kind(X0) | patient(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (kind(X0) & ~patient(X0)))) [flattening 50]
56. ! [X0] : (((patient(X0) | ~patient(X0)) | ~funny(X0)) & (funny(X0) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
57. ! [X0] : ((patient(X0) | ~patient(X0) | ~funny(X0)) & (funny(X0) | (~patient(X0) & patient(X0)))) [flattening 56]
58. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [flattening 58]
64. ! [X0] : ((~kind(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | kind(X0))) [nnf transformation 14]
65. ! [X0] : (((generous(X0) | ~quiet(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 15]
66. ! [X0] : ((generous(X0) | ~quiet(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (~generous(X0) & quiet(X0)))) [flattening 65]
80. ~humble(alice) | ~brave(X0) | ~funny(X0) [cnf transformation 41]
82. rich(X0) | brave(X0) | quiet(X0) [cnf transformation 43]
90. ~quiet(X0) | ~patient(X0) [cnf transformation 33]
96. ~kind(X0) | patient(X0) | ~funny(X0) [cnf transformation 51]
102. funny(X0) | patient(X0) [cnf transformation 57]
103. ~patient(X0) | funny(X0) [cnf transformation 57]
106. ~funny(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 59]
114. ~quiet(X0) | strong(X0) | kind(X0) [cnf transformation 64]
118. strong(X0) | quiet(X0) [cnf transformation 66]
125. humble(alice) | patient(alice) [cnf transformation 17]
131. patient(paul) | ~strong(paul) [cnf transformation 21]
134. ~brave(alice) [cnf transformation 24]
136. 1 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition]
137. ~brave(X0) | ~funny(X0) <- (1) [avatar component clause 136]
139. 2 <=> humble(alice) [avatar definition]
142. 1 | ~2 [avatar split clause 80,139,136]
197. funny(X0) [subsumption resolution 102,103]
198. ~rich(X0) | ~patient(X0) [subsumption resolution 106,197]
223. 20 <=> patient(alice) [avatar definition]
225. patient(alice) <- (20) [avatar component clause 223]
226. 20 | 2 [avatar split clause 125,139,223]
229. 21 <=> strong(paul) [avatar definition]
231. ~strong(paul) <- (~21) [avatar component clause 229]
233. 22 <=> patient(paul) [avatar definition]
234. ~patient(paul) <- (~22) [avatar component clause 233]
235. patient(paul) <- (22) [avatar component clause 233]
236. ~21 | 22 [avatar split clause 131,233,229]
253. quiet(paul) <- (~21) [resolution 118,231]
262. brave(X0) | quiet(X0) | ~patient(X0) [resolution 82,198]
272. ~patient(X0) | brave(X0) [subsumption resolution 262,90]
301. brave(alice) <- (20) [resolution 272,225]
302. $false <- (20) [subsumption resolution 301,134]
303. ~20 [avatar contradiction clause 302]
304. ~brave(X0) <- (1) [subsumption resolution 137,197]
315. strong(paul) | kind(paul) <- (~21) [resolution 114,253]
316. kind(paul) <- (~21) [subsumption resolution 315,231]
319. patient(paul) | ~funny(paul) <- (~21) [resolution 316,96]
321. ~funny(paul) <- (~21, ~22) [subsumption resolution 319,234]
322. $false <- (~21, ~22) [subsumption resolution 321,197]
323. 21 | 22 [avatar contradiction clause 322]
336. brave(paul) <- (22) [resolution 235,272]
339. $false <- (1, 22) [subsumption resolution 336,304]
340. ~1 | ~22 [avatar contradiction clause 339]
341. $false [avatar sat refutation 142,226,236,303,323,340]
% SZS output end Proof for 8030296497043391836697642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either happy or creative then someone is strong and vice versa.
If mary is not humble or happy then someone is not curious and vice versa.
If someone is either not kind or creative then john is either brave or wise.
If someone is either calm or not strong then mary is quiet.
Everyone who is both not wise and not calm is not old or patient and vice versa.
Everyone who is both rich and not brave is patient and vice versa.
If someone is not old then paul is not kind and vice versa.
Everyone who is humble or not generous is either not kind or not funny.
Everyone who is quiet is happy or not wise and vice versa.
Everyone who is patient or not kind is wise or not quiet.
If john is either kind or curious then someone is not happy or happy and vice versa.
Everyone who is calm or not rich is both not strong and humble.
Everyone who is both funny and rich is not wise or not happy and vice versa.
If someone is both not rich and tall then someone is both tall and quiet and vice versa.
Everyone who is both not strong and not wise is both strong and old and vice versa.
Everyone who is not patient or not calm is not rich and vice versa.
Mary is either wise or not brave.
Fred is both not kind and not creative.
Someone is not curious or calm.
Someone is either calm or not curious.
Paul is either not curious or not brave. | Paul is not funny. | entailment | (((happy(alice)<~>creative(alice)))<=>(?[X]:(strong(X))))&
(((~humble(mary)|happy(mary)))<=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)<~>creative(X))))=>((brave(john)<~>wise(john))))&
((?[X]:((calm(X)<~>~strong(X))))=>(quiet(mary)))&
(![X]:((~wise(X)&~calm(X))<=>(~old(X)|patient(X))))&
(![X]:((rich(X)&~brave(X))<=>patient(X)))&
((?[X]:(~old(X)))<=>(~kind(paul)))&
(![X]:((humble(X)|~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:(quiet(X)<=>(happy(X)|~wise(X))))&
(![X]:((patient(X)|~kind(X))=>(wise(X)|~quiet(X))))&
(((kind(john)<~>curious(john)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((calm(X)|~rich(X))=>(~strong(X)&humble(X))))&
(![X]:((funny(X)&rich(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~strong(X)&~wise(X))<=>(strong(X)&old(X))))&
(![X]:((~patient(X)|~calm(X))<=>~rich(X)))&
((wise(mary)<~>~brave(mary)))&
((~kind(fred)&~creative(fred)))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
((~curious(paul)<~>~brave(paul))) | ~funny(paul) | [
"p0",
"p4",
"p6",
"p7",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4184739065229290424838859
% SZS output start Proof for 4184739065229290424838859
1. (happy(alice) <~> creative(alice)) <=> ? [X0] : strong(X0) [input p0]
5. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> (patient(X0) | ~old(X0))) [input p4]
7. ? [X0] : ~old(X0) <=> ~kind(paul) [input p6]
8. ! [X0] : ((~generous(X0) | humble(X0)) => (~kind(X0) <~> ~funny(X0))) [input p7]
12. ! [X0] : ((~rich(X0) | calm(X0)) => (humble(X0) & ~strong(X0))) [input p11]
15. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> (old(X0) & strong(X0))) [input p14]
16. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> ~rich(X0)) [input p15]
22. funny(paul) [input hypothesis]
24. ! [X0] : (humble(X0) => (~kind(X0) <~> ~funny(X0))) [pure predicate removal 8]
27. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | ~humble(X0)) [ennf transformation 24]
30. ! [X0] : ((humble(X0) & ~strong(X0)) | (rich(X0) & ~calm(X0))) [ennf transformation 12]
31. (((~creative(alice) | ~happy(alice)) & (creative(alice) | happy(alice))) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ((happy(alice) | ~creative(alice)) & (creative(alice) | ~happy(alice)))) [nnf transformation 1]
32. (((~creative(alice) | ~happy(alice)) & (creative(alice) | happy(alice))) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ((happy(alice) | ~creative(alice)) & (creative(alice) | ~happy(alice)))) [rectify 31]
33. ? [X1] : strong(X1) => strong(sK0) [choice axiom]
34. (((~creative(alice) | ~happy(alice)) & (creative(alice) | happy(alice))) | ! [X0] : ~strong(X0)) & (strong(sK0) | ((happy(alice) | ~creative(alice)) & (creative(alice) | ~happy(alice)))) [skolemisation 32,33]
42. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~patient(X0) & old(X0))) & ((patient(X0) | ~old(X0)) | (calm(X0) | wise(X0)))) [nnf transformation 5]
43. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~patient(X0) & old(X0))) & (patient(X0) | ~old(X0) | calm(X0) | wise(X0))) [flattening 42]
46. (? [X0] : ~old(X0) | kind(paul)) & (~kind(paul) | ! [X0] : old(X0)) [nnf transformation 7]
47. (? [X0] : ~old(X0) | kind(paul)) & (~kind(paul) | ! [X1] : old(X1)) [rectify 46]
48. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
49. (~old(sK2) | kind(paul)) & (~kind(paul) | ! [X1] : old(X1)) [skolemisation 47,48]
50. ! [X0] : (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~humble(X0)) [nnf transformation 27]
64. ! [X0] : (((~wise(X0) & ~strong(X0)) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | (wise(X0) | strong(X0)))) [nnf transformation 15]
65. ! [X0] : (((~wise(X0) & ~strong(X0)) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | wise(X0) | strong(X0))) [flattening 64]
66. ! [X0] : (((~calm(X0) | ~patient(X0)) | rich(X0)) & (~rich(X0) | (calm(X0) & patient(X0)))) [nnf transformation 16]
67. ! [X0] : ((~calm(X0) | ~patient(X0) | rich(X0)) & (~rich(X0) | (calm(X0) & patient(X0)))) [flattening 66]
75. strong(sK0) | creative(alice) | ~happy(alice) [cnf transformation 34]
76. strong(sK0) | happy(alice) | ~creative(alice) [cnf transformation 34]
77. creative(alice) | happy(alice) | ~strong(X0) [cnf transformation 34]
78. ~creative(alice) | ~happy(alice) | ~strong(X0) [cnf transformation 34]
89. ~wise(X0) | old(X0) [cnf transformation 43]
92. ~patient(X0) | ~calm(X0) [cnf transformation 43]
97. ~old(sK2) | kind(paul) [cnf transformation 49]
98. ~funny(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 50]
112. ~strong(X0) | rich(X0) [cnf transformation 30]
113. ~calm(X0) | humble(X0) [cnf transformation 30]
114. rich(X0) | humble(X0) [cnf transformation 30]
125. old(X0) | wise(X0) | strong(X0) [cnf transformation 65]
128. ~rich(X0) | patient(X0) [cnf transformation 67]
129. ~rich(X0) | calm(X0) [cnf transformation 67]
140. funny(paul) [cnf transformation 22]
144. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
145. ~strong(X0) <- (1) [avatar component clause 144]
147. 2 <=> happy(alice) [avatar definition]
151. 3 <=> creative(alice) [avatar definition]
154. 1 | ~2 | ~3 [avatar split clause 78,151,147,144]
155. 1 | 2 | 3 [avatar split clause 77,151,147,144]
157. 4 <=> strong(sK0) [avatar definition]
159. strong(sK0) <- (4) [avatar component clause 157]
160. ~3 | 2 | 4 [avatar split clause 76,157,147,151]
161. ~2 | 3 | 4 [avatar split clause 75,157,151,147]
211. 16 <=> kind(paul) [avatar definition]
213. kind(paul) <- (16) [avatar component clause 211]
215. 17 <=> old(sK2) [avatar definition]
217. ~old(sK2) <- (~17) [avatar component clause 215]
218. 16 | ~17 [avatar split clause 97,215,211]
271. old(X0) | strong(X0) [subsumption resolution 125,89]
312. rich(sK0) <- (4) [resolution 112,159]
313. patient(sK0) <- (4) [resolution 128,312]
317. calm(sK0) <- (4) [resolution 129,312]
320. calm(X2) | humble(X2) [resolution 129,114]
321. humble(X2) [subsumption resolution 320,113]
336. ~calm(sK0) <- (4) [resolution 313,92]
338. $false <- (4) [subsumption resolution 336,317]
339. ~4 [avatar contradiction clause 338]
361. strong(sK2) <- (~17) [resolution 271,217]
363. $false <- (1, ~17) [subsumption resolution 361,145]
364. ~1 | 17 [avatar contradiction clause 363]
383. ~kind(paul) | ~humble(paul) [resolution 98,140]
386. ~humble(paul) <- (16) [subsumption resolution 383,213]
387. $false <- (16) [subsumption resolution 386,321]
388. ~16 [avatar contradiction clause 387]
389. $false [avatar sat refutation 154,155,160,161,218,339,364,388]
% SZS output end Proof for 4184739065229290424838859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either generous or not quiet.
If susan is not generous or quiet then someone is humble and vice versa.
Everyone who is both not strong and not quiet is both not kind and generous and vice versa.
Everyone who is both quiet and not patient is either not rich or not humble and vice versa.
Everyone who is either quiet or humble is both not strong and curious and vice versa.
Everyone who is not funny or kind is both brave and generous.
Everyone who is both quiet and not patient is not tall or not wise.
Everyone who is kind or humble is not strong and vice versa.
Everyone who is wise or calm is not generous or not creative and vice versa.
Everyone who is funny is generous.
Everyone who is either patient or not curious is not happy and vice versa.
If someone is not quiet then someone is either not calm or not rich and vice versa.
If someone is both quiet and strong then mary is not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Someone is not old or generous.
Someone is either not brave or not happy.
Alice is not strong or not patient.
Someone is not patient or quiet.
Someone is both not calm and curious.
Someone is not patient.
Someone is curious. | John is tall. | neutral | (![X]:(~rich(X)=>(generous(X)<~>~quiet(X))))&
(((~generous(susan)|quiet(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~strong(X)&~quiet(X))<=>(~kind(X)&generous(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)|kind(X))=>(brave(X)&generous(X))))&
(![X]:((quiet(X)&~patient(X))=>(~tall(X)|~wise(X))))&
(![X]:((kind(X)|humble(X))<=>~strong(X)))&
(![X]:((wise(X)|calm(X))<=>(~generous(X)|~creative(X))))&
(![X]:(funny(X)=>generous(X)))&
(![X]:((patient(X)<~>~curious(X))<=>~happy(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:((quiet(X)&strong(X))))<=>(~tall(mary)))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((~strong(alice)|~patient(alice)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((~calm(X)&curious(X))))&
(?[X]:(~patient(X)))&
(?[X]:(curious(X))) | tall(john) | [] | null | 0 |
If lucy is old or humble then someone is not old. Everyone who is not strong is kind and vice versa. Everyone who is either not tall or not quiet is both happy and curious and vice versa. Everyone who is not humble or not brave is both not quiet and brave. If lucy is happy or rich then someone is either not quiet or not tall and vice versa. Everyone who is both not quiet and patient is either not curious or not wise and vice versa. If susan is tall or kind then john is both strong and not calm and vice versa. If fred is either curious or not kind then someone is strong. Everyone who is both curious and not tall is tall or not brave. If susan is not curious or calm then someone is both creative and funny and vice versa. Everyone who is not wise or happy is not humble and vice versa. Everyone who is kind or funny is either not curious or not kind and vice versa. Everyone who is both brave and tall is both not tall and creative. If lucy is both kind and strong then someone is both brave and not quiet. Everyone who is both old and not generous is both not quiet and tall and vice versa. Someone is happy. Someone is rich or not funny. Someone is both not calm and not humble. Someone is both not rich and creative. Someone is not creative. Fred is not rich. John is either not rich or old. Someone is either funny or wise. | Lucy is not curious. | entailment | (((old(lucy)|humble(lucy)))=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~tall(X)<~>~quiet(X))<=>(happy(X)&curious(X))))&
(![X]:((~humble(X)|~brave(X))=>(~quiet(X)&brave(X))))&
(((happy(lucy)|rich(lucy)))<=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((~quiet(X)&patient(X))<=>(~curious(X)<~>~wise(X))))&
(((tall(susan)|kind(susan)))<=>((strong(john)&~calm(john))))&
(((curious(fred)<~>~kind(fred)))=>(?[X]:(strong(X))))&
(![X]:((curious(X)&~tall(X))=>(tall(X)|~brave(X))))&
(((~curious(susan)|calm(susan)))<=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((~wise(X)|happy(X))<=>~humble(X)))&
(![X]:((kind(X)|funny(X))<=>(~curious(X)<~>~kind(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)&creative(X))))&
(((kind(lucy)&strong(lucy)))=>(?[X]:((brave(X)&~quiet(X)))))&
(![X]:((old(X)&~generous(X))<=>(~quiet(X)&tall(X))))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)|~funny(X))))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~rich(X)&creative(X))))&
(?[X]:(~creative(X)))&
(~rich(fred))&
((~rich(john)<~>old(john)))&
(?[X]:((funny(X)<~>wise(X)))) | ~curious(lucy) | [
"p3",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8034641923782810904945057
% SZS output start Proof for 8034641923782810904945057
4. ! [X0] : ((~brave(X0) | ~humble(X0)) => (brave(X0) & ~quiet(X0))) [input p3]
9. ! [X0] : ((~tall(X0) & curious(X0)) => (~brave(X0) | tall(X0))) [input p8]
13. ! [X0] : ((tall(X0) & brave(X0)) => (creative(X0) & ~tall(X0))) [input p12]
24. curious(lucy) [input hypothesis]
26. ! [X0] : ((brave(X0) & ~quiet(X0)) | (brave(X0) & humble(X0))) [ennf transformation 4]
28. ! [X0] : ((~brave(X0) | tall(X0)) | (tall(X0) | ~curious(X0))) [ennf transformation 9]
29. ! [X0] : (~brave(X0) | tall(X0) | tall(X0) | ~curious(X0)) [flattening 28]
30. ! [X0] : ((creative(X0) & ~tall(X0)) | (~tall(X0) | ~brave(X0))) [ennf transformation 13]
31. ! [X0] : ((creative(X0) & ~tall(X0)) | ~tall(X0) | ~brave(X0)) [flattening 30]
91. brave(X0) | brave(X0) [cnf transformation 26]
111. ~brave(X0) | tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 29]
126. ~tall(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 31]
146. curious(lucy) [cnf transformation 24]
147. ~tall(X0) | ~brave(X0) [duplicate literal removal 126]
150. ~brave(X0) | tall(X0) | ~curious(X0) [duplicate literal removal 111]
151. brave(X0) [duplicate literal removal 91]
229. ~curious(X0) | tall(X0) [subsumption resolution 150,151]
255. ~tall(X0) [subsumption resolution 147,151]
294. tall(lucy) [resolution 229,146]
296. $false [subsumption resolution 294,255]
% SZS output end Proof for 8034641923782810904945057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and vice versa.
If john is not strong or patient then susan is strong and vice versa.
Everyone who is not strong is tall and vice versa.
If someone is not old then john is not humble.
If someone is not old then alice is not curious.
Everyone who is either not curious or not humble is both creative and not calm.
If someone is not wise or calm then someone is both not wise and not quiet and vice versa.
If paul is creative or curious then someone is both not wise and not generous.
Everyone who is either wise or old is both strong and not curious.
Everyone who is either not strong or kind is both not generous and kind.
Everyone who is strong or not generous is either not brave or not wise and vice versa.
If lucy is not old then susan is either wise or not happy and vice versa.
Everyone who is both generous and not curious is not happy.
If someone is either not humble or not generous then fred is either tall or calm and vice versa.
Everyone who is not calm or not rich is tall or humble and vice versa.
Everyone who is both not curious and tall is not kind.
Lucy is rich or not quiet.
John is both not quiet and not humble.
Someone is either not curious or funny.
Someone is either curious or not patient.
Someone is funny or curious.
John is strong or not creative.
Paul is either not humble or not wise.
John is wise. | John is not brave. | entailment | (![X]:(~humble(X)<=>happy(X)))&
(((~strong(john)|patient(john)))<=>(strong(susan)))&
(![X]:(~strong(X)<=>tall(X)))&
((?[X]:(~old(X)))=>(~humble(john)))&
((?[X]:(~old(X)))=>(~curious(alice)))&
(![X]:((~curious(X)<~>~humble(X))=>(creative(X)&~calm(X))))&
((?[X]:((~wise(X)|calm(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(((creative(paul)|curious(paul)))=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((wise(X)<~>old(X))=>(strong(X)&~curious(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~generous(X)&kind(X))))&
(![X]:((strong(X)|~generous(X))<=>(~brave(X)<~>~wise(X))))&
((~old(lucy))<=>((wise(susan)<~>~happy(susan))))&
(![X]:((generous(X)&~curious(X))=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&tall(X))=>~kind(X)))&
((rich(lucy)|~quiet(lucy)))&
((~quiet(john)&~humble(john)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john)))&
((~humble(paul)<~>~wise(paul)))&
(wise(john)) | ~brave(john) | [
"p0",
"p5",
"p10",
"p12",
"p17",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6782393385522288965350926
% SZS output start Proof for 6782393385522288965350926
1. ! [X0] : (~humble(X0) <=> happy(X0)) [input p0]
6. ! [X0] : ((~curious(X0) <~> ~humble(X0)) => (~calm(X0) & creative(X0))) [input p5]
11. ! [X0] : ((~generous(X0) | strong(X0)) <=> (~brave(X0) <~> ~wise(X0))) [input p10]
13. ! [X0] : ((~curious(X0) & generous(X0)) => ~happy(X0)) [input p12]
18. ~humble(john) & ~quiet(john) [input p17]
22. ~creative(john) | strong(john) [input p21]
24. wise(john) [input p23]
25. brave(john) [input hypothesis]
29. ! [X0] : ((~calm(X0) & creative(X0)) | (~curious(X0) <=> ~humble(X0))) [ennf transformation 6]
33. ! [X0] : (~happy(X0) | (curious(X0) | ~generous(X0))) [ennf transformation 13]
34. ! [X0] : (~happy(X0) | curious(X0) | ~generous(X0)) [flattening 33]
37. ! [X0] : ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) & creative(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) [nnf transformation 29]
51. ! [X0] : (((~generous(X0) | strong(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 11]
52. ! [X0] : ((~generous(X0) | strong(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (generous(X0) & ~strong(X0)))) [flattening 51]
69. happy(X0) | humble(X0) [cnf transformation 37]
79. ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 41]
99. ~brave(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 52]
100. ~brave(X0) | ~wise(X0) | generous(X0) [cnf transformation 52]
109. ~generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 34]
125. ~humble(john) [cnf transformation 18]
131. ~creative(john) | strong(john) [cnf transformation 22]
134. wise(john) [cnf transformation 24]
135. brave(john) [cnf transformation 25]
142. 2 <=> strong(john) [avatar definition]
156. 5 <=> humble(john) [avatar definition]
158. ~humble(john) <- (~5) [avatar component clause 156]
270. ~5 [avatar split clause 125,156]
301. 35 <=> creative(john) [avatar definition]
303. ~creative(john) <- (~35) [avatar component clause 301]
304. 2 | ~35 [avatar split clause 131,301,142]
362. 44 <=> curious(john) [avatar definition]
363. curious(john) <- (44) [avatar component clause 362]
364. ~curious(john) <- (~44) [avatar component clause 362]
381. ~wise(john) | ~strong(john) [resolution 99,135]
382. ~strong(john) [subsumption resolution 381,134]
385. ~2 [avatar split clause 382,142]
387. ~wise(john) | generous(john) [resolution 100,135]
388. generous(john) [subsumption resolution 387,134]
407. curious(john) | ~happy(john) [resolution 109,388]
408. ~happy(john) <- (~44) [subsumption resolution 407,364]
414. humble(john) <- (~44) [resolution 408,69]
415. $false <- (~5, ~44) [subsumption resolution 414,158]
416. 5 | 44 [avatar contradiction clause 415]
423. creative(john) | humble(john) <- (44) [resolution 363,79]
424. humble(john) <- (~35, 44) [subsumption resolution 423,303]
425. $false <- (~5, ~35, 44) [subsumption resolution 424,158]
426. 5 | 35 | ~44 [avatar contradiction clause 425]
427. $false [avatar sat refutation 270,304,385,416,426]
% SZS output end Proof for 6782393385522288965350926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative then someone is both not generous and kind. Everyone who is either not old or not quiet is either not funny or not old. Everyone who is strong is not tall or not creative. If mary is brave then someone is either not creative or quiet and vice versa. Everyone who is not humble is either creative or not strong. Everyone who is both not funny and not quiet is both not kind and calm and vice versa. If someone is humble or not tall then susan is tall or creative. If someone is funny then john is not happy or not wise and vice versa. Everyone who is both not calm and patient is not tall. Everyone who is both funny and humble is either wise or brave and vice versa. If someone is either rich or not creative then someone is either not wise or not generous and vice versa. Everyone who is not funny is either rich or happy. Everyone who is either not brave or not calm is not patient and vice versa. Everyone who is either not happy or not curious is both not creative and not calm and vice versa. Everyone who is both old and calm is tall. Everyone who is either funny or patient is tall or funny and vice versa. Someone is both generous and wise. Someone is not happy or funny. Paul is not generous. Someone is not brave or strong. John is both not rich and not brave. Someone is calm. Someone is not old or not calm. Someone is either not wise or not curious. | Mary is brave. | neutral | ((creative(mary))=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((~old(X)<~>~quiet(X))=>(~funny(X)<~>~old(X))))&
(![X]:(strong(X)=>(~tall(X)|~creative(X))))&
((brave(mary))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(creative(X)<~>~strong(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(~kind(X)&calm(X))))&
((?[X]:((humble(X)|~tall(X))))=>((tall(susan)|creative(susan))))&
((?[X]:(funny(X)))<=>((~happy(john)|~wise(john))))&
(![X]:((~calm(X)&patient(X))=>~tall(X)))&
(![X]:((funny(X)&humble(X))<=>(wise(X)<~>brave(X))))&
((?[X]:((rich(X)<~>~creative(X))))<=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:(~funny(X)=>(rich(X)<~>happy(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>~patient(X)))&
(![X]:((~happy(X)<~>~curious(X))<=>(~creative(X)&~calm(X))))&
(![X]:((old(X)&calm(X))=>tall(X)))&
(![X]:((funny(X)<~>patient(X))<=>(tall(X)|funny(X))))&
(?[X]:((generous(X)&wise(X))))&
(?[X]:((~happy(X)|funny(X))))&
(~generous(paul))&
(?[X]:((~brave(X)|strong(X))))&
((~rich(john)&~brave(john)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)|~calm(X))))&
(?[X]:((~wise(X)<~>~curious(X)))) | brave(mary) | [] | null | 0 |
Everyone who is both not tall and curious is either not brave or old and vice versa.
If someone is not calm then someone is not tall or wise and vice versa.
If john is rich then john is either brave or not quiet.
Everyone who is either not kind or not wise is either wise or not quiet and vice versa.
Everyone who is both not patient and not wise is not funny or rich.
Everyone who is both not curious and not calm is not creative and vice versa.
Everyone who is either not calm or not happy is not patient.
If paul is not kind or curious then someone is brave or not kind and vice versa.
If alice is not tall then someone is brave.
Everyone who is rich or calm is both not funny and not tall.
Everyone who is not quiet is patient.
If susan is both not wise and brave then fred is strong or wise.
If susan is both not generous and quiet then someone is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Everyone who is either happy or tall is either not quiet or not tall.
Mary is patient.
Someone is both brave and kind.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative.
Fred is kind. | John is not curious. | neutral | (![X]:((~tall(X)&curious(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)|wise(X)))))&
((rich(john))=>((brave(john)<~>~quiet(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~patient(X)&~wise(X))=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>~creative(X)))&
(![X]:((~calm(X)<~>~happy(X))=>~patient(X)))&
(((~kind(paul)|curious(paul)))<=>(?[X]:((brave(X)|~kind(X)))))&
((~tall(alice))=>(?[X]:(brave(X))))&
(![X]:((rich(X)|calm(X))=>(~funny(X)&~tall(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(((~wise(susan)&brave(susan)))=>((strong(fred)|wise(fred))))&
(((~generous(susan)&quiet(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
(![X]:((happy(X)<~>tall(X))=>(~quiet(X)<~>~tall(X))))&
(patient(mary))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john)))&
(kind(fred)) | ~curious(john) | [] | null | 0 |
Everyone who is strong is not old and vice versa. Everyone who is rich or not generous is not funny or strong. Everyone who is not patient or strong is both not rich and rich and vice versa. If someone is both strong and kind then someone is not tall or kind. Everyone who is patient is both quiet and not kind. Everyone who is not patient is either quiet or wise and vice versa. Everyone who is both not humble and strong is brave and vice versa. If alice is both not curious and calm then someone is not kind or strong. Everyone who is not generous is not tall. If mary is either not curious or old then someone is both not brave and not quiet and vice versa. If someone is not creative then someone is either not creative or not happy and vice versa. If someone is both not patient and not quiet then paul is either not generous or not kind and vice versa. If lucy is both rich and not old then someone is either patient or not generous and vice versa. Everyone who is not happy or not rich is not funny or not curious. Someone is not rich. Someone is either strong or not tall. Someone is both humble and happy. Someone is either creative or not brave. Mary is humble. Mary is not wise or happy. Someone is either not old or not kind. | Lucy is generous. | contradiction | (![X]:(strong(X)<=>~old(X)))&
(![X]:((rich(X)|~generous(X))=>(~funny(X)|strong(X))))&
(![X]:((~patient(X)|strong(X))<=>(~rich(X)&rich(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(patient(X)=>(quiet(X)&~kind(X))))&
(![X]:(~patient(X)<=>(quiet(X)<~>wise(X))))&
(![X]:((~humble(X)&strong(X))<=>brave(X)))&
(((~curious(alice)&calm(alice)))=>(?[X]:((~kind(X)|strong(X)))))&
(![X]:(~generous(X)=>~tall(X)))&
(((~curious(mary)<~>old(mary)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((~patient(X)&~quiet(X))))<=>((~generous(paul)<~>~kind(paul))))&
(((rich(lucy)&~old(lucy)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
(![X]:((~happy(X)|~rich(X))=>(~funny(X)|~curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((humble(X)&happy(X))))&
(?[X]:((creative(X)<~>~brave(X))))&
(humble(mary))&
((~wise(mary)|happy(mary)))&
(?[X]:((~old(X)<~>~kind(X)))) | generous(lucy) | [
"p0",
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1829572476352482661399633
% SZS output start Proof for 1829572476352482661399633
1. ! [X0] : (strong(X0) <=> ~old(X0)) [input p0]
3. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (rich(X0) & ~rich(X0))) [input p2]
13. (~old(lucy) & rich(lucy)) <=> ? [X0] : (patient(X0) <~> ~generous(X0)) [input p12]
22. generous(lucy) [input hypothesis]
31. ! [X0] : ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0))) [nnf transformation 1]
32. ! [X0] : (((strong(X0) | ~patient(X0)) | (~rich(X0) | rich(X0))) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 3]
33. ! [X0] : ((strong(X0) | ~patient(X0) | ~rich(X0) | rich(X0)) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & patient(X0)))) [flattening 32]
53. ((~old(lucy) & rich(lucy)) | ! [X0] : ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (? [X0] : ((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (old(lucy) | ~rich(lucy))) [nnf transformation 13]
54. ((~old(lucy) & rich(lucy)) | ! [X0] : ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (? [X0] : ((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | old(lucy) | ~rich(lucy)) [flattening 53]
55. ((~old(lucy) & rich(lucy)) | ! [X0] : ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (? [X1] : ((generous(X1) | ~patient(X1)) & (~generous(X1) | patient(X1))) | old(lucy) | ~rich(lucy)) [rectify 54]
56. ? [X1] : ((generous(X1) | ~patient(X1)) & (~generous(X1) | patient(X1))) => ((generous(sK5) | ~patient(sK5)) & (~generous(sK5) | patient(sK5))) [choice axiom]
57. ((~old(lucy) & rich(lucy)) | ! [X0] : ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(sK5) | ~patient(sK5)) & (~generous(sK5) | patient(sK5))) | old(lucy) | ~rich(lucy)) [skolemisation 55,56]
72. old(X0) | strong(X0) [cnf transformation 31]
73. ~rich(X0) | patient(X0) [cnf transformation 33]
74. ~rich(X0) | ~strong(X0) [cnf transformation 33]
75. rich(X0) | patient(X0) [cnf transformation 33]
76. rich(X0) | ~strong(X0) [cnf transformation 33]
109. ~old(lucy) | ~generous(X0) | ~patient(X0) [cnf transformation 57]
122. generous(lucy) [cnf transformation 22]
123. ~strong(X0) [subsumption resolution 74,76]
124. patient(X0) [subsumption resolution 73,75]
169. ~old(lucy) | ~generous(X0) [subsumption resolution 109,124]
171. 9 <=> ! [X0] : ~generous(X0) [avatar definition]
172. ~generous(X0) <- (9) [avatar component clause 171]
174. 10 <=> old(lucy) [avatar definition]
176. ~old(lucy) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 169,174,171]
196. $false <- (9) [resolution 172,122]
197. ~9 [avatar contradiction clause 196]
200. strong(lucy) <- (~10) [resolution 72,176]
204. $false <- (~10) [subsumption resolution 200,123]
205. 10 [avatar contradiction clause 204]
206. $false [avatar sat refutation 177,197,205]
% SZS output end Proof for 1829572476352482661399633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and brave is either not brave or happy.
If mary is not kind then john is either not wise or humble.
Everyone who is not wise or not patient is both not old and old and vice versa.
Everyone who is either generous or curious is either not funny or rich and vice versa.
Everyone who is brave or not brave is not funny or humble.
Everyone who is either curious or kind is either not kind or not patient and vice versa.
Everyone who is both not old and not kind is not strong and vice versa.
Everyone who is not tall is both not old and calm and vice versa.
Everyone who is not curious or not humble is rich.
Everyone who is both not quiet and wise is curious and vice versa.
If john is not generous then someone is either tall or curious.
Everyone who is not generous is both not rich and brave.
Everyone who is not patient or not brave is tall and vice versa.
If susan is both brave and wise then someone is not humble or calm and vice versa.
Everyone who is either generous or old is either not patient or creative and vice versa.
Everyone who is not funny or not curious is either wise or not calm.
Someone is both calm and wise.
Fred is both not humble and kind.
Someone is not brave or not calm.
Someone is either kind or wise.
Someone is not brave.
Alice is either humble or funny.
Lucy is either happy or not patient. | Lucy is strong. | neutral | (![X]:((creative(X)&brave(X))=>(~brave(X)<~>happy(X))))&
((~kind(mary))=>((~wise(john)<~>humble(john))))&
(![X]:((~wise(X)|~patient(X))<=>(~old(X)&old(X))))&
(![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(?[X]:((calm(X)&wise(X))))&
((~humble(fred)&kind(fred)))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~brave(X)))&
((humble(alice)<~>funny(alice)))&
((happy(lucy)<~>~patient(lucy))) | strong(lucy) | [] | null | 0 |
If someone is both not creative and humble then mary is either calm or not old and vice versa. Everyone who is either strong or old is both not creative and not curious. Everyone who is both not curious and humble is either humble or creative and vice versa. If lucy is calm then mary is not curious or curious and vice versa. Everyone who is not wise or strong is not creative and vice versa. If lucy is not brave or not curious then someone is not tall or not patient. Everyone who is both not curious and rich is both not creative and not kind. Everyone who is either not strong or not humble is both funny and not tall and vice versa. Everyone who is either creative or not wise is both strong and not curious and vice versa. Everyone who is both generous and not kind is both not tall and not funny and vice versa. Everyone who is not funny is both not generous and not brave. Everyone who is either not rich or not tall is not patient and vice versa. If paul is both strong and not happy then lucy is not old or not rich. If fred is either creative or not generous then alice is both not strong and curious. Everyone who is happy is both old and not funny. Everyone who is not kind is both humble and kind and vice versa. Lucy is not curious. Someone is both quiet and not calm. Someone is strong or not happy. | Paul is not funny. | contradiction | ((?[X]:((~creative(X)&humble(X))))<=>((calm(mary)<~>~old(mary))))&
(![X]:((strong(X)<~>old(X))=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&humble(X))<=>(humble(X)<~>creative(X))))&
((calm(lucy))<=>((~curious(mary)|curious(mary))))&
(![X]:((~wise(X)|strong(X))<=>~creative(X)))&
(((~brave(lucy)|~curious(lucy)))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((~curious(X)&rich(X))=>(~creative(X)&~kind(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(funny(X)&~tall(X))))&
(![X]:((creative(X)<~>~wise(X))<=>(strong(X)&~curious(X))))&
(![X]:((generous(X)&~kind(X))<=>(~tall(X)&~funny(X))))&
(![X]:(~funny(X)=>(~generous(X)&~brave(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>~patient(X)))&
(((strong(paul)&~happy(paul)))=>((~old(lucy)|~rich(lucy))))&
(((creative(fred)<~>~generous(fred)))=>((~strong(alice)&curious(alice))))&
(![X]:(happy(X)=>(old(X)&~funny(X))))&
(![X]:(~kind(X)<=>(humble(X)&kind(X))))&
(~curious(lucy))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((strong(X)|~happy(X)))) | ~funny(paul) | [
"p0",
"p2",
"p4",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2500761312872998379152
% SZS output start Proof for 2500761312872998379152
1. ? [X0] : (humble(X0) & ~creative(X0)) <=> (calm(mary) <~> ~old(mary)) [input p0]
3. ! [X0] : ((humble(X0) & ~curious(X0)) <=> (humble(X0) <~> creative(X0))) [input p2]
5. ! [X0] : ((strong(X0) | ~wise(X0)) <=> ~creative(X0)) [input p4]
8. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (~tall(X0) & funny(X0))) [input p7]
9. ! [X0] : ((creative(X0) <~> ~wise(X0)) <=> (~curious(X0) & strong(X0))) [input p8]
16. ! [X0] : (~kind(X0) <=> (kind(X0) & humble(X0))) [input p15]
20. ~funny(paul) [input hypothesis]
33. (? [X0] : (humble(X0) & ~creative(X0)) | ((calm(mary) | old(mary)) & (~old(mary) | ~calm(mary)))) & (((old(mary) | ~calm(mary)) & (~old(mary) | calm(mary))) | ! [X0] : (~humble(X0) | creative(X0))) [nnf transformation 1]
34. (? [X0] : (humble(X0) & ~creative(X0)) | ((calm(mary) | old(mary)) & (~old(mary) | ~calm(mary)))) & (((old(mary) | ~calm(mary)) & (~old(mary) | calm(mary))) | ! [X1] : (~humble(X1) | creative(X1))) [rectify 33]
35. ? [X0] : (humble(X0) & ~creative(X0)) => (humble(sK0) & ~creative(sK0)) [choice axiom]
36. ((humble(sK0) & ~creative(sK0)) | ((calm(mary) | old(mary)) & (~old(mary) | ~calm(mary)))) & (((old(mary) | ~calm(mary)) & (~old(mary) | calm(mary))) | ! [X1] : (~humble(X1) | creative(X1))) [skolemisation 34,35]
38. ! [X0] : (((humble(X0) & ~curious(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~humble(X0) | curious(X0)))) [nnf transformation 3]
39. ! [X0] : (((humble(X0) & ~curious(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ~humble(X0) | curious(X0))) [flattening 38]
42. ! [X0] : (((strong(X0) | ~wise(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) & wise(X0)))) [nnf transformation 5]
43. ! [X0] : ((strong(X0) | ~wise(X0) | creative(X0)) & (~creative(X0) | (~strong(X0) & wise(X0)))) [flattening 42]
46. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 8]
47. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 46]
48. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (curious(X0) | ~strong(X0))) & ((~curious(X0) & strong(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [nnf transformation 9]
49. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | curious(X0) | ~strong(X0)) & ((~curious(X0) & strong(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [flattening 48]
54. ! [X0] : ((~kind(X0) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | kind(X0))) [nnf transformation 16]
55. ! [X0] : ((~kind(X0) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | kind(X0))) [flattening 54]
60. ~old(mary) | calm(mary) | ~humble(X1) | creative(X1) [cnf transformation 36]
61. old(mary) | ~calm(mary) | ~humble(X1) | creative(X1) [cnf transformation 36]
64. humble(sK0) | ~old(mary) | ~calm(mary) [cnf transformation 36]
65. humble(sK0) | calm(mary) | old(mary) [cnf transformation 36]
71. ~creative(X0) | ~humble(X0) | ~humble(X0) | curious(X0) [cnf transformation 39]
75. humble(X0) | humble(X0) | ~creative(X0) [cnf transformation 39]
79. ~creative(X0) | wise(X0) [cnf transformation 43]
81. ~wise(X0) | strong(X0) | creative(X0) [cnf transformation 43]
87. ~strong(X0) | funny(X0) | humble(X0) [cnf transformation 47]
93. strong(X0) | creative(X0) | wise(X0) [cnf transformation 49]
94. ~curious(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 49]
114. kind(X0) | kind(X0) [cnf transformation 55]
115. ~kind(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 55]
119. ~funny(paul) [cnf transformation 20]
120. kind(X0) [duplicate literal removal 114]
121. ~kind(X0) | ~humble(X0) [duplicate literal removal 115]
122. ~creative(X0) | ~humble(X0) | curious(X0) [duplicate literal removal 71]
123. ~creative(X0) | humble(X0) [duplicate literal removal 75]
125. 1 <=> old(mary) [avatar definition]
129. 2 <=> calm(mary) [avatar definition]
133. 3 <=> humble(sK0) [avatar definition]
135. humble(sK0) <- (3) [avatar component clause 133]
136. 1 | 2 | 3 [avatar split clause 65,133,129,125]
137. ~2 | ~1 | 3 [avatar split clause 64,133,125,129]
145. 5 <=> ! [X1] : (~humble(X1) | creative(X1)) [avatar definition]
146. ~humble(X1) | creative(X1) <- (5) [avatar component clause 145]
147. 5 | ~2 | 1 [avatar split clause 61,125,129,145]
148. 5 | 2 | ~1 [avatar split clause 60,125,129,145]
149. ~creative(X0) | curious(X0) [subsumption resolution 122,123]
180. ~wise(X0) | ~creative(X0) [subsumption resolution 94,149]
181. ~creative(X0) [subsumption resolution 180,79]
182. wise(X0) | strong(X0) [subsumption resolution 93,181]
226. ~humble(X1) <- (5) [subsumption resolution 146,181]
228. ~humble(X0) [resolution 121,120]
230. strong(X0) | creative(X0) | strong(X0) [resolution 81,182]
231. strong(X0) | creative(X0) [duplicate literal removal 230]
232. strong(X0) [subsumption resolution 231,181]
236. funny(X0) | humble(X0) [resolution 87,232]
237. funny(X0) <- (5) [subsumption resolution 236,226]
238. $false <- (5) [resolution 237,119]
239. ~5 [avatar contradiction clause 238]
240. $false <- (3) [subsumption resolution 135,228]
241. ~3 [avatar contradiction clause 240]
242. $false [avatar sat refutation 136,137,147,148,239,241]
% SZS output end Proof for 2500761312872998379152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not tall is not brave.
Everyone who is calm or quiet is old.
Everyone who is not humble is both rich and funny.
Everyone who is either tall or not quiet is rich or happy and vice versa.
Everyone who is brave or not patient is both not generous and strong and vice versa.
Everyone who is wise is either quiet or not generous and vice versa.
If john is humble then someone is both old and curious.
If someone is both generous and not rich then alice is not generous and vice versa.
Everyone who is humble or not calm is not wise and vice versa.
Everyone who is rich or not curious is both brave and not old and vice versa.
Everyone who is both not quiet and not patient is creative or tall.
If lucy is either not generous or not quiet then someone is both curious and not calm.
If lucy is both creative and not kind then lucy is either not quiet or kind.
Everyone who is not happy or not creative is both kind and not calm.
If alice is either not kind or not funny then lucy is both not kind and not humble and vice versa.
Everyone who is not humble or not happy is quiet.
Fred is both happy and brave.
Alice is both curious and not creative.
Someone is tall or not kind.
Susan is either quiet or creative.
Someone is brave or not humble.
Fred is patient.
Lucy is curious. | Fred is old. | entailment | (![X]:((~old(X)<~>~tall(X))=>~brave(X)))&
(![X]:((calm(X)|quiet(X))=>old(X)))&
(![X]:(~humble(X)=>(rich(X)&funny(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>(rich(X)|happy(X))))&
(![X]:((brave(X)|~patient(X))<=>(~generous(X)&strong(X))))&
(![X]:(wise(X)<=>(quiet(X)<~>~generous(X))))&
((humble(john))=>(?[X]:((old(X)&curious(X)))))&
((?[X]:((generous(X)&~rich(X))))<=>(~generous(alice)))&
(![X]:((humble(X)|~calm(X))<=>~wise(X)))&
(![X]:((rich(X)|~curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~quiet(X)&~patient(X))=>(creative(X)|tall(X))))&
(((~generous(lucy)<~>~quiet(lucy)))=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(lucy)&~kind(lucy)))=>((~quiet(lucy)<~>kind(lucy))))&
(![X]:((~happy(X)|~creative(X))=>(kind(X)&~calm(X))))&
(((~kind(alice)<~>~funny(alice)))<=>((~kind(lucy)&~humble(lucy))))&
(![X]:((~humble(X)|~happy(X))=>quiet(X)))&
((happy(fred)&brave(fred)))&
((curious(alice)&~creative(alice)))&
(?[X]:((tall(X)|~kind(X))))&
((quiet(susan)<~>creative(susan)))&
(?[X]:((brave(X)|~humble(X))))&
(patient(fred))&
(curious(lucy)) | old(fred) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8360014816127638934658921
% SZS output start Proof for 8360014816127638934658921
1. ! [X0] : ((~old(X0) <~> ~tall(X0)) => ~brave(X0)) [input p0]
4. ! [X0] : ((tall(X0) <~> ~quiet(X0)) <=> (happy(X0) | rich(X0))) [input p3]
5. ! [X0] : ((~patient(X0) | brave(X0)) <=> (strong(X0) & ~generous(X0))) [input p4]
6. ! [X0] : (wise(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p5]
9. ! [X0] : ((~calm(X0) | humble(X0)) <=> ~wise(X0)) [input p8]
16. ! [X0] : ((~happy(X0) | ~humble(X0)) => quiet(X0)) [input p15]
17. brave(fred) & happy(fred) [input p16]
24. ~old(fred) [input hypothesis]
25. ! [X0] : (~brave(X0) | (~old(X0) <=> ~tall(X0))) [ennf transformation 1]
35. ! [X0] : (quiet(X0) | (happy(X0) & humble(X0))) [ennf transformation 16]
36. ! [X0] : (~brave(X0) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) [nnf transformation 25]
37. ! [X0] : ((((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))))) [nnf transformation 4]
38. ! [X0] : ((((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))))) [flattening 37]
39. ! [X0] : (((~patient(X0) | brave(X0)) | (~strong(X0) | generous(X0))) & ((strong(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 5]
40. ! [X0] : ((~patient(X0) | brave(X0) | ~strong(X0) | generous(X0)) & ((strong(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [flattening 39]
41. ! [X0] : ((wise(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~wise(X0))) [nnf transformation 6]
48. ! [X0] : (((~calm(X0) | humble(X0)) | wise(X0)) & (~wise(X0) | (calm(X0) & ~humble(X0)))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | humble(X0) | wise(X0)) & (~wise(X0) | (calm(X0) & ~humble(X0)))) [flattening 48]
63. ~brave(X0) | ~tall(X0) | old(X0) [cnf transformation 36]
72. ~happy(X0) | tall(X0) | ~quiet(X0) [cnf transformation 38]
75. ~generous(X0) | ~brave(X0) [cnf transformation 40]
83. wise(X0) | quiet(X0) | generous(X0) [cnf transformation 41]
89. ~wise(X0) | ~humble(X0) [cnf transformation 49]
114. humble(X0) | quiet(X0) [cnf transformation 35]
116. happy(fred) [cnf transformation 17]
117. brave(fred) [cnf transformation 17]
126. ~old(fred) [cnf transformation 24]
264. ~tall(fred) | old(fred) [resolution 63,117]
265. ~tall(fred) [subsumption resolution 264,126]
270. tall(fred) | ~quiet(fred) [resolution 72,116]
273. ~quiet(fred) [subsumption resolution 270,265]
303. quiet(X3) | generous(X3) | ~humble(X3) [resolution 83,89]
306. generous(X3) | quiet(X3) [subsumption resolution 303,114]
468. ~brave(X2) | quiet(X2) [resolution 306,75]
531. quiet(fred) [resolution 468,117]
533. $false [subsumption resolution 531,273]
% SZS output end Proof for 8360014816127638934658921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is funny or not tall.
If someone is either not calm or not kind then susan is both not kind and kind.
Everyone who is humble or wise is either not humble or strong and vice versa.
Everyone who is generous or wise is old and vice versa.
If someone is not creative or creative then fred is both not creative and not strong.
Everyone who is not old or tall is not funny.
Everyone who is not wise is both not rich and rich and vice versa.
Everyone who is either wise or not curious is not calm or wise and vice versa.
If paul is not kind or brave then someone is both not funny and not brave and vice versa.
If someone is not curious or strong then mary is both patient and curious and vice versa.
Everyone who is both quiet and not happy is both not creative and generous and vice versa.
Everyone who is either not patient or not quiet is not creative.
Everyone who is tall or wise is not patient or funny and vice versa.
Everyone who is both happy and brave is both patient and not wise and vice versa.
Everyone who is both wise and tall is both not calm and strong and vice versa.
Fred is either strong or not patient.
Susan is not tall.
Someone is funny or creative.
Someone is either strong or creative.
Susan is not rich.
Someone is either tall or generous.
John is both rich and not funny. | Fred is strong. | contradiction | (![X]:(~funny(X)=>(funny(X)|~tall(X))))&
((?[X]:((~calm(X)<~>~kind(X))))=>((~kind(susan)&kind(susan))))&
(![X]:((humble(X)|wise(X))<=>(~humble(X)<~>strong(X))))&
(![X]:((generous(X)|wise(X))<=>old(X)))&
((?[X]:((~creative(X)|creative(X))))=>((~creative(fred)&~strong(fred))))&
(![X]:((~old(X)|tall(X))=>~funny(X)))&
(![X]:(~wise(X)<=>(~rich(X)&rich(X))))&
(![X]:((wise(X)<~>~curious(X))<=>(~calm(X)|wise(X))))&
(((~kind(paul)|brave(paul)))<=>(?[X]:((~funny(X)&~brave(X)))))&
((?[X]:((~curious(X)|strong(X))))<=>((patient(mary)&curious(mary))))&
(![X]:((quiet(X)&~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~patient(X)<~>~quiet(X))=>~creative(X)))&
(![X]:((tall(X)|wise(X))<=>(~patient(X)|funny(X))))&
(![X]:((happy(X)&brave(X))<=>(patient(X)&~wise(X))))&
(![X]:((wise(X)&tall(X))<=>(~calm(X)&strong(X))))&
((strong(fred)<~>~patient(fred)))&
(~tall(susan))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((strong(X)<~>creative(X))))&
(~rich(susan))&
(?[X]:((tall(X)<~>generous(X))))&
((rich(john)&~funny(john))) | strong(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1169290592063860167760517
% SZS output start Proof for 1169290592063860167760517
5. ? [X0] : (creative(X0) | ~creative(X0)) => (~strong(fred) & ~creative(fred)) [input p4]
23. strong(fred) [input hypothesis]
30. (~strong(fred) & ~creative(fred)) | ! [X0] : (~creative(X0) & creative(X0)) [ennf transformation 5]
82. ~strong(fred) | creative(X0) [cnf transformation 30]
83. ~strong(fred) | ~creative(X0) [cnf transformation 30]
134. strong(fred) [cnf transformation 23]
155. 4 <=> ! [X0] : ~creative(X0) [avatar definition]
156. ~creative(X0) <- (4) [avatar component clause 155]
158. 5 <=> strong(fred) [avatar definition]
161. 4 | ~5 [avatar split clause 83,158,155]
163. 6 <=> ! [X0] : creative(X0) [avatar definition]
164. creative(X0) <- (6) [avatar component clause 163]
165. 6 | ~5 [avatar split clause 82,158,163]
243. 5 [avatar split clause 134,158]
244. $false <- (4, 6) [subsumption resolution 156,164]
245. ~4 | ~6 [avatar contradiction clause 244]
246. $false [avatar sat refutation 161,165,243,245]
% SZS output end Proof for 1169290592063860167760517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and rich is either brave or creative.
If someone is not rich then someone is both creative and quiet and vice versa.
If alice is both not tall and not creative then lucy is not funny and vice versa.
Everyone who is either old or funny is either not old or not tall and vice versa.
If susan is both wise and not tall then someone is strong and vice versa.
Everyone who is either strong or calm is either calm or old and vice versa.
If someone is either not funny or not patient then lucy is both not rich and rich and vice versa.
Everyone who is both not patient and quiet is not kind and vice versa.
If someone is strong or kind then paul is not brave or humble.
If someone is both not rich and patient then fred is not curious.
Everyone who is not old or not brave is not brave or not happy and vice versa.
If someone is kind or creative then paul is not creative or funny and vice versa.
Everyone who is not tall is funny.
If mary is either not happy or not rich then mary is not kind or humble.
If paul is both creative and not kind then someone is both not tall and not old.
Everyone who is both happy and not wise is either not generous or quiet and vice versa.
Someone is both not generous and curious.
Susan is either not brave or old.
Fred is happy or creative.
Alice is not wise or not brave.
Fred is either not old or not wise.
Someone is either happy or calm.
Fred is either not tall or curious.
Paul is old or not old. | Fred is not wise. | contradiction | (![X]:((~wise(X)&rich(X))=>(brave(X)<~>creative(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((creative(X)&quiet(X)))))&
(((~tall(alice)&~creative(alice)))<=>(~funny(lucy)))&
(![X]:((old(X)<~>funny(X))<=>(~old(X)<~>~tall(X))))&
(((wise(susan)&~tall(susan)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)<~>calm(X))<=>(calm(X)<~>old(X))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>((~rich(lucy)&rich(lucy))))&
(![X]:((~patient(X)&quiet(X))<=>~kind(X)))&
((?[X]:((strong(X)|kind(X))))=>((~brave(paul)|humble(paul))))&
((?[X]:((~rich(X)&patient(X))))=>(~curious(fred)))&
(![X]:((~old(X)|~brave(X))<=>(~brave(X)|~happy(X))))&
((?[X]:((kind(X)|creative(X))))<=>((~creative(paul)|funny(paul))))&
(![X]:(~tall(X)=>funny(X)))&
(((~happy(mary)<~>~rich(mary)))=>((~kind(mary)|humble(mary))))&
(((creative(paul)&~kind(paul)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((happy(X)&~wise(X))<=>(~generous(X)<~>quiet(X))))&
(?[X]:((~generous(X)&curious(X))))&
((~brave(susan)<~>old(susan)))&
((happy(fred)|creative(fred)))&
((~wise(alice)|~brave(alice)))&
((~old(fred)<~>~wise(fred)))&
(?[X]:((happy(X)<~>calm(X))))&
((~tall(fred)<~>curious(fred)))&
((old(paul)|~old(paul))) | ~wise(fred) | [
"p3",
"p4",
"p5",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3781381401611498402153577
% SZS output start Proof for 3781381401611498402153577
4. ! [X0] : ((old(X0) <~> funny(X0)) <=> (~old(X0) <~> ~tall(X0))) [input p3]
5. (~tall(susan) & wise(susan)) <=> ? [X0] : strong(X0) [input p4]
6. ! [X0] : ((strong(X0) <~> calm(X0)) <=> (calm(X0) <~> old(X0))) [input p5]
13. ! [X0] : (~tall(X0) => funny(X0)) [input p12]
21. ~old(fred) <~> ~wise(fred) [input p20]
25. ~wise(fred) [input hypothesis]
32. ! [X0] : (funny(X0) | tall(X0)) [ennf transformation 13]
43. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 4]
44. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (tall(susan) | ~wise(susan))) [nnf transformation 5]
45. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | tall(susan) | ~wise(susan)) [flattening 44]
46. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | tall(susan) | ~wise(susan)) [rectify 45]
47. ? [X1] : strong(X1) => strong(sK2) [choice axiom]
48. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (strong(sK2) | tall(susan) | ~wise(susan)) [skolemisation 46,47]
49. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0)))) & (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [nnf transformation 6]
71. (wise(fred) | old(fred)) & (~wise(fred) | ~old(fred)) [nnf transformation 21]
87. tall(X0) | old(X0) | old(X0) | ~funny(X0) [cnf transformation 43]
91. ~funny(X0) | ~old(X0) | ~old(X0) | tall(X0) [cnf transformation 43]
94. ~tall(susan) | ~strong(X0) [cnf transformation 48]
98. ~old(X0) | ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 49]
100. calm(X0) | strong(X0) | calm(X0) | ~old(X0) [cnf transformation 49]
121. funny(X0) | tall(X0) [cnf transformation 32]
137. wise(fred) | old(fred) [cnf transformation 71]
143. ~wise(fred) [cnf transformation 25]
145. ~old(X0) | ~calm(X0) | strong(X0) [duplicate literal removal 98]
146. calm(X0) | strong(X0) | ~old(X0) [duplicate literal removal 100]
149. tall(X0) | old(X0) | ~funny(X0) [duplicate literal removal 87]
151. ~funny(X0) | ~old(X0) | tall(X0) [duplicate literal removal 91]
188. ~funny(X0) | tall(X0) [subsumption resolution 149,151]
191. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
192. ~strong(X0) <- (9) [avatar component clause 191]
194. 10 <=> tall(susan) [avatar definition]
196. ~tall(susan) <- (~10) [avatar component clause 194]
197. 9 | ~10 [avatar split clause 94,194,191]
208. ~old(X0) | strong(X0) [subsumption resolution 145,146]
258. tall(X0) [subsumption resolution 121,188]
299. 32 <=> old(fred) [avatar definition]
301. old(fred) <- (32) [avatar component clause 299]
303. 33 <=> wise(fred) [avatar definition]
306. 32 | 33 [avatar split clause 137,303,299]
320. ~33 [avatar split clause 143,303]
325. strong(fred) <- (32) [resolution 208,301]
326. $false <- (9, 32) [subsumption resolution 325,192]
327. ~9 | ~32 [avatar contradiction clause 326]
328. $false <- (~10) [subsumption resolution 196,258]
329. 10 [avatar contradiction clause 328]
330. $false [avatar sat refutation 197,306,320,327,329]
% SZS output end Proof for 3781381401611498402153577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and wise then someone is not quiet.
If someone is patient or tall then someone is both not tall and not strong.
Everyone who is not wise or not patient is either old or humble.
Everyone who is not kind is either humble or not creative and vice versa.
Everyone who is either not old or not brave is curious or tall.
Everyone who is either not humble or happy is both not brave and not wise and vice versa.
If fred is not strong then mary is both curious and not tall and vice versa.
If someone is not patient then mary is both old and not wise and vice versa.
Everyone who is both not old and humble is funny.
Everyone who is funny is both creative and not humble and vice versa.
Everyone who is rich or not wise is either not wise or funny and vice versa.
Everyone who is not rich or not calm is both wise and not funny and vice versa.
Everyone who is either tall or not funny is either not rich or strong and vice versa.
Everyone who is either not rich or patient is either not rich or not wise and vice versa.
Everyone who is not generous or not wise is either not generous or kind.
Someone is not brave or not rich.
Paul is either happy or not tall.
Paul is not curious or curious.
Alice is tall or strong.
Paul is either kind or tall.
Alice is rich. | Paul is not creative. | entailment | ((?[X]:((tall(X)&wise(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((patient(X)|tall(X))))=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~wise(X)|~patient(X))=>(old(X)<~>humble(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)<~>~brave(X))=>(curious(X)|tall(X))))&
(![X]:((~humble(X)<~>happy(X))<=>(~brave(X)&~wise(X))))&
((~strong(fred))<=>((curious(mary)&~tall(mary))))&
((?[X]:(~patient(X)))<=>((old(mary)&~wise(mary))))&
(![X]:((~old(X)&humble(X))=>funny(X)))&
(![X]:(funny(X)<=>(creative(X)&~humble(X))))&
(![X]:((rich(X)|~wise(X))<=>(~wise(X)<~>funny(X))))&
(![X]:((~rich(X)|~calm(X))<=>(wise(X)&~funny(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~generous(X)|~wise(X))=>(~generous(X)<~>kind(X))))&
(?[X]:((~brave(X)|~rich(X))))&
((happy(paul)<~>~tall(paul)))&
((~curious(paul)|curious(paul)))&
((tall(alice)|strong(alice)))&
((kind(paul)<~>tall(paul)))&
(rich(alice)) | ~creative(paul) | [
"p2",
"p3",
"p5",
"p8",
"p9",
"p10",
"p11",
"p13",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3102479400639312557244564
% SZS output start Proof for 3102479400639312557244564
3. ! [X0] : ((~patient(X0) | ~wise(X0)) => (old(X0) <~> humble(X0))) [input p2]
4. ! [X0] : (~kind(X0) <=> (humble(X0) <~> ~creative(X0))) [input p3]
6. ! [X0] : ((~humble(X0) <~> happy(X0)) <=> (~wise(X0) & ~brave(X0))) [input p5]
9. ! [X0] : ((humble(X0) & ~old(X0)) => funny(X0)) [input p8]
10. ! [X0] : (funny(X0) <=> (~humble(X0) & creative(X0))) [input p9]
11. ! [X0] : ((~wise(X0) | rich(X0)) <=> (~wise(X0) <~> funny(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~funny(X0) & wise(X0))) [input p11]
14. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p13]
17. happy(paul) <~> ~tall(paul) [input p16]
20. kind(paul) <~> tall(paul) [input p19]
22. creative(paul) [input hypothesis]
27. ! [X0] : ((old(X0) <~> humble(X0)) | (patient(X0) & wise(X0))) [ennf transformation 3]
30. ! [X0] : (funny(X0) | (~humble(X0) | old(X0))) [ennf transformation 9]
31. ! [X0] : (funny(X0) | ~humble(X0) | old(X0)) [flattening 30]
36. ! [X0] : (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (patient(X0) & wise(X0))) [nnf transformation 27]
37. ! [X0] : ((~kind(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | kind(X0))) [nnf transformation 4]
39. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [nnf transformation 6]
40. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [flattening 39]
48. ! [X0] : ((funny(X0) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | ~funny(X0))) [nnf transformation 10]
49. ! [X0] : ((funny(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~funny(X0))) [flattening 48]
50. ! [X0] : (((~wise(X0) | rich(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (wise(X0) & ~rich(X0)))) [nnf transformation 11]
51. ! [X0] : ((~wise(X0) | rich(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) & (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (wise(X0) & ~rich(X0)))) [flattening 50]
52. ! [X0] : (((~calm(X0) | ~rich(X0)) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | (calm(X0) & rich(X0)))) [nnf transformation 12]
53. ! [X0] : ((~calm(X0) | ~rich(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | (calm(X0) & rich(X0)))) [flattening 52]
55. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 14]
59. (tall(paul) | ~happy(paul)) & (~tall(paul) | happy(paul)) [nnf transformation 17]
60. (~tall(paul) | ~kind(paul)) & (tall(paul) | kind(paul)) [nnf transformation 20]
66. humble(X0) | old(X0) | patient(X0) [cnf transformation 36]
67. ~humble(X0) | ~old(X0) | wise(X0) [cnf transformation 36]
68. ~humble(X0) | ~old(X0) | patient(X0) [cnf transformation 36]
69. ~creative(X0) | humble(X0) | kind(X0) [cnf transformation 37]
71. ~creative(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 37]
77. ~wise(X0) | happy(X0) | humble(X0) [cnf transformation 40]
78. ~happy(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 40]
87. ~humble(X0) | funny(X0) | old(X0) [cnf transformation 31]
90. ~creative(X0) | humble(X0) | funny(X0) [cnf transformation 49]
94. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 51]
97. rich(X0) | wise(X0) [cnf transformation 53]
111. ~wise(X0) | ~rich(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 55]
116. ~patient(X0) | rich(X0) | ~wise(X0) | rich(X0) [cnf transformation 55]
123. ~tall(paul) | happy(paul) [cnf transformation 59]
124. tall(paul) | ~happy(paul) [cnf transformation 59]
127. tall(paul) | kind(paul) [cnf transformation 60]
128. ~tall(paul) | ~kind(paul) [cnf transformation 60]
130. creative(paul) [cnf transformation 22]
132. ~wise(X0) | ~rich(X0) | ~patient(X0) [duplicate literal removal 111]
135. ~patient(X0) | rich(X0) | ~wise(X0) [duplicate literal removal 116]
136. ~funny(X0) | wise(X0) [duplicate literal removal 94]
193. ~patient(X0) | rich(X0) [subsumption resolution 135,97]
195. ~patient(X0) | ~wise(X0) [subsumption resolution 132,193]
206. 14 <=> happy(paul) [avatar definition]
207. happy(paul) <- (14) [avatar component clause 206]
208. ~happy(paul) <- (~14) [avatar component clause 206]
210. 15 <=> tall(paul) [avatar definition]
213. ~14 | 15 [avatar split clause 124,210,206]
214. 14 | ~15 [avatar split clause 123,210,206]
225. 18 <=> kind(paul) [avatar definition]
227. ~kind(paul) <- (~18) [avatar component clause 225]
228. ~18 | ~15 [avatar split clause 128,210,225]
229. 18 | 15 [avatar split clause 127,210,225]
240. humble(paul) | kind(paul) [resolution 69,130]
241. humble(paul) <- (~18) [subsumption resolution 240,227]
245. ~old(paul) | patient(paul) <- (~18) [resolution 241,68]
246. ~old(paul) | wise(paul) <- (~18) [resolution 241,67]
248. 19 <=> patient(paul) [avatar definition]
250. patient(paul) <- (19) [avatar component clause 248]
252. 20 <=> old(paul) [avatar definition]
254. ~old(paul) <- (~20) [avatar component clause 252]
255. 19 | ~20 | 18 [avatar split clause 245,225,252,248]
257. 21 <=> wise(paul) [avatar definition]
258. ~wise(paul) <- (~21) [avatar component clause 257]
259. wise(paul) <- (21) [avatar component clause 257]
260. 21 | ~20 | 18 [avatar split clause 246,225,252,257]
261. ~kind(paul) | ~humble(paul) [resolution 71,130]
339. humble(paul) | funny(paul) [resolution 90,130]
415. 41 <=> funny(paul) [avatar definition]
416. ~funny(paul) <- (~41) [avatar component clause 415]
417. funny(paul) <- (41) [avatar component clause 415]
419. 42 <=> humble(paul) [avatar definition]
420. ~humble(paul) <- (~42) [avatar component clause 419]
421. humble(paul) <- (42) [avatar component clause 419]
422. 41 | 42 [avatar split clause 339,419,415]
423. ~42 | ~18 [avatar split clause 261,225,419]
424. 18 | 42 [avatar split clause 240,419,225]
438. ~humble(paul) | ~wise(paul) <- (14) [resolution 207,78]
440. ~wise(paul) <- (14, 42) [subsumption resolution 438,421]
441. ~21 | ~14 | ~42 [avatar split clause 440,419,206,257]
462. wise(paul) <- (41) [resolution 417,136]
467. $false <- (~21, 41) [subsumption resolution 462,258]
468. 21 | ~41 [avatar contradiction clause 467]
476. funny(paul) | old(paul) <- (42) [resolution 421,87]
480. old(paul) <- (~41, 42) [subsumption resolution 476,416]
481. $false <- (~20, ~41, 42) [subsumption resolution 480,254]
482. 20 | 41 | ~42 [avatar contradiction clause 481]
497. old(paul) | patient(paul) <- (~42) [resolution 420,66]
499. 19 | 20 | 42 [avatar split clause 497,419,252,248]
547. ~wise(paul) <- (19) [resolution 250,195]
549. $false <- (19, 21) [subsumption resolution 547,259]
550. ~19 | ~21 [avatar contradiction clause 549]
604. happy(paul) | humble(paul) <- (21) [resolution 259,77]
605. humble(paul) <- (~14, 21) [subsumption resolution 604,208]
606. $false <- (~14, 21, ~42) [subsumption resolution 605,420]
607. 14 | ~21 | 42 [avatar contradiction clause 606]
608. $false [avatar sat refutation 213,214,228,229,255,260,422,423,424,441,468,482,499,550,607]
% SZS output end Proof for 3102479400639312557244564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or brave is rich.
If paul is wise or not strong then susan is rich.
If someone is both not humble and happy then someone is funny.
Everyone who is either not funny or humble is either not strong or not humble and vice versa.
Everyone who is not happy is humble and vice versa.
Everyone who is either not strong or happy is not happy or brave and vice versa.
If someone is tall or quiet then someone is either quiet or generous and vice versa.
If someone is either quiet or not curious then someone is both not humble and quiet.
Everyone who is kind is curious or not old and vice versa.
If someone is either not generous or wise then someone is either not happy or not brave and vice versa.
Everyone who is both not humble and not curious is not humble.
If john is both humble and kind then someone is either old or brave.
Everyone who is not calm or not quiet is either not brave or not calm and vice versa.
Everyone who is either quiet or rich is either not old or not curious.
John is either not generous or quiet.
Someone is not brave or rich.
John is wise or humble.
Lucy is either quiet or not strong.
Alice is both not curious and not generous.
Susan is either rich or not patient. | Paul is not rich. | contradiction | (![X]:((~brave(X)<~>brave(X))=>rich(X)))&
(((wise(paul)|~strong(paul)))=>(rich(susan)))&
((?[X]:((~humble(X)&happy(X))))=>(?[X]:(funny(X))))&
(![X]:((~funny(X)<~>humble(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:(~happy(X)<=>humble(X)))&
(![X]:((~strong(X)<~>happy(X))<=>(~happy(X)|brave(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:(kind(X)<=>(curious(X)|~old(X))))&
((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((~happy(X)<~>~brave(X)))))&
(![X]:((~humble(X)&~curious(X))=>~humble(X)))&
(((humble(john)&kind(john)))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>rich(X))=>(~old(X)<~>~curious(X))))&
((~generous(john)<~>quiet(john)))&
(?[X]:((~brave(X)|rich(X))))&
((wise(john)|humble(john)))&
((quiet(lucy)<~>~strong(lucy)))&
((~curious(alice)&~generous(alice)))&
((rich(susan)<~>~patient(susan))) | ~rich(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3861128542874857888771161
% SZS output start Proof for 3861128542874857888771161
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => rich(X0)) [input p0]
21. ~rich(paul) [input hypothesis]
27. ! [X0] : (rich(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
37. ! [X0] : (rich(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 27]
70. rich(X0) | brave(X0) | brave(X0) [cnf transformation 37]
71. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
134. ~rich(paul) [cnf transformation 21]
143. rich(X0) | brave(X0) [duplicate literal removal 70]
144. rich(X0) | ~brave(X0) [duplicate literal removal 71]
145. rich(X0) [subsumption resolution 143,144]
291. $false [subsumption resolution 134,145]
% SZS output end Proof for 3861128542874857888771161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or strong then john is not rich.
Everyone who is not old is not tall and vice versa.
Everyone who is both not generous and not old is both curious and not old and vice versa.
Everyone who is not rich or not funny is calm and vice versa.
If susan is not brave or rich then someone is either curious or not old and vice versa.
Everyone who is both not wise and not kind is either funny or quiet and vice versa.
Everyone who is not kind or rich is both not creative and humble.
If lucy is generous then someone is either kind or not creative.
Everyone who is either creative or not generous is rich or humble and vice versa.
If alice is not calm then someone is tall.
Everyone who is both not generous and not calm is not curious or old and vice versa.
If john is both calm and old then someone is both happy and curious.
Everyone who is either not kind or humble is both old and strong.
Everyone who is either not rich or not calm is both not wise and creative.
Everyone who is not generous or not humble is either not wise or strong and vice versa.
If susan is either not tall or not creative then someone is not creative.
Someone is either not strong or patient.
Someone is both not quiet and not patient.
Someone is either patient or not tall.
Someone is not humble.
Mary is either strong or funny.
Someone is either curious or not humble.
Someone is both not happy and rich. | Susan is strong. | contradiction | ((?[X]:((~rich(X)|strong(X))))=>(~rich(john)))&
(![X]:(~old(X)<=>~tall(X)))&
(![X]:((~generous(X)&~old(X))<=>(curious(X)&~old(X))))&
(![X]:((~rich(X)|~funny(X))<=>calm(X)))&
(((~brave(susan)|rich(susan)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~wise(X)&~kind(X))<=>(funny(X)<~>quiet(X))))&
(![X]:((~kind(X)|rich(X))=>(~creative(X)&humble(X))))&
((generous(lucy))=>(?[X]:((kind(X)<~>~creative(X)))))&
(![X]:((creative(X)<~>~generous(X))<=>(rich(X)|humble(X))))&
((~calm(alice))=>(?[X]:(tall(X))))&
(![X]:((~generous(X)&~calm(X))<=>(~curious(X)|old(X))))&
(((calm(john)&old(john)))=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((~kind(X)<~>humble(X))=>(old(X)&strong(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~wise(X)&creative(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~wise(X)<~>strong(X))))&
(((~tall(susan)<~>~creative(susan)))=>(?[X]:(~creative(X))))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((~quiet(X)&~patient(X))))&
(?[X]:((patient(X)<~>~tall(X))))&
(?[X]:(~humble(X)))&
((strong(mary)<~>funny(mary)))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:((~happy(X)&rich(X)))) | strong(susan) | [
"p2",
"p3",
"p4",
"p6",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5672467691537085605597465
% SZS output start Proof for 5672467691537085605597465
3. ! [X0] : ((~old(X0) & ~generous(X0)) <=> (~old(X0) & curious(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> calm(X0)) [input p3]
5. (rich(susan) | ~brave(susan)) <=> ? [X0] : (curious(X0) <~> ~old(X0)) [input p4]
7. ! [X0] : ((rich(X0) | ~kind(X0)) => (humble(X0) & ~creative(X0))) [input p6]
11. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (old(X0) | ~curious(X0))) [input p10]
14. ! [X0] : ((~rich(X0) <~> ~calm(X0)) => (creative(X0) & ~wise(X0))) [input p13]
15. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> (~wise(X0) <~> strong(X0))) [input p14]
24. strong(susan) [input hypothesis]
26. ! [X0] : ((humble(X0) & ~creative(X0)) | (~rich(X0) & kind(X0))) [ennf transformation 7]
32. ! [X0] : ((creative(X0) & ~wise(X0)) | (~rich(X0) <=> ~calm(X0))) [ennf transformation 14]
35. ! [X0] : (((~old(X0) & ~generous(X0)) | (old(X0) | ~curious(X0))) & ((~old(X0) & curious(X0)) | (old(X0) | generous(X0)))) [nnf transformation 3]
36. ! [X0] : (((~old(X0) & ~generous(X0)) | old(X0) | ~curious(X0)) & ((~old(X0) & curious(X0)) | old(X0) | generous(X0))) [flattening 35]
37. ! [X0] : (((~funny(X0) | ~rich(X0)) | ~calm(X0)) & (calm(X0) | (funny(X0) & rich(X0)))) [nnf transformation 4]
38. ! [X0] : ((~funny(X0) | ~rich(X0) | ~calm(X0)) & (calm(X0) | (funny(X0) & rich(X0)))) [flattening 37]
39. ((rich(susan) | ~brave(susan)) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (~rich(susan) & brave(susan))) [nnf transformation 5]
40. (rich(susan) | ~brave(susan) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (~rich(susan) & brave(susan))) [flattening 39]
41. (rich(susan) | ~brave(susan) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) | (~rich(susan) & brave(susan))) [rectify 40]
42. ? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) => ((old(sK0) | ~curious(sK0)) & (~old(sK0) | curious(sK0))) [choice axiom]
43. (rich(susan) | ~brave(susan) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(sK0) | ~curious(sK0)) & (~old(sK0) | curious(sK0))) | (~rich(susan) & brave(susan))) [skolemisation 41,42]
53. ! [X0] : (((~calm(X0) & ~generous(X0)) | (~old(X0) & curious(X0))) & ((old(X0) | ~curious(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~calm(X0) & ~generous(X0)) | (~old(X0) & curious(X0))) & (old(X0) | ~curious(X0) | calm(X0) | generous(X0))) [flattening 53]
58. ! [X0] : ((creative(X0) & ~wise(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0)))) [nnf transformation 32]
59. ! [X0] : (((~humble(X0) | ~generous(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | (humble(X0) & generous(X0)))) [nnf transformation 15]
60. ! [X0] : ((~humble(X0) | ~generous(X0) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | (humble(X0) & generous(X0)))) [flattening 59]
86. ~curious(X0) | old(X0) | ~generous(X0) [cnf transformation 36]
88. calm(X0) | rich(X0) [cnf transformation 38]
94. old(sK0) | ~curious(sK0) | ~rich(susan) [cnf transformation 43]
104. ~creative(X0) | ~rich(X0) [cnf transformation 26]
119. ~calm(X0) | curious(X0) [cnf transformation 54]
120. ~calm(X0) | ~old(X0) [cnf transformation 54]
127. ~wise(X0) | ~calm(X0) | rich(X0) [cnf transformation 58]
128. ~wise(X0) | ~rich(X0) | calm(X0) [cnf transformation 58]
130. creative(X0) | ~rich(X0) | calm(X0) [cnf transformation 58]
133. ~strong(X0) | wise(X0) | generous(X0) [cnf transformation 60]
152. strong(susan) [cnf transformation 24]
173. 6 <=> rich(susan) [avatar definition]
182. 8 <=> curious(sK0) [avatar definition]
184. ~curious(sK0) <- (~8) [avatar component clause 182]
186. 9 <=> old(sK0) [avatar definition]
188. old(sK0) <- (9) [avatar component clause 186]
189. ~6 | ~8 | 9 [avatar split clause 94,186,182,173]
219. creative(X0) | calm(X0) [subsumption resolution 130,88]
221. ~wise(X0) | calm(X0) [subsumption resolution 128,88]
222. ~wise(X0) | rich(X0) [subsumption resolution 127,221]
287. calm(X0) | ~rich(X0) [resolution 219,104]
289. calm(X0) [subsumption resolution 287,88]
295. ~old(X0) [resolution 289,120]
296. curious(X1) [resolution 289,119]
348. $false <- (~8) [resolution 296,184]
350. old(X0) | ~generous(X0) [resolution 296,86]
352. 8 [avatar contradiction clause 348]
353. ~generous(X0) [subsumption resolution 350,295]
380. wise(susan) | generous(susan) [resolution 133,152]
382. wise(susan) [subsumption resolution 380,353]
387. rich(susan) [resolution 382,222]
400. 6 [avatar split clause 387,173]
401. $false <- (9) [subsumption resolution 188,295]
402. ~9 [avatar contradiction clause 401]
403. $false [avatar sat refutation 189,352,400,402]
% SZS output end Proof for 5672467691537085605597465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not creative is both not patient and wise and vice versa.
If someone is not kind then someone is kind and vice versa.
If fred is both creative and not humble then someone is curious or patient and vice versa.
Everyone who is both not funny and not strong is patient or curious and vice versa.
If someone is both wise and calm then fred is both patient and not brave.
If john is not humble or not quiet then someone is either not kind or old.
Everyone who is both not humble and creative is either not funny or not patient and vice versa.
If someone is both not happy and not calm then mary is quiet or patient and vice versa.
If someone is not humble then fred is not kind or generous and vice versa.
Everyone who is both not creative and not rich is curious or rich.
Everyone who is not calm or not brave is either not rich or rich and vice versa.
Everyone who is not humble is either brave or calm and vice versa.
If fred is both not tall and calm then someone is both patient and not creative.
Everyone who is either funny or not humble is strong or not patient and vice versa.
Everyone who is either humble or not strong is humble and vice versa.
Everyone who is both curious and not generous is either not quiet or rich and vice versa.
Someone is either not happy or not generous.
Someone is both not creative and not calm.
Someone is not quiet.
Someone is rich or not brave. | Fred is not happy. | contradiction | (![X]:((~generous(X)|~creative(X))<=>(~patient(X)&wise(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X)))) | ~happy(fred) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7623474919377400451480051
% SZS output start Proof for 7623474919377400451480051
1. ! [X0] : ((~creative(X0) | ~generous(X0)) <=> (wise(X0) & ~patient(X0))) [input p0]
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p3]
5. ? [X0] : (calm(X0) & wise(X0)) => (~brave(fred) & patient(fred)) [input p4]
7. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p6]
8. ? [X0] : (~calm(X0) & ~happy(X0)) <=> (patient(mary) | quiet(mary)) [input p7]
10. ! [X0] : ((~rich(X0) & ~creative(X0)) => (rich(X0) | curious(X0))) [input p9]
11. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~rich(X0) <~> rich(X0))) [input p10]
12. ! [X0] : (~humble(X0) <=> (brave(X0) <~> calm(X0))) [input p11]
14. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p13]
15. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> humble(X0)) [input p14]
16. ! [X0] : ((~generous(X0) & curious(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p15]
21. ~happy(fred) [input hypothesis]
24. (~brave(fred) & patient(fred)) | ! [X0] : (~calm(X0) | ~wise(X0)) [ennf transformation 5]
26. ! [X0] : ((rich(X0) | curious(X0)) | (rich(X0) | creative(X0))) [ennf transformation 10]
27. ! [X0] : (rich(X0) | curious(X0) | rich(X0) | creative(X0)) [flattening 26]
28. ! [X0] : (((~creative(X0) | ~generous(X0)) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [nnf transformation 1]
29. ! [X0] : ((~creative(X0) | ~generous(X0) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [flattening 28]
40. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 40]
45. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & ((patient(mary) | quiet(mary)) | ! [X0] : (calm(X0) | happy(X0))) [nnf transformation 8]
48. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X0] : (calm(X0) | happy(X0))) [flattening 47]
49. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X1] : (calm(X1) | happy(X1))) [rectify 48]
50. ? [X0] : (~calm(X0) & ~happy(X0)) => (~calm(sK4) & ~happy(sK4)) [choice axiom]
51. ((~calm(sK4) & ~happy(sK4)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X1] : (calm(X1) | happy(X1))) [skolemisation 49,50]
57. ! [X0] : (((~brave(X0) | ~calm(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (brave(X0) & calm(X0)))) [nnf transformation 11]
58. ! [X0] : ((~brave(X0) | ~calm(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (brave(X0) & calm(X0)))) [flattening 57]
59. ! [X0] : ((~humble(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | humble(X0))) [nnf transformation 12]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 14]
61. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 60]
62. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (generous(X0) | ~curious(X0)))) [nnf transformation 16]
64. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | generous(X0) | ~curious(X0))) [flattening 63]
77. wise(X0) | creative(X0) [cnf transformation 29]
87. ~funny(X0) | ~patient(X0) [cnf transformation 41]
89. ~strong(X0) | ~patient(X0) [cnf transformation 41]
90. ~strong(X0) | ~curious(X0) [cnf transformation 41]
91. patient(fred) | ~calm(X0) | ~wise(X0) [cnf transformation 24]
98. ~creative(X0) | funny(X0) | patient(X0) | humble(X0) [cnf transformation 46]
99. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 46]
100. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 46]
103. patient(mary) | quiet(mary) | calm(X1) | happy(X1) [cnf transformation 51]
111. rich(X0) | curious(X0) | rich(X0) | creative(X0) [cnf transformation 27]
116. ~brave(X0) | ~calm(X0) | rich(X0) | rich(X0) [cnf transformation 58]
117. ~brave(X0) | ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
118. brave(X0) | calm(X0) | humble(X0) [cnf transformation 59]
123. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 61]
125. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 61]
127. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 61]
129. humble(X0) | humble(X0) | strong(X0) [cnf transformation 62]
135. ~rich(X0) | ~quiet(X0) | curious(X0) [cnf transformation 64]
144. ~happy(fred) [cnf transformation 21]
145. humble(X0) | strong(X0) [duplicate literal removal 129]
147. ~brave(X0) | ~calm(X0) | rich(X0) [duplicate literal removal 116]
148. ~rich(X0) | ~calm(X0) | ~brave(X0) [duplicate literal removal 117]
149. rich(X0) | curious(X0) | creative(X0) [duplicate literal removal 111]
167. 5 <=> ! [X0] : ~patient(X0) [avatar definition]
168. ~patient(X0) <- (5) [avatar component clause 167]
175. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
176. ~curious(X0) <- (7) [avatar component clause 175]
179. 8 <=> creative(fred) [avatar definition]
180. ~creative(fred) <- (~8) [avatar component clause 179]
181. creative(fred) <- (8) [avatar component clause 179]
194. 11 <=> ! [X0] : (~calm(X0) | ~wise(X0)) [avatar definition]
195. ~calm(X0) | ~wise(X0) <- (11) [avatar component clause 194]
197. 12 <=> brave(fred) [avatar definition]
198. brave(fred) <- (12) [avatar component clause 197]
199. ~brave(fred) <- (~12) [avatar component clause 197]
202. 13 <=> patient(fred) [avatar definition]
204. patient(fred) <- (13) [avatar component clause 202]
205. 11 | 13 [avatar split clause 91,202,194]
227. ~funny(X0) | ~humble(X0) [subsumption resolution 100,87]
228. ~humble(X0) | ~patient(X0) [subsumption resolution 99,227]
230. 18 <=> patient(mary) [avatar definition]
231. patient(mary) <- (18) [avatar component clause 230]
239. 20 <=> quiet(mary) [avatar definition]
240. quiet(mary) <- (20) [avatar component clause 239]
250. 22 <=> ! [X1] : (calm(X1) | happy(X1)) [avatar definition]
251. happy(X1) | calm(X1) <- (22) [avatar component clause 250]
252. 22 | 20 | 18 [avatar split clause 103,230,239,250]
271. ~brave(X0) | ~calm(X0) [subsumption resolution 147,148]
274. humble(X0) | ~funny(X0) [subsumption resolution 127,87]
275. ~funny(X0) [subsumption resolution 274,227]
276. ~humble(X0) | patient(X0) [subsumption resolution 125,275]
277. ~humble(X0) [subsumption resolution 276,228]
278. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 123,275]
279. ~patient(X0) | strong(X0) [subsumption resolution 278,277]
280. ~patient(X0) [subsumption resolution 279,89]
281. 5 [avatar split clause 280,167]
282. strong(X0) [subsumption resolution 145,277]
306. $false <- (5, 18) [resolution 231,168]
307. ~5 | ~18 [avatar contradiction clause 306]
309. ~curious(X0) [resolution 90,282]
330. curious(X2) | creative(X2) | ~quiet(X2) | curious(X2) [resolution 149,135]
331. curious(X2) | creative(X2) | ~quiet(X2) [duplicate literal removal 330]
333. ~quiet(X2) | creative(X2) <- (7) [subsumption resolution 331,176]
336. creative(mary) <- (7, 20) [resolution 333,240]
341. funny(mary) | patient(mary) | humble(mary) <- (7, 20) [resolution 98,336]
346. patient(mary) | humble(mary) <- (7, 20) [subsumption resolution 341,275]
347. humble(mary) <- (5, 7, 20) [subsumption resolution 346,168]
348. $false <- (5, 7, 20) [subsumption resolution 347,277]
349. ~5 | ~7 | ~20 [avatar contradiction clause 348]
350. 7 [avatar split clause 309,175]
351. $false <- (5, 13) [subsumption resolution 204,168]
352. ~5 | ~13 [avatar contradiction clause 351]
353. funny(fred) | patient(fred) | humble(fred) <- (8) [resolution 181,98]
354. patient(fred) | humble(fred) <- (8) [subsumption resolution 353,275]
355. humble(fred) <- (5, 8) [subsumption resolution 354,168]
356. $false <- (5, 8) [subsumption resolution 355,277]
357. ~5 | ~8 [avatar contradiction clause 356]
360. calm(fred) | humble(fred) <- (~12) [resolution 199,118]
361. calm(fred) <- (~12) [subsumption resolution 360,277]
379. ~wise(fred) <- (11, ~12) [resolution 195,361]
380. calm(fred) <- (22) [resolution 251,144]
393. creative(fred) <- (11, ~12) [resolution 379,77]
395. $false <- (~8, 11, ~12) [subsumption resolution 393,180]
396. 8 | ~11 | 12 [avatar contradiction clause 395]
399. ~calm(fred) <- (12) [resolution 198,271]
400. $false <- (12, 22) [subsumption resolution 399,380]
401. ~12 | ~22 [avatar contradiction clause 400]
402. $false [avatar sat refutation 205,252,281,307,349,350,352,357,396,401]
% SZS output end Proof for 7623474919377400451480051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or kind is funny and vice versa. If susan is either curious or kind then paul is both not creative and not brave. If someone is both strong and rich then someone is both kind and not old. Everyone who is either curious or not old is either quiet or not humble. Everyone who is both not happy and rich is both not kind and not brave. Everyone who is not happy is old. Everyone who is creative is either not wise or wise. If mary is either tall or not brave then someone is either strong or not rich and vice versa. Everyone who is kind or happy is either not strong or patient. Everyone who is either quiet or not funny is not strong or not rich. Everyone who is both not wise and patient is brave or not calm and vice versa. Everyone who is not calm or not kind is not happy. Everyone who is both not curious and happy is not calm. If john is not creative or tall then susan is not curious or quiet. Everyone who is either brave or happy is not funny or not tall and vice versa. If someone is both not humble and not calm then john is both not curious and old. Mary is either tall or generous. Someone is either not happy or creative. Someone is either happy or not happy. Someone is both brave and not quiet. Fred is creative or not strong. Lucy is either not funny or generous. Someone is either not old or not calm. Someone is either patient or not generous. | Fred is not funny. | contradiction | (![X]:((patient(X)|kind(X))<=>funny(X)))&
(((curious(susan)<~>kind(susan)))=>((~creative(paul)&~brave(paul))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((curious(X)<~>~old(X))=>(quiet(X)<~>~humble(X))))&
(![X]:((~happy(X)&rich(X))=>(~kind(X)&~brave(X))))&
(![X]:(~happy(X)=>old(X)))&
(![X]:(creative(X)=>(~wise(X)<~>wise(X))))&
(((tall(mary)<~>~brave(mary)))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((kind(X)|happy(X))=>(~strong(X)<~>patient(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(~strong(X)|~rich(X))))&
(![X]:((~wise(X)&patient(X))<=>(brave(X)|~calm(X))))&
(![X]:((~calm(X)|~kind(X))=>~happy(X)))&
(![X]:((~curious(X)&happy(X))=>~calm(X)))&
(((~creative(john)|tall(john)))=>((~curious(susan)|quiet(susan))))&
(![X]:((brave(X)<~>happy(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((~humble(X)&~calm(X))))=>((~curious(john)&old(john))))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((brave(X)&~quiet(X))))&
((creative(fred)|~strong(fred)))&
((~funny(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((patient(X)<~>~generous(X)))) | ~funny(fred) | [
"p0",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3136337485957137877594947
% SZS output start Proof for 3136337485957137877594947
1. ! [X0] : ((kind(X0) | patient(X0)) <=> funny(X0)) [input p0]
11. ! [X0] : ((patient(X0) & ~wise(X0)) <=> (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~calm(X0)) => ~happy(X0)) [input p11]
15. ! [X0] : ((brave(X0) <~> happy(X0)) <=> (~tall(X0) | ~funny(X0))) [input p14]
25. ~funny(fred) [input hypothesis]
37. ! [X0] : (~happy(X0) | (kind(X0) & calm(X0))) [ennf transformation 12]
43. ! [X0] : (((kind(X0) | patient(X0)) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | patient(X0) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [flattening 43]
57. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (~patient(X0) | wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | ~patient(X0) | wise(X0))) [flattening 57]
59. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [nnf transformation 15]
60. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [flattening 59]
77. ~patient(X0) | funny(X0) [cnf transformation 44]
78. ~kind(X0) | funny(X0) [cnf transformation 44]
112. ~brave(X0) | patient(X0) [cnf transformation 58]
115. ~happy(X0) | kind(X0) [cnf transformation 37]
121. happy(X0) | brave(X0) | funny(X0) [cnf transformation 60]
142. ~funny(fred) [cnf transformation 25]
307. brave(X3) | funny(X3) | kind(X3) [resolution 121,115]
320. brave(X3) | funny(X3) [subsumption resolution 307,78]
372. funny(X0) | patient(X0) [resolution 320,112]
374. funny(X0) [subsumption resolution 372,77]
395. $false [resolution 374,142]
% SZS output end Proof for 3136337485957137877594947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and creative then mary is either not curious or old.
If someone is both old and kind then someone is tall or not humble and vice versa.
If john is both not calm and not patient then someone is both not strong and quiet.
Everyone who is both funny and not kind is either not patient or not curious and vice versa.
If someone is both calm and not strong then alice is both not patient and not creative.
If paul is both not patient and not rich then paul is funny and vice versa.
Everyone who is not quiet or not patient is not creative or old.
Everyone who is both funny and not rich is old.
If someone is curious then lucy is either generous or curious.
If fred is either kind or not quiet then susan is happy.
Everyone who is both tall and wise is both old and generous and vice versa.
If someone is happy then someone is both not creative and not funny and vice versa.
If john is either kind or quiet then fred is either not humble or not happy.
Everyone who is either happy or not kind is either patient or strong and vice versa.
Everyone who is both patient and not strong is calm or not strong.
If john is either not creative or calm then someone is not kind.
Lucy is not generous or happy.
Fred is patient.
Someone is either happy or not wise.
Someone is either creative or not rich.
Someone is not happy.
Someone is calm.
Someone is both brave and not happy.
John is not wise. | Mary is quiet. | neutral | ((?[X]:((~tall(X)&creative(X))))=>((~curious(mary)<~>old(mary))))&
((?[X]:((old(X)&kind(X))))<=>(?[X]:((tall(X)|~humble(X)))))&
(((~calm(john)&~patient(john)))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((funny(X)&~kind(X))<=>(~patient(X)<~>~curious(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~patient(alice)&~creative(alice))))&
(((~patient(paul)&~rich(paul)))<=>(funny(paul)))&
(![X]:((~quiet(X)|~patient(X))=>(~creative(X)|old(X))))&
(![X]:((funny(X)&~rich(X))=>old(X)))&
((?[X]:(curious(X)))=>((generous(lucy)<~>curious(lucy))))&
(((kind(fred)<~>~quiet(fred)))=>(happy(susan)))&
(![X]:((tall(X)&wise(X))<=>(old(X)&generous(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)&~funny(X)))))&
(((kind(john)<~>quiet(john)))=>((~humble(fred)<~>~happy(fred))))&
(![X]:((happy(X)<~>~kind(X))<=>(patient(X)<~>strong(X))))&
(![X]:((patient(X)&~strong(X))=>(calm(X)|~strong(X))))&
(((~creative(john)<~>calm(john)))=>(?[X]:(~kind(X))))&
((~generous(lucy)|happy(lucy)))&
(patient(fred))&
(?[X]:((happy(X)<~>~wise(X))))&
(?[X]:((creative(X)<~>~rich(X))))&
(?[X]:(~happy(X)))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)&~happy(X))))&
(~wise(john)) | quiet(mary) | [] | null | 0 |
Everyone who is creative or not funny is funny and vice versa. If someone is not creative or not humble then paul is either not generous or not rich and vice versa. Everyone who is not old is either not curious or quiet and vice versa. Everyone who is both patient and not kind is either not rich or happy. If paul is not humble or not tall then someone is kind and vice versa. Everyone who is both not generous and humble is both not brave and not creative. If someone is rich then someone is either old or rich. Everyone who is wise is either not rich or patient and vice versa. If someone is tall or brave then lucy is either generous or not happy and vice versa. If paul is not generous or brave then someone is funny. If susan is generous or wise then someone is both funny and creative. Everyone who is not humble is not wise or funny and vice versa. Everyone who is kind is either happy or generous and vice versa. Everyone who is both generous and brave is either not happy or rich. If paul is both not quiet and not humble then someone is not creative or curious and vice versa. If lucy is both quiet and not calm then someone is generous or not curious. Susan is both not quiet and strong. Someone is both not kind and not patient. Lucy is either not creative or not patient. John is calm. Fred is happy or wise. Someone is either not old or not generous. Someone is both not curious and rich. Fred is either strong or not rich. | Paul is funny. | entailment | (![X]:((creative(X)|~funny(X))<=>funny(X)))&
((?[X]:((~creative(X)|~humble(X))))<=>((~generous(paul)<~>~rich(paul))))&
(![X]:(~old(X)<=>(~curious(X)<~>quiet(X))))&
(![X]:((patient(X)&~kind(X))=>(~rich(X)<~>happy(X))))&
(((~humble(paul)|~tall(paul)))<=>(?[X]:(kind(X))))&
(![X]:((~generous(X)&humble(X))=>(~brave(X)&~creative(X))))&
((?[X]:(rich(X)))=>(?[X]:((old(X)<~>rich(X)))))&
(![X]:(wise(X)<=>(~rich(X)<~>patient(X))))&
((?[X]:((tall(X)|brave(X))))<=>((generous(lucy)<~>~happy(lucy))))&
(((~generous(paul)|brave(paul)))=>(?[X]:(funny(X))))&
(((generous(susan)|wise(susan)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:(~humble(X)<=>(~wise(X)|funny(X))))&
(![X]:(kind(X)<=>(happy(X)<~>generous(X))))&
(![X]:((generous(X)&brave(X))=>(~happy(X)<~>rich(X))))&
(((~quiet(paul)&~humble(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((quiet(lucy)&~calm(lucy)))=>(?[X]:((generous(X)|~curious(X)))))&
((~quiet(susan)&strong(susan)))&
(?[X]:((~kind(X)&~patient(X))))&
((~creative(lucy)<~>~patient(lucy)))&
(calm(john))&
((happy(fred)|wise(fred)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~curious(X)&rich(X))))&
((strong(fred)<~>~rich(fred))) | funny(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1106136781998209993637669
% SZS output start Proof for 1106136781998209993637669
1. ! [X0] : ((~funny(X0) | creative(X0)) <=> funny(X0)) [input p0]
25. ~funny(paul) [input hypothesis]
38. ! [X0] : (((~funny(X0) | creative(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 1]
39. ! [X0] : ((~funny(X0) | creative(X0) | ~funny(X0)) & (funny(X0) | (funny(X0) & ~creative(X0)))) [flattening 38]
83. funny(X0) | funny(X0) [cnf transformation 39]
147. ~funny(paul) [cnf transformation 25]
148. funny(X0) [duplicate literal removal 83]
310. $false [subsumption resolution 147,148]
% SZS output end Proof for 1106136781998209993637669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not humble is not calm or not creative and vice versa. If paul is both creative and not strong then someone is patient or not quiet and vice versa. Everyone who is both curious and not patient is either wise or quiet and vice versa. If someone is either not humble or not old then mary is not rich. If fred is either not funny or not brave then paul is not quiet or calm. If someone is not funny or not generous then someone is not quiet and vice versa. Everyone who is either not brave or old is not old or rich. Everyone who is either calm or not kind is both not strong and rich. If someone is both brave and not patient then john is not patient. Everyone who is not curious or creative is both not brave and strong. If someone is either calm or not curious then someone is wise or not generous. If paul is either kind or patient then someone is not happy. Everyone who is not calm is not tall or patient. If lucy is both not kind and patient then paul is not calm and vice versa. Everyone who is both creative and not tall is not tall or not funny and vice versa. If someone is either not brave or not quiet then susan is both quiet and not creative. Someone is rich or not tall. Lucy is curious. Someone is not curious or strong. Someone is not calm. Someone is either calm or not old. Someone is either humble or generous. Fred is either not brave or quiet. | Fred is calm. | entailment | (![X]:((generous(X)&~humble(X))<=>(~calm(X)|~creative(X))))&
(((creative(paul)&~strong(paul)))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((curious(X)&~patient(X))<=>(wise(X)<~>quiet(X))))&
((?[X]:((~humble(X)<~>~old(X))))=>(~rich(mary)))&
(((~funny(fred)<~>~brave(fred)))=>((~quiet(paul)|calm(paul))))&
((?[X]:((~funny(X)|~generous(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)<~>old(X))=>(~old(X)|rich(X))))&
(![X]:((calm(X)<~>~kind(X))=>(~strong(X)&rich(X))))&
((?[X]:((brave(X)&~patient(X))))=>(~patient(john)))&
(![X]:((~curious(X)|creative(X))=>(~brave(X)&strong(X))))&
((?[X]:((calm(X)<~>~curious(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(((kind(paul)<~>patient(paul)))=>(?[X]:(~happy(X))))&
(![X]:(~calm(X)=>(~tall(X)|patient(X))))&
(((~kind(lucy)&patient(lucy)))<=>(~calm(paul)))&
(![X]:((creative(X)&~tall(X))<=>(~tall(X)|~funny(X))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>((quiet(susan)&~creative(susan))))&
(?[X]:((rich(X)|~tall(X))))&
(curious(lucy))&
(?[X]:((~curious(X)|strong(X))))&
(?[X]:(~calm(X)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((humble(X)<~>generous(X))))&
((~brave(fred)<~>quiet(fred))) | calm(fred) | [
"p1",
"p9",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9115348588293860489384561
% SZS output start Proof for 9115348588293860489384561
2. (~strong(paul) & creative(paul)) <=> ? [X0] : (~quiet(X0) | patient(X0)) [input p1]
10. ! [X0] : ((creative(X0) | ~curious(X0)) => (strong(X0) & ~brave(X0))) [input p9]
13. ! [X0] : (~calm(X0) => (patient(X0) | ~tall(X0))) [input p12]
15. ! [X0] : ((~tall(X0) & creative(X0)) <=> (~funny(X0) | ~tall(X0))) [input p14]
23. ~brave(fred) <~> quiet(fred) [input p22]
24. ~calm(fred) [input hypothesis]
35. ! [X0] : ((strong(X0) & ~brave(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 10]
37. ! [X0] : ((patient(X0) | ~tall(X0)) | calm(X0)) [ennf transformation 13]
38. ! [X0] : (patient(X0) | ~tall(X0) | calm(X0)) [flattening 37]
42. ((~strong(paul) & creative(paul)) | ! [X0] : (quiet(X0) & ~patient(X0))) & (? [X0] : (~quiet(X0) | patient(X0)) | (strong(paul) | ~creative(paul))) [nnf transformation 2]
43. ((~strong(paul) & creative(paul)) | ! [X0] : (quiet(X0) & ~patient(X0))) & (? [X0] : (~quiet(X0) | patient(X0)) | strong(paul) | ~creative(paul)) [flattening 42]
44. ((~strong(paul) & creative(paul)) | ! [X0] : (quiet(X0) & ~patient(X0))) & (? [X1] : (~quiet(X1) | patient(X1)) | strong(paul) | ~creative(paul)) [rectify 43]
45. ? [X1] : (~quiet(X1) | patient(X1)) => (~quiet(sK0) | patient(sK0)) [choice axiom]
46. ((~strong(paul) & creative(paul)) | ! [X0] : (quiet(X0) & ~patient(X0))) & ((~quiet(sK0) | patient(sK0)) | strong(paul) | ~creative(paul)) [skolemisation 44,45]
64. ! [X0] : (((~tall(X0) & creative(X0)) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | (tall(X0) | ~creative(X0)))) [nnf transformation 15]
65. ! [X0] : (((~tall(X0) & creative(X0)) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | tall(X0) | ~creative(X0))) [flattening 64]
79. (~quiet(fred) | brave(fred)) & (quiet(fred) | ~brave(fred)) [nnf transformation 23]
86. creative(paul) | ~patient(X0) [cnf transformation 46]
87. creative(paul) | quiet(X0) [cnf transformation 46]
88. ~strong(paul) | ~patient(X0) [cnf transformation 46]
89. ~strong(paul) | quiet(X0) [cnf transformation 46]
111. ~brave(X0) | ~creative(X0) [cnf transformation 35]
113. ~creative(X0) | strong(X0) [cnf transformation 35]
116. ~tall(X0) | patient(X0) | calm(X0) [cnf transformation 38]
121. tall(X0) | creative(X0) [cnf transformation 65]
138. ~quiet(fred) | brave(fred) [cnf transformation 79]
139. ~calm(fred) [cnf transformation 24]
142. 1 <=> ! [X0] : quiet(X0) [avatar definition]
143. quiet(X0) <- (1) [avatar component clause 142]
145. 2 <=> strong(paul) [avatar definition]
148. 1 | ~2 [avatar split clause 89,145,142]
150. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
151. ~patient(X0) <- (3) [avatar component clause 150]
152. 3 | ~2 [avatar split clause 88,145,150]
154. 4 <=> creative(paul) [avatar definition]
156. creative(paul) <- (4) [avatar component clause 154]
157. 1 | 4 [avatar split clause 87,154,142]
158. 3 | 4 [avatar split clause 86,154,150]
181. 10 <=> brave(fred) [avatar definition]
183. brave(fred) <- (10) [avatar component clause 181]
303. 37 <=> quiet(fred) [avatar definition]
305. ~quiet(fred) <- (~37) [avatar component clause 303]
306. 10 | ~37 [avatar split clause 138,303,181]
313. strong(paul) <- (4) [resolution 113,156]
318. 2 | ~4 [avatar split clause 313,154,145]
321. $false <- (1, ~37) [resolution 143,305]
322. ~1 | 37 [avatar contradiction clause 321]
325. ~creative(fred) <- (10) [resolution 183,111]
381. patient(X0) | calm(X0) | creative(X0) [resolution 116,121]
383. creative(X0) | calm(X0) <- (3) [subsumption resolution 381,151]
421. calm(fred) <- (3, 10) [resolution 383,325]
423. $false <- (3, 10) [subsumption resolution 421,139]
424. ~3 | ~10 [avatar contradiction clause 423]
425. $false [avatar sat refutation 148,152,157,158,306,318,322,424]
% SZS output end Proof for 9115348588293860489384561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is old. Everyone who is not calm is both funny and not patient. If someone is not curious or generous then lucy is either curious or kind. Everyone who is either calm or not funny is not kind or not brave and vice versa. Everyone who is humble or not creative is either patient or happy. If john is not humble or strong then someone is not happy. If someone is both not quiet and not calm then susan is both generous and not quiet and vice versa. Everyone who is not funny is not quiet. Everyone who is either not quiet or not kind is either happy or not kind and vice versa. If john is either calm or generous then someone is curious and vice versa. Everyone who is not kind or happy is both not humble and happy. Everyone who is kind is humble and vice versa. Everyone who is both not wise and not patient is either not happy or not quiet. Everyone who is strong or not quiet is not old. If fred is both not strong and curious then someone is not humble or kind and vice versa. Everyone who is either old or not kind is both funny and not happy and vice versa. Someone is not funny or not tall. John is either not generous or generous. Lucy is both curious and creative. Alice is kind or happy. Someone is wise. Fred is both kind and calm. | Fred is not quiet. | contradiction | (![X]:(~brave(X)=>old(X)))&
(![X]:(~calm(X)=>(funny(X)&~patient(X))))&
((?[X]:((~curious(X)|generous(X))))=>((curious(lucy)<~>kind(lucy))))&
(![X]:((calm(X)<~>~funny(X))<=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)|~creative(X))=>(patient(X)<~>happy(X))))&
(((~humble(john)|strong(john)))=>(?[X]:(~happy(X))))&
((?[X]:((~quiet(X)&~calm(X))))<=>((generous(susan)&~quiet(susan))))&
(![X]:(~funny(X)=>~quiet(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(happy(X)<~>~kind(X))))&
(((calm(john)<~>generous(john)))<=>(?[X]:(curious(X))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(?[X]:((~funny(X)|~tall(X))))&
((~generous(john)<~>generous(john)))&
((curious(lucy)&creative(lucy)))&
((kind(alice)|happy(alice)))&
(?[X]:(wise(X)))&
((kind(fred)&calm(fred))) | ~quiet(fred) | [
"p8",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4182076444641506583271450
% SZS output start Proof for 4182076444641506583271450
9. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (happy(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p10]
12. ! [X0] : (kind(X0) <=> humble(X0)) [input p11]
22. calm(fred) & kind(fred) [input p21]
23. ~quiet(fred) [input hypothesis]
35. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 11]
48. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) & (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 9]
53. ! [X0] : ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))) [nnf transformation 12]
84. ~kind(X0) | happy(X0) | ~kind(X0) | quiet(X0) [cnf transformation 48]
91. kind(X0) | quiet(X0) | happy(X0) | kind(X0) [cnf transformation 48]
97. ~happy(X0) | ~humble(X0) [cnf transformation 35]
100. ~kind(X0) | humble(X0) [cnf transformation 53]
119. kind(fred) [cnf transformation 22]
121. ~quiet(fred) [cnf transformation 23]
122. ~kind(X0) | happy(X0) | quiet(X0) [duplicate literal removal 84]
125. kind(X0) | quiet(X0) | happy(X0) [duplicate literal removal 91]
186. quiet(X0) | happy(X0) [subsumption resolution 122,125]
232. humble(fred) [resolution 100,119]
245. happy(fred) [resolution 186,121]
251. ~humble(fred) [resolution 245,97]
252. $false [subsumption resolution 251,232]
% SZS output end Proof for 4182076444641506583271450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or tall is not happy or not quiet.
If someone is brave or not curious then fred is both not patient and not humble.
Everyone who is wise is both not rich and not quiet and vice versa.
Everyone who is not brave is tall or not generous.
Everyone who is either not kind or wise is both brave and rich.
If paul is rich then someone is not happy or not old and vice versa.
Everyone who is not calm is either not kind or not old.
If susan is either old or brave then someone is both not kind and not calm and vice versa.
If lucy is humble then someone is either not strong or not humble.
Everyone who is either humble or not wise is either patient or not brave and vice versa.
If fred is either not happy or not humble then lucy is either not wise or curious and vice versa.
If someone is not old or generous then someone is both calm and funny.
If someone is not calm then mary is both not creative and calm.
Everyone who is both not calm and calm is not funny or not humble and vice versa.
Everyone who is generous or not patient is either quiet or not funny and vice versa.
If someone is either not quiet or not funny then alice is either not generous or not creative.
Someone is not generous.
Someone is not calm.
Someone is generous.
Someone is not patient or humble.
Susan is funny.
Fred is not generous or not rich.
Someone is either kind or not strong.
Someone is both not brave and not calm. | Fred is wise. | contradiction | (![X]:((~happy(X)|tall(X))=>(~happy(X)|~quiet(X))))&
((?[X]:((brave(X)|~curious(X))))=>((~patient(fred)&~humble(fred))))&
(![X]:(wise(X)<=>(~rich(X)&~quiet(X))))&
(![X]:(~brave(X)=>(tall(X)|~generous(X))))&
(![X]:((~kind(X)<~>wise(X))=>(brave(X)&rich(X))))&
((rich(paul))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:(~calm(X)=>(~kind(X)<~>~old(X))))&
(((old(susan)<~>brave(susan)))<=>(?[X]:((~kind(X)&~calm(X)))))&
((humble(lucy))=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>~wise(X))<=>(patient(X)<~>~brave(X))))&
(((~happy(fred)<~>~humble(fred)))<=>((~wise(lucy)<~>curious(lucy))))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((calm(X)&funny(X)))))&
((?[X]:(~calm(X)))=>((~creative(mary)&calm(mary))))&
(![X]:((~calm(X)&calm(X))<=>(~funny(X)|~humble(X))))&
(![X]:((generous(X)|~patient(X))<=>(quiet(X)<~>~funny(X))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>((~generous(alice)<~>~creative(alice))))&
(?[X]:(~generous(X)))&
(?[X]:(~calm(X)))&
(?[X]:(generous(X)))&
(?[X]:((~patient(X)|humble(X))))&
(funny(susan))&
((~generous(fred)|~rich(fred)))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((~brave(X)&~calm(X)))) | wise(fred) | [
"p1",
"p2",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3737420887974040102883057
% SZS output start Proof for 3737420887974040102883057
2. ? [X0] : (~curious(X0) | brave(X0)) => (~humble(fred) & ~patient(fred)) [input p1]
3. ! [X0] : (wise(X0) <=> (~quiet(X0) & ~rich(X0))) [input p2]
10. ! [X0] : ((humble(X0) <~> ~wise(X0)) <=> (patient(X0) <~> ~brave(X0))) [input p9]
14. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~humble(X0) | ~funny(X0))) [input p13]
15. ! [X0] : ((~patient(X0) | generous(X0)) <=> (quiet(X0) <~> ~funny(X0))) [input p14]
25. wise(fred) [input hypothesis]
29. (~humble(fred) & ~patient(fred)) | ! [X0] : (curious(X0) & ~brave(X0)) [ennf transformation 2]
38. ! [X0] : ((wise(X0) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | ~wise(X0))) [nnf transformation 3]
39. ! [X0] : ((wise(X0) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | ~wise(X0))) [flattening 38]
53. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [nnf transformation 10]
58. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & ((~humble(X0) | ~funny(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 14]
59. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & (~humble(X0) | ~funny(X0) | ~calm(X0) | calm(X0))) [flattening 58]
60. ! [X0] : (((~patient(X0) | generous(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (patient(X0) & ~generous(X0)))) [nnf transformation 15]
61. ! [X0] : ((~patient(X0) | generous(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (patient(X0) & ~generous(X0)))) [flattening 60]
78. ~patient(fred) | ~brave(X0) [cnf transformation 29]
83. ~wise(X0) | ~quiet(X0) [cnf transformation 39]
105. ~wise(X0) | ~patient(X0) | brave(X0) | ~humble(X0) [cnf transformation 53]
126. ~calm(X0) | funny(X0) [cnf transformation 59]
127. ~calm(X0) | humble(X0) [cnf transformation 59]
128. funny(X0) | calm(X0) [cnf transformation 59]
129. calm(X0) | humble(X0) [cnf transformation 59]
131. ~funny(X0) | quiet(X0) | patient(X0) [cnf transformation 61]
150. wise(fred) [cnf transformation 25]
160. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
161. ~brave(X0) <- (3) [avatar component clause 160]
164. 4 <=> patient(fred) [avatar definition]
165. patient(fred) <- (4) [avatar component clause 164]
166. ~patient(fred) <- (~4) [avatar component clause 164]
168. 3 | ~4 [avatar split clause 78,164,160]
278. humble(X0) [subsumption resolution 127,129]
279. funny(X0) [subsumption resolution 126,128]
281. patient(X0) | quiet(X0) [subsumption resolution 131,279]
338. ~quiet(fred) [resolution 83,150]
349. quiet(fred) <- (~4) [resolution 281,166]
350. $false <- (~4) [subsumption resolution 349,338]
351. 4 [avatar contradiction clause 350]
405. ~patient(fred) | brave(fred) | ~humble(fred) [resolution 105,150]
409. brave(fred) | ~humble(fred) <- (4) [subsumption resolution 405,165]
410. ~humble(fred) <- (3, 4) [subsumption resolution 409,161]
411. $false <- (3, 4) [subsumption resolution 410,278]
412. ~3 | ~4 [avatar contradiction clause 411]
419. $false [avatar sat refutation 168,351,412]
% SZS output end Proof for 3737420887974040102883057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is both curious and generous.
If someone is not humble then someone is both not generous and not patient.
If lucy is generous or not tall then someone is not brave or old.
If lucy is either calm or strong then someone is not wise and vice versa.
If someone is kind or humble then lucy is both brave and not happy and vice versa.
Everyone who is either rich or patient is both tall and not funny and vice versa.
If lucy is both brave and not curious then john is either funny or creative and vice versa.
If john is funny then someone is both not brave and not patient.
Everyone who is happy is either not funny or humble.
Everyone who is both not wise and funny is either not tall or not strong and vice versa.
If someone is both funny and not old then someone is quiet.
Everyone who is not curious or not humble is old.
Everyone who is both tall and rich is either kind or creative and vice versa.
Everyone who is either happy or not calm is old and vice versa.
Everyone who is quiet is not old or not strong and vice versa.
Everyone who is both not quiet and humble is not funny or not strong and vice versa.
Someone is funny or not funny.
Someone is quiet or not wise.
Someone is calm or rich.
Someone is either not kind or not old.
Lucy is not brave or patient.
Lucy is both patient and strong.
Someone is not generous.
Alice is kind or not old. | Lucy is not rich. | neutral | (![X]:(kind(X)=>(curious(X)&generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~generous(X)&~patient(X)))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~brave(X)|old(X)))))&
(((calm(lucy)<~>strong(lucy)))<=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|humble(X))))<=>((brave(lucy)&~happy(lucy))))&
(![X]:((rich(X)<~>patient(X))<=>(tall(X)&~funny(X))))&
(((brave(lucy)&~curious(lucy)))<=>((funny(john)<~>creative(john))))&
((funny(john))=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:(happy(X)=>(~funny(X)<~>humble(X))))&
(![X]:((~wise(X)&funny(X))<=>(~tall(X)<~>~strong(X))))&
((?[X]:((funny(X)&~old(X))))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)|~humble(X))=>old(X)))&
(![X]:((tall(X)&rich(X))<=>(kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>~calm(X))<=>old(X)))&
(![X]:(quiet(X)<=>(~old(X)|~strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~funny(X)|~strong(X))))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
((~brave(lucy)|patient(lucy)))&
((patient(lucy)&strong(lucy)))&
(?[X]:(~generous(X)))&
((kind(alice)|~old(alice))) | ~rich(lucy) | [] | null | 0 |
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