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 not funny or wise then lucy is either not old or not brave.
Everyone who is both curious and humble is not brave or happy and vice versa.
If someone is both quiet and strong then susan is not curious or not rich.
Everyone who is not kind is both calm and not wise and vice versa.
Everyone who is both not brave and not generous is not happy or quiet and vice versa.
Everyone who is both not humble and quiet is rich or happy.
Everyone who is not patient or patient is both patient and not kind and vice versa.
Everyone who is not tall is either not old or not strong and vice versa.
If someone is both calm and old then someone is wise.
Everyone who is humble or not old is not quiet and vice versa.
If someone is happy then someone is tall and vice versa.
If someone is both not generous and rich then someone is either not tall or humble and vice versa.
If susan is not humble then someone is creative.
Everyone who is not curious or not patient is either quiet or kind.
Someone is both generous and funny.
Someone is calm or not curious.
Someone is either happy or old.
Susan is not funny.
Someone is either patient or not creative. | Lucy is happy. | entailment | ((?[X]:((~funny(X)|wise(X))))=>((~old(lucy)<~>~brave(lucy))))&
(![X]:((curious(X)&humble(X))<=>(~brave(X)|happy(X))))&
((?[X]:((quiet(X)&strong(X))))=>((~curious(susan)|~rich(susan))))&
(![X]:(~kind(X)<=>(calm(X)&~wise(X))))&
(![X]:((~brave(X)&~generous(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~humble(X)&quiet(X))=>(rich(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(patient(X)&~kind(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>~strong(X))))&
((?[X]:((calm(X)&old(X))))=>(?[X]:(wise(X))))&
(![X]:((humble(X)|~old(X))<=>~quiet(X)))&
((?[X]:(happy(X)))<=>(?[X]:(tall(X))))&
((?[X]:((~generous(X)&rich(X))))<=>(?[X]:((~tall(X)<~>humble(X)))))&
((~humble(susan))=>(?[X]:(creative(X))))&
(![X]:((~curious(X)|~patient(X))=>(quiet(X)<~>kind(X))))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((calm(X)|~curious(X))))&
(?[X]:((happy(X)<~>old(X))))&
(~funny(susan))&
(?[X]:((patient(X)<~>~creative(X)))) | happy(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7250181354338957582768718
% SZS output start Proof for 7250181354338957582768718
1. ? [X0] : (wise(X0) | ~funny(X0)) => (~old(lucy) <~> ~brave(lucy)) [input p0]
4. ! [X0] : (~kind(X0) <=> (~wise(X0) & calm(X0))) [input p3]
5. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (quiet(X0) | ~happy(X0))) [input p4]
7. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~kind(X0) & patient(X0))) [input p6]
9. ? [X0] : (old(X0) & calm(X0)) => ? [X0] : wise(X0) [input p8]
18. ~funny(susan) [input p17]
20. ~happy(lucy) [input hypothesis]
21. ? [X0] : (old(X0) & calm(X0)) => ? [X1] : wise(X1) [rectify 9]
24. (~old(lucy) <~> ~brave(lucy)) | ! [X0] : (~wise(X0) & funny(X0)) [ennf transformation 1]
29. ? [X1] : wise(X1) | ! [X0] : (~old(X0) | ~calm(X0)) [ennf transformation 21]
32. ((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X0] : (~wise(X0) & funny(X0)) [nnf transformation 24]
35. ! [X0] : ((~kind(X0) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | kind(X0))) [nnf transformation 4]
36. ! [X0] : ((~kind(X0) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | kind(X0))) [flattening 35]
37. ! [X0] : (((~generous(X0) & ~brave(X0)) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | (generous(X0) | brave(X0)))) [nnf transformation 5]
38. ! [X0] : (((~generous(X0) & ~brave(X0)) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | generous(X0) | brave(X0))) [flattening 37]
39. ! [X0] : (((patient(X0) | ~patient(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 7]
40. ! [X0] : ((patient(X0) | ~patient(X0) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 39]
42. ? [X0] : wise(X0) | ! [X1] : (~old(X1) | ~calm(X1)) [rectify 29]
43. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
44. wise(sK0) | ! [X1] : (~old(X1) | ~calm(X1)) [skolemisation 42,43]
72. brave(lucy) | old(lucy) | funny(X0) [cnf transformation 32]
80. calm(X0) | kind(X0) [cnf transformation 36]
81. ~wise(X0) | kind(X0) [cnf transformation 36]
84. ~brave(X0) | happy(X0) [cnf transformation 38]
91. ~kind(X0) | patient(X0) [cnf transformation 40]
92. ~patient(X0) | ~kind(X0) [cnf transformation 40]
98. wise(sK0) | ~old(X1) | ~calm(X1) [cnf transformation 44]
120. ~funny(susan) [cnf transformation 18]
123. ~happy(lucy) [cnf transformation 20]
130. 2 <=> old(lucy) [avatar definition]
132. old(lucy) <- (2) [avatar component clause 130]
134. 3 <=> brave(lucy) [avatar definition]
136. brave(lucy) <- (3) [avatar component clause 134]
139. 4 <=> ! [X0] : funny(X0) [avatar definition]
140. funny(X0) <- (4) [avatar component clause 139]
141. 4 | 2 | 3 [avatar split clause 72,134,130,139]
157. ~kind(X0) [subsumption resolution 91,92]
159. 8 <=> ! [X1] : (~old(X1) | ~calm(X1)) [avatar definition]
160. ~calm(X1) | ~old(X1) <- (8) [avatar component clause 159]
162. 9 <=> wise(sK0) [avatar definition]
164. wise(sK0) <- (9) [avatar component clause 162]
165. 8 | 9 [avatar split clause 98,162,159]
268. ~old(X0) | kind(X0) <- (8) [resolution 160,80]
270. ~old(X0) <- (8) [subsumption resolution 268,157]
275. $false <- (2, 8) [resolution 270,132]
276. ~2 | ~8 [avatar contradiction clause 275]
277. kind(sK0) <- (9) [resolution 164,81]
278. $false <- (9) [subsumption resolution 277,157]
279. ~9 [avatar contradiction clause 278]
280. happy(lucy) <- (3) [resolution 136,84]
281. $false <- (3) [subsumption resolution 280,123]
282. ~3 [avatar contradiction clause 281]
283. $false <- (4) [resolution 140,120]
284. ~4 [avatar contradiction clause 283]
285. $false [avatar sat refutation 141,165,276,279,282,284]
% SZS output end Proof for 7250181354338957582768718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not generous and strong is not rich or not curious. Everyone who is both brave and strong is both patient and brave and vice versa. Everyone who is not brave is not humble. If john is either humble or quiet then alice is both creative and not old and vice versa. Everyone who is either brave or not patient is old or wise. Everyone who is patient is not strong or not brave and vice versa. Everyone who is both wise and happy is not old or kind and vice versa. Everyone who is either not old or not curious is not wise or not funny and vice versa. If someone is either not strong or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. If alice is calm or rich then fred is not humble or curious and vice versa. Susan is tall. Mary is not funny or not rich. Someone is strong. Mary is either quiet or kind. Lucy is not calm or patient. Someone is both funny and not kind. | Lucy is creative. | neutral | (![X]:((~generous(X)&strong(X))=>(~rich(X)|~curious(X))))&
(![X]:((brave(X)&strong(X))<=>(patient(X)&brave(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(((humble(john)<~>quiet(john)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(tall(susan))&
((~funny(mary)|~rich(mary)))&
(?[X]:(strong(X)))&
((quiet(mary)<~>kind(mary)))&
((~calm(lucy)|patient(lucy)))&
(?[X]:((funny(X)&~kind(X)))) | creative(lucy) | [] | null | 0 |
If someone is not quiet then alice is either not wise or wise and vice versa.
Everyone who is curious or patient is both humble and not rich.
Everyone who is both not calm and humble is not curious or tall and vice versa.
Everyone who is not old or not curious is strong and vice versa.
If someone is either not curious or not creative then someone is both tall and creative and vice versa.
Everyone who is both not strong and funny is either not old or kind and vice versa.
Everyone who is not rich is both curious and tall and vice versa.
Everyone who is not tall is not brave or not strong and vice versa.
If someone is both funny and not humble then alice is both not creative and creative.
If susan is either rich or not funny then someone is not curious or wise and vice versa.
If someone is not rich then someone is creative and vice versa.
Everyone who is either not happy or not rich is both not generous and old and vice versa.
If susan is not humble then lucy is not quiet or not old and vice versa.
If alice is not patient then susan is tall.
If someone is patient or not patient then mary is both rich and not happy and vice versa.
Someone is both creative and not generous.
Paul is either wise or curious.
John is rich or not curious.
Someone is either rich or not funny.
Lucy is either not old or old.
Someone is either not funny or not tall. | Alice is not rich. | neutral | ((?[X]:(~quiet(X)))<=>((~wise(alice)<~>wise(alice))))&
(![X]:((curious(X)|patient(X))=>(humble(X)&~rich(X))))&
(![X]:((~calm(X)&humble(X))<=>(~curious(X)|tall(X))))&
(![X]:((~old(X)|~curious(X))<=>strong(X)))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((tall(X)&creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)<~>kind(X))))&
(![X]:(~rich(X)<=>(curious(X)&tall(X))))&
(![X]:(~tall(X)<=>(~brave(X)|~strong(X))))&
((?[X]:((funny(X)&~humble(X))))=>((~creative(alice)&creative(alice))))&
(((rich(susan)<~>~funny(susan)))<=>(?[X]:((~curious(X)|wise(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(creative(X))))&
(![X]:((~happy(X)<~>~rich(X))<=>(~generous(X)&old(X))))&
((~humble(susan))<=>((~quiet(lucy)|~old(lucy))))&
((~patient(alice))=>(tall(susan)))&
((?[X]:((patient(X)|~patient(X))))<=>((rich(mary)&~happy(mary))))&
(?[X]:((creative(X)&~generous(X))))&
((wise(paul)<~>curious(paul)))&
((rich(john)|~curious(john)))&
(?[X]:((rich(X)<~>~funny(X))))&
((~old(lucy)<~>old(lucy)))&
(?[X]:((~funny(X)<~>~tall(X)))) | ~rich(alice) | [] | null | 0 |
If someone is either not old or not generous then lucy is both old and not old and vice versa.
Everyone who is not wise is calm and vice versa.
If alice is both not old and patient then fred is both not strong and curious and vice versa.
Everyone who is either patient or creative is creative or patient and vice versa.
Everyone who is not patient or kind is humble.
Everyone who is not patient is humble and vice versa.
Everyone who is not curious is either rich or not generous and vice versa.
If mary is both tall and humble then someone is both not creative and not tall and vice versa.
Everyone who is either not quiet or not strong is both not wise and tall and vice versa.
Everyone who is not old is either kind or patient.
If someone is both not strong and not quiet then alice is not rich and vice versa.
Everyone who is both humble and not quiet is not kind and vice versa.
Everyone who is not quiet or generous is kind.
If someone is either not strong or quiet then someone is not brave.
If alice is either tall or not generous then mary is both not creative and not patient.
Everyone who is either brave or strong is either not funny or not strong.
Fred is not old.
Someone is either not funny or wise.
Someone is both not calm and not creative.
John is either not tall or not creative.
Someone is both happy and calm. | Fred is strong. | neutral | ((?[X]:((~old(X)<~>~generous(X))))<=>((old(lucy)&~old(lucy))))&
(![X]:(~wise(X)<=>calm(X)))&
(((~old(alice)&patient(alice)))<=>((~strong(fred)&curious(fred))))&
(![X]:((patient(X)<~>creative(X))<=>(creative(X)|patient(X))))&
(![X]:((~patient(X)|kind(X))=>humble(X)))&
(![X]:(~patient(X)<=>humble(X)))&
(![X]:(~curious(X)<=>(rich(X)<~>~generous(X))))&
(((tall(mary)&humble(mary)))<=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(~wise(X)&tall(X))))&
(![X]:(~old(X)=>(kind(X)<~>patient(X))))&
((?[X]:((~strong(X)&~quiet(X))))<=>(~rich(alice)))&
(![X]:((humble(X)&~quiet(X))<=>~kind(X)))&
(![X]:((~quiet(X)|generous(X))=>kind(X)))&
((?[X]:((~strong(X)<~>quiet(X))))=>(?[X]:(~brave(X))))&
(((tall(alice)<~>~generous(alice)))=>((~creative(mary)&~patient(mary))))&
(![X]:((brave(X)<~>strong(X))=>(~funny(X)<~>~strong(X))))&
(~old(fred))&
(?[X]:((~funny(X)<~>wise(X))))&
(?[X]:((~calm(X)&~creative(X))))&
((~tall(john)<~>~creative(john)))&
(?[X]:((happy(X)&calm(X)))) | strong(fred) | [] | null | 0 |
Everyone who is tall is not creative or not strong and vice versa. Everyone who is either not funny or curious is both not old and not wise. If susan is both humble and rich then john is either not old or humble and vice versa. Everyone who is brave or happy is generous. If paul is not rich then someone is brave or rich and vice versa. Everyone who is both not generous and patient is either not tall or patient and vice versa. Everyone who is not happy or strong is brave. If someone is not humble then someone is both not generous and not quiet and vice versa. Everyone who is both creative and not kind is both tall and brave and vice versa. Everyone who is happy or not patient is not humble or not patient. If someone is not patient or not creative then john is either not tall or wise. Everyone who is kind or brave is either funny or generous. Everyone who is calm or not patient is either not kind or old and vice versa. Everyone who is not happy or not generous is not quiet or not calm. If fred is both quiet and not humble then someone is both tall and happy and vice versa. Everyone who is both wise and not rich is wise. Alice is old or strong. Someone is not strong. Someone is either not rich or quiet. Paul is either not wise or rich. Mary is not patient or not generous. Alice is not curious or strong. Someone is curious or tall. | Alice is strong. | entailment | (![X]:(tall(X)<=>(~creative(X)|~strong(X))))&
(![X]:((~funny(X)<~>curious(X))=>(~old(X)&~wise(X))))&
(((humble(susan)&rich(susan)))<=>((~old(john)<~>humble(john))))&
(![X]:((brave(X)|happy(X))=>generous(X)))&
((~rich(paul))<=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((~generous(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
(![X]:((~happy(X)|strong(X))=>brave(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~generous(X)&~quiet(X)))))&
(![X]:((creative(X)&~kind(X))<=>(tall(X)&brave(X))))&
(![X]:((happy(X)|~patient(X))=>(~humble(X)|~patient(X))))&
((?[X]:((~patient(X)|~creative(X))))=>((~tall(john)<~>wise(john))))&
(![X]:((kind(X)|brave(X))=>(funny(X)<~>generous(X))))&
(![X]:((calm(X)|~patient(X))<=>(~kind(X)<~>old(X))))&
(![X]:((~happy(X)|~generous(X))=>(~quiet(X)|~calm(X))))&
(((quiet(fred)&~humble(fred)))<=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((wise(X)&~rich(X))=>wise(X)))&
((old(alice)|strong(alice)))&
(?[X]:(~strong(X)))&
(?[X]:((~rich(X)<~>quiet(X))))&
((~wise(paul)<~>rich(paul)))&
((~patient(mary)|~generous(mary)))&
((~curious(alice)|strong(alice)))&
(?[X]:((curious(X)|tall(X)))) | strong(alice) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"p11",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6425168404077029765876509
% SZS output start Proof for 6425168404077029765876509
1. ! [X0] : (tall(X0) <=> (~strong(X0) | ~creative(X0))) [input p0]
2. ! [X0] : ((~funny(X0) <~> curious(X0)) => (~wise(X0) & ~old(X0))) [input p1]
4. ! [X0] : ((happy(X0) | brave(X0)) => generous(X0)) [input p3]
7. ! [X0] : ((strong(X0) | ~happy(X0)) => brave(X0)) [input p6]
8. ? [X0] : ~humble(X0) <=> ? [X0] : (~quiet(X0) & ~generous(X0)) [input p7]
12. ! [X0] : ((brave(X0) | kind(X0)) => (funny(X0) <~> generous(X0))) [input p11]
15. (~humble(fred) & quiet(fred)) <=> ? [X0] : (happy(X0) & tall(X0)) [input p14]
17. strong(alice) | old(alice) [input p16]
22. strong(alice) | ~curious(alice) [input p21]
24. ~strong(alice) [input hypothesis]
25. ? [X0] : ~humble(X0) <=> ? [X1] : (~quiet(X1) & ~generous(X1)) [rectify 8]
26. ! [X0] : ((~wise(X0) & ~old(X0)) | (~funny(X0) <=> curious(X0))) [ennf transformation 2]
27. ! [X0] : (generous(X0) | (~happy(X0) & ~brave(X0))) [ennf transformation 4]
28. ! [X0] : (brave(X0) | (~strong(X0) & happy(X0))) [ennf transformation 7]
32. ! [X0] : ((funny(X0) <~> generous(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 12]
37. ! [X0] : ((tall(X0) | (strong(X0) & creative(X0))) & ((~strong(X0) | ~creative(X0)) | ~tall(X0))) [nnf transformation 1]
38. ! [X0] : ((tall(X0) | (strong(X0) & creative(X0))) & (~strong(X0) | ~creative(X0) | ~tall(X0))) [flattening 37]
39. ! [X0] : ((~wise(X0) & ~old(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [nnf transformation 26]
48. (? [X0] : ~humble(X0) | ! [X1] : (quiet(X1) | generous(X1))) & (? [X1] : (~quiet(X1) & ~generous(X1)) | ! [X0] : humble(X0)) [nnf transformation 25]
49. (? [X0] : ~humble(X0) | ! [X1] : (quiet(X1) | generous(X1))) & (? [X2] : (~quiet(X2) & ~generous(X2)) | ! [X3] : humble(X3)) [rectify 48]
50. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
51. ? [X2] : (~quiet(X2) & ~generous(X2)) => (~quiet(sK2) & ~generous(sK2)) [choice axiom]
52. (~humble(sK1) | ! [X1] : (quiet(X1) | generous(X1))) & ((~quiet(sK2) & ~generous(sK2)) | ! [X3] : humble(X3)) [skolemisation 49,51,50]
56. ! [X0] : (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~brave(X0) & ~kind(X0))) [nnf transformation 32]
59. ((~humble(fred) & quiet(fred)) | ! [X0] : (~happy(X0) | ~tall(X0))) & (? [X0] : (happy(X0) & tall(X0)) | (humble(fred) | ~quiet(fred))) [nnf transformation 15]
60. ((~humble(fred) & quiet(fred)) | ! [X0] : (~happy(X0) | ~tall(X0))) & (? [X0] : (happy(X0) & tall(X0)) | humble(fred) | ~quiet(fred)) [flattening 59]
61. ((~humble(fred) & quiet(fred)) | ! [X0] : (~happy(X0) | ~tall(X0))) & (? [X1] : (happy(X1) & tall(X1)) | humble(fred) | ~quiet(fred)) [rectify 60]
62. ? [X1] : (happy(X1) & tall(X1)) => (happy(sK3) & tall(sK3)) [choice axiom]
63. ((~humble(fred) & quiet(fred)) | ! [X0] : (~happy(X0) | ~tall(X0))) & ((happy(sK3) & tall(sK3)) | humble(fred) | ~quiet(fred)) [skolemisation 61,62]
74. strong(X0) | tall(X0) [cnf transformation 38]
75. ~old(X0) | curious(X0) | funny(X0) [cnf transformation 39]
85. ~brave(X0) | generous(X0) [cnf transformation 27]
86. ~happy(X0) | generous(X0) [cnf transformation 27]
96. happy(X0) | brave(X0) [cnf transformation 28]
97. ~strong(X0) | brave(X0) [cnf transformation 28]
98. ~generous(sK2) | humble(X3) [cnf transformation 52]
114. ~generous(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 56]
126. ~humble(fred) | ~happy(X0) | ~tall(X0) [cnf transformation 63]
128. strong(alice) | old(alice) [cnf transformation 17]
135. strong(alice) | ~curious(alice) [cnf transformation 22]
137. ~strong(alice) [cnf transformation 24]
193. 12 <=> ! [X3] : humble(X3) [avatar definition]
194. humble(X3) <- (12) [avatar component clause 193]
201. 14 <=> generous(sK2) [avatar definition]
203. ~generous(sK2) <- (~14) [avatar component clause 201]
204. 12 | ~14 [avatar split clause 98,201,193]
225. ~brave(X0) | ~funny(X0) [subsumption resolution 114,85]
227. 19 <=> ! [X0] : (~happy(X0) | ~tall(X0)) [avatar definition]
228. ~happy(X0) | ~tall(X0) <- (19) [avatar component clause 227]
230. 20 <=> humble(fred) [avatar definition]
232. ~humble(fred) <- (~20) [avatar component clause 230]
233. 19 | ~20 [avatar split clause 126,230,227]
250. 24 <=> old(alice) [avatar definition]
252. old(alice) <- (24) [avatar component clause 250]
254. 25 <=> strong(alice) [avatar definition]
257. 24 | 25 [avatar split clause 128,254,250]
284. 31 <=> curious(alice) [avatar definition]
286. ~curious(alice) <- (~31) [avatar component clause 284]
287. ~31 | 25 [avatar split clause 135,254,284]
297. ~25 [avatar split clause 137,254]
301. brave(X0) | generous(X0) [resolution 96,86]
302. generous(X0) [subsumption resolution 301,85]
303. $false <- (~14) [resolution 302,203]
306. 14 [avatar contradiction clause 303]
313. brave(X0) | tall(X0) [resolution 97,74]
317. ~tall(X0) | brave(X0) <- (19) [resolution 228,96]
318. brave(X0) <- (19) [subsumption resolution 317,313]
320. ~funny(X0) <- (19) [resolution 318,225]
324. curious(alice) | funny(alice) <- (24) [resolution 75,252]
325. funny(alice) <- (24, ~31) [subsumption resolution 324,286]
326. $false <- (19, 24, ~31) [subsumption resolution 325,320]
327. ~19 | ~24 | 31 [avatar contradiction clause 326]
328. $false <- (12, ~20) [subsumption resolution 232,194]
329. ~12 | 20 [avatar contradiction clause 328]
330. $false [avatar sat refutation 204,233,257,287,297,306,327,329]
% SZS output end Proof for 6425168404077029765876509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and funny is both not humble and not brave.
Everyone who is either creative or not brave is both not creative and brave and vice versa.
Everyone who is not tall or creative is tall or not kind.
If someone is humble or patient then someone is either not tall or not curious and vice versa.
Everyone who is both curious and not calm is not humble or not happy and vice versa.
If fred is either not humble or rich then someone is both kind and not brave.
If someone is either calm or not creative then fred is both not tall and old.
Everyone who is both curious and tall is brave or not old and vice versa.
Everyone who is either not funny or not brave is either calm or not happy and vice versa.
Everyone who is both rich and curious is not quiet or not rich.
Everyone who is not rich is wise.
Everyone who is wise is not curious or calm.
Everyone who is both not generous and not humble is patient or not happy and vice versa.
Everyone who is either rich or not old is not creative or not curious.
If someone is not kind or patient then paul is not kind or not rich.
If someone is both calm and not happy then alice is not strong or not rich and vice versa.
John is either not kind or not calm.
John is humble or not rich.
Someone is both not calm and tall.
Someone is generous or not kind.
Someone is either curious or not creative.
Someone is either not calm or generous.
Someone is not rich.
John is not brave or brave. | John is happy. | entailment | (![X]:((~tall(X)&funny(X))=>(~humble(X)&~brave(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~creative(X)&brave(X))))&
(![X]:((~tall(X)|creative(X))=>(tall(X)|~kind(X))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
(![X]:((curious(X)&~calm(X))<=>(~humble(X)|~happy(X))))&
(((~humble(fred)<~>rich(fred)))=>(?[X]:((kind(X)&~brave(X)))))&
((?[X]:((calm(X)<~>~creative(X))))=>((~tall(fred)&old(fred))))&
(![X]:((curious(X)&tall(X))<=>(brave(X)|~old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((rich(X)&curious(X))=>(~quiet(X)|~rich(X))))&
(![X]:(~rich(X)=>wise(X)))&
(![X]:(wise(X)=>(~curious(X)|calm(X))))&
(![X]:((~generous(X)&~humble(X))<=>(patient(X)|~happy(X))))&
(![X]:((rich(X)<~>~old(X))=>(~creative(X)|~curious(X))))&
((?[X]:((~kind(X)|patient(X))))=>((~kind(paul)|~rich(paul))))&
((?[X]:((calm(X)&~happy(X))))<=>((~strong(alice)|~rich(alice))))&
((~kind(john)<~>~calm(john)))&
((humble(john)|~rich(john)))&
(?[X]:((~calm(X)&tall(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:((~calm(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
((~brave(john)|brave(john))) | happy(john) | [
"p4",
"p10",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2044563809882720161317744
% SZS output start Proof for 2044563809882720161317744
5. ! [X0] : ((~calm(X0) & curious(X0)) <=> (~happy(X0) | ~humble(X0))) [input p4]
11. ! [X0] : (~rich(X0) => wise(X0)) [input p10]
12. ! [X0] : (wise(X0) => (calm(X0) | ~curious(X0))) [input p11]
13. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (~happy(X0) | patient(X0))) [input p12]
18. ~rich(john) | humble(john) [input p17]
25. ~happy(john) [input hypothesis]
34. ! [X0] : (wise(X0) | rich(X0)) [ennf transformation 11]
35. ! [X0] : ((calm(X0) | ~curious(X0)) | ~wise(X0)) [ennf transformation 12]
36. ! [X0] : (calm(X0) | ~curious(X0) | ~wise(X0)) [flattening 35]
48. ! [X0] : (((~calm(X0) & curious(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (calm(X0) | ~curious(X0)))) [nnf transformation 5]
49. ! [X0] : (((~calm(X0) & curious(X0)) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | calm(X0) | ~curious(X0))) [flattening 48]
57. ! [X0] : (((~humble(X0) & ~generous(X0)) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 13]
58. ! [X0] : (((~humble(X0) & ~generous(X0)) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | humble(X0) | generous(X0))) [flattening 57]
96. happy(X0) | curious(X0) [cnf transformation 49]
97. ~calm(X0) | humble(X0) [cnf transformation 49]
120. wise(X0) | rich(X0) [cnf transformation 34]
121. ~wise(X0) | ~curious(X0) | calm(X0) [cnf transformation 36]
126. ~humble(X0) | happy(X0) [cnf transformation 58]
138. ~rich(john) | humble(john) [cnf transformation 18]
148. ~happy(john) [cnf transformation 25]
266. 23 <=> calm(john) [avatar definition]
268. calm(john) <- (23) [avatar component clause 266]
272. 24 <=> humble(john) [avatar definition]
274. humble(john) <- (24) [avatar component clause 272]
276. 25 <=> rich(john) [avatar definition]
279. 24 | ~25 [avatar split clause 138,276,272]
301. curious(john) [resolution 96,148]
317. ~curious(X0) | calm(X0) | rich(X0) [resolution 121,120]
389. calm(john) | rich(john) [resolution 317,301]
407. humble(john) <- (23) [resolution 268,97]
410. 24 | ~23 [avatar split clause 407,266,272]
411. 25 | 23 [avatar split clause 389,266,276]
414. happy(john) <- (24) [resolution 274,126]
415. $false <- (24) [subsumption resolution 414,148]
416. ~24 [avatar contradiction clause 415]
417. $false [avatar sat refutation 279,410,411,416]
% SZS output end Proof for 2044563809882720161317744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not brave then someone is both creative and not humble and vice versa.
Everyone who is both quiet and wise is both not calm and not quiet.
Everyone who is either rich or old is not tall or old.
Everyone who is not happy is strong and vice versa.
Everyone who is not brave or not calm is both not kind and not patient and vice versa.
Everyone who is strong or happy is not strong and vice versa.
If paul is old or kind then someone is funny or kind.
Everyone who is not patient is either quiet or curious and vice versa.
Everyone who is brave is not kind or strong and vice versa.
If alice is not generous or not tall then paul is not kind or not brave.
Everyone who is both old and not wise is not patient or kind.
If lucy is not calm then someone is both not tall and not quiet and vice versa.
Everyone who is not old is both curious and tall.
If someone is both not happy and generous then lucy is not rich and vice versa.
If someone is not funny then alice is both not tall and strong and vice versa.
If someone is generous then susan is both not funny and calm and vice versa.
Someone is wise.
Someone is either not happy or quiet.
Someone is either not brave or curious.
Susan is either curious or not brave.
Mary is happy or not tall.
Lucy is either calm or tall. | Mary is not quiet. | neutral | ((?[X]:((tall(X)<~>~brave(X))))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((quiet(X)&wise(X))=>(~calm(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))=>(~tall(X)|old(X))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((~brave(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
(![X]:((strong(X)|happy(X))<=>~strong(X)))&
(((old(paul)|kind(paul)))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:(~patient(X)<=>(quiet(X)<~>curious(X))))&
(![X]:(brave(X)<=>(~kind(X)|strong(X))))&
(((~generous(alice)|~tall(alice)))=>((~kind(paul)|~brave(paul))))&
(![X]:((old(X)&~wise(X))=>(~patient(X)|kind(X))))&
((~calm(lucy))<=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:(~old(X)=>(curious(X)&tall(X))))&
((?[X]:((~happy(X)&generous(X))))<=>(~rich(lucy)))&
((?[X]:(~funny(X)))<=>((~tall(alice)&strong(alice))))&
((?[X]:(generous(X)))<=>((~funny(susan)&calm(susan))))&
(?[X]:(wise(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
((curious(susan)<~>~brave(susan)))&
((happy(mary)|~tall(mary)))&
((calm(lucy)<~>tall(lucy))) | ~quiet(mary) | [] | null | 0 |
Everyone who is either not creative or funny is rich and vice versa.
If fred is either not funny or not old then lucy is tall or not rich.
If lucy is either old or brave then paul is not funny or not old.
If someone is not patient then paul is not kind or strong.
Everyone who is not generous or not old is not rich or wise and vice versa.
Everyone who is either funny or not old is both not rich and calm.
Everyone who is not calm is either not creative or quiet and vice versa.
Everyone who is wise or patient is both not happy and strong.
If mary is not old or happy then someone is both rich and not funny and vice versa.
If susan is curious or not curious then someone is calm.
Everyone who is both curious and not generous is either curious or old.
If fred is strong then fred is not generous.
Everyone who is not strong or not quiet is wise or quiet and vice versa.
If someone is both kind and generous then mary is not brave or not curious and vice versa.
If someone is creative then someone is not curious or not brave and vice versa.
If susan is creative or happy then someone is brave or not calm.
Susan is curious.
John is both brave and happy.
Someone is both humble and not kind.
John is old or not kind.
Someone is not happy.
Susan is either calm or patient.
John is either curious or not rich.
Someone is not kind. | Paul is not kind. | neutral | (![X]:((~creative(X)<~>funny(X))<=>rich(X)))&
(((~funny(fred)<~>~old(fred)))=>((tall(lucy)|~rich(lucy))))&
(((old(lucy)<~>brave(lucy)))=>((~funny(paul)|~old(paul))))&
((?[X]:(~patient(X)))=>((~kind(paul)|strong(paul))))&
(![X]:((~generous(X)|~old(X))<=>(~rich(X)|wise(X))))&
(![X]:((funny(X)<~>~old(X))=>(~rich(X)&calm(X))))&
(![X]:(~calm(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((wise(X)|patient(X))=>(~happy(X)&strong(X))))&
(((~old(mary)|happy(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(((curious(susan)|~curious(susan)))=>(?[X]:(calm(X))))&
(![X]:((curious(X)&~generous(X))=>(curious(X)<~>old(X))))&
((strong(fred))=>(~generous(fred)))&
(![X]:((~strong(X)|~quiet(X))<=>(wise(X)|quiet(X))))&
((?[X]:((kind(X)&generous(X))))<=>((~brave(mary)|~curious(mary))))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)|~brave(X)))))&
(((creative(susan)|happy(susan)))=>(?[X]:((brave(X)|~calm(X)))))&
(curious(susan))&
((brave(john)&happy(john)))&
(?[X]:((humble(X)&~kind(X))))&
((old(john)|~kind(john)))&
(?[X]:(~happy(X)))&
((calm(susan)<~>patient(susan)))&
((curious(john)<~>~rich(john)))&
(?[X]:(~kind(X))) | ~kind(paul) | [] | null | 0 |
Everyone who is either happy or not tall is both not calm and not kind.
Everyone who is not happy is calm and vice versa.
If someone is either calm or not calm then paul is either not old or not strong.
Everyone who is not generous is either rich or curious.
Everyone who is either not curious or wise is generous or not calm and vice versa.
If lucy is not kind or not generous then someone is either humble or tall and vice versa.
Everyone who is quiet is not patient or not old.
Everyone who is not rich is happy and vice versa.
If fred is not creative then lucy is not brave and vice versa.
If someone is wise or not old then alice is both not happy and not calm and vice versa.
Everyone who is either strong or brave is both not kind and not funny and vice versa.
If someone is not brave or generous then john is quiet.
If john is either not humble or not creative then someone is not creative.
Everyone who is kind or not strong is rich or not tall and vice versa.
If someone is either curious or creative then susan is not kind and vice versa.
If someone is either not rich or not happy then someone is generous or not wise and vice versa.
Susan is curious or brave.
Alice is either not quiet or not curious.
Susan is calm or not old.
Susan is patient or not happy. | John is tall. | neutral | (![X]:((happy(X)<~>~tall(X))=>(~calm(X)&~kind(X))))&
(![X]:(~happy(X)<=>calm(X)))&
((?[X]:((calm(X)<~>~calm(X))))=>((~old(paul)<~>~strong(paul))))&
(![X]:(~generous(X)=>(rich(X)<~>curious(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(generous(X)|~calm(X))))&
(((~kind(lucy)|~generous(lucy)))<=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:(quiet(X)=>(~patient(X)|~old(X))))&
(![X]:(~rich(X)<=>happy(X)))&
((~creative(fred))<=>(~brave(lucy)))&
((?[X]:((wise(X)|~old(X))))<=>((~happy(alice)&~calm(alice))))&
(![X]:((strong(X)<~>brave(X))<=>(~kind(X)&~funny(X))))&
((?[X]:((~brave(X)|generous(X))))=>(quiet(john)))&
(((~humble(john)<~>~creative(john)))=>(?[X]:(~creative(X))))&
(![X]:((kind(X)|~strong(X))<=>(rich(X)|~tall(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>(~kind(susan)))&
((?[X]:((~rich(X)<~>~happy(X))))<=>(?[X]:((generous(X)|~wise(X)))))&
((curious(susan)|brave(susan)))&
((~quiet(alice)<~>~curious(alice)))&
((calm(susan)|~old(susan)))&
((patient(susan)|~happy(susan))) | tall(john) | [] | null | 0 |
If someone is both not funny and not quiet then someone is either not happy or not strong and vice versa. If someone is not strong or not generous then lucy is not calm or not quiet. Everyone who is both not brave and not tall is humble or old. Everyone who is either calm or not patient is not kind or curious and vice versa. If alice is both generous and not funny then someone is either patient or not patient and vice versa. If someone is curious then mary is rich or not creative. Everyone who is both patient and humble is both not kind and creative and vice versa. If john is generous or brave then someone is either generous or quiet. Everyone who is both old and tall is both kind and rich and vice versa. If someone is both not strong and wise then mary is not generous and vice versa. If someone is brave or strong then someone is generous. If someone is funny or curious then paul is both not humble and not old and vice versa. If someone is both not tall and not patient then susan is quiet and vice versa. Everyone who is generous or old is either tall or not wise. If lucy is both kind and not humble then fred is not funny or brave. Everyone who is both not generous and wise is both tall and patient. Someone is creative. Lucy is wise. Mary is patient or not calm. John is both not kind and not wise. Lucy is either brave or patient. Susan is both curious and humble. Someone is not strong. Someone is both not wise and not generous. | Paul is not old. | entailment | ((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
((?[X]:((~strong(X)|~generous(X))))=>((~calm(lucy)|~quiet(lucy))))&
(![X]:((~brave(X)&~tall(X))=>(humble(X)|old(X))))&
(![X]:((calm(X)<~>~patient(X))<=>(~kind(X)|curious(X))))&
(((generous(alice)&~funny(alice)))<=>(?[X]:((patient(X)<~>~patient(X)))))&
((?[X]:(curious(X)))=>((rich(mary)|~creative(mary))))&
(![X]:((patient(X)&humble(X))<=>(~kind(X)&creative(X))))&
(((generous(john)|brave(john)))=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((old(X)&tall(X))<=>(kind(X)&rich(X))))&
((?[X]:((~strong(X)&wise(X))))<=>(~generous(mary)))&
((?[X]:((brave(X)|strong(X))))=>(?[X]:(generous(X))))&
((?[X]:((funny(X)|curious(X))))<=>((~humble(paul)&~old(paul))))&
((?[X]:((~tall(X)&~patient(X))))<=>(quiet(susan)))&
(![X]:((generous(X)|old(X))=>(tall(X)<~>~wise(X))))&
(((kind(lucy)&~humble(lucy)))=>((~funny(fred)|brave(fred))))&
(![X]:((~generous(X)&wise(X))=>(tall(X)&patient(X))))&
(?[X]:(creative(X)))&
(wise(lucy))&
((patient(mary)|~calm(mary)))&
((~kind(john)&~wise(john)))&
((brave(lucy)<~>patient(lucy)))&
((curious(susan)&humble(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((~wise(X)&~generous(X)))) | ~old(paul) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7764435097697183181844641
% SZS output start Proof for 7764435097697183181844641
12. ? [X0] : (curious(X0) | funny(X0)) <=> (~old(paul) & ~humble(paul)) [input p11]
22. humble(susan) & curious(susan) [input p21]
25. old(paul) [input hypothesis]
67. (? [X0] : (curious(X0) | funny(X0)) | (old(paul) | humble(paul))) & ((~old(paul) & ~humble(paul)) | ! [X0] : (~curious(X0) & ~funny(X0))) [nnf transformation 12]
68. (? [X0] : (curious(X0) | funny(X0)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X0] : (~curious(X0) & ~funny(X0))) [flattening 67]
69. (? [X0] : (curious(X0) | funny(X0)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X1] : (~curious(X1) & ~funny(X1))) [rectify 68]
70. ? [X0] : (curious(X0) | funny(X0)) => (curious(sK6) | funny(sK6)) [choice axiom]
71. ((curious(sK6) | funny(sK6)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X1] : (~curious(X1) & ~funny(X1))) [skolemisation 69,70]
126. ~old(paul) | ~curious(X1) [cnf transformation 71]
145. curious(susan) [cnf transformation 22]
150. old(paul) [cnf transformation 25]
221. 16 <=> ! [X0] : ~curious(X0) [avatar definition]
222. ~curious(X0) <- (16) [avatar component clause 221]
287. 31 <=> old(paul) [avatar definition]
299. 16 | ~31 [avatar split clause 126,287,221]
361. 31 [avatar split clause 150,287]
367. $false <- (16) [resolution 222,145]
368. ~16 [avatar contradiction clause 367]
369. $false [avatar sat refutation 299,361,368]
% SZS output end Proof for 7764435097697183181844641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or rich is tall or not calm and vice versa. Everyone who is curious or brave is not patient and vice versa. Everyone who is not brave or patient is either not rich or not creative. Everyone who is either brave or calm is curious. Everyone who is both strong and rich is quiet or generous. If lucy is not creative or tall then susan is either happy or kind and vice versa. If fred is both strong and not happy then susan is both generous and not calm. Everyone who is either generous or curious is not tall or not quiet. Everyone who is funny or tall is not creative and vice versa. If someone is either humble or calm then someone is not wise or old. Everyone who is both calm and not curious is either kind or strong. Everyone who is either not brave or creative is happy or brave and vice versa. If someone is either not tall or humble then someone is both not brave and wise and vice versa. Everyone who is both not happy and strong is generous and vice versa. Everyone who is tall or not calm is both not brave and happy. If someone is not rich then someone is not kind and vice versa. Susan is either not wise or strong. Someone is both humble and not rich. Mary is not rich or kind. Lucy is both curious and not kind. Someone is not kind. Lucy is humble or generous. Fred is calm or happy. | Susan is not kind. | neutral | (![X]:((kind(X)|rich(X))<=>(tall(X)|~calm(X))))&
(![X]:((curious(X)|brave(X))<=>~patient(X)))&
(![X]:((~brave(X)|patient(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((brave(X)<~>calm(X))=>curious(X)))&
(![X]:((strong(X)&rich(X))=>(quiet(X)|generous(X))))&
(((~creative(lucy)|tall(lucy)))<=>((happy(susan)<~>kind(susan))))&
(((strong(fred)&~happy(fred)))=>((generous(susan)&~calm(susan))))&
(![X]:((generous(X)<~>curious(X))=>(~tall(X)|~quiet(X))))&
(![X]:((funny(X)|tall(X))<=>~creative(X)))&
((?[X]:((humble(X)<~>calm(X))))=>(?[X]:((~wise(X)|old(X)))))&
(![X]:((calm(X)&~curious(X))=>(kind(X)<~>strong(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(happy(X)|brave(X))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:((~happy(X)&strong(X))<=>generous(X)))&
(![X]:((tall(X)|~calm(X))=>(~brave(X)&happy(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~kind(X))))&
((~wise(susan)<~>strong(susan)))&
(?[X]:((humble(X)&~rich(X))))&
((~rich(mary)|kind(mary)))&
((curious(lucy)&~kind(lucy)))&
(?[X]:(~kind(X)))&
((humble(lucy)|generous(lucy)))&
((calm(fred)|happy(fred))) | ~kind(susan) | [] | null | 0 |
Everyone who is old is both wise and not funny and vice versa.
Everyone who is either not humble or not generous is kind or not humble.
If lucy is not wise then someone is both patient and not patient.
If someone is both strong and not strong then someone is both not brave and kind.
Everyone who is either not humble or not patient is both patient and not creative.
Everyone who is either calm or not calm is not strong.
Everyone who is humble is either happy or kind and vice versa.
Everyone who is both strong and happy is not rich or creative.
Everyone who is not brave is both not rich and kind and vice versa.
If someone is curious then someone is both not old and humble.
If alice is patient or not tall then alice is not strong.
Everyone who is both not calm and not patient is patient or curious.
Everyone who is not brave is either not old or funny and vice versa.
Everyone who is both tall and brave is either not rich or not tall.
If paul is not quiet then someone is not humble.
If lucy is not humble or not funny then someone is both not quiet and creative and vice versa.
John is funny.
John is both curious and not happy.
Someone is not brave.
Fred is not humble or not old.
Someone is both not happy and patient.
Someone is either calm or happy.
Someone is tall or kind.
Alice is brave. | Alice is not tall. | neutral | (![X]:(old(X)<=>(wise(X)&~funny(X))))&
(![X]:((~humble(X)<~>~generous(X))=>(kind(X)|~humble(X))))&
((~wise(lucy))=>(?[X]:((patient(X)&~patient(X)))))&
((?[X]:((strong(X)&~strong(X))))=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:((~humble(X)<~>~patient(X))=>(patient(X)&~creative(X))))&
(![X]:((calm(X)<~>~calm(X))=>~strong(X)))&
(![X]:(humble(X)<=>(happy(X)<~>kind(X))))&
(![X]:((strong(X)&happy(X))=>(~rich(X)|creative(X))))&
(![X]:(~brave(X)<=>(~rich(X)&kind(X))))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)&humble(X)))))&
(((patient(alice)|~tall(alice)))=>(~strong(alice)))&
(![X]:((~calm(X)&~patient(X))=>(patient(X)|curious(X))))&
(![X]:(~brave(X)<=>(~old(X)<~>funny(X))))&
(![X]:((tall(X)&brave(X))=>(~rich(X)<~>~tall(X))))&
((~quiet(paul))=>(?[X]:(~humble(X))))&
(((~humble(lucy)|~funny(lucy)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(funny(john))&
((curious(john)&~happy(john)))&
(?[X]:(~brave(X)))&
((~humble(fred)|~old(fred)))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((tall(X)|kind(X))))&
(brave(alice)) | ~tall(alice) | [] | null | 0 |
Everyone who is both curious and calm is either calm or not happy and vice versa.
Everyone who is kind or not strong is either not curious or old.
If lucy is both not patient and not happy then someone is both not strong and not brave and vice versa.
If paul is either strong or calm then fred is either not old or tall and vice versa.
Everyone who is quiet is not brave or curious and vice versa.
Everyone who is not funny or creative is both not old and not curious and vice versa.
If someone is either not old or strong then someone is both not kind and not generous.
Everyone who is brave is both not funny and not brave and vice versa.
Everyone who is both not quiet and old is not kind or not patient.
Everyone who is creative or not brave is brave or not patient.
If someone is kind or tall then someone is both not tall and strong and vice versa.
If someone is either funny or kind then paul is either patient or generous.
Everyone who is both happy and not rich is not brave or not strong.
Everyone who is either strong or not rich is not strong or patient and vice versa.
Everyone who is not happy is either not tall or curious and vice versa.
Everyone who is both tall and curious is not funny or not curious and vice versa.
Someone is not humble.
Alice is either curious or not humble.
Lucy is brave or curious.
Mary is not tall.
John is not tall or quiet. | Lucy is not funny. | contradiction | (![X]:((curious(X)&calm(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((kind(X)|~strong(X))=>(~curious(X)<~>old(X))))&
(((~patient(lucy)&~happy(lucy)))<=>(?[X]:((~strong(X)&~brave(X)))))&
(((strong(paul)<~>calm(paul)))<=>((~old(fred)<~>tall(fred))))&
(![X]:(quiet(X)<=>(~brave(X)|curious(X))))&
(![X]:((~funny(X)|creative(X))<=>(~old(X)&~curious(X))))&
((?[X]:((~old(X)<~>strong(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(brave(X)<=>(~funny(X)&~brave(X))))&
(![X]:((~quiet(X)&old(X))=>(~kind(X)|~patient(X))))&
(![X]:((creative(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((funny(X)<~>kind(X))))=>((patient(paul)<~>generous(paul))))&
(![X]:((happy(X)&~rich(X))=>(~brave(X)|~strong(X))))&
(![X]:((strong(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:(~happy(X)<=>(~tall(X)<~>curious(X))))&
(![X]:((tall(X)&curious(X))<=>(~funny(X)|~curious(X))))&
(?[X]:(~humble(X)))&
((curious(alice)<~>~humble(alice)))&
((brave(lucy)|curious(lucy)))&
(~tall(mary))&
((~tall(john)|quiet(john))) | ~funny(lucy) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4006560368344243003914580
% SZS output start Proof for 4006560368344243003914580
6. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (~curious(X0) & ~old(X0))) [input p5]
16. ! [X0] : ((curious(X0) & tall(X0)) <=> (~curious(X0) | ~funny(X0))) [input p15]
22. ~funny(lucy) [input hypothesis]
46. ! [X0] : (((creative(X0) | ~funny(X0)) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 6]
47. ! [X0] : ((creative(X0) | ~funny(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | (~creative(X0) & funny(X0)))) [flattening 46]
63. ! [X0] : (((curious(X0) & tall(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 16]
64. ! [X0] : (((curious(X0) & tall(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~curious(X0) | ~tall(X0))) [flattening 63]
93. ~curious(X0) | funny(X0) [cnf transformation 47]
130. curious(X0) | curious(X0) [cnf transformation 64]
137. ~funny(lucy) [cnf transformation 22]
139. curious(X0) [duplicate literal removal 130]
272. funny(X0) [resolution 93,139]
273. $false [resolution 272,137]
% SZS output end Proof for 4006560368344243003914580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not patient is both humble and not wise.
Everyone who is creative or not funny is either old or not strong.
If someone is not rich or not curious then fred is either happy or creative.
Everyone who is not calm is either not old or tall and vice versa.
Everyone who is not rich or not humble is either not rich or not curious and vice versa.
If susan is both not tall and not wise then susan is both not humble and not curious and vice versa.
Everyone who is both not calm and not happy is not rich or not patient and vice versa.
Everyone who is either not wise or not creative is both funny and kind and vice versa.
Everyone who is calm or not kind is both rich and kind and vice versa.
If someone is both not curious and old then someone is both not patient and quiet and vice versa.
If mary is either not wise or not creative then john is either not kind or not curious.
If someone is not creative or not tall then susan is not quiet or not tall and vice versa.
If alice is either brave or not kind then someone is not humble or not old.
If susan is both not patient and not wise then susan is not funny.
Everyone who is not curious or funny is wise.
If someone is both not curious and old then fred is both not kind and humble.
Someone is strong or patient.
John is not quiet.
Alice is either not curious or not quiet.
Fred is both funny and wise.
Someone is not humble.
Alice is creative or not wise.
Someone is humble or happy. | Fred is not calm. | contradiction | (![X]:((strong(X)<~>~patient(X))=>(humble(X)&~wise(X))))&
(![X]:((creative(X)|~funny(X))=>(old(X)<~>~strong(X))))&
((?[X]:((~rich(X)|~curious(X))))=>((happy(fred)<~>creative(fred))))&
(![X]:(~calm(X)<=>(~old(X)<~>tall(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~rich(X)<~>~curious(X))))&
(((~tall(susan)&~wise(susan)))<=>((~humble(susan)&~curious(susan))))&
(![X]:((~calm(X)&~happy(X))<=>(~rich(X)|~patient(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(funny(X)&kind(X))))&
(![X]:((calm(X)|~kind(X))<=>(rich(X)&kind(X))))&
((?[X]:((~curious(X)&old(X))))<=>(?[X]:((~patient(X)&quiet(X)))))&
(((~wise(mary)<~>~creative(mary)))=>((~kind(john)<~>~curious(john))))&
((?[X]:((~creative(X)|~tall(X))))<=>((~quiet(susan)|~tall(susan))))&
(((brave(alice)<~>~kind(alice)))=>(?[X]:((~humble(X)|~old(X)))))&
(((~patient(susan)&~wise(susan)))=>(~funny(susan)))&
(![X]:((~curious(X)|funny(X))=>wise(X)))&
((?[X]:((~curious(X)&old(X))))=>((~kind(fred)&humble(fred))))&
(?[X]:((strong(X)|patient(X))))&
(~quiet(john))&
((~curious(alice)<~>~quiet(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:(~humble(X)))&
((creative(alice)|~wise(alice)))&
(?[X]:((humble(X)|happy(X)))) | ~calm(fred) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 601313277483009330209758
% SZS output start Proof for 601313277483009330209758
3. ? [X0] : (~curious(X0) | ~rich(X0)) => (happy(fred) <~> creative(fred)) [input p2]
5. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~rich(X0) <~> ~curious(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~patient(X0) | ~rich(X0))) [input p6]
8. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> (kind(X0) & funny(X0))) [input p7]
9. ! [X0] : ((~kind(X0) | calm(X0)) <=> (kind(X0) & rich(X0))) [input p8]
15. ! [X0] : ((funny(X0) | ~curious(X0)) => wise(X0)) [input p14]
20. wise(fred) & funny(fred) [input p19]
21. ? [X0] : ~humble(X0) [input p20]
24. ~calm(fred) [input hypothesis]
28. (happy(fred) <~> creative(fred)) | ! [X0] : (curious(X0) & rich(X0)) [ennf transformation 3]
33. ! [X0] : (wise(X0) | (~funny(X0) & curious(X0))) [ennf transformation 15]
37. ((~creative(fred) | ~happy(fred)) & (creative(fred) | happy(fred))) | ! [X0] : (curious(X0) & rich(X0)) [nnf transformation 28]
39. ! [X0] : (((~humble(X0) | ~rich(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) & (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | (humble(X0) & rich(X0)))) [nnf transformation 5]
40. ! [X0] : ((~humble(X0) | ~rich(X0) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) & (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | (humble(X0) & rich(X0)))) [flattening 39]
43. ! [X0] : (((~happy(X0) & ~calm(X0)) | (patient(X0) & rich(X0))) & ((~patient(X0) | ~rich(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 7]
44. ! [X0] : (((~happy(X0) & ~calm(X0)) | (patient(X0) & rich(X0))) & (~patient(X0) | ~rich(X0) | happy(X0) | calm(X0))) [flattening 43]
45. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 8]
46. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [flattening 45]
47. ! [X0] : (((~kind(X0) | calm(X0)) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | (kind(X0) & ~calm(X0)))) [nnf transformation 9]
48. ! [X0] : ((~kind(X0) | calm(X0) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | (kind(X0) & ~calm(X0)))) [flattening 47]
66. ? [X0] : ~humble(X0) => ~humble(sK5) [choice axiom]
67. ~humble(sK5) [skolemisation 21,66]
78. creative(fred) | happy(fred) | rich(X0) [cnf transformation 37]
79. creative(fred) | happy(fred) | curious(X0) [cnf transformation 37]
87. ~curious(X0) | ~rich(X0) | humble(X0) [cnf transformation 40]
99. ~happy(X0) | rich(X0) [cnf transformation 44]
105. ~kind(X0) | ~wise(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 46]
110. kind(X0) | kind(X0) [cnf transformation 48]
111. ~kind(X0) | calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 48]
128. ~funny(X0) | wise(X0) [cnf transformation 33]
135. funny(fred) [cnf transformation 20]
137. ~humble(sK5) [cnf transformation 67]
140. ~calm(fred) [cnf transformation 24]
141. kind(X0) [duplicate literal removal 110]
142. ~kind(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 111]
146. 1 <=> ! [X0] : curious(X0) [avatar definition]
147. curious(X0) <- (1) [avatar component clause 146]
149. 2 <=> happy(fred) [avatar definition]
150. happy(fred) <- (2) [avatar component clause 149]
153. 3 <=> creative(fred) [avatar definition]
158. 4 <=> ! [X0] : rich(X0) [avatar definition]
159. rich(X0) <- (4) [avatar component clause 158]
161. 1 | 2 | 3 [avatar split clause 79,153,149,146]
162. 4 | 2 | 3 [avatar split clause 78,153,149,158]
314. rich(fred) <- (2) [resolution 99,150]
439. ~rich(X0) | calm(X0) [resolution 142,141]
440. calm(fred) <- (2) [resolution 439,314]
443. $false <- (2) [subsumption resolution 440,140]
444. ~2 [avatar contradiction clause 443]
458. ~wise(X0) | ~creative(X0) | ~funny(X0) [resolution 105,141]
459. ~funny(X0) | ~creative(X0) [subsumption resolution 458,128]
474. ~creative(fred) [resolution 459,135]
478. ~3 [avatar split clause 474,153]
479. ~rich(X0) | humble(X0) <- (1) [resolution 147,87]
482. humble(X0) <- (1, 4) [subsumption resolution 479,159]
491. $false <- (1, 4) [resolution 482,137]
494. ~1 | ~4 [avatar contradiction clause 491]
495. $false [avatar sat refutation 161,162,444,478,494]
% SZS output end Proof for 601313277483009330209758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and funny is either kind or not quiet and vice versa. Everyone who is both not patient and patient is creative or funny and vice versa. Everyone who is wise or patient is both humble and not strong. If paul is not rich then someone is both not rich and kind. If someone is both not quiet and strong then lucy is tall or kind. Everyone who is kind is either not strong or not rich. Everyone who is both calm and rich is either not brave or not calm. Everyone who is rich is curious and vice versa. If mary is strong then mary is not wise and vice versa. If john is both not rich and not calm then someone is wise or generous and vice versa. Everyone who is not brave is both not kind and not rich and vice versa. Everyone who is not creative is not generous or not brave and vice versa. Everyone who is both not strong and brave is both not kind and not quiet. If someone is both calm and generous then someone is old or not funny. Everyone who is funny is both calm and not tall. Everyone who is not rich is both kind and wise. Paul is rich. Fred is either not generous or wise. Someone is either creative or quiet. Someone is rich. Paul is not funny. Someone is either not funny or calm. | Fred is not curious. | contradiction | (![X]:((~creative(X)&funny(X))<=>(kind(X)<~>~quiet(X))))&
(![X]:((~patient(X)&patient(X))<=>(creative(X)|funny(X))))&
(![X]:((wise(X)|patient(X))=>(humble(X)&~strong(X))))&
((~rich(paul))=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((~quiet(X)&strong(X))))=>((tall(lucy)|kind(lucy))))&
(![X]:(kind(X)=>(~strong(X)<~>~rich(X))))&
(![X]:((calm(X)&rich(X))=>(~brave(X)<~>~calm(X))))&
(![X]:(rich(X)<=>curious(X)))&
((strong(mary))<=>(~wise(mary)))&
(((~rich(john)&~calm(john)))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(~brave(X)<=>(~kind(X)&~rich(X))))&
(![X]:(~creative(X)<=>(~generous(X)|~brave(X))))&
(![X]:((~strong(X)&brave(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((old(X)|~funny(X)))))&
(![X]:(funny(X)=>(calm(X)&~tall(X))))&
(![X]:(~rich(X)=>(kind(X)&wise(X))))&
(rich(paul))&
((~generous(fred)<~>wise(fred)))&
(?[X]:((creative(X)<~>quiet(X))))&
(?[X]:(rich(X)))&
(~funny(paul))&
(?[X]:((~funny(X)<~>calm(X)))) | ~curious(fred) | [
"p2",
"p7",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 642805985561231199737526
% SZS output start Proof for 642805985561231199737526
3. ! [X0] : ((patient(X0) | wise(X0)) => (~strong(X0) & humble(X0))) [input p2]
8. ! [X0] : (rich(X0) <=> curious(X0)) [input p7]
10. (~calm(john) & ~rich(john)) <=> ? [X0] : (generous(X0) | wise(X0)) [input p9]
11. ! [X0] : (~brave(X0) <=> (~rich(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((brave(X0) & ~strong(X0)) => (~quiet(X0) & ~kind(X0))) [input p12]
16. ! [X0] : (~rich(X0) => (wise(X0) & kind(X0))) [input p15]
23. ~curious(fred) [input hypothesis]
26. ! [X0] : ((patient(X0) | wise(X0)) => ~strong(X0)) [pure predicate removal 3]
27. ! [X0] : (~strong(X0) | (~patient(X0) & ~wise(X0))) [ennf transformation 26]
34. ! [X0] : ((~quiet(X0) & ~kind(X0)) | (~brave(X0) | strong(X0))) [ennf transformation 13]
35. ! [X0] : ((~quiet(X0) & ~kind(X0)) | ~brave(X0) | strong(X0)) [flattening 34]
37. ! [X0] : ((wise(X0) & kind(X0)) | rich(X0)) [ennf transformation 16]
46. ! [X0] : ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))) [nnf transformation 8]
48. ((~calm(john) & ~rich(john)) | ! [X0] : (~generous(X0) & ~wise(X0))) & (? [X0] : (generous(X0) | wise(X0)) | (calm(john) | rich(john))) [nnf transformation 10]
49. ((~calm(john) & ~rich(john)) | ! [X0] : (~generous(X0) & ~wise(X0))) & (? [X0] : (generous(X0) | wise(X0)) | calm(john) | rich(john)) [flattening 48]
50. ((~calm(john) & ~rich(john)) | ! [X0] : (~generous(X0) & ~wise(X0))) & (? [X1] : (generous(X1) | wise(X1)) | calm(john) | rich(john)) [rectify 49]
51. ? [X1] : (generous(X1) | wise(X1)) => (generous(sK1) | wise(sK1)) [choice axiom]
52. ((~calm(john) & ~rich(john)) | ! [X0] : (~generous(X0) & ~wise(X0))) & ((generous(sK1) | wise(sK1)) | calm(john) | rich(john)) [skolemisation 50,51]
53. ! [X0] : ((~brave(X0) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | brave(X0))) [nnf transformation 11]
54. ! [X0] : ((~brave(X0) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | brave(X0))) [flattening 53]
77. ~strong(X0) | ~wise(X0) [cnf transformation 27]
86. ~rich(X0) | curious(X0) [cnf transformation 46]
91. ~rich(john) | ~wise(X0) [cnf transformation 52]
95. ~kind(X0) | brave(X0) [cnf transformation 54]
101. ~kind(X0) | ~brave(X0) | strong(X0) [cnf transformation 35]
105. rich(X0) | kind(X0) [cnf transformation 37]
106. rich(X0) | wise(X0) [cnf transformation 37]
116. ~curious(fred) [cnf transformation 23]
164. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
165. ~wise(X0) <- (11) [avatar component clause 164]
168. 12 <=> rich(john) [avatar definition]
170. ~rich(john) <- (~12) [avatar component clause 168]
172. 11 | ~12 [avatar split clause 91,168,164]
183. ~kind(X0) | strong(X0) [subsumption resolution 101,95]
211. wise(X1) | curious(X1) [resolution 106,86]
212. curious(X1) <- (11) [subsumption resolution 211,165]
214. $false <- (11) [resolution 212,116]
216. ~11 [avatar contradiction clause 214]
218. wise(john) <- (~12) [resolution 170,106]
219. kind(john) <- (~12) [resolution 170,105]
222. strong(john) <- (~12) [resolution 219,183]
226. ~wise(john) <- (~12) [resolution 222,77]
227. $false <- (~12) [subsumption resolution 226,218]
228. 12 [avatar contradiction clause 227]
229. $false [avatar sat refutation 172,216,228]
% SZS output end Proof for 642805985561231199737526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both brave and wise then someone is tall.
If someone is both not funny and not patient then mary is either not brave or tall and vice versa.
If john is not wise or kind then someone is not wise and vice versa.
Everyone who is not generous is both not calm and not quiet and vice versa.
If someone is not happy or patient then someone is not brave or quiet and vice versa.
If paul is both brave and generous then someone is patient or strong.
Everyone who is both strong and not kind is either not funny or not patient.
Everyone who is not kind is both quiet and not quiet.
If someone is not funny or not curious then paul is not wise.
Everyone who is not generous or not tall is either curious or not calm.
If someone is both brave and not strong then lucy is not creative and vice versa.
Everyone who is not tall or tall is not strong.
Everyone who is both wise and not happy is not quiet or wise and vice versa.
If someone is either not wise or kind then susan is brave and vice versa.
Everyone who is not funny is either not generous or not tall and vice versa.
Everyone who is patient or creative is not brave or not funny and vice versa.
Someone is curious or not curious.
Lucy is patient.
John is curious or not brave.
Someone is either not quiet or not old.
Fred is either not tall or not wise.
Someone is brave.
Someone is funny or happy.
John is either brave or not happy. | John is kind. | entailment | (((brave(fred)&wise(fred)))=>(?[X]:(tall(X))))&
((?[X]:((~funny(X)&~patient(X))))<=>((~brave(mary)<~>tall(mary))))&
(((~wise(john)|kind(john)))<=>(?[X]:(~wise(X))))&
(![X]:(~generous(X)<=>(~calm(X)&~quiet(X))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~brave(X)|quiet(X)))))&
(((brave(paul)&generous(paul)))=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)<~>~patient(X))))&
(![X]:(~kind(X)=>(quiet(X)&~quiet(X))))&
((?[X]:((~funny(X)|~curious(X))))=>(~wise(paul)))&
(![X]:((~generous(X)|~tall(X))=>(curious(X)<~>~calm(X))))&
((?[X]:((brave(X)&~strong(X))))<=>(~creative(lucy)))&
(![X]:((~tall(X)|tall(X))=>~strong(X)))&
(![X]:((wise(X)&~happy(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(brave(susan)))&
(![X]:(~funny(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((patient(X)|creative(X))<=>(~brave(X)|~funny(X))))&
(?[X]:((curious(X)|~curious(X))))&
(patient(lucy))&
((curious(john)|~brave(john)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~tall(fred)<~>~wise(fred)))&
(?[X]:(brave(X)))&
(?[X]:((funny(X)|happy(X))))&
((brave(john)<~>~happy(john))) | kind(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2803505137049780729317161
% SZS output start Proof for 2803505137049780729317161
8. ! [X0] : (~kind(X0) => (~quiet(X0) & quiet(X0))) [input p7]
25. ~kind(john) [input hypothesis]
33. ! [X0] : ((~quiet(X0) & quiet(X0)) | kind(X0)) [ennf transformation 8]
103. quiet(X0) | kind(X0) [cnf transformation 33]
104. ~quiet(X0) | kind(X0) [cnf transformation 33]
144. ~kind(john) [cnf transformation 25]
250. kind(X0) [subsumption resolution 103,104]
338. $false [subsumption resolution 144,250]
% SZS output end Proof for 2803505137049780729317161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or creative then mary is not creative or not generous and vice versa.
Everyone who is either not strong or creative is wise.
Everyone who is not calm is both not funny and calm and vice versa.
If alice is wise or patient then someone is wise or not quiet.
If someone is not quiet then mary is both not wise and kind.
If someone is either happy or not rich then someone is old or not kind and vice versa.
Everyone who is either rich or not wise is not generous or happy and vice versa.
Everyone who is either old or not quiet is either not quiet or not kind.
If john is both not curious and not generous then susan is not calm.
Everyone who is both kind and funny is rich.
Everyone who is rich is quiet or not funny.
If susan is tall then someone is either brave or generous and vice versa.
Everyone who is not funny is either strong or not humble.
Everyone who is not wise or kind is both not strong and tall and vice versa.
If someone is both strong and rich then mary is not rich or kind and vice versa.
Everyone who is old is not calm or curious.
Someone is not brave.
Someone is either humble or strong.
Someone is humble or tall.
Someone is wise.
Lucy is tall or calm.
Someone is either not happy or generous. | Mary is not funny. | contradiction | ((?[X]:((quiet(X)|creative(X))))<=>((~creative(mary)|~generous(mary))))&
(![X]:((~strong(X)<~>creative(X))=>wise(X)))&
(![X]:(~calm(X)<=>(~funny(X)&calm(X))))&
(((wise(alice)|patient(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:(~quiet(X)))=>((~wise(mary)&kind(mary))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~generous(X)|happy(X))))&
(![X]:((old(X)<~>~quiet(X))=>(~quiet(X)<~>~kind(X))))&
(((~curious(john)&~generous(john)))=>(~calm(susan)))&
(![X]:((kind(X)&funny(X))=>rich(X)))&
(![X]:(rich(X)=>(quiet(X)|~funny(X))))&
((tall(susan))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(~funny(X)=>(strong(X)<~>~humble(X))))&
(![X]:((~wise(X)|kind(X))<=>(~strong(X)&tall(X))))&
((?[X]:((strong(X)&rich(X))))<=>((~rich(mary)|kind(mary))))&
(![X]:(old(X)=>(~calm(X)|curious(X))))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:(wise(X)))&
((tall(lucy)|calm(lucy)))&
(?[X]:((~happy(X)<~>generous(X)))) | ~funny(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2779228364892980965675965
% SZS output start Proof for 2779228364892980965675965
3. ! [X0] : (~calm(X0) <=> (calm(X0) & ~funny(X0))) [input p2]
23. ~funny(mary) [input hypothesis]
43. ! [X0] : ((~calm(X0) | (~calm(X0) | funny(X0))) & ((calm(X0) & ~funny(X0)) | calm(X0))) [nnf transformation 3]
44. ! [X0] : ((~calm(X0) | ~calm(X0) | funny(X0)) & ((calm(X0) & ~funny(X0)) | calm(X0))) [flattening 43]
86. calm(X0) | calm(X0) [cnf transformation 44]
87. ~calm(X0) | ~calm(X0) | funny(X0) [cnf transformation 44]
133. ~funny(mary) [cnf transformation 23]
136. calm(X0) [duplicate literal removal 86]
137. ~calm(X0) | funny(X0) [duplicate literal removal 87]
299. funny(X0) [resolution 137,136]
300. $false [resolution 299,133]
% SZS output end Proof for 2779228364892980965675965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not happy then mary is rich or old and vice versa.
Everyone who is both not happy and curious is both happy and not strong and vice versa.
If someone is both not quiet and humble then susan is not wise and vice versa.
Everyone who is both not quiet and rich is not creative.
If someone is either wise or calm then lucy is either not calm or generous.
If someone is old or not patient then someone is not creative.
If someone is not happy or not kind then susan is tall or creative.
Everyone who is both funny and curious is either not rich or not kind.
If someone is funny or curious then someone is either happy or not brave and vice versa.
Everyone who is not happy or quiet is both old and not brave and vice versa.
Everyone who is both curious and not strong is not kind or not happy and vice versa.
Everyone who is patient is not generous and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not quiet or creative is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
Susan is not brave.
Alice is calm.
Someone is rich or kind.
Mary is not creative or not humble.
Someone is not humble or wise.
Someone is both brave and curious.
Someone is either humble or not patient. | Lucy is wise. | neutral | ((?[X]:((rich(X)|~happy(X))))<=>((rich(mary)|old(mary))))&
(![X]:((~happy(X)&curious(X))<=>(happy(X)&~strong(X))))&
((?[X]:((~quiet(X)&humble(X))))<=>(~wise(susan)))&
(![X]:((~quiet(X)&rich(X))=>~creative(X)))&
((?[X]:((wise(X)<~>calm(X))))=>((~calm(lucy)<~>generous(lucy))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((tall(susan)|creative(susan))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
(~brave(susan))&
(calm(alice))&
(?[X]:((rich(X)|kind(X))))&
((~creative(mary)|~humble(mary)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is brave or happy is both quiet and not quiet and vice versa.
If mary is either creative or happy then paul is funny or not humble.
If someone is not curious then someone is both not curious and not calm and vice versa.
If someone is not generous or funny then john is not curious.
If alice is either creative or wise then someone is either old or creative.
If someone is not curious or not funny then someone is both not calm and not patient and vice versa.
If alice is not creative or not humble then paul is patient.
Everyone who is generous or quiet is either brave or humble and vice versa.
If someone is quiet or creative then susan is patient or humble.
Everyone who is not funny or not generous is both happy and creative.
If someone is not calm then someone is kind and vice versa.
Everyone who is both not patient and not rich is not humble and vice versa.
If someone is both humble and patient then mary is either not happy or not rich.
If someone is either quiet or not calm then someone is both not old and funny.
Everyone who is creative or patient is either not old or happy and vice versa.
Everyone who is both strong and quiet is either not quiet or funny and vice versa.
John is either tall or not patient.
Paul is not curious or not happy.
Someone is either not humble or curious.
Alice is calm or tall.
John is tall.
Someone is old.
Mary is either creative or not happy.
John is calm. | Mary is not humble. | contradiction | (![X]:((brave(X)|happy(X))<=>(quiet(X)&~quiet(X))))&
(((creative(mary)<~>happy(mary)))=>((funny(paul)|~humble(paul))))&
((?[X]:(~curious(X)))<=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~generous(X)|funny(X))))=>(~curious(john)))&
(((creative(alice)<~>wise(alice)))=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~creative(alice)|~humble(alice)))=>(patient(paul)))&
(![X]:((generous(X)|quiet(X))<=>(brave(X)<~>humble(X))))&
((?[X]:((quiet(X)|creative(X))))=>((patient(susan)|humble(susan))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)&~rich(X))<=>~humble(X)))&
((?[X]:((humble(X)&patient(X))))=>((~happy(mary)<~>~rich(mary))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>happy(X))))&
(![X]:((strong(X)&quiet(X))<=>(~quiet(X)<~>funny(X))))&
((tall(john)<~>~patient(john)))&
((~curious(paul)|~happy(paul)))&
(?[X]:((~humble(X)<~>curious(X))))&
((calm(alice)|tall(alice)))&
(tall(john))&
(?[X]:(old(X)))&
((creative(mary)<~>~happy(mary)))&
(calm(john)) | ~humble(mary) | [
"p0",
"p11",
"p12",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4764624283641090795468698
% SZS output start Proof for 4764624283641090795468698
1. ! [X0] : ((happy(X0) | brave(X0)) <=> (~quiet(X0) & quiet(X0))) [input p0]
12. ! [X0] : ((~rich(X0) & ~patient(X0)) <=> ~humble(X0)) [input p11]
13. ? [X0] : (patient(X0) & humble(X0)) => (~happy(mary) <~> ~rich(mary)) [input p12]
17. tall(john) <~> ~patient(john) [input p16]
21. tall(john) [input p20]
25. ~humble(mary) [input hypothesis]
38. (~happy(mary) <~> ~rich(mary)) | ! [X0] : (~patient(X0) | ~humble(X0)) [ennf transformation 13]
40. ! [X0] : (((happy(X0) | brave(X0)) | (quiet(X0) | ~quiet(X0))) & ((~quiet(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 1]
41. ! [X0] : ((happy(X0) | brave(X0) | quiet(X0) | ~quiet(X0)) & ((~quiet(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 40]
63. ! [X0] : (((~rich(X0) & ~patient(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) | patient(X0)))) [nnf transformation 12]
64. ! [X0] : (((~rich(X0) & ~patient(X0)) | humble(X0)) & (~humble(X0) | rich(X0) | patient(X0))) [flattening 63]
65. ((rich(mary) | happy(mary)) & (~rich(mary) | ~happy(mary))) | ! [X0] : (~patient(X0) | ~humble(X0)) [nnf transformation 38]
74. (patient(john) | ~tall(john)) & (~patient(john) | tall(john)) [nnf transformation 17]
82. quiet(X0) | ~happy(X0) [cnf transformation 41]
84. ~quiet(X0) | ~happy(X0) [cnf transformation 41]
119. ~patient(X0) | humble(X0) [cnf transformation 64]
120. ~rich(X0) | humble(X0) [cnf transformation 64]
122. rich(mary) | happy(mary) | ~patient(X0) | ~humble(X0) [cnf transformation 65]
140. patient(john) | ~tall(john) [cnf transformation 74]
145. tall(john) [cnf transformation 21]
150. ~humble(mary) [cnf transformation 25]
153. ~happy(X0) [subsumption resolution 82,84]
298. rich(mary) | ~patient(X0) | ~humble(X0) [subsumption resolution 122,153]
299. rich(mary) | ~patient(X0) [subsumption resolution 298,119]
301. 32 <=> ! [X0] : ~patient(X0) [avatar definition]
302. ~patient(X0) <- (32) [avatar component clause 301]
304. 33 <=> rich(mary) [avatar definition]
306. rich(mary) <- (33) [avatar component clause 304]
307. 32 | 33 [avatar split clause 299,304,301]
331. 38 <=> tall(john) [avatar definition]
335. 39 <=> patient(john) [avatar definition]
337. patient(john) <- (39) [avatar component clause 335]
338. ~38 | 39 [avatar split clause 140,335,331]
359. 38 [avatar split clause 145,331]
374. $false <- (32, 39) [resolution 337,302]
375. ~32 | ~39 [avatar contradiction clause 374]
377. humble(mary) <- (33) [resolution 120,306]
378. $false <- (33) [subsumption resolution 377,150]
379. ~33 [avatar contradiction clause 378]
380. $false [avatar sat refutation 307,338,359,375,379]
% SZS output end Proof for 4764624283641090795468698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or funny then someone is not old and vice versa.
If someone is rich then someone is funny or not rich.
Everyone who is rich or calm is either patient or not kind.
Everyone who is not kind is wise.
Everyone who is not generous is both not rich and humble.
If someone is not rich or generous then someone is both patient and not creative.
Everyone who is not calm is both not calm and patient and vice versa.
Everyone who is humble or generous is not generous and vice versa.
If someone is curious then someone is brave or not old and vice versa.
Everyone who is quiet is either kind or creative and vice versa.
Everyone who is either not old or not kind is either not strong or not rich.
Everyone who is either not patient or not rich is both funny and not quiet and vice versa.
If paul is humble or not old then someone is not patient.
Everyone who is both rich and not funny is both not curious and not tall.
If fred is both kind and not patient then someone is not wise and vice versa.
If someone is not curious or not humble then someone is either calm or strong and vice versa.
John is brave or not quiet.
Paul is either not tall or old.
Someone is not wise or not rich.
Mary is not creative or brave.
Someone is not creative or not patient.
Someone is either funny or humble.
Someone is both not tall and humble. | Paul is not rich. | entailment | ((?[X]:((wise(X)|funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:(rich(X)))=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((rich(X)|calm(X))=>(patient(X)<~>~kind(X))))&
(![X]:(~kind(X)=>wise(X)))&
(![X]:(~generous(X)=>(~rich(X)&humble(X))))&
((?[X]:((~rich(X)|generous(X))))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:(~calm(X)<=>(~calm(X)&patient(X))))&
(![X]:((humble(X)|generous(X))<=>~generous(X)))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)|~old(X)))))&
(![X]:(quiet(X)<=>(kind(X)<~>creative(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~strong(X)<~>~rich(X))))&
(![X]:((~patient(X)<~>~rich(X))<=>(funny(X)&~quiet(X))))&
(((humble(paul)|~old(paul)))=>(?[X]:(~patient(X))))&
(![X]:((rich(X)&~funny(X))=>(~curious(X)&~tall(X))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(~wise(X))))&
((?[X]:((~curious(X)|~humble(X))))<=>(?[X]:((calm(X)<~>strong(X)))))&
((brave(john)|~quiet(john)))&
((~tall(paul)<~>old(paul)))&
(?[X]:((~wise(X)|~rich(X))))&
((~creative(mary)|brave(mary)))&
(?[X]:((~creative(X)|~patient(X))))&
(?[X]:((funny(X)<~>humble(X))))&
(?[X]:((~tall(X)&humble(X)))) | ~rich(paul) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3449581160365280445126498
% SZS output start Proof for 3449581160365280445126498
5. ! [X0] : (~generous(X0) => (humble(X0) & ~rich(X0))) [input p4]
8. ! [X0] : ((generous(X0) | humble(X0)) <=> ~generous(X0)) [input p7]
24. rich(paul) [input hypothesis]
33. ! [X0] : ((humble(X0) & ~rich(X0)) | generous(X0)) [ennf transformation 5]
53. ! [X0] : (((generous(X0) | humble(X0)) | generous(X0)) & (~generous(X0) | (~generous(X0) & ~humble(X0)))) [nnf transformation 8]
54. ! [X0] : ((generous(X0) | humble(X0) | generous(X0)) & (~generous(X0) | (~generous(X0) & ~humble(X0)))) [flattening 53]
95. ~rich(X0) | generous(X0) [cnf transformation 33]
105. ~generous(X0) | ~generous(X0) [cnf transformation 54]
147. rich(paul) [cnf transformation 24]
148. ~generous(X0) [duplicate literal removal 105]
187. 10 <=> ! [X1] : ~generous(X1) [avatar definition]
188. ~generous(X1) <- (10) [avatar component clause 187]
204. 10 [avatar split clause 148,187]
351. generous(paul) [resolution 95,147]
353. $false <- (10) [subsumption resolution 351,188]
354. ~10 [avatar contradiction clause 353]
357. $false [avatar sat refutation 204,354]
% SZS output end Proof for 3449581160365280445126498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and funny then someone is both funny and humble.
If someone is not calm then lucy is either not happy or not generous.
Everyone who is rich is both patient and old.
Everyone who is humble or strong is both not calm and wise and vice versa.
If someone is both not calm and generous then susan is not happy or not patient.
Everyone who is either curious or generous is generous and vice versa.
If someone is either calm or creative then someone is both not creative and not old.
Everyone who is not quiet is either not calm or funny and vice versa.
Everyone who is not funny or strong is both not curious and patient.
If susan is not happy then fred is both patient and not patient and vice versa.
If someone is both not creative and creative then someone is both quiet and patient and vice versa.
If mary is not curious or not old then someone is not humble or not calm.
If someone is happy or not kind then lucy is either not funny or brave.
Everyone who is humble or not generous is not patient and vice versa.
If lucy is rich then mary is either not kind or not old and vice versa.
If someone is both rich and humble then john is rich and vice versa.
Someone is both not curious and strong.
Someone is not curious or brave.
Someone is creative.
Fred is not tall or not quiet.
Lucy is both not calm and funny.
Fred is both not happy and not humble.
Someone is not kind or rich.
Someone is brave. | Lucy is rich. | contradiction | ((?[X]:((tall(X)&funny(X))))=>(?[X]:((funny(X)&humble(X)))))&
((?[X]:(~calm(X)))=>((~happy(lucy)<~>~generous(lucy))))&
(![X]:(rich(X)=>(patient(X)&old(X))))&
(![X]:((humble(X)|strong(X))<=>(~calm(X)&wise(X))))&
((?[X]:((~calm(X)&generous(X))))=>((~happy(susan)|~patient(susan))))&
(![X]:((curious(X)<~>generous(X))<=>generous(X)))&
((?[X]:((calm(X)<~>creative(X))))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:(~quiet(X)<=>(~calm(X)<~>funny(X))))&
(![X]:((~funny(X)|strong(X))=>(~curious(X)&patient(X))))&
((~happy(susan))<=>((patient(fred)&~patient(fred))))&
((?[X]:((~creative(X)&creative(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(((~curious(mary)|~old(mary)))=>(?[X]:((~humble(X)|~calm(X)))))&
((?[X]:((happy(X)|~kind(X))))=>((~funny(lucy)<~>brave(lucy))))&
(![X]:((humble(X)|~generous(X))<=>~patient(X)))&
((rich(lucy))<=>((~kind(mary)<~>~old(mary))))&
((?[X]:((rich(X)&humble(X))))<=>(rich(john)))&
(?[X]:((~curious(X)&strong(X))))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:(creative(X)))&
((~tall(fred)|~quiet(fred)))&
((~calm(lucy)&funny(lucy)))&
((~happy(fred)&~humble(fred)))&
(?[X]:((~kind(X)|rich(X))))&
(?[X]:(brave(X))) | rich(lucy) | [
"p2",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1283620166677978146781596
% SZS output start Proof for 1283620166677978146781596
3. ! [X0] : (rich(X0) => (old(X0) & patient(X0))) [input p2]
8. ! [X0] : (~quiet(X0) <=> (~calm(X0) <~> funny(X0))) [input p7]
11. ? [X0] : (creative(X0) & ~creative(X0)) <=> ? [X0] : (patient(X0) & quiet(X0)) [input p10]
21. funny(lucy) & ~calm(lucy) [input p20]
25. rich(lucy) [input hypothesis]
28. ? [X0] : (creative(X0) & ~creative(X0)) <=> ? [X1] : (patient(X1) & quiet(X1)) [rectify 11]
32. ! [X0] : ((old(X0) & patient(X0)) | ~rich(X0)) [ennf transformation 3]
47. ! [X0] : ((~quiet(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | quiet(X0))) [nnf transformation 8]
50. (? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : (~patient(X1) | ~quiet(X1))) & (? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : (~creative(X0) | creative(X0))) [nnf transformation 28]
51. (? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : (~patient(X1) | ~quiet(X1))) & (? [X2] : (patient(X2) & quiet(X2)) | ! [X3] : (~creative(X3) | creative(X3))) [rectify 50]
52. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK1) & ~creative(sK1)) [choice axiom]
53. ? [X2] : (patient(X2) & quiet(X2)) => (patient(sK2) & quiet(sK2)) [choice axiom]
54. ((creative(sK1) & ~creative(sK1)) | ! [X1] : (~patient(X1) | ~quiet(X1))) & ((patient(sK2) & quiet(sK2)) | ! [X3] : (~creative(X3) | creative(X3))) [skolemisation 51,53,52]
77. ~rich(X0) | patient(X0) [cnf transformation 32]
94. ~funny(X0) | calm(X0) | quiet(X0) [cnf transformation 47]
106. ~creative(sK1) | ~patient(X1) | ~quiet(X1) [cnf transformation 54]
107. creative(sK1) | ~patient(X1) | ~quiet(X1) [cnf transformation 54]
128. ~calm(lucy) [cnf transformation 21]
129. funny(lucy) [cnf transformation 21]
134. rich(lucy) [cnf transformation 25]
188. 12 <=> ! [X1] : (~patient(X1) | ~quiet(X1)) [avatar definition]
189. ~quiet(X1) | ~patient(X1) <- (12) [avatar component clause 188]
191. 13 <=> creative(sK1) [avatar definition]
194. 12 | 13 [avatar split clause 107,191,188]
195. 12 | ~13 [avatar split clause 106,191,188]
200. 15 <=> funny(lucy) [avatar definition]
202. funny(lucy) <- (15) [avatar component clause 200]
223. 20 <=> rich(lucy) [avatar definition]
225. rich(lucy) <- (20) [avatar component clause 223]
248. 15 [avatar split clause 129,200]
258. 20 [avatar split clause 134,223]
259. patient(lucy) <- (20) [resolution 77,225]
287. calm(lucy) | quiet(lucy) <- (15) [resolution 94,202]
289. quiet(lucy) <- (15) [subsumption resolution 287,128]
299. ~patient(lucy) <- (12, 15) [resolution 289,189]
300. $false <- (12, 15, 20) [subsumption resolution 299,259]
301. ~12 | ~15 | ~20 [avatar contradiction clause 300]
302. $false [avatar sat refutation 194,195,248,258,301]
% SZS output end Proof for 1283620166677978146781596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or generous then john is not creative and vice versa.
Everyone who is generous or not quiet is either not strong or not funny.
If someone is both not creative and wise then john is quiet and vice versa.
Everyone who is not rich is not calm or not wise.
Everyone who is both generous and not patient is patient and vice versa.
If someone is not strong or not brave then john is both not patient and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
Someone is not wise or creative.
Alice is both not old and funny.
Susan is either happy or old.
Someone is both not rich and strong.
Someone is quiet or old. | Alice is not rich. | contradiction | ((?[X]:((~humble(X)<~>generous(X))))<=>(~creative(john)))&
(![X]:((generous(X)|~quiet(X))=>(~strong(X)<~>~funny(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(quiet(john)))&
(![X]:(~rich(X)=>(~calm(X)|~wise(X))))&
(![X]:((generous(X)&~patient(X))<=>patient(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>((~patient(john)&creative(john))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
(?[X]:((~wise(X)|creative(X))))&
((~old(alice)&funny(alice)))&
((happy(susan)<~>old(susan)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((quiet(X)|old(X)))) | ~rich(alice) | [
"p3",
"p4",
"p7",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6166609069430060160490677
% SZS output start Proof for 6166609069430060160490677
4. ! [X0] : (~rich(X0) => (~wise(X0) | ~calm(X0))) [input p3]
5. ! [X0] : ((~patient(X0) & generous(X0)) <=> patient(X0)) [input p4]
8. ! [X0] : ((funny(X0) <~> ~creative(X0)) <=> (calm(X0) <~> wise(X0))) [input p7]
13. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p12]
17. funny(alice) & ~old(alice) [input p16]
21. ~rich(alice) [input hypothesis]
25. ! [X0] : ((~wise(X0) | ~calm(X0)) | rich(X0)) [ennf transformation 4]
26. ! [X0] : (~wise(X0) | ~calm(X0) | rich(X0)) [flattening 25]
30. ! [X0] : ((generous(X0) & creative(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 13]
40. ! [X0] : (((~patient(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | ~generous(X0)))) [nnf transformation 5]
41. ! [X0] : (((~patient(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | ~generous(X0))) [flattening 40]
49. ! [X0] : ((((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) & (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))))) [nnf transformation 8]
86. ~calm(X0) | ~wise(X0) | rich(X0) [cnf transformation 26]
87. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 41]
89. ~patient(X0) | ~patient(X0) [cnf transformation 41]
104. ~calm(X0) | ~funny(X0) | wise(X0) | creative(X0) [cnf transformation 49]
124. generous(X0) | ~creative(X0) [cnf transformation 30]
125. generous(X0) | calm(X0) [cnf transformation 30]
140. funny(alice) [cnf transformation 17]
146. ~rich(alice) [cnf transformation 21]
149. patient(X0) | ~generous(X0) [duplicate literal removal 87]
150. ~patient(X0) [duplicate literal removal 89]
191. ~generous(X0) [subsumption resolution 149,150]
213. 14 <=> ! [X1] : ~creative(X1) [avatar definition]
214. ~creative(X1) <- (14) [avatar component clause 213]
249. calm(X0) [subsumption resolution 125,191]
250. ~creative(X0) [subsumption resolution 124,191]
251. 14 [avatar split clause 250,213]
324. ~wise(X0) | rich(X0) [resolution 86,249]
407. ~funny(X1) | wise(X1) | creative(X1) [resolution 104,249]
409. ~funny(X1) | wise(X1) <- (14) [subsumption resolution 407,214]
431. wise(alice) <- (14) [resolution 409,140]
437. rich(alice) <- (14) [resolution 431,324]
438. $false <- (14) [subsumption resolution 437,146]
439. ~14 [avatar contradiction clause 438]
440. $false [avatar sat refutation 251,439]
% SZS output end Proof for 6166609069430060160490677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or funny is not calm and vice versa. If mary is either calm or not funny then john is both curious and kind. If susan is both old and humble then fred is either patient or happy. Everyone who is both rich and not old is either wise or calm and vice versa. Everyone who is humble is not happy and vice versa. If someone is funny then someone is not kind or not old. If someone is both not brave and funny then mary is brave. If alice is not rich or generous then alice is both strong and creative and vice versa. Everyone who is not strong is generous or not calm. Everyone who is both kind and happy is either generous or humble and vice versa. Everyone who is both not tall and not generous is both not wise and kind. Everyone who is both not curious and not rich is either not rich or not funny and vice versa. Everyone who is both not wise and happy is creative or not patient and vice versa. If mary is humble then someone is rich. Everyone who is not calm or tall is not calm. If someone is both rich and not kind then someone is both not kind and not funny and vice versa. Susan is both not strong and tall. Someone is not funny. Alice is not brave. John is not kind or not happy. Someone is either not old or strong. Paul is wise. Alice is not generous or not kind. Alice is creative. | Mary is brave. | entailment | (![X]:((humble(X)|funny(X))<=>~calm(X)))&
(((calm(mary)<~>~funny(mary)))=>((curious(john)&kind(john))))&
(((old(susan)&humble(susan)))=>((patient(fred)<~>happy(fred))))&
(![X]:((rich(X)&~old(X))<=>(wise(X)<~>calm(X))))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:(funny(X)))=>(?[X]:((~kind(X)|~old(X)))))&
((?[X]:((~brave(X)&funny(X))))=>(brave(mary)))&
(((~rich(alice)|generous(alice)))<=>((strong(alice)&creative(alice))))&
(![X]:(~strong(X)=>(generous(X)|~calm(X))))&
(![X]:((kind(X)&happy(X))<=>(generous(X)<~>humble(X))))&
(![X]:((~tall(X)&~generous(X))=>(~wise(X)&kind(X))))&
(![X]:((~curious(X)&~rich(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((~wise(X)&happy(X))<=>(creative(X)|~patient(X))))&
((humble(mary))=>(?[X]:(rich(X))))&
(![X]:((~calm(X)|tall(X))=>~calm(X)))&
((?[X]:((rich(X)&~kind(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
((~strong(susan)&tall(susan)))&
(?[X]:(~funny(X)))&
(~brave(alice))&
((~kind(john)|~happy(john)))&
(?[X]:((~old(X)<~>strong(X))))&
(wise(paul))&
((~generous(alice)|~kind(alice)))&
(creative(alice)) | brave(mary) | [
"p0",
"p3",
"p4",
"p6",
"p11",
"p12",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7638100264218057472956412
% SZS output start Proof for 7638100264218057472956412
1. ! [X0] : ((funny(X0) | humble(X0)) <=> ~calm(X0)) [input p0]
4. ! [X0] : ((~old(X0) & rich(X0)) <=> (wise(X0) <~> calm(X0))) [input p3]
5. ! [X0] : (humble(X0) <=> ~happy(X0)) [input p4]
7. ? [X0] : (funny(X0) & ~brave(X0)) => brave(mary) [input p6]
12. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p11]
13. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~patient(X0) | creative(X0))) [input p12]
19. ~brave(alice) [input p18]
24. creative(alice) [input p23]
25. ~brave(mary) [input hypothesis]
32. brave(mary) | ! [X0] : (~funny(X0) | brave(X0)) [ennf transformation 7]
39. ! [X0] : (((funny(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (~funny(X0) & ~humble(X0)))) [nnf transformation 1]
40. ! [X0] : ((funny(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (~funny(X0) & ~humble(X0)))) [flattening 39]
43. ! [X0] : (((~old(X0) & rich(X0)) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0)))) & (((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 4]
44. ! [X0] : (((~old(X0) & rich(X0)) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0)))) & (((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | old(X0) | ~rich(X0))) [flattening 43]
45. ! [X0] : ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))) [nnf transformation 5]
53. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (rich(X0) | curious(X0)))) [nnf transformation 12]
54. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | rich(X0) | curious(X0))) [flattening 53]
55. ! [X0] : (((happy(X0) & ~wise(X0)) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 13]
56. ! [X0] : (((happy(X0) & ~wise(X0)) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ~happy(X0) | wise(X0))) [flattening 55]
71. calm(X0) | humble(X0) | funny(X0) [cnf transformation 40]
81. ~calm(X0) | wise(X0) | rich(X0) [cnf transformation 44]
84. ~happy(X0) | ~humble(X0) [cnf transformation 45]
87. brave(mary) | ~funny(X0) | brave(X0) [cnf transformation 32]
107. ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 54]
109. ~creative(X0) | ~wise(X0) [cnf transformation 56]
111. ~creative(X0) | happy(X0) [cnf transformation 56]
123. ~brave(alice) [cnf transformation 19]
129. creative(alice) [cnf transformation 24]
130. ~brave(mary) [cnf transformation 25]
132. ~rich(X0) | funny(X0) [duplicate literal removal 107]
182. 12 <=> ! [X0] : (~funny(X0) | brave(X0)) [avatar definition]
183. ~funny(X0) | brave(X0) <- (12) [avatar component clause 182]
185. 13 <=> brave(mary) [avatar definition]
188. 12 | 13 [avatar split clause 87,185,182]
194. 15 <=> creative(alice) [avatar definition]
195. creative(alice) <- (15) [avatar component clause 194]
268. 15 [avatar split clause 129,194]
269. ~13 [avatar split clause 130,185]
275. ~wise(alice) <- (15) [resolution 109,195]
277. happy(alice) <- (15) [resolution 111,195]
278. ~humble(alice) <- (15) [resolution 277,84]
305. wise(X0) | rich(X0) | humble(X0) | funny(X0) [resolution 81,71]
315. wise(X0) | humble(X0) | funny(X0) [subsumption resolution 305,132]
523. humble(alice) | funny(alice) <- (15) [resolution 315,275]
529. funny(alice) <- (15) [subsumption resolution 523,278]
573. brave(alice) <- (12, 15) [resolution 529,183]
574. $false <- (12, 15) [subsumption resolution 573,123]
575. ~12 | ~15 [avatar contradiction clause 574]
576. $false [avatar sat refutation 188,268,269,575]
% SZS output end Proof for 7638100264218057472956412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not happy or not wise then lucy is both tall and not tall. If susan is calm then someone is tall and vice versa. Everyone who is either not generous or not happy is rich and vice versa. If someone is both generous and creative then someone is brave or not calm. Everyone who is rich is tall. If someone is not wise or not calm then someone is either rich or wise and vice versa. If susan is not tall then susan is both generous and funny. Everyone who is either patient or not generous is not tall or not happy and vice versa. If susan is either quiet or not strong then mary is either curious or not wise and vice versa. Everyone who is either not tall or not creative is either creative or quiet and vice versa. If someone is either not old or not calm then someone is not funny and vice versa. Everyone who is not old or calm is humble. Everyone who is not humble or tall is either rich or not creative and vice versa. Everyone who is not humble or not funny is either wise or not funny. Everyone who is curious or humble is both creative and quiet. Everyone who is both not strong and happy is either not strong or not calm and vice versa. Someone is not tall. John is generous or not rich. Someone is either not brave or wise. Someone is either happy or not old. Someone is not patient. Someone is either not humble or not tall. Someone is not calm or strong. | John is not strong. | neutral | (((~happy(susan)|~wise(susan)))=>((tall(lucy)&~tall(lucy))))&
((calm(susan))<=>(?[X]:(tall(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>rich(X)))&
((?[X]:((generous(X)&creative(X))))=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:(rich(X)=>tall(X)))&
((?[X]:((~wise(X)|~calm(X))))<=>(?[X]:((rich(X)<~>wise(X)))))&
((~tall(susan))=>((generous(susan)&funny(susan))))&
(![X]:((patient(X)<~>~generous(X))<=>(~tall(X)|~happy(X))))&
(((quiet(susan)<~>~strong(susan)))<=>((curious(mary)<~>~wise(mary))))&
(![X]:((~tall(X)<~>~creative(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)|calm(X))=>humble(X)))&
(![X]:((~humble(X)|tall(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((~humble(X)|~funny(X))=>(wise(X)<~>~funny(X))))&
(![X]:((curious(X)|humble(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)&happy(X))<=>(~strong(X)<~>~calm(X))))&
(?[X]:(~tall(X)))&
((generous(john)|~rich(john)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((~calm(X)|strong(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is not tall or not calm is humble or not humble and vice versa. If someone is either happy or not happy then someone is not generous. Everyone who is not creative or not quiet is both humble and not brave. Everyone who is both wise and not rich is generous. Everyone who is patient or not quiet is not kind or not curious. Everyone who is not funny or not humble is both not patient and humble. Everyone who is not tall or wise is either not humble or tall and vice versa. Everyone who is not tall is both not wise and not strong. Everyone who is either funny or rich is calm or rich and vice versa. Everyone who is both strong and not wise is not funny or humble. Everyone who is both not brave and not strong is not funny or wise. If lucy is both not strong and not patient then paul is not humble and vice versa. If paul is either brave or not funny then someone is both calm and not quiet and vice versa. If mary is both not patient and brave then lucy is either tall or not tall. Everyone who is both not funny and curious is either kind or funny and vice versa. Everyone who is humble is both happy and kind and vice versa. Mary is either not patient or not wise. Susan is not tall or not funny. Fred is curious. Someone is either brave or generous. Someone is both not rich and strong. Someone is both not calm and not old. Susan is both not old and not generous. Someone is either old or curious. | Mary is not humble. | contradiction | (![X]:((~tall(X)|~calm(X))<=>(humble(X)|~humble(X))))&
((?[X]:((happy(X)<~>~happy(X))))=>(?[X]:(~generous(X))))&
(![X]:((~creative(X)|~quiet(X))=>(humble(X)&~brave(X))))&
(![X]:((wise(X)&~rich(X))=>generous(X)))&
(![X]:((patient(X)|~quiet(X))=>(~kind(X)|~curious(X))))&
(![X]:((~funny(X)|~humble(X))=>(~patient(X)&humble(X))))&
(![X]:((~tall(X)|wise(X))<=>(~humble(X)<~>tall(X))))&
(![X]:(~tall(X)=>(~wise(X)&~strong(X))))&
(![X]:((funny(X)<~>rich(X))<=>(calm(X)|rich(X))))&
(![X]:((strong(X)&~wise(X))=>(~funny(X)|humble(X))))&
(![X]:((~brave(X)&~strong(X))=>(~funny(X)|wise(X))))&
(((~strong(lucy)&~patient(lucy)))<=>(~humble(paul)))&
(((brave(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&~quiet(X)))))&
(((~patient(mary)&brave(mary)))=>((tall(lucy)<~>~tall(lucy))))&
(![X]:((~funny(X)&curious(X))<=>(kind(X)<~>funny(X))))&
(![X]:(humble(X)<=>(happy(X)&kind(X))))&
((~patient(mary)<~>~wise(mary)))&
((~tall(susan)|~funny(susan)))&
(curious(fred))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((~calm(X)&~old(X))))&
((~old(susan)&~generous(susan)))&
(?[X]:((old(X)<~>curious(X)))) | ~humble(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5755734363980771423859824
% SZS output start Proof for 5755734363980771423859824
6. ! [X0] : ((~humble(X0) | ~funny(X0)) => (humble(X0) & ~patient(X0))) [input p5]
25. ~humble(mary) [input hypothesis]
34. ! [X0] : ((humble(X0) & ~patient(X0)) | (humble(X0) & funny(X0))) [ennf transformation 6]
88. humble(X0) | humble(X0) [cnf transformation 34]
139. ~humble(mary) [cnf transformation 25]
146. humble(X0) [duplicate literal removal 88]
236. $false [subsumption resolution 139,146]
% SZS output end Proof for 5755734363980771423859824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is rich and vice versa.
If paul is funny or not tall then susan is either not brave or not quiet.
If someone is both not funny and patient then someone is wise.
Everyone who is both not humble and not happy is both not wise and not quiet.
Everyone who is both rich and not strong is not tall or rich and vice versa.
If paul is not calm or not rich then someone is either not wise or brave.
If mary is not old then lucy is either strong or quiet.
Everyone who is either funny or generous is both not old and not brave.
If john is humble then mary is either not patient or not happy.
Everyone who is not calm is not strong.
If someone is either not generous or wise then someone is both patient and not old.
Everyone who is humble or brave is kind and vice versa.
Everyone who is tall is both patient and tall and vice versa.
Everyone who is not old is both not calm and quiet and vice versa.
Everyone who is happy or not quiet is funny or tall.
If paul is either not funny or not happy then alice is either not happy or not rich.
John is not brave.
Susan is brave or not brave.
Someone is both not tall and generous.
Someone is tall or not tall.
Paul is not rich or tall.
Someone is both not creative and not generous.
Mary is not generous or old.
Paul is both not strong and kind. | Paul is tall. | entailment | ((calm(mary))<=>(?[X]:(rich(X))))&
(((funny(paul)|~tall(paul)))=>((~brave(susan)<~>~quiet(susan))))&
((?[X]:((~funny(X)&patient(X))))=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~happy(X))=>(~wise(X)&~quiet(X))))&
(![X]:((rich(X)&~strong(X))<=>(~tall(X)|rich(X))))&
(((~calm(paul)|~rich(paul)))=>(?[X]:((~wise(X)<~>brave(X)))))&
((~old(mary))=>((strong(lucy)<~>quiet(lucy))))&
(![X]:((funny(X)<~>generous(X))=>(~old(X)&~brave(X))))&
((humble(john))=>((~patient(mary)<~>~happy(mary))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((humble(X)|brave(X))<=>kind(X)))&
(![X]:(tall(X)<=>(patient(X)&tall(X))))&
(![X]:(~old(X)<=>(~calm(X)&quiet(X))))&
(![X]:((happy(X)|~quiet(X))=>(funny(X)|tall(X))))&
(((~funny(paul)<~>~happy(paul)))=>((~happy(alice)<~>~rich(alice))))&
(~brave(john))&
((brave(susan)|~brave(susan)))&
(?[X]:((~tall(X)&generous(X))))&
(?[X]:((tall(X)|~tall(X))))&
((~rich(paul)|tall(paul)))&
(?[X]:((~creative(X)&~generous(X))))&
((~generous(mary)|old(mary)))&
((~strong(paul)&kind(paul))) | tall(paul) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5986157009297372588241900
% SZS output start Proof for 5986157009297372588241900
5. ! [X0] : ((~strong(X0) & rich(X0)) <=> (rich(X0) | ~tall(X0))) [input p4]
21. tall(paul) | ~rich(paul) [input p20]
25. ~tall(paul) [input hypothesis]
53. ! [X0] : (((~strong(X0) & rich(X0)) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | (strong(X0) | ~rich(X0)))) [nnf transformation 5]
54. ! [X0] : (((~strong(X0) & rich(X0)) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | strong(X0) | ~rich(X0))) [flattening 53]
86. rich(X0) | tall(X0) [cnf transformation 54]
125. tall(paul) | ~rich(paul) [cnf transformation 21]
130. ~tall(paul) [cnf transformation 25]
145. 4 <=> tall(paul) [avatar definition]
254. tall(paul) [subsumption resolution 125,86]
255. 4 [avatar split clause 254,145]
261. ~4 [avatar split clause 130,145]
262. $false [avatar sat refutation 255,261]
% SZS output end Proof for 5986157009297372588241900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is happy or generous and vice versa. If someone is either not wise or not generous then someone is either not strong or not quiet. Everyone who is humble or tall is tall or funny and vice versa. Everyone who is either not brave or rich is not rich or patient and vice versa. Everyone who is wise or not patient is both curious and humble. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. If susan is both curious and generous then someone is curious and vice versa. Everyone who is both generous and not humble is not strong and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Everyone who is either strong or creative is both generous and curious. If someone is not tall then fred is not wise or not rich and vice versa. If someone is either not wise or not rich then someone is rich or not funny. John is happy. Someone is either rich or not kind. Someone is not quiet or not old. Mary is either not patient or not wise. Someone is not funny or kind. Alice is strong. | Fred is strong. | entailment | (![X]:(~generous(X)<=>(happy(X)|generous(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))<=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(happy(john))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|~old(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(strong(alice)) | strong(fred) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6419493819250125166396044
% SZS output start Proof for 6419493819250125166396044
1. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p0]
11. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p10]
22. ~strong(fred) [input hypothesis]
30. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 1]
31. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 30]
54. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 11]
55. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 54]
78. ~generous(X0) | ~generous(X0) [cnf transformation 31]
123. generous(X0) | strong(X0) [cnf transformation 55]
148. ~strong(fred) [cnf transformation 22]
152. ~generous(X0) [duplicate literal removal 78]
199. strong(X0) [subsumption resolution 123,152]
274. $false [subsumption resolution 148,199]
% SZS output end Proof for 6419493819250125166396044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is kind and vice versa.
If paul is not strong or funny then susan is not rich or not tall and vice versa.
If someone is both not happy and generous then susan is not calm or patient and vice versa.
Everyone who is rich or creative is both not strong and not wise.
Everyone who is not happy is both not generous and not brave and vice versa.
Everyone who is either not kind or not tall is creative or not patient.
If someone is either generous or not funny then john is either creative or happy.
If someone is either rich or strong then john is both funny and old.
Everyone who is either happy or not kind is either not old or creative and vice versa.
If someone is old or not tall then alice is either tall or not happy.
Everyone who is both creative and kind is curious and vice versa.
Everyone who is both quiet and funny is both not happy and wise and vice versa.
Everyone who is not creative or happy is both not strong and not rich and vice versa.
If someone is happy or old then alice is both generous and quiet.
Everyone who is either calm or not funny is both not generous and not quiet.
If someone is both kind and not creative then someone is both funny and not humble and vice versa.
Someone is either not humble or generous.
Lucy is both not creative and old.
Someone is both happy and humble.
Someone is either not creative or not patient.
Fred is strong or patient.
Someone is old or not strong.
Fred is not happy.
Lucy is kind or patient. | Susan is not strong. | entailment | (![X]:(~quiet(X)<=>kind(X)))&
(((~strong(paul)|funny(paul)))<=>((~rich(susan)|~tall(susan))))&
((?[X]:((~happy(X)&generous(X))))<=>((~calm(susan)|patient(susan))))&
(![X]:((rich(X)|creative(X))=>(~strong(X)&~wise(X))))&
(![X]:(~happy(X)<=>(~generous(X)&~brave(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(creative(X)|~patient(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>((creative(john)<~>happy(john))))&
((?[X]:((rich(X)<~>strong(X))))=>((funny(john)&old(john))))&
(![X]:((happy(X)<~>~kind(X))<=>(~old(X)<~>creative(X))))&
((?[X]:((old(X)|~tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((creative(X)&kind(X))<=>curious(X)))&
(![X]:((quiet(X)&funny(X))<=>(~happy(X)&wise(X))))&
(![X]:((~creative(X)|happy(X))<=>(~strong(X)&~rich(X))))&
((?[X]:((happy(X)|old(X))))=>((generous(alice)&quiet(alice))))&
(![X]:((calm(X)<~>~funny(X))=>(~generous(X)&~quiet(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:((funny(X)&~humble(X)))))&
(?[X]:((~humble(X)<~>generous(X))))&
((~creative(lucy)&old(lucy)))&
(?[X]:((happy(X)&humble(X))))&
(?[X]:((~creative(X)<~>~patient(X))))&
((strong(fred)|patient(fred)))&
(?[X]:((old(X)|~strong(X))))&
(~happy(fred))&
((kind(lucy)|patient(lucy))) | ~strong(susan) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5506008038885651939292511
% SZS output start Proof for 5506008038885651939292511
4. ! [X0] : ((creative(X0) | rich(X0)) => (~wise(X0) & ~strong(X0))) [input p3]
13. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~rich(X0) & ~strong(X0))) [input p12]
25. strong(susan) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~strong(X0)) | (~creative(X0) & ~rich(X0))) [ennf transformation 4]
52. ! [X0] : (((happy(X0) | ~creative(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 13]
53. ! [X0] : ((happy(X0) | ~creative(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [flattening 52]
82. ~strong(X0) | ~creative(X0) [cnf transformation 27]
114. ~strong(X0) | creative(X0) [cnf transformation 53]
143. strong(susan) [cnf transformation 25]
209. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
210. ~strong(X0) <- (14) [avatar component clause 209]
248. ~strong(X0) [subsumption resolution 114,82]
249. 14 [avatar split clause 248,209]
341. $false <- (14) [resolution 210,143]
342. ~14 [avatar contradiction clause 341]
343. $false [avatar sat refutation 249,342]
% SZS output end Proof for 5506008038885651939292511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is tall or not calm then someone is not calm or humble. Everyone who is either not brave or not kind is either old or not kind and vice versa. If someone is not strong or wise then alice is brave or old and vice versa. If alice is not happy then someone is not patient. Everyone who is funny is both not humble and happy. Everyone who is either not brave or old is both curious and brave. If fred is both not tall and creative then susan is both generous and not brave. Everyone who is either not wise or rich is both not wise and not funny and vice versa. If someone is both not old and not tall then someone is humble or not wise. If fred is not funny or not humble then mary is either brave or not creative and vice versa. If paul is humble then someone is either old or not wise. If someone is not rich then fred is not rich. If alice is not kind or not brave then paul is not kind or not rich and vice versa. Everyone who is either not brave or not strong is not old and vice versa. If someone is either not brave or funny then someone is either quiet or strong. If lucy is not brave or wise then paul is either not wise or not kind. Lucy is not generous or kind. Lucy is both not creative and not old. Alice is either tall or not creative. Someone is not old. Susan is either not strong or not rich. Susan is not humble or patient. Someone is either funny or humble. Susan is kind. | Susan is funny. | entailment | (((tall(fred)|~calm(fred)))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(old(X)<~>~kind(X))))&
((?[X]:((~strong(X)|wise(X))))<=>((brave(alice)|old(alice))))&
((~happy(alice))=>(?[X]:(~patient(X))))&
(![X]:(funny(X)=>(~humble(X)&happy(X))))&
(![X]:((~brave(X)<~>old(X))=>(curious(X)&brave(X))))&
(((~tall(fred)&creative(fred)))=>((generous(susan)&~brave(susan))))&
(![X]:((~wise(X)<~>rich(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((~old(X)&~tall(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(((~funny(fred)|~humble(fred)))<=>((brave(mary)<~>~creative(mary))))&
((humble(paul))=>(?[X]:((old(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))=>(~rich(fred)))&
(((~kind(alice)|~brave(alice)))<=>((~kind(paul)|~rich(paul))))&
(![X]:((~brave(X)<~>~strong(X))<=>~old(X)))&
((?[X]:((~brave(X)<~>funny(X))))=>(?[X]:((quiet(X)<~>strong(X)))))&
(((~brave(lucy)|wise(lucy)))=>((~wise(paul)<~>~kind(paul))))&
((~generous(lucy)|kind(lucy)))&
((~creative(lucy)&~old(lucy)))&
((tall(alice)<~>~creative(alice)))&
(?[X]:(~old(X)))&
((~strong(susan)<~>~rich(susan)))&
((~humble(susan)|patient(susan)))&
(?[X]:((funny(X)<~>humble(X))))&
(kind(susan)) | funny(susan) | [
"p1",
"p7",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 769115768739440475111248
% SZS output start Proof for 769115768739440475111248
2. ! [X0] : ((~brave(X0) <~> ~kind(X0)) <=> (old(X0) <~> ~kind(X0))) [input p1]
8. ! [X0] : ((~wise(X0) <~> rich(X0)) <=> (~funny(X0) & ~wise(X0))) [input p7]
14. ! [X0] : ((~brave(X0) <~> ~strong(X0)) <=> ~old(X0)) [input p13]
21. ~strong(susan) <~> ~rich(susan) [input p20]
25. ~funny(susan) [input hypothesis]
44. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [nnf transformation 2]
51. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [flattening 51]
63. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | old(X0)) & (~old(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [nnf transformation 14]
72. (rich(susan) | strong(susan)) & (~rich(susan) | ~strong(susan)) [nnf transformation 21]
78. ~kind(X0) | old(X0) | ~kind(X0) | brave(X0) [cnf transformation 44]
81. kind(X0) | ~old(X0) | ~brave(X0) | kind(X0) [cnf transformation 44]
82. ~kind(X0) | ~brave(X0) | ~kind(X0) | ~old(X0) [cnf transformation 44]
85. kind(X0) | brave(X0) | old(X0) | kind(X0) [cnf transformation 44]
96. ~wise(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 52]
100. ~rich(X0) | wise(X0) | funny(X0) | wise(X0) [cnf transformation 52]
115. ~old(X0) | ~strong(X0) | brave(X0) [cnf transformation 63]
117. ~strong(X0) | ~brave(X0) | old(X0) [cnf transformation 63]
134. rich(susan) | strong(susan) [cnf transformation 72]
138. ~funny(susan) [cnf transformation 25]
139. ~rich(X0) | ~wise(X0) [duplicate literal removal 96]
140. ~rich(X0) | wise(X0) | funny(X0) [duplicate literal removal 100]
142. ~kind(X0) | old(X0) | brave(X0) [duplicate literal removal 78]
143. kind(X0) | ~old(X0) | ~brave(X0) [duplicate literal removal 81]
144. ~kind(X0) | ~brave(X0) | ~old(X0) [duplicate literal removal 82]
145. kind(X0) | brave(X0) | old(X0) [duplicate literal removal 85]
164. ~old(X0) | ~brave(X0) [subsumption resolution 143,144]
165. old(X0) | brave(X0) [subsumption resolution 142,145]
189. 10 <=> brave(susan) [avatar definition]
190. brave(susan) <- (10) [avatar component clause 189]
268. ~strong(X0) | old(X0) [subsumption resolution 117,165]
269. ~strong(X0) | brave(X0) [subsumption resolution 115,268]
324. 38 <=> strong(susan) [avatar definition]
326. strong(susan) <- (38) [avatar component clause 324]
328. 39 <=> rich(susan) [avatar definition]
330. rich(susan) <- (39) [avatar component clause 328]
331. 38 | 39 [avatar split clause 134,328,324]
348. old(susan) <- (38) [resolution 268,326]
349. brave(susan) <- (38) [resolution 269,326]
350. 10 | ~38 [avatar split clause 349,324,189]
361. ~brave(susan) <- (38) [resolution 348,164]
362. $false <- (10, 38) [subsumption resolution 361,190]
363. ~10 | ~38 [avatar contradiction clause 362]
364. ~wise(susan) <- (39) [resolution 330,139]
366. wise(susan) | funny(susan) <- (39) [resolution 140,330]
367. funny(susan) <- (39) [subsumption resolution 366,364]
368. $false <- (39) [subsumption resolution 367,138]
369. ~39 [avatar contradiction clause 368]
370. $false [avatar sat refutation 331,350,363,369]
% SZS output end Proof for 769115768739440475111248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or patient is not calm or brave and vice versa. If someone is either not generous or not calm then someone is both curious and patient. If mary is both kind and wise then susan is not funny. If john is either wise or rich then john is both not wise and calm and vice versa. Everyone who is humble is either not curious or not quiet. If someone is both not kind and quiet then fred is either happy or calm. If someone is tall or quiet then paul is both not brave and not rich. Everyone who is not funny or not creative is either humble or wise. Everyone who is both not calm and brave is not happy or not curious and vice versa. Everyone who is not kind or rich is either patient or not quiet and vice versa. Everyone who is not patient or not brave is either not calm or not strong and vice versa. Everyone who is either not quiet or not kind is not generous. Everyone who is either strong or wise is either not funny or kind and vice versa. Everyone who is curious is not old and vice versa. Everyone who is not brave is not quiet or not calm and vice versa. If someone is happy or funny then fred is either not old or old. Mary is either not kind or rich. Mary is either not quiet or creative. Someone is not brave or not old. Someone is either not quiet or not humble. Someone is not calm. Paul is either not kind or curious. Someone is not generous or curious. | Paul is not old. | entailment | (![X]:((~calm(X)<~>patient(X))<=>(~calm(X)|brave(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((curious(X)&patient(X)))))&
(((kind(mary)&wise(mary)))=>(~funny(susan)))&
(((wise(john)<~>rich(john)))<=>((~wise(john)&calm(john))))&
(![X]:(humble(X)=>(~curious(X)<~>~quiet(X))))&
((?[X]:((~kind(X)&quiet(X))))=>((happy(fred)<~>calm(fred))))&
((?[X]:((tall(X)|quiet(X))))=>((~brave(paul)&~rich(paul))))&
(![X]:((~funny(X)|~creative(X))=>(humble(X)<~>wise(X))))&
(![X]:((~calm(X)&brave(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~kind(X)|rich(X))<=>(patient(X)<~>~quiet(X))))&
(![X]:((~patient(X)|~brave(X))<=>(~calm(X)<~>~strong(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>~generous(X)))&
(![X]:((strong(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:(curious(X)<=>~old(X)))&
(![X]:(~brave(X)<=>(~quiet(X)|~calm(X))))&
((?[X]:((happy(X)|funny(X))))=>((~old(fred)<~>old(fred))))&
((~kind(mary)<~>rich(mary)))&
((~quiet(mary)<~>creative(mary)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:(~calm(X)))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X)))) | ~old(paul) | [
"p6",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3492658351782452774666977
% SZS output start Proof for 3492658351782452774666977
7. ? [X0] : (quiet(X0) | tall(X0)) => (~rich(paul) & ~brave(paul)) [input p6]
9. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (~curious(X0) | ~happy(X0))) [input p8]
14. ! [X0] : (curious(X0) <=> ~old(X0)) [input p13]
15. ! [X0] : (~brave(X0) <=> (~calm(X0) | ~quiet(X0))) [input p14]
24. old(paul) [input hypothesis]
26. ? [X0] : quiet(X0) => (~rich(paul) & ~brave(paul)) [pure predicate removal 7]
32. (~rich(paul) & ~brave(paul)) | ! [X0] : ~quiet(X0) [ennf transformation 26]
47. ! [X0] : (((brave(X0) & ~calm(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (~brave(X0) | calm(X0)))) [nnf transformation 9]
48. ! [X0] : (((brave(X0) & ~calm(X0)) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | ~brave(X0) | calm(X0))) [flattening 47]
55. ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))) [nnf transformation 14]
56. ! [X0] : ((~brave(X0) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | brave(X0))) [nnf transformation 15]
57. ! [X0] : ((~brave(X0) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | brave(X0))) [flattening 56]
92. ~brave(paul) | ~quiet(X0) [cnf transformation 32]
102. curious(X0) | brave(X0) [cnf transformation 48]
125. ~old(X0) | ~curious(X0) [cnf transformation 55]
128. ~brave(X0) | quiet(X0) [cnf transformation 57]
145. old(paul) [cnf transformation 24]
212. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
213. ~quiet(X0) <- (14) [avatar component clause 212]
220. 16 <=> brave(paul) [avatar definition]
221. brave(paul) <- (16) [avatar component clause 220]
223. 14 | ~16 [avatar split clause 92,220,212]
267. 25 <=> curious(paul) [avatar definition]
269. ~curious(paul) <- (~25) [avatar component clause 267]
281. brave(paul) <- (~25) [resolution 102,269]
284. 16 | 25 [avatar split clause 281,267,220]
287. ~curious(paul) [resolution 125,145]
289. quiet(paul) <- (16) [resolution 128,221]
290. $false <- (14, 16) [subsumption resolution 289,213]
291. ~14 | ~16 [avatar contradiction clause 290]
292. ~25 [avatar split clause 287,267]
293. $false [avatar sat refutation 223,284,291,292]
% SZS output end Proof for 3492658351782452774666977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is tall or curious then susan is not kind and vice versa. Everyone who is wise is funny. If someone is both humble and curious then alice is either happy or not happy. If fred is not generous then someone is not humble or not strong and vice versa. If susan is not strong then john is kind. If lucy is creative then someone is both happy and funny. Everyone who is both quiet and humble is both not old and not funny and vice versa. Everyone who is old is both humble and not tall and vice versa. If mary is not curious or funny then john is either wise or kind and vice versa. If alice is both wise and not calm then alice is funny. Everyone who is calm is both not generous and curious and vice versa. If someone is quiet then paul is generous or humble and vice versa. Everyone who is quiet or not wise is old and vice versa. Everyone who is not creative or creative is not old or quiet and vice versa. Everyone who is quiet is curious or not brave and vice versa. Everyone who is creative or not kind is not wise or not curious. Someone is both creative and not strong. Someone is creative or not humble. Lucy is not creative. Someone is not tall. Someone is patient. | Susan is not funny. | contradiction | ((?[X]:((tall(X)|curious(X))))<=>(~kind(susan)))&
(![X]:(wise(X)=>funny(X)))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)<~>~happy(alice))))&
((~generous(fred))<=>(?[X]:((~humble(X)|~strong(X)))))&
((~strong(susan))=>(kind(john)))&
((creative(lucy))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(old(X)<=>(humble(X)&~tall(X))))&
(((~curious(mary)|funny(mary)))<=>((wise(john)<~>kind(john))))&
(((wise(alice)&~calm(alice)))=>(funny(alice)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
((?[X]:(quiet(X)))<=>((generous(paul)|humble(paul))))&
(![X]:((quiet(X)|~wise(X))<=>old(X)))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(?[X]:((creative(X)&~strong(X))))&
(?[X]:((creative(X)|~humble(X))))&
(~creative(lucy))&
(?[X]:(~tall(X)))&
(?[X]:(patient(X))) | ~funny(susan) | [
"p1",
"p6",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 879025937771487038679827
% SZS output start Proof for 879025937771487038679827
2. ! [X0] : (wise(X0) => funny(X0)) [input p1]
7. ! [X0] : ((humble(X0) & quiet(X0)) <=> (~funny(X0) & ~old(X0))) [input p6]
8. ! [X0] : (old(X0) <=> (~tall(X0) & humble(X0))) [input p7]
13. ! [X0] : ((~wise(X0) | quiet(X0)) <=> old(X0)) [input p12]
14. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | ~old(X0))) [input p13]
22. ~funny(susan) [input hypothesis]
25. ! [X0] : (funny(X0) | ~wise(X0)) [ennf transformation 2]
45. ! [X0] : (((humble(X0) & quiet(X0)) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | (~humble(X0) | ~quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((humble(X0) & quiet(X0)) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~humble(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : ((old(X0) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | ~old(X0))) [nnf transformation 8]
48. ! [X0] : ((old(X0) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | ~old(X0))) [flattening 47]
56. ! [X0] : (((~wise(X0) | quiet(X0)) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 13]
57. ! [X0] : ((~wise(X0) | quiet(X0) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [flattening 56]
58. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 14]
59. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (~creative(X0) & creative(X0)))) [flattening 58]
71. ~wise(X0) | funny(X0) [cnf transformation 25]
80. ~old(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 46]
84. ~old(X0) | humble(X0) [cnf transformation 48]
100. old(X0) | wise(X0) [cnf transformation 57]
102. quiet(X0) | ~old(X0) | creative(X0) [cnf transformation 59]
103. quiet(X0) | ~old(X0) | ~creative(X0) [cnf transformation 59]
116. ~funny(susan) [cnf transformation 22]
218. ~old(X0) | quiet(X0) [subsumption resolution 102,103]
231. wise(X1) | humble(X1) [resolution 100,84]
234. quiet(X0) | wise(X0) [resolution 218,100]
237. ~humble(X0) | ~quiet(X0) | wise(X0) [resolution 80,100]
239. ~quiet(X0) | wise(X0) [subsumption resolution 237,231]
240. wise(X0) [subsumption resolution 239,234]
245. funny(X0) [resolution 240,71]
258. $false [resolution 245,116]
% SZS output end Proof for 879025937771487038679827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or not happy then someone is both not funny and creative.
If lucy is humble then susan is happy and vice versa.
Everyone who is not rich or humble is either creative or not rich.
If someone is either strong or not calm then someone is either rich or humble and vice versa.
If alice is quiet then alice is creative or quiet and vice versa.
Everyone who is either not curious or curious is both happy and wise.
If someone is both not funny and wise then john is not rich and vice versa.
If someone is either not patient or not tall then someone is both not tall and brave.
Everyone who is not quiet is not creative and vice versa.
If someone is either humble or not generous then mary is strong and vice versa.
Everyone who is creative is either funny or quiet and vice versa.
Everyone who is both not brave and generous is not patient or tall and vice versa.
Everyone who is either generous or not humble is old.
Everyone who is both generous and wise is both not old and patient and vice versa.
If john is both tall and not happy then mary is either kind or not generous and vice versa.
If fred is creative then someone is not curious.
John is brave.
Someone is either not quiet or not kind.
Someone is quiet.
Someone is humble or wise.
Fred is either not wise or not rich.
Fred is not kind or happy. | Mary is not patient. | contradiction | ((?[X]:((~calm(X)|~happy(X))))=>(?[X]:((~funny(X)&creative(X)))))&
((humble(lucy))<=>(happy(susan)))&
(![X]:((~rich(X)|humble(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((quiet(alice))<=>((creative(alice)|quiet(alice))))&
(![X]:((~curious(X)<~>curious(X))=>(happy(X)&wise(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(~rich(john)))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~creative(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(strong(mary)))&
(![X]:(creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)&generous(X))<=>(~patient(X)|tall(X))))&
(![X]:((generous(X)<~>~humble(X))=>old(X)))&
(![X]:((generous(X)&wise(X))<=>(~old(X)&patient(X))))&
(((tall(john)&~happy(john)))<=>((kind(mary)<~>~generous(mary))))&
((creative(fred))=>(?[X]:(~curious(X))))&
(brave(john))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|wise(X))))&
((~wise(fred)<~>~rich(fred)))&
((~kind(fred)|happy(fred))) | ~patient(mary) | [
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 117930232135952742150520
% SZS output start Proof for 117930232135952742150520
6. ! [X0] : ((~curious(X0) <~> curious(X0)) => (wise(X0) & happy(X0))) [input p5]
12. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (tall(X0) | ~patient(X0))) [input p11]
14. ! [X0] : ((wise(X0) & generous(X0)) <=> (patient(X0) & ~old(X0))) [input p13]
23. ~patient(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & happy(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 6]
45. ! [X0] : ((wise(X0) & happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 29]
60. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & ((tall(X0) | ~patient(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & (tall(X0) | ~patient(X0) | ~generous(X0) | brave(X0))) [flattening 60]
63. ! [X0] : (((wise(X0) & generous(X0)) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 14]
64. ! [X0] : (((wise(X0) & generous(X0)) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ~wise(X0) | ~generous(X0))) [flattening 63]
100. wise(X0) | curious(X0) | curious(X0) [cnf transformation 45]
101. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
122. generous(X0) | patient(X0) [cnf transformation 61]
127. patient(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 64]
145. ~patient(mary) [cnf transformation 23]
148. wise(X0) | curious(X0) [duplicate literal removal 100]
149. wise(X0) | ~curious(X0) [duplicate literal removal 101]
224. wise(X0) [subsumption resolution 148,149]
284. patient(X0) | ~generous(X0) [subsumption resolution 127,224]
285. patient(X0) [subsumption resolution 284,122]
338. $false [subsumption resolution 145,285]
% SZS output end Proof for 117930232135952742150520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
If someone is not curious or not generous then fred is both creative and old and vice versa.
If someone is funny then alice is not brave or not wise.
If someone is either not calm or rich then susan is not calm and vice versa.
Everyone who is either not generous or rich is not funny or wise and vice versa.
If paul is either rich or not brave then alice is not generous.
If mary is either not funny or quiet then someone is both brave and creative and vice versa.
Everyone who is both kind and not wise is both not rich and curious.
If fred is both calm and not calm then lucy is rich or strong and vice versa.
If someone is both not generous and not quiet then alice is both not rich and curious and vice versa.
Susan is both kind and not quiet.
Fred is not calm.
Paul is not generous or kind.
Someone is calm or not strong.
John is either not happy or old.
Mary is both quiet and strong.
Someone is both not humble and happy. | Paul is generous. | entailment | ((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
((?[X]:(funny(X)))=>((~brave(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>rich(X))))<=>(~calm(susan)))&
(![X]:((~generous(X)<~>rich(X))<=>(~funny(X)|wise(X))))&
(((rich(paul)<~>~brave(paul)))=>(~generous(alice)))&
(((~funny(mary)<~>quiet(mary)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((kind(X)&~wise(X))=>(~rich(X)&curious(X))))&
(((calm(fred)&~calm(fred)))<=>((rich(lucy)|strong(lucy))))&
((?[X]:((~generous(X)&~quiet(X))))<=>((~rich(alice)&curious(alice))))&
((kind(susan)&~quiet(susan)))&
(~calm(fred))&
((~generous(paul)|kind(paul)))&
(?[X]:((calm(X)|~strong(X))))&
((~happy(john)<~>old(john)))&
((quiet(mary)&strong(mary)))&
(?[X]:((~humble(X)&happy(X)))) | generous(paul) | [
"p3",
"p7",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3371609999037188971538078
% SZS output start Proof for 3371609999037188971538078
4. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p3]
8. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p7]
15. (~calm(fred) & calm(fred)) <=> (strong(lucy) | rich(lucy)) [input p14]
18. ~calm(fred) [input p17]
24. ~generous(paul) [input hypothesis]
38. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 4]
39. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 38]
46. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 8]
47. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 46]
48. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 47]
49. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK1) | ~curious(sK1)) [choice axiom]
50. ((~generous(sK1) | ~curious(sK1)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 48,49]
62. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & ((strong(lucy) | rich(lucy)) | (calm(fred) | ~calm(fred))) [nnf transformation 15]
63. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & (strong(lucy) | rich(lucy) | calm(fred) | ~calm(fred)) [flattening 62]
89. strong(lucy) | ~old(fred) [cnf transformation 39]
105. old(fred) | generous(X1) [cnf transformation 50]
130. calm(fred) | ~strong(lucy) [cnf transformation 63]
139. ~calm(fred) [cnf transformation 18]
148. ~generous(paul) [cnf transformation 24]
193. 10 <=> old(fred) [avatar definition]
202. 12 <=> strong(lucy) [avatar definition]
205. ~10 | 12 [avatar split clause 89,202,193]
221. 16 <=> ! [X1] : generous(X1) [avatar definition]
222. generous(X1) <- (16) [avatar component clause 221]
223. 16 | 10 [avatar split clause 105,193,221]
300. 33 <=> calm(fred) [avatar definition]
309. ~12 | 33 [avatar split clause 130,300,202]
335. ~33 [avatar split clause 139,300]
337. 40 <=> generous(paul) [avatar definition]
339. ~generous(paul) <- (~40) [avatar component clause 337]
365. ~40 [avatar split clause 148,337]
374. $false <- (16, ~40) [resolution 339,222]
375. ~16 | 40 [avatar contradiction clause 374]
376. $false [avatar sat refutation 205,223,309,335,365,375]
% SZS output end Proof for 3371609999037188971538078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or calm is not quiet or not wise and vice versa. If someone is not old or kind then john is not wise or not creative and vice versa. If someone is not quiet then someone is strong or kind. If fred is not patient then someone is calm. Everyone who is not happy or not patient is not old or not generous. Everyone who is both not funny and not calm is either not creative or not tall and vice versa. If paul is not strong then someone is not happy and vice versa. Everyone who is either not patient or funny is not quiet. Everyone who is not kind or rich is both strong and generous. If someone is not happy then mary is both kind and not kind. If someone is not quiet or funny then paul is both not tall and not wise. Everyone who is not kind is not calm or not kind and vice versa. Everyone who is either humble or wise is not curious or creative. Everyone who is not creative is either not calm or not wise and vice versa. Everyone who is both strong and not funny is rich and vice versa. If fred is tall then someone is brave and vice versa. Someone is patient. Someone is creative or strong. Fred is not brave. Mary is kind or quiet. Someone is either not rich or creative. Someone is both brave and not curious. Paul is wise. Susan is either patient or wise. | Susan is tall. | contradiction | (![X]:((creative(X)<~>calm(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((~old(X)|kind(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)|kind(X)))))&
((~patient(fred))=>(?[X]:(calm(X))))&
(![X]:((~happy(X)|~patient(X))=>(~old(X)|~generous(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~creative(X)<~>~tall(X))))&
((~strong(paul))<=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)<~>funny(X))=>~quiet(X)))&
(![X]:((~kind(X)|rich(X))=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))=>((kind(mary)&~kind(mary))))&
((?[X]:((~quiet(X)|funny(X))))=>((~tall(paul)&~wise(paul))))&
(![X]:(~kind(X)<=>(~calm(X)|~kind(X))))&
(![X]:((humble(X)<~>wise(X))=>(~curious(X)|creative(X))))&
(![X]:(~creative(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~funny(X))<=>rich(X)))&
((tall(fred))<=>(?[X]:(brave(X))))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)|strong(X))))&
(~brave(fred))&
((kind(mary)|quiet(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((brave(X)&~curious(X))))&
(wise(paul))&
((patient(susan)<~>wise(susan))) | tall(susan) | [
"p0",
"p5",
"p7",
"p10",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4618056966890566711440822
% SZS output start Proof for 4618056966890566711440822
1. ! [X0] : ((creative(X0) <~> calm(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p0]
6. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p5]
8. ! [X0] : ((~patient(X0) <~> funny(X0)) => ~quiet(X0)) [input p7]
11. ? [X0] : (funny(X0) | ~quiet(X0)) => (~wise(paul) & ~tall(paul)) [input p10]
23. wise(paul) [input p22]
24. patient(susan) <~> wise(susan) [input p23]
25. tall(susan) [input hypothesis]
33. ! [X0] : (~quiet(X0) | (~patient(X0) <=> funny(X0))) [ennf transformation 8]
36. (~wise(paul) & ~tall(paul)) | ! [X0] : (~funny(X0) & quiet(X0)) [ennf transformation 11]
37. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [flattening 37]
49. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (calm(X0) | funny(X0)))) [nnf transformation 6]
50. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | calm(X0) | funny(X0))) [flattening 49]
55. ! [X0] : (~quiet(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) [nnf transformation 33]
74. (~wise(susan) | ~patient(susan)) & (wise(susan) | patient(susan)) [nnf transformation 24]
78. wise(X0) | creative(X0) | calm(X0) [cnf transformation 38]
80. ~calm(X0) | ~creative(X0) | wise(X0) [cnf transformation 38]
89. ~tall(X0) | ~creative(X0) | calm(X0) | funny(X0) [cnf transformation 50]
93. ~tall(X0) | ~calm(X0) | creative(X0) [cnf transformation 50]
97. ~quiet(X0) | funny(X0) | patient(X0) [cnf transformation 55]
107. ~wise(paul) | quiet(X0) [cnf transformation 36]
108. ~wise(paul) | ~funny(X0) [cnf transformation 36]
128. wise(paul) [cnf transformation 23]
130. ~wise(susan) | ~patient(susan) [cnf transformation 74]
131. tall(susan) [cnf transformation 25]
159. 7 <=> ! [X1] : quiet(X1) [avatar definition]
160. quiet(X1) <- (7) [avatar component clause 159]
199. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
200. ~funny(X0) <- (16) [avatar component clause 199]
202. 17 <=> wise(paul) [avatar definition]
205. 16 | ~17 [avatar split clause 108,202,199]
206. 7 | ~17 [avatar split clause 107,202,159]
250. 17 [avatar split clause 128,202]
252. 27 <=> patient(susan) [avatar definition]
254. ~patient(susan) <- (~27) [avatar component clause 252]
256. 28 <=> wise(susan) [avatar definition]
258. ~wise(susan) <- (~28) [avatar component clause 256]
259. ~27 | ~28 [avatar split clause 130,256,252]
266. creative(susan) | calm(susan) <- (~28) [resolution 78,258]
268. 29 <=> calm(susan) [avatar definition]
270. calm(susan) <- (29) [avatar component clause 268]
272. 30 <=> creative(susan) [avatar definition]
274. creative(susan) <- (30) [avatar component clause 272]
275. 29 | 30 | 28 [avatar split clause 266,256,272,268]
291. ~calm(susan) | creative(susan) [resolution 93,131]
293. 30 | ~29 [avatar split clause 291,268,272]
305. funny(X1) | patient(X1) <- (7) [resolution 97,160]
307. patient(X1) <- (7, 16) [subsumption resolution 305,200]
308. $false <- (7, 16, ~27) [resolution 307,254]
309. ~7 | ~16 | 27 [avatar contradiction clause 308]
347. ~creative(susan) | calm(susan) | funny(susan) [resolution 89,131]
349. calm(susan) | funny(susan) <- (30) [subsumption resolution 347,274]
356. calm(susan) <- (16, 30) [subsumption resolution 349,200]
357. 29 | ~16 | ~30 [avatar split clause 356,272,199,268]
359. ~creative(susan) | wise(susan) <- (29) [resolution 270,80]
361. wise(susan) <- (29, 30) [subsumption resolution 359,274]
362. $false <- (~28, 29, 30) [subsumption resolution 361,258]
363. 28 | ~29 | ~30 [avatar contradiction clause 362]
364. $false [avatar sat refutation 205,206,250,259,275,293,309,357,363]
% SZS output end Proof for 4618056966890566711440822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or creative then someone is either not patient or old. Everyone who is brave is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Everyone who is either not generous or not happy is either not creative or brave and vice versa. Everyone who is calm or rich is both not creative and not strong and vice versa. Everyone who is not old or not generous is both happy and wise. If someone is either kind or not kind then mary is either generous or not wise and vice versa. Everyone who is either not patient or not funny is either creative or calm and vice versa. If alice is either not wise or patient then john is not generous or not calm and vice versa. Everyone who is either not patient or creative is both kind and strong and vice versa. Everyone who is either not happy or not generous is patient or humble and vice versa. Everyone who is not quiet or kind is not kind or quiet. Everyone who is funny or not brave is rich. Someone is funny. Fred is not old or not funny. Someone is either not brave or quiet. Susan is either not creative or curious. John is both curious and not quiet. Someone is not kind. Fred is curious or quiet. Lucy is not happy. | John is not patient. | contradiction | ((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((generous(mary)<~>~wise(mary))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((funny(X)|~brave(X))=>rich(X)))&
(?[X]:(funny(X)))&
((~old(fred)|~funny(fred)))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~creative(susan)<~>curious(susan)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X)))&
((curious(fred)|quiet(fred)))&
(~happy(lucy)) | ~patient(john) | [
"p7",
"p10",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4595924534351202033283640
% SZS output start Proof for 4595924534351202033283640
8. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p7]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p12]
15. ! [X0] : ((kind(X0) | ~quiet(X0)) => (quiet(X0) | ~kind(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | funny(X0)) => rich(X0)) [input p15]
21. ~quiet(john) & curious(john) [input p20]
25. ~patient(john) [input hypothesis]
32. ! [X0] : ((quiet(X0) | ~kind(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 15]
33. ! [X0] : (quiet(X0) | ~kind(X0) | (~kind(X0) & quiet(X0))) [flattening 32]
34. ! [X0] : (rich(X0) | (brave(X0) & ~funny(X0))) [ennf transformation 16]
51. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 51]
57. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 60]
104. ~calm(X0) | ~creative(X0) [cnf transformation 52]
105. ~rich(X0) | ~creative(X0) [cnf transformation 52]
107. ~strong(X0) | ~rich(X0) [cnf transformation 52]
127. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 57]
128. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
135. kind(X0) | creative(X0) | patient(X0) [cnf transformation 61]
137. strong(X0) | creative(X0) | patient(X0) [cnf transformation 61]
148. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 33]
149. ~funny(X0) | rich(X0) [cnf transformation 34]
158. ~quiet(john) [cnf transformation 21]
162. ~patient(john) [cnf transformation 25]
164. ~kind(X0) | quiet(X0) [duplicate literal removal 148]
266. ~calm(X0) | patient(X0) | funny(X0) [subsumption resolution 128,104]
267. ~creative(X0) | patient(X0) | funny(X0) [subsumption resolution 127,266]
381. quiet(X0) | patient(X0) | creative(X0) [resolution 135,164]
401. creative(X0) | patient(X0) | ~rich(X0) [resolution 137,107]
639. ~rich(X0) | patient(X0) [subsumption resolution 401,105]
777. patient(john) | creative(john) [resolution 381,158]
779. creative(john) [subsumption resolution 777,162]
816. patient(john) | funny(john) [resolution 779,267]
818. funny(john) [subsumption resolution 816,162]
949. rich(john) [resolution 818,149]
1043. patient(john) [resolution 949,639]
1045. $false [subsumption resolution 1043,162]
% SZS output end Proof for 4595924534351202033283640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble or not curious then someone is either not calm or not creative.
Everyone who is either not strong or patient is tall.
If someone is not generous or not rich then someone is either not strong or generous.
Everyone who is funny is both humble and curious and vice versa.
Everyone who is not calm or patient is either not tall or not strong and vice versa.
Everyone who is both not strong and not tall is both humble and happy.
Everyone who is not curious or not patient is humble.
If lucy is quiet or not tall then someone is both rich and not kind.
Everyone who is either not kind or not curious is both not happy and creative.
If someone is not humble or funny then susan is both not rich and rich.
Everyone who is not old or not curious is not calm.
If someone is both not brave and creative then someone is kind or calm and vice versa.
If someone is funny or calm then mary is both wise and not creative and vice versa.
If paul is both not creative and brave then someone is both strong and not calm and vice versa.
Everyone who is either not wise or generous is tall or brave.
If someone is not patient then someone is either funny or not brave and vice versa.
John is not generous.
Someone is both not old and not happy.
Someone is wise.
Alice is either not strong or not old.
Paul is strong.
Lucy is both humble and kind.
Someone is either not kind or creative.
John is not curious or funny. | Lucy is creative. | entailment | (((~humble(john)|~curious(john)))=>(?[X]:((~calm(X)<~>~creative(X)))))&
(![X]:((~strong(X)<~>patient(X))=>tall(X)))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(funny(X)<=>(humble(X)&curious(X))))&
(![X]:((~calm(X)|patient(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:((~strong(X)&~tall(X))=>(humble(X)&happy(X))))&
(![X]:((~curious(X)|~patient(X))=>humble(X)))&
(((quiet(lucy)|~tall(lucy)))=>(?[X]:((rich(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~curious(X))=>(~happy(X)&creative(X))))&
((?[X]:((~humble(X)|funny(X))))=>((~rich(susan)&rich(susan))))&
(![X]:((~old(X)|~curious(X))=>~calm(X)))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((wise(mary)&~creative(mary))))&
(((~creative(paul)&brave(paul)))<=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((~wise(X)<~>generous(X))=>(tall(X)|brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(~generous(john))&
(?[X]:((~old(X)&~happy(X))))&
(?[X]:(wise(X)))&
((~strong(alice)<~>~old(alice)))&
(strong(paul))&
((humble(lucy)&kind(lucy)))&
(?[X]:((~kind(X)<~>creative(X))))&
((~curious(john)|funny(john))) | creative(lucy) | [
"p3",
"p8",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 228563482554212431569415
% SZS output start Proof for 228563482554212431569415
4. ! [X0] : (funny(X0) <=> (curious(X0) & humble(X0))) [input p3]
9. ! [X0] : ((~kind(X0) <~> ~curious(X0)) => (creative(X0) & ~happy(X0))) [input p8]
10. ? [X0] : (funny(X0) | ~humble(X0)) => (rich(susan) & ~rich(susan)) [input p9]
22. kind(lucy) & humble(lucy) [input p21]
25. ~creative(lucy) [input hypothesis]
37. ! [X0] : ((creative(X0) & ~happy(X0)) | (~kind(X0) <=> ~curious(X0))) [ennf transformation 9]
38. (rich(susan) & ~rich(susan)) | ! [X0] : (~funny(X0) & humble(X0)) [ennf transformation 10]
50. ! [X0] : ((funny(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | ~funny(X0))) [nnf transformation 4]
51. ! [X0] : ((funny(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | ~funny(X0))) [flattening 50]
56. ! [X0] : ((creative(X0) & ~happy(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) [nnf transformation 37]
98. ~curious(X0) | funny(X0) | ~humble(X0) [cnf transformation 51]
114. ~kind(X0) | creative(X0) | curious(X0) [cnf transformation 56]
116. ~rich(susan) | ~funny(X0) [cnf transformation 38]
118. rich(susan) | ~funny(X0) [cnf transformation 38]
148. humble(lucy) [cnf transformation 22]
149. kind(lucy) [cnf transformation 22]
153. ~creative(lucy) [cnf transformation 25]
211. 12 <=> ! [X0] : ~funny(X0) [avatar definition]
212. ~funny(X0) <- (12) [avatar component clause 211]
214. 13 <=> rich(susan) [avatar definition]
217. 12 | 13 [avatar split clause 118,214,211]
222. 12 | ~13 [avatar split clause 116,214,211]
400. 44 <=> curious(lucy) [avatar definition]
402. curious(lucy) <- (44) [avatar component clause 400]
449. creative(lucy) | curious(lucy) [resolution 114,149]
451. curious(lucy) [subsumption resolution 449,153]
452. 44 [avatar split clause 451,400]
455. funny(lucy) | ~humble(lucy) <- (44) [resolution 402,98]
456. ~humble(lucy) <- (12, 44) [subsumption resolution 455,212]
457. $false <- (12, 44) [subsumption resolution 456,148]
458. ~12 | ~44 [avatar contradiction clause 457]
459. $false [avatar sat refutation 217,222,452,458]
% SZS output end Proof for 228563482554212431569415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or not happy then someone is either generous or not funny.
Everyone who is patient or generous is both not tall and rich and vice versa.
If someone is either not creative or kind then alice is humble or strong and vice versa.
If john is either not brave or not generous then someone is not tall or humble and vice versa.
Everyone who is not generous is both quiet and kind.
Everyone who is either happy or not creative is both curious and rich.
If someone is not quiet then lucy is creative or rich and vice versa.
Everyone who is both not patient and not humble is strong or not old and vice versa.
Everyone who is brave is curious.
If someone is curious or old then someone is either not wise or not patient and vice versa.
Everyone who is kind is not kind or brave and vice versa.
Everyone who is both rich and patient is quiet.
If someone is either rich or generous then someone is not generous or not brave.
Everyone who is both not funny and funny is either not humble or calm.
If someone is rich or not humble then mary is not brave and vice versa.
If susan is not creative then someone is either not strong or not quiet and vice versa.
Someone is tall.
Alice is quiet or patient.
Susan is either humble or not funny.
Someone is either not wise or not calm.
Fred is not calm.
Someone is not rich or not kind. | Mary is generous. | contradiction | ((?[X]:((~wise(X)<~>~happy(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((patient(X)|generous(X))<=>(~tall(X)&rich(X))))&
((?[X]:((~creative(X)<~>kind(X))))<=>((humble(alice)|strong(alice))))&
(((~brave(john)<~>~generous(john)))<=>(?[X]:((~tall(X)|humble(X)))))&
(![X]:(~generous(X)=>(quiet(X)&kind(X))))&
(![X]:((happy(X)<~>~creative(X))=>(curious(X)&rich(X))))&
((?[X]:(~quiet(X)))<=>((creative(lucy)|rich(lucy))))&
(![X]:((~patient(X)&~humble(X))<=>(strong(X)|~old(X))))&
(![X]:(brave(X)=>curious(X)))&
((?[X]:((curious(X)|old(X))))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~kind(X)|brave(X))))&
(![X]:((rich(X)&patient(X))=>quiet(X)))&
((?[X]:((rich(X)<~>generous(X))))=>(?[X]:((~generous(X)|~brave(X)))))&
(![X]:((~funny(X)&funny(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(~brave(mary)))&
((~creative(susan))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(?[X]:(tall(X)))&
((quiet(alice)|patient(alice)))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((~wise(X)<~>~calm(X))))&
(~calm(fred))&
(?[X]:((~rich(X)|~kind(X)))) | generous(mary) | [
"p1",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7503453990961226725902135
% SZS output start Proof for 7503453990961226725902135
2. ! [X0] : ((generous(X0) | patient(X0)) <=> (rich(X0) & ~tall(X0))) [input p1]
11. ! [X0] : (kind(X0) <=> (brave(X0) | ~kind(X0))) [input p10]
15. ? [X0] : (~humble(X0) | rich(X0)) <=> ~brave(mary) [input p14]
23. generous(mary) [input hypothesis]
40. ! [X0] : (((generous(X0) | patient(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 2]
41. ! [X0] : ((generous(X0) | patient(X0) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | (~generous(X0) & ~patient(X0)))) [flattening 40]
64. ! [X0] : ((kind(X0) | (~brave(X0) & kind(X0))) & ((brave(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 11]
65. ! [X0] : ((kind(X0) | (~brave(X0) & kind(X0))) & (brave(X0) | ~kind(X0) | ~kind(X0))) [flattening 64]
71. (? [X0] : (~humble(X0) | rich(X0)) | brave(mary)) & (~brave(mary) | ! [X0] : (humble(X0) & ~rich(X0))) [nnf transformation 15]
72. (? [X0] : (~humble(X0) | rich(X0)) | brave(mary)) & (~brave(mary) | ! [X1] : (humble(X1) & ~rich(X1))) [rectify 71]
73. ? [X0] : (~humble(X0) | rich(X0)) => (~humble(sK7) | rich(sK7)) [choice axiom]
74. ((~humble(sK7) | rich(sK7)) | brave(mary)) & (~brave(mary) | ! [X1] : (humble(X1) & ~rich(X1))) [skolemisation 72,73]
94. ~generous(X0) | rich(X0) [cnf transformation 41]
129. brave(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 65]
130. kind(X0) | kind(X0) [cnf transformation 65]
137. ~brave(mary) | ~rich(X1) [cnf transformation 74]
152. generous(mary) [cnf transformation 23]
153. brave(X0) | ~kind(X0) [duplicate literal removal 129]
154. kind(X0) [duplicate literal removal 130]
281. brave(X0) [subsumption resolution 153,154]
293. ~rich(X1) [subsumption resolution 137,281]
334. rich(mary) [resolution 94,152]
335. $false [subsumption resolution 334,293]
% SZS output end Proof for 7503453990961226725902135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not happy and funny then someone is both happy and not strong and vice versa.
If someone is either not old or not curious then someone is rich or not tall and vice versa.
Everyone who is either not calm or funny is calm.
If paul is either kind or not calm then susan is not strong or generous.
Everyone who is both not wise and wise is both not generous and not strong and vice versa.
Everyone who is happy or not calm is either not wise or not happy and vice versa.
Everyone who is either wise or patient is kind or strong and vice versa.
If susan is kind or not patient then susan is calm or humble and vice versa.
Everyone who is either not wise or curious is brave or not quiet.
If someone is not generous or happy then lucy is both not kind and not curious and vice versa.
Everyone who is not generous is wise or not patient.
Everyone who is both old and calm is not curious or not old and vice versa.
Everyone who is not kind or not quiet is either calm or not wise and vice versa.
If someone is not quiet then someone is either not strong or humble and vice versa.
If alice is either not patient or funny then someone is curious or not strong and vice versa.
If fred is either creative or quiet then someone is happy and vice versa.
Lucy is happy or quiet.
Mary is not creative or quiet.
Someone is calm or patient.
Someone is curious.
Someone is either patient or quiet.
Someone is both wise and brave.
Someone is old.
Fred is both not happy and creative. | Alice is brave. | entailment | (((~happy(paul)&funny(paul)))<=>(?[X]:((happy(X)&~strong(X)))))&
((?[X]:((~old(X)<~>~curious(X))))<=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:((~calm(X)<~>funny(X))=>calm(X)))&
(((kind(paul)<~>~calm(paul)))=>((~strong(susan)|generous(susan))))&
(![X]:((~wise(X)&wise(X))<=>(~generous(X)&~strong(X))))&
(![X]:((happy(X)|~calm(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((wise(X)<~>patient(X))<=>(kind(X)|strong(X))))&
(((kind(susan)|~patient(susan)))<=>((calm(susan)|humble(susan))))&
(![X]:((~wise(X)<~>curious(X))=>(brave(X)|~quiet(X))))&
((?[X]:((~generous(X)|happy(X))))<=>((~kind(lucy)&~curious(lucy))))&
(![X]:(~generous(X)=>(wise(X)|~patient(X))))&
(![X]:((old(X)&calm(X))<=>(~curious(X)|~old(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(calm(X)<~>~wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(((~patient(alice)<~>funny(alice)))<=>(?[X]:((curious(X)|~strong(X)))))&
(((creative(fred)<~>quiet(fred)))<=>(?[X]:(happy(X))))&
((happy(lucy)|quiet(lucy)))&
((~creative(mary)|quiet(mary)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:(old(X)))&
((~happy(fred)&creative(fred))) | brave(alice) | [
"p5",
"p8",
"p11",
"p12",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4763174674595361623912328
% SZS output start Proof for 4763174674595361623912328
6. ! [X0] : ((~calm(X0) | happy(X0)) <=> (~wise(X0) <~> ~happy(X0))) [input p5]
9. ! [X0] : ((~wise(X0) <~> curious(X0)) => (~quiet(X0) | brave(X0))) [input p8]
12. ! [X0] : ((calm(X0) & old(X0)) <=> (~old(X0) | ~curious(X0))) [input p11]
13. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p12]
16. (creative(fred) <~> quiet(fred)) <=> ? [X0] : happy(X0) [input p15]
24. creative(fred) & ~happy(fred) [input p23]
25. ~brave(alice) [input hypothesis]
31. ! [X0] : ((~quiet(X0) | brave(X0)) | (~wise(X0) <=> curious(X0))) [ennf transformation 9]
32. ! [X0] : (~quiet(X0) | brave(X0) | (~wise(X0) <=> curious(X0))) [flattening 31]
49. ! [X0] : (((~calm(X0) | happy(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [nnf transformation 6]
50. ! [X0] : ((~calm(X0) | happy(X0) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (calm(X0) & ~happy(X0)))) [flattening 49]
55. ! [X0] : (~quiet(X0) | brave(X0) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) [nnf transformation 32]
61. ! [X0] : (((calm(X0) & old(X0)) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | (~calm(X0) | ~old(X0)))) [nnf transformation 12]
62. ! [X0] : (((calm(X0) & old(X0)) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | ~calm(X0) | ~old(X0))) [flattening 61]
63. ! [X0] : (((~quiet(X0) | ~kind(X0)) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (quiet(X0) & kind(X0)))) [nnf transformation 13]
64. ! [X0] : ((~quiet(X0) | ~kind(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (quiet(X0) & kind(X0)))) [flattening 63]
74. (((~quiet(fred) | ~creative(fred)) & (quiet(fred) | creative(fred))) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ((creative(fred) | ~quiet(fred)) & (quiet(fred) | ~creative(fred)))) [nnf transformation 16]
75. (((~quiet(fred) | ~creative(fred)) & (quiet(fred) | creative(fred))) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ((creative(fred) | ~quiet(fred)) & (quiet(fred) | ~creative(fred)))) [rectify 74]
76. ? [X1] : happy(X1) => happy(sK7) [choice axiom]
77. (((~quiet(fred) | ~creative(fred)) & (quiet(fred) | creative(fred))) | ! [X0] : ~happy(X0)) & (happy(sK7) | ((creative(fred) | ~quiet(fred)) & (quiet(fred) | ~creative(fred)))) [skolemisation 75,76]
107. ~happy(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 50]
110. wise(X0) | happy(X0) | calm(X0) [cnf transformation 50]
112. ~calm(X0) | happy(X0) | ~wise(X0) | happy(X0) [cnf transformation 50]
123. ~quiet(X0) | brave(X0) | curious(X0) | wise(X0) [cnf transformation 55]
124. ~quiet(X0) | brave(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 55]
131. ~old(X0) | ~curious(X0) | ~calm(X0) | ~old(X0) [cnf transformation 62]
133. old(X0) | old(X0) [cnf transformation 62]
134. calm(X0) | curious(X0) [cnf transformation 62]
137. ~wise(X0) | calm(X0) | quiet(X0) [cnf transformation 64]
139. ~calm(X0) | wise(X0) | quiet(X0) [cnf transformation 64]
155. ~quiet(fred) | ~creative(fred) | ~happy(X0) [cnf transformation 77]
165. ~happy(fred) [cnf transformation 24]
166. creative(fred) [cnf transformation 24]
167. ~brave(alice) [cnf transformation 25]
168. ~old(X0) | ~curious(X0) | ~calm(X0) [duplicate literal removal 131]
169. old(X0) [duplicate literal removal 133]
170. ~wise(X0) | ~happy(X0) [duplicate literal removal 107]
171. ~wise(X0) | happy(X0) | ~calm(X0) [duplicate literal removal 112]
287. 26 <=> ! [X1] : ~happy(X1) [avatar definition]
288. ~happy(X1) <- (26) [avatar component clause 287]
296. ~calm(X0) | ~curious(X0) [subsumption resolution 168,169]
351. 40 <=> creative(fred) [avatar definition]
355. 41 <=> quiet(fred) [avatar definition]
357. ~quiet(fred) <- (~41) [avatar component clause 355]
358. 26 | ~40 | ~41 [avatar split clause 155,355,351,287]
403. 40 [avatar split clause 166,351]
485. calm(X0) | quiet(X0) | happy(X0) | calm(X0) [resolution 137,110]
488. quiet(X0) | calm(X0) | happy(X0) [duplicate literal removal 485]
529. quiet(X2) | wise(X2) | curious(X2) [resolution 139,134]
636. calm(fred) | happy(fred) <- (~41) [resolution 488,357]
639. calm(X2) | happy(X2) | brave(X2) | ~wise(X2) | ~curious(X2) [resolution 488,124]
651. calm(fred) <- (~41) [subsumption resolution 636,165]
652. happy(X2) | brave(X2) | ~wise(X2) | ~curious(X2) [subsumption resolution 639,171]
653. ~wise(X2) | brave(X2) | ~curious(X2) [subsumption resolution 652,170]
700. 75 <=> wise(fred) [avatar definition]
702. wise(fred) <- (75) [avatar component clause 700]
706. wise(fred) | curious(fred) <- (~41) [resolution 529,357]
710. wise(X3) | curious(X3) | brave(X3) | curious(X3) | wise(X3) [resolution 529,123]
711. brave(X3) | curious(X3) | wise(X3) [duplicate literal removal 710]
719. 77 <=> curious(fred) [avatar definition]
722. 77 | 75 | 41 [avatar split clause 706,355,700,719]
725. ~curious(fred) <- (~41) [resolution 651,296]
726. ~77 | 41 [avatar split clause 725,355,719]
758. happy(fred) | ~calm(fred) <- (75) [resolution 702,171]
776. ~calm(fred) <- (75) [subsumption resolution 758,165]
777. $false <- (~41, 75) [subsumption resolution 776,651]
778. 41 | ~75 [avatar contradiction clause 777]
1041. brave(X2) | ~curious(X2) | happy(X2) | calm(X2) [resolution 653,110]
1048. brave(X2) | ~curious(X2) | calm(X2) <- (26) [subsumption resolution 1041,288]
1049. brave(X2) | calm(X2) <- (26) [subsumption resolution 1048,134]
1077. curious(alice) | wise(alice) [resolution 711,167]
1119. 96 <=> calm(alice) [avatar definition]
1121. calm(alice) <- (96) [avatar component clause 1119]
1138. calm(alice) <- (26) [resolution 1049,167]
1142. 97 <=> wise(alice) [avatar definition]
1144. wise(alice) <- (97) [avatar component clause 1142]
1146. 98 <=> curious(alice) [avatar definition]
1148. curious(alice) <- (98) [avatar component clause 1146]
1149. 97 | 98 [avatar split clause 1077,1146,1142]
1151. 96 | ~26 [avatar split clause 1138,287,1119]
1167. happy(alice) | ~calm(alice) <- (97) [resolution 1144,171]
1170. ~calm(alice) <- (26, 97) [subsumption resolution 1167,288]
1171. $false <- (26, 96, 97) [subsumption resolution 1170,1121]
1172. ~26 | ~96 | ~97 [avatar contradiction clause 1171]
1201. ~curious(alice) <- (96) [resolution 1121,296]
1202. $false <- (96, 98) [subsumption resolution 1201,1148]
1203. ~96 | ~98 [avatar contradiction clause 1202]
1204. $false [avatar sat refutation 358,403,722,726,778,1149,1151,1172,1203]
% SZS output end Proof for 4763174674595361623912328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not strong is either curious or quiet.
If alice is not wise then someone is brave or wise and vice versa.
Everyone who is not happy or curious is curious.
Everyone who is both generous and patient is not calm or not happy and vice versa.
Everyone who is quiet or not wise is either not generous or not calm.
Everyone who is not old or strong is both not generous and curious and vice versa.
If someone is both not creative and not old then someone is either not patient or rich and vice versa.
If fred is not rich then someone is kind and vice versa.
Everyone who is not curious is both not curious and brave.
Everyone who is not humble is wise.
If someone is either not humble or not calm then lucy is either not generous or not old and vice versa.
Everyone who is either rich or calm is curious.
If someone is old or generous then someone is either old or not curious.
Everyone who is not happy is both quiet and brave.
Everyone who is both not creative and happy is either quiet or old.
Everyone who is either humble or not patient is both not patient and funny and vice versa.
Someone is rich.
Alice is calm.
Someone is both not kind and old.
Fred is not brave.
Fred is not wise or not old.
Susan is either funny or patient.
Someone is either calm or funny.
John is either funny or patient. | John is wise. | entailment | (![X]:((~curious(X)|~strong(X))=>(curious(X)<~>quiet(X))))&
((~wise(alice))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:((~happy(X)|curious(X))=>curious(X)))&
(![X]:((generous(X)&patient(X))<=>(~calm(X)|~happy(X))))&
(![X]:((quiet(X)|~wise(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((~old(X)|strong(X))<=>(~generous(X)&curious(X))))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((~rich(fred))<=>(?[X]:(kind(X))))&
(![X]:(~curious(X)=>(~curious(X)&brave(X))))&
(![X]:(~humble(X)=>wise(X)))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((~generous(lucy)<~>~old(lucy))))&
(![X]:((rich(X)<~>calm(X))=>curious(X)))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:(~happy(X)=>(quiet(X)&brave(X))))&
(![X]:((~creative(X)&happy(X))=>(quiet(X)<~>old(X))))&
(![X]:((humble(X)<~>~patient(X))<=>(~patient(X)&funny(X))))&
(?[X]:(rich(X)))&
(calm(alice))&
(?[X]:((~kind(X)&old(X))))&
(~brave(fred))&
((~wise(fred)|~old(fred)))&
((funny(susan)<~>patient(susan)))&
(?[X]:((calm(X)<~>funny(X))))&
((funny(john)<~>patient(john))) | wise(john) | [
"p9",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8121430958379549064610431
% SZS output start Proof for 8121430958379549064610431
10. ! [X0] : (~humble(X0) => wise(X0)) [input p9]
16. ! [X0] : ((humble(X0) <~> ~patient(X0)) <=> (funny(X0) & ~patient(X0))) [input p15]
24. funny(john) <~> patient(john) [input p23]
25. ~wise(john) [input hypothesis]
32. ! [X0] : (wise(X0) | humble(X0)) [ennf transformation 10]
67. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [nnf transformation 16]
68. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [flattening 67]
77. (~patient(john) | ~funny(john)) & (patient(john) | funny(john)) [nnf transformation 24]
111. humble(X0) | wise(X0) [cnf transformation 32]
130. ~patient(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 68]
135. patient(X0) | ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 68]
146. patient(john) | funny(john) [cnf transformation 77]
148. ~wise(john) [cnf transformation 25]
149. ~humble(X0) | ~patient(X0) [duplicate literal removal 130]
150. ~funny(X0) | ~humble(X0) | patient(X0) [duplicate literal removal 135]
302. 32 <=> funny(john) [avatar definition]
303. funny(john) <- (32) [avatar component clause 302]
306. 33 <=> patient(john) [avatar definition]
307. patient(john) <- (33) [avatar component clause 306]
308. ~patient(john) <- (~33) [avatar component clause 306]
310. 32 | 33 [avatar split clause 146,306,302]
329. ~patient(X0) | wise(X0) [resolution 149,111]
383. ~humble(john) | patient(john) <- (32) [resolution 150,303]
392. ~humble(john) <- (32, ~33) [subsumption resolution 383,308]
539. wise(john) <- (32, ~33) [resolution 392,111]
540. $false <- (32, ~33) [subsumption resolution 539,148]
541. ~32 | 33 [avatar contradiction clause 540]
543. wise(john) <- (33) [resolution 307,329]
544. $false <- (33) [subsumption resolution 543,148]
545. ~33 [avatar contradiction clause 544]
546. $false [avatar sat refutation 310,541,545]
% SZS output end Proof for 8121430958379549064610431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not brave is both not creative and not quiet. Everyone who is either not tall or not funny is both humble and not generous and vice versa. Everyone who is happy is not calm or strong and vice versa. Everyone who is both brave and not curious is patient or not patient. Everyone who is not tall is old or generous. Everyone who is either not funny or old is not patient or not tall and vice versa. If paul is both wise and not quiet then alice is either not kind or not curious and vice versa. Everyone who is both not quiet and not funny is patient and vice versa. Everyone who is not wise is both wise and not calm. If someone is not creative then someone is both not funny and not calm. If someone is both wise and not funny then someone is either not curious or kind. Everyone who is tall or not humble is both not quiet and not wise. Everyone who is both not generous and funny is both not wise and patient. Everyone who is both not calm and not kind is either not calm or brave and vice versa. If someone is not patient then someone is either patient or brave. Mary is not tall. Someone is kind. Fred is either not wise or happy. Someone is not patient. Susan is funny or humble. Paul is either not creative or curious. Susan is either not strong or not happy. | Alice is not tall. | entailment | (![X]:((generous(X)<~>~brave(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(humble(X)&~generous(X))))&
(![X]:(happy(X)<=>(~calm(X)|strong(X))))&
(![X]:((brave(X)&~curious(X))=>(patient(X)|~patient(X))))&
(![X]:(~tall(X)=>(old(X)|generous(X))))&
(![X]:((~funny(X)<~>old(X))<=>(~patient(X)|~tall(X))))&
(((wise(paul)&~quiet(paul)))<=>((~kind(alice)<~>~curious(alice))))&
(![X]:((~quiet(X)&~funny(X))<=>patient(X)))&
(![X]:(~wise(X)=>(wise(X)&~calm(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~funny(X)&~calm(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((tall(X)|~humble(X))=>(~quiet(X)&~wise(X))))&
(![X]:((~generous(X)&funny(X))=>(~wise(X)&patient(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(~patient(X)))=>(?[X]:((patient(X)<~>brave(X)))))&
(~tall(mary))&
(?[X]:(kind(X)))&
((~wise(fred)<~>happy(fred)))&
(?[X]:(~patient(X)))&
((funny(susan)|humble(susan)))&
((~creative(paul)<~>curious(paul)))&
((~strong(susan)<~>~happy(susan))) | ~tall(alice) | [
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6527776516537586012607142
% SZS output start Proof for 6527776516537586012607142
9. ! [X0] : (~wise(X0) => (~calm(X0) & wise(X0))) [input p8]
12. ! [X0] : ((~humble(X0) | tall(X0)) => (~wise(X0) & ~quiet(X0))) [input p11]
23. tall(alice) [input hypothesis]
32. ! [X0] : ((~calm(X0) & wise(X0)) | wise(X0)) [ennf transformation 9]
35. ! [X0] : ((~wise(X0) & ~quiet(X0)) | (humble(X0) & ~tall(X0))) [ennf transformation 12]
100. wise(X0) | wise(X0) [cnf transformation 32]
108. ~wise(X0) | ~tall(X0) [cnf transformation 35]
130. tall(alice) [cnf transformation 23]
133. wise(X0) [duplicate literal removal 100]
185. ~tall(X0) [subsumption resolution 108,133]
214. $false [subsumption resolution 130,185]
% SZS output end Proof for 6527776516537586012607142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or quiet is both not calm and not kind and vice versa.
Everyone who is funny or not patient is not creative or wise and vice versa.
If someone is strong then someone is not tall and vice versa.
Everyone who is not brave or not humble is either not generous or not calm and vice versa.
Everyone who is not calm is humble.
Everyone who is either quiet or not kind is both patient and not funny and vice versa.
Everyone who is either brave or old is patient and vice versa.
If someone is either old or not tall then someone is kind and vice versa.
Everyone who is either creative or curious is rich and vice versa.
If someone is both patient and not creative then someone is not curious.
Everyone who is either not curious or strong is either not rich or patient and vice versa.
Everyone who is both rich and humble is both brave and tall.
If lucy is strong then lucy is both old and calm and vice versa.
If someone is either wise or rich then someone is not generous or curious.
Everyone who is not happy or not rich is brave or kind.
Everyone who is not quiet or tall is not strong or humble and vice versa.
Someone is not brave or happy.
Alice is both strong and not wise.
Someone is either calm or generous.
Alice is not humble.
Someone is both happy and not old.
Someone is not tall.
Someone is either curious or not rich.
Paul is either happy or tall. | Alice is not funny. | contradiction | (![X]:((~wise(X)<~>quiet(X))<=>(~calm(X)&~kind(X))))&
(![X]:((funny(X)|~patient(X))<=>(~creative(X)|wise(X))))&
((?[X]:(strong(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>(patient(X)&~funny(X))))&
(![X]:((brave(X)<~>old(X))<=>patient(X)))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((creative(X)<~>curious(X))<=>rich(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((rich(X)&humble(X))=>(brave(X)&tall(X))))&
((strong(lucy))<=>((old(lucy)&calm(lucy))))&
((?[X]:((wise(X)<~>rich(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~happy(X)|~rich(X))=>(brave(X)|kind(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~strong(X)|humble(X))))&
(?[X]:((~brave(X)|happy(X))))&
((strong(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>generous(X))))&
(~humble(alice))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
((happy(paul)<~>tall(paul))) | ~funny(alice) | [
"p1",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8828253095860892357558867
% SZS output start Proof for 8828253095860892357558867
2. ! [X0] : ((~patient(X0) | funny(X0)) <=> (wise(X0) | ~creative(X0))) [input p1]
9. ! [X0] : ((creative(X0) <~> curious(X0)) <=> rich(X0)) [input p8]
11. ! [X0] : ((~curious(X0) <~> strong(X0)) <=> (~rich(X0) <~> patient(X0))) [input p10]
18. ~wise(alice) & strong(alice) [input p17]
25. ~funny(alice) [input hypothesis]
39. ! [X0] : (((~patient(X0) | funny(X0)) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | (patient(X0) & ~funny(X0)))) [nnf transformation 2]
40. ! [X0] : ((~patient(X0) | funny(X0) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | (patient(X0) & ~funny(X0)))) [flattening 39]
56. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | ~rich(X0)) & (rich(X0) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 9]
60. ! [X0] : ((((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0))))) [nnf transformation 11]
89. ~creative(X0) | wise(X0) | patient(X0) [cnf transformation 40]
90. ~patient(X0) | funny(X0) | creative(X0) [cnf transformation 40]
115. ~creative(X0) | curious(X0) | rich(X0) [cnf transformation 56]
116. ~curious(X0) | creative(X0) | rich(X0) [cnf transformation 56]
117. ~rich(X0) | creative(X0) | curious(X0) [cnf transformation 56]
118. ~rich(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 56]
121. ~rich(X0) | patient(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 60]
123. ~curious(X0) | rich(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 60]
126. ~strong(X0) | curious(X0) | patient(X0) | rich(X0) [cnf transformation 60]
127. ~rich(X0) | curious(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 60]
142. strong(alice) [cnf transformation 18]
143. ~wise(alice) [cnf transformation 18]
154. ~funny(alice) [cnf transformation 25]
562. curious(alice) | patient(alice) | rich(alice) [resolution 126,142]
565. 61 <=> rich(alice) [avatar definition]
566. ~rich(alice) <- (~61) [avatar component clause 565]
567. rich(alice) <- (61) [avatar component clause 565]
569. 62 <=> patient(alice) [avatar definition]
570. ~patient(alice) <- (~62) [avatar component clause 569]
571. patient(alice) <- (62) [avatar component clause 569]
573. 63 <=> curious(alice) [avatar definition]
575. curious(alice) <- (63) [avatar component clause 573]
576. 61 | 62 | 63 [avatar split clause 562,573,569,565]
629. creative(alice) | curious(alice) <- (61) [resolution 567,117]
630. ~creative(alice) | ~curious(alice) <- (61) [resolution 567,118]
632. patient(alice) | ~curious(alice) | ~strong(alice) <- (61) [resolution 567,121]
634. curious(alice) | ~strong(alice) | ~patient(alice) <- (61) [resolution 567,127]
638. 71 <=> creative(alice) [avatar definition]
640. creative(alice) <- (71) [avatar component clause 638]
641. 63 | 71 | ~61 [avatar split clause 629,565,638,573]
642. ~63 | ~71 | ~61 [avatar split clause 630,565,638,573]
643. patient(alice) | ~curious(alice) <- (61) [subsumption resolution 632,142]
644. ~63 | 62 | ~61 [avatar split clause 643,565,569,573]
645. curious(alice) | ~patient(alice) <- (61) [subsumption resolution 634,142]
646. ~62 | 63 | ~61 [avatar split clause 645,565,573,569]
706. wise(alice) | patient(alice) <- (71) [resolution 640,89]
708. patient(alice) <- (71) [subsumption resolution 706,143]
709. $false <- (~62, 71) [subsumption resolution 708,570]
710. 62 | ~71 [avatar contradiction clause 709]
726. funny(alice) | creative(alice) <- (62) [resolution 571,90]
732. creative(alice) <- (62) [subsumption resolution 726,154]
733. 71 | ~62 [avatar split clause 732,569,638]
766. curious(alice) | rich(alice) <- (71) [resolution 640,115]
772. curious(alice) <- (~61, 71) [subsumption resolution 766,566]
773. 63 | 61 | ~71 [avatar split clause 772,638,565,573]
775. rich(alice) | ~patient(alice) | ~strong(alice) <- (63) [resolution 575,123]
776. creative(alice) | rich(alice) <- (63) [resolution 575,116]
777. ~patient(alice) | ~strong(alice) <- (~61, 63) [subsumption resolution 775,566]
781. ~patient(alice) <- (~61, 63) [subsumption resolution 777,142]
782. ~62 | 61 | ~63 [avatar split clause 781,573,565,569]
783. creative(alice) <- (~61, 63) [subsumption resolution 776,566]
784. 71 | 61 | ~63 [avatar split clause 783,573,565,638]
785. $false [avatar sat refutation 576,641,642,644,646,710,733,773,782,784]
% SZS output end Proof for 8828253095860892357558867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is not humble and vice versa. Everyone who is curious is not calm and vice versa. Everyone who is both not calm and humble is either calm or not old and vice versa. Everyone who is either calm or tall is either not patient or not kind and vice versa. Everyone who is funny or quiet is not kind and vice versa. If someone is not humble or not quiet then paul is either not calm or not strong and vice versa. Everyone who is tall or not curious is both not patient and not quiet. Everyone who is both humble and creative is rich or not brave and vice versa. If someone is both old and tall then someone is creative or not generous. If someone is funny or kind then susan is curious and vice versa. If someone is not rich then someone is not curious. If someone is either not creative or not brave then lucy is both not calm and not happy and vice versa. Everyone who is both not old and not humble is both creative and patient. If john is not wise then mary is either not quiet or calm. Everyone who is not wise is not rich and vice versa. Someone is either kind or quiet. Someone is happy or not brave. Fred is both tall and strong. John is not tall. Alice is tall or not quiet. Someone is either kind or not quiet. | Alice is not calm. | entailment | (![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:((tall(X)|~curious(X))=>(~patient(X)&~quiet(X))))&
(![X]:((humble(X)&creative(X))<=>(rich(X)|~brave(X))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((creative(X)|~generous(X)))))&
((?[X]:((funny(X)|kind(X))))<=>(curious(susan)))&
((?[X]:(~rich(X)))=>(?[X]:(~curious(X))))&
((?[X]:((~creative(X)<~>~brave(X))))<=>((~calm(lucy)&~happy(lucy))))&
(![X]:((~old(X)&~humble(X))=>(creative(X)&patient(X))))&
((~wise(john))=>((~quiet(mary)<~>calm(mary))))&
(![X]:(~wise(X)<=>~rich(X)))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((happy(X)|~brave(X))))&
((tall(fred)&strong(fred)))&
(~tall(john))&
((tall(alice)|~quiet(alice)))&
(?[X]:((kind(X)<~>~quiet(X)))) | ~calm(alice) | [
"p0",
"p1",
"p2",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4599102316580270517470444
% SZS output start Proof for 4599102316580270517470444
1. ! [X0] : (calm(X0) <=> ~humble(X0)) [input p0]
2. ! [X0] : (curious(X0) <=> ~calm(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (calm(X0) <~> ~old(X0))) [input p2]
7. ! [X0] : ((~curious(X0) | tall(X0)) => (~quiet(X0) & ~patient(X0))) [input p6]
13. ! [X0] : ((~humble(X0) & ~old(X0)) => (patient(X0) & creative(X0))) [input p12]
22. calm(alice) [input hypothesis]
27. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (curious(X0) & ~tall(X0))) [ennf transformation 7]
29. ! [X0] : ((patient(X0) & creative(X0)) | (humble(X0) | old(X0))) [ennf transformation 13]
30. ! [X0] : ((patient(X0) & creative(X0)) | humble(X0) | old(X0)) [flattening 29]
33. ! [X0] : ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))) [nnf transformation 1]
34. ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 2]
35. ! [X0] : (((humble(X0) & ~calm(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (~humble(X0) | calm(X0)))) [nnf transformation 3]
36. ! [X0] : (((humble(X0) & ~calm(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ~humble(X0) | calm(X0))) [flattening 35]
67. ~humble(X0) | ~calm(X0) [cnf transformation 33]
69. ~curious(X0) | ~calm(X0) [cnf transformation 34]
70. curious(X0) | calm(X0) [cnf transformation 34]
75. humble(X0) | ~old(X0) | ~calm(X0) [cnf transformation 36]
95. ~patient(X0) | curious(X0) [cnf transformation 27]
114. patient(X0) | humble(X0) | old(X0) [cnf transformation 30]
127. calm(alice) [cnf transformation 22]
130. ~old(X0) | ~calm(X0) [subsumption resolution 75,67]
313. old(X0) | humble(X0) | curious(X0) [resolution 114,95]
474. humble(X1) | curious(X1) | ~calm(X1) [resolution 313,130]
475. curious(X1) | ~calm(X1) [subsumption resolution 474,67]
476. curious(X1) [subsumption resolution 475,70]
505. ~calm(X0) [resolution 476,69]
543. $false [resolution 505,127]
% SZS output end Proof for 4599102316580270517470444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not patient and vice versa.
If someone is not rich then someone is wise or not calm.
Everyone who is either kind or brave is either not wise or not quiet and vice versa.
If someone is both not old and curious then mary is not kind.
Everyone who is either not quiet or not old is not creative.
If lucy is not calm then alice is both quiet and not brave and vice versa.
If mary is tall or not generous then someone is both not tall and patient.
Everyone who is either patient or curious is calm or not happy.
Everyone who is either strong or rich is happy or generous and vice versa.
Everyone who is either kind or brave is calm or not humble and vice versa.
If someone is either not curious or not brave then paul is both not funny and not strong.
Everyone who is kind is rich.
Everyone who is quiet or happy is either patient or not happy.
Everyone who is both not patient and kind is either funny or not creative and vice versa.
If someone is both creative and not old then lucy is both quiet and not strong.
If fred is calm then fred is quiet.
Someone is not quiet.
Alice is wise.
Someone is either humble or not rich.
Someone is both old and not humble.
Someone is not creative.
Paul is both curious and strong.
Someone is kind or not rich.
Susan is not tall or curious. | Lucy is quiet. | neutral | (![X]:(~happy(X)<=>~patient(X)))&
((?[X]:(~rich(X)))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((kind(X)<~>brave(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((~old(X)&curious(X))))=>(~kind(mary)))&
(![X]:((~quiet(X)<~>~old(X))=>~creative(X)))&
((~calm(lucy))<=>((quiet(alice)&~brave(alice))))&
(((tall(mary)|~generous(mary)))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((patient(X)<~>curious(X))=>(calm(X)|~happy(X))))&
(![X]:((strong(X)<~>rich(X))<=>(happy(X)|generous(X))))&
(![X]:((kind(X)<~>brave(X))<=>(calm(X)|~humble(X))))&
((?[X]:((~curious(X)<~>~brave(X))))=>((~funny(paul)&~strong(paul))))&
(![X]:(kind(X)=>rich(X)))&
(![X]:((quiet(X)|happy(X))=>(patient(X)<~>~happy(X))))&
(![X]:((~patient(X)&kind(X))<=>(funny(X)<~>~creative(X))))&
((?[X]:((creative(X)&~old(X))))=>((quiet(lucy)&~strong(lucy))))&
((calm(fred))=>(quiet(fred)))&
(?[X]:(~quiet(X)))&
(wise(alice))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((old(X)&~humble(X))))&
(?[X]:(~creative(X)))&
((curious(paul)&strong(paul)))&
(?[X]:((kind(X)|~rich(X))))&
((~tall(susan)|curious(susan))) | quiet(lucy) | [] | null | 0 |
If susan is rich or tall then someone is not old or not humble and vice versa.
If someone is old then paul is both curious and not curious and vice versa.
If susan is either calm or creative then fred is either not humble or tall and vice versa.
If paul is both happy and strong then someone is both not rich and old and vice versa.
If mary is rich or tall then someone is funny or not wise and vice versa.
If john is not humble then someone is either funny or not quiet.
If someone is both humble and not rich then someone is humble.
Everyone who is both not humble and happy is not rich and vice versa.
Everyone who is both not tall and not curious is old or not generous and vice versa.
If someone is not happy then someone is not quiet or not wise and vice versa.
Everyone who is either kind or wise is happy or calm.
If alice is either patient or strong then someone is either happy or not generous and vice versa.
If fred is not patient or not generous then fred is either not wise or happy.
Everyone who is both not rich and curious is both not rich and wise and vice versa.
If someone is not rich then fred is humble or not creative.
Everyone who is curious is creative or not funny.
Mary is not creative.
Someone is either happy or not quiet.
Lucy is both not curious and not strong.
Lucy is both creative and tall.
Alice is both tall and quiet.
Alice is not creative or generous.
Someone is both tall and not curious.
Paul is not happy or wise. | Mary is old. | contradiction | (((rich(susan)|tall(susan)))<=>(?[X]:((~old(X)|~humble(X)))))&
((?[X]:(old(X)))<=>((curious(paul)&~curious(paul))))&
(((calm(susan)<~>creative(susan)))<=>((~humble(fred)<~>tall(fred))))&
(((happy(paul)&strong(paul)))<=>(?[X]:((~rich(X)&old(X)))))&
(((rich(mary)|tall(mary)))<=>(?[X]:((funny(X)|~wise(X)))))&
((~humble(john))=>(?[X]:((funny(X)<~>~quiet(X)))))&
((?[X]:((humble(X)&~rich(X))))=>(?[X]:(humble(X))))&
(![X]:((~humble(X)&happy(X))<=>~rich(X)))&
(![X]:((~tall(X)&~curious(X))<=>(old(X)|~generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:((kind(X)<~>wise(X))=>(happy(X)|calm(X))))&
(((patient(alice)<~>strong(alice)))<=>(?[X]:((happy(X)<~>~generous(X)))))&
(((~patient(fred)|~generous(fred)))=>((~wise(fred)<~>happy(fred))))&
(![X]:((~rich(X)&curious(X))<=>(~rich(X)&wise(X))))&
((?[X]:(~rich(X)))=>((humble(fred)|~creative(fred))))&
(![X]:(curious(X)=>(creative(X)|~funny(X))))&
(~creative(mary))&
(?[X]:((happy(X)<~>~quiet(X))))&
((~curious(lucy)&~strong(lucy)))&
((creative(lucy)&tall(lucy)))&
((tall(alice)&quiet(alice)))&
((~creative(alice)|generous(alice)))&
(?[X]:((tall(X)&~curious(X))))&
((~happy(paul)|wise(paul))) | old(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8261390020536037963625670
% SZS output start Proof for 8261390020536037963625670
2. ? [X0] : old(X0) <=> (~curious(paul) & curious(paul)) [input p1]
25. old(mary) [input hypothesis]
42. (? [X0] : old(X0) | (curious(paul) | ~curious(paul))) & ((~curious(paul) & curious(paul)) | ! [X0] : ~old(X0)) [nnf transformation 2]
43. (? [X0] : old(X0) | curious(paul) | ~curious(paul)) & ((~curious(paul) & curious(paul)) | ! [X0] : ~old(X0)) [flattening 42]
44. (? [X0] : old(X0) | curious(paul) | ~curious(paul)) & ((~curious(paul) & curious(paul)) | ! [X1] : ~old(X1)) [rectify 43]
45. ? [X0] : old(X0) => old(sK1) [choice axiom]
46. (old(sK1) | curious(paul) | ~curious(paul)) & ((~curious(paul) & curious(paul)) | ! [X1] : ~old(X1)) [skolemisation 44,45]
90. curious(paul) | ~old(X1) [cnf transformation 46]
91. ~curious(paul) | ~old(X1) [cnf transformation 46]
156. old(mary) [cnf transformation 25]
184. 7 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (7) [avatar component clause 184]
187. 8 <=> curious(paul) [avatar definition]
190. 7 | ~8 [avatar split clause 91,187,184]
191. 7 | 8 [avatar split clause 90,187,184]
391. $false <- (7) [resolution 185,156]
392. ~7 [avatar contradiction clause 391]
393. $false [avatar sat refutation 190,191,392]
% SZS output end Proof for 8261390020536037963625670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not wise is both kind and wise and vice versa.
Everyone who is brave or strong is both not old and tall and vice versa.
If mary is either generous or rich then susan is not rich.
Everyone who is not kind or not old is both not wise and not creative and vice versa.
Everyone who is either kind or not patient is either not creative or not curious and vice versa.
Everyone who is both not kind and quiet is both patient and curious and vice versa.
If paul is creative then fred is not patient.
Everyone who is happy is not quiet and vice versa.
Everyone who is both wise and not rich is not tall and vice versa.
Everyone who is either not creative or calm is not patient.
If paul is not tall or rich then someone is rich.
If susan is humble then fred is both funny and not happy and vice versa.
If someone is happy then someone is either not funny or brave and vice versa.
If paul is both not wise and humble then someone is not quiet or patient and vice versa.
If fred is not brave or humble then john is either wise or not wise.
Alice is not patient.
Paul is either generous or kind.
Mary is not generous.
Lucy is both not generous and quiet.
Someone is not rich. | John is not quiet. | neutral | (![X]:((brave(X)<~>~wise(X))<=>(kind(X)&wise(X))))&
(![X]:((brave(X)|strong(X))<=>(~old(X)&tall(X))))&
(((generous(mary)<~>rich(mary)))=>(~rich(susan)))&
(![X]:((~kind(X)|~old(X))<=>(~wise(X)&~creative(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(~creative(X)<~>~curious(X))))&
(![X]:((~kind(X)&quiet(X))<=>(patient(X)&curious(X))))&
((creative(paul))=>(~patient(fred)))&
(![X]:(happy(X)<=>~quiet(X)))&
(![X]:((wise(X)&~rich(X))<=>~tall(X)))&
(![X]:((~creative(X)<~>calm(X))=>~patient(X)))&
(((~tall(paul)|rich(paul)))=>(?[X]:(rich(X))))&
((humble(susan))<=>((funny(fred)&~happy(fred))))&
((?[X]:(happy(X)))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(((~wise(paul)&humble(paul)))<=>(?[X]:((~quiet(X)|patient(X)))))&
(((~brave(fred)|humble(fred)))=>((wise(john)<~>~wise(john))))&
(~patient(alice))&
((generous(paul)<~>kind(paul)))&
(~generous(mary))&
((~generous(lucy)&quiet(lucy)))&
(?[X]:(~rich(X))) | ~quiet(john) | [] | null | 0 |
Everyone who is kind or tall is not generous or humble and vice versa.
Everyone who is either creative or curious is old or not tall and vice versa.
Everyone who is either brave or curious is humble and vice versa.
If someone is both kind and not wise then someone is both funny and not funny and vice versa.
Everyone who is either rich or not humble is not curious.
If fred is not humble then john is not generous and vice versa.
If john is both funny and wise then fred is funny or patient.
Everyone who is either happy or wise is not tall.
Everyone who is both not creative and not quiet is not creative or generous and vice versa.
Everyone who is not old or generous is patient and vice versa.
Everyone who is either not kind or not old is both brave and not humble.
Everyone who is both not quiet and brave is both not curious and not patient and vice versa.
If john is tall or not humble then someone is not kind or not brave and vice versa.
Everyone who is both strong and old is either rich or generous and vice versa.
If john is both not quiet and wise then someone is either not strong or not brave and vice versa.
Everyone who is not rich is either not patient or not quiet.
Alice is happy.
Alice is not quiet.
Susan is both calm and wise.
Susan is not wise or kind.
John is not funny or not generous.
Someone is both not strong and humble.
Fred is not rich or not creative.
Someone is either not old or not patient. | Fred is not kind. | neutral | (![X]:((kind(X)|tall(X))<=>(~generous(X)|humble(X))))&
(![X]:((creative(X)<~>curious(X))<=>(old(X)|~tall(X))))&
(![X]:((brave(X)<~>curious(X))<=>humble(X)))&
((?[X]:((kind(X)&~wise(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((rich(X)<~>~humble(X))=>~curious(X)))&
((~humble(fred))<=>(~generous(john)))&
(((funny(john)&wise(john)))=>((funny(fred)|patient(fred))))&
(![X]:((happy(X)<~>wise(X))=>~tall(X)))&
(![X]:((~creative(X)&~quiet(X))<=>(~creative(X)|generous(X))))&
(![X]:((~old(X)|generous(X))<=>patient(X)))&
(![X]:((~kind(X)<~>~old(X))=>(brave(X)&~humble(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~curious(X)&~patient(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:((strong(X)&old(X))<=>(rich(X)<~>generous(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~rich(X)=>(~patient(X)<~>~quiet(X))))&
(happy(alice))&
(~quiet(alice))&
((calm(susan)&wise(susan)))&
((~wise(susan)|kind(susan)))&
((~funny(john)|~generous(john)))&
(?[X]:((~strong(X)&humble(X))))&
((~rich(fred)|~creative(fred)))&
(?[X]:((~old(X)<~>~patient(X)))) | ~kind(fred) | [] | null | 0 |
Everyone who is both funny and not patient is not calm or not brave and vice versa.
If john is not rich then someone is both rich and curious and vice versa.
If someone is patient then someone is either humble or not funny.
If susan is not old or calm then susan is old.
Everyone who is not old or generous is not brave and vice versa.
Everyone who is rich or not strong is curious or not tall and vice versa.
If lucy is both happy and quiet then mary is either not brave or not old and vice versa.
If mary is both curious and not funny then mary is brave or not funny and vice versa.
Everyone who is either not brave or not wise is either kind or not calm and vice versa.
If someone is either not creative or not generous then someone is old.
Everyone who is both brave and not calm is not kind or not wise and vice versa.
Everyone who is either brave or not happy is not tall or generous.
Everyone who is either not old or tall is both not generous and patient and vice versa.
Everyone who is both kind and brave is not patient.
If paul is strong then alice is quiet or not wise.
Everyone who is either funny or brave is either patient or happy and vice versa.
Someone is both tall and not creative.
John is funny or not creative.
Alice is not wise or patient.
John is both calm and not tall.
Someone is not wise.
Alice is not curious or wise. | John is not happy. | contradiction | (![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((~rich(john))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(((~old(susan)|calm(susan)))=>(old(susan)))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(((curious(mary)&~funny(mary)))<=>((brave(mary)|~funny(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((brave(X)&~calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((kind(X)&brave(X))=>~patient(X)))&
((strong(paul))=>((quiet(alice)|~wise(alice))))&
(![X]:((funny(X)<~>brave(X))<=>(patient(X)<~>happy(X))))&
(?[X]:((tall(X)&~creative(X))))&
((funny(john)|~creative(john)))&
((~wise(alice)|patient(alice)))&
((calm(john)&~tall(john)))&
(?[X]:(~wise(X)))&
((~curious(alice)|wise(alice))) | ~happy(john) | [
"p0",
"p8",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1330194770555615366294687
% SZS output start Proof for 1330194770555615366294687
1. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~brave(X0) | ~calm(X0))) [input p0]
9. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p8]
11. ! [X0] : ((~calm(X0) & brave(X0)) <=> (~wise(X0) | ~kind(X0))) [input p10]
16. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (patient(X0) <~> happy(X0))) [input p15]
20. ~tall(john) & calm(john) [input p19]
23. ~happy(john) [input hypothesis]
35. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 1]
36. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | patient(X0) | ~funny(X0))) [flattening 35]
53. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 9]
58. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0))) [flattening 58]
63. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) & (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 16]
70. brave(X0) | funny(X0) [cnf transformation 36]
72. ~patient(X0) | brave(X0) [cnf transformation 36]
102. ~wise(X0) | ~brave(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 53]
108. ~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0) [cnf transformation 59]
111. ~calm(X0) | kind(X0) [cnf transformation 59]
112. ~calm(X0) | wise(X0) [cnf transformation 59]
123. happy(X0) | patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
135. calm(john) [cnf transformation 20]
139. ~happy(john) [cnf transformation 23]
227. ~kind(X0) | ~wise(X0) | ~brave(X0) [subsumption resolution 108,102]
246. happy(X0) | brave(X0) | ~funny(X0) [subsumption resolution 123,72]
247. happy(X0) | brave(X0) [subsumption resolution 246,70]
272. kind(john) [resolution 111,135]
275. wise(john) [resolution 112,135]
279. brave(john) [resolution 247,139]
348. ~wise(john) | ~brave(john) [resolution 227,272]
349. ~brave(john) [subsumption resolution 348,275]
350. $false [subsumption resolution 349,279]
% SZS output end Proof for 1330194770555615366294687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is rich or not generous then paul is not quiet. Everyone who is either patient or rich is not curious or quiet. Everyone who is both old and calm is happy or not old. Everyone who is both brave and happy is either not brave or generous. Everyone who is both not curious and not old is curious and vice versa. Everyone who is not generous is not creative and vice versa. Everyone who is patient is not strong or rich. If someone is both patient and not quiet then mary is both not strong and not tall. Everyone who is calm is both humble and not patient and vice versa. If someone is calm then someone is funny. If someone is brave or generous then someone is both not patient and not calm. Everyone who is wise is patient or not rich and vice versa. Everyone who is both not rich and not curious is either not kind or humble. Everyone who is happy or not generous is both not strong and not happy. If someone is either humble or not humble then fred is not patient and vice versa. If someone is wise then mary is not rich. Someone is not old or humble. Someone is either rich or not curious. Someone is funny or not wise. Someone is both quiet and generous. Alice is both not curious and not wise. | Paul is patient. | neutral | (((rich(paul)|~generous(paul)))=>(~quiet(paul)))&
(![X]:((patient(X)<~>rich(X))=>(~curious(X)|quiet(X))))&
(![X]:((old(X)&calm(X))=>(happy(X)|~old(X))))&
(![X]:((brave(X)&happy(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&~old(X))<=>curious(X)))&
(![X]:(~generous(X)<=>~creative(X)))&
(![X]:(patient(X)=>(~strong(X)|rich(X))))&
((?[X]:((patient(X)&~quiet(X))))=>((~strong(mary)&~tall(mary))))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
((?[X]:(calm(X)))=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:(wise(X)<=>(patient(X)|~rich(X))))&
(![X]:((~rich(X)&~curious(X))=>(~kind(X)<~>humble(X))))&
(![X]:((happy(X)|~generous(X))=>(~strong(X)&~happy(X))))&
((?[X]:((humble(X)<~>~humble(X))))<=>(~patient(fred)))&
((?[X]:(wise(X)))=>(~rich(mary)))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((rich(X)<~>~curious(X))))&
(?[X]:((funny(X)|~wise(X))))&
(?[X]:((quiet(X)&generous(X))))&
((~curious(alice)&~wise(alice))) | patient(paul) | [] | null | 0 |
If someone is not calm then alice is funny or not happy. If alice is either creative or strong then someone is either humble or not curious and vice versa. Everyone who is funny or generous is either rich or not curious and vice versa. If susan is either not kind or brave then paul is either kind or generous and vice versa. Everyone who is either not happy or not rich is not kind and vice versa. Everyone who is not kind is both not happy and happy. Everyone who is wise or not calm is not wise or calm and vice versa. Everyone who is both not old and patient is either patient or not quiet and vice versa. Everyone who is either not quiet or not wise is not generous. Everyone who is either humble or brave is both not curious and quiet and vice versa. If mary is brave or not kind then someone is not curious and vice versa. If someone is both not happy and not rich then paul is humble or patient and vice versa. If mary is not funny or brave then john is both not kind and happy. If lucy is kind then someone is not calm or not old. If susan is both not wise and not calm then lucy is either brave or wise. Everyone who is generous is not patient. John is both strong and creative. Someone is wise. Someone is not creative. Mary is old or kind. Someone is not strong. Someone is either calm or not tall. | Mary is patient. | neutral | ((?[X]:(~calm(X)))=>((funny(alice)|~happy(alice))))&
(((creative(alice)<~>strong(alice)))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((funny(X)|generous(X))<=>(rich(X)<~>~curious(X))))&
(((~kind(susan)<~>brave(susan)))<=>((kind(paul)<~>generous(paul))))&
(![X]:((~happy(X)<~>~rich(X))<=>~kind(X)))&
(![X]:(~kind(X)=>(~happy(X)&happy(X))))&
(![X]:((wise(X)|~calm(X))<=>(~wise(X)|calm(X))))&
(![X]:((~old(X)&patient(X))<=>(patient(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~wise(X))=>~generous(X)))&
(![X]:((humble(X)<~>brave(X))<=>(~curious(X)&quiet(X))))&
(((brave(mary)|~kind(mary)))<=>(?[X]:(~curious(X))))&
((?[X]:((~happy(X)&~rich(X))))<=>((humble(paul)|patient(paul))))&
(((~funny(mary)|brave(mary)))=>((~kind(john)&happy(john))))&
((kind(lucy))=>(?[X]:((~calm(X)|~old(X)))))&
(((~wise(susan)&~calm(susan)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:(generous(X)=>~patient(X)))&
((strong(john)&creative(john)))&
(?[X]:(wise(X)))&
(?[X]:(~creative(X)))&
((old(mary)|kind(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)<~>~tall(X)))) | patient(mary) | [] | null | 0 |
Everyone who is generous or not kind is both not curious and wise and vice versa.
Everyone who is either not happy or not creative is generous or kind and vice versa.
Everyone who is generous or happy is either not strong or not wise.
If mary is both generous and not creative then paul is both not tall and not creative and vice versa.
Everyone who is both not happy and not humble is not brave or rich and vice versa.
Everyone who is both strong and not old is both not humble and not kind.
If someone is wise or generous then someone is not humble and vice versa.
Everyone who is either humble or not strong is either not kind or not curious.
If paul is either not tall or funny then mary is old and vice versa.
If someone is both not happy and funny then someone is not creative or not humble and vice versa.
Everyone who is strong is not funny.
Everyone who is wise or calm is both not quiet and creative and vice versa.
If john is either not creative or not kind then fred is either humble or funny and vice versa.
Everyone who is not humble or happy is both not tall and quiet and vice versa.
If someone is either not kind or not generous then fred is both happy and not creative.
If someone is either not brave or not funny then someone is either not curious or not strong and vice versa.
Someone is either quiet or brave.
Someone is tall.
Fred is both not rich and not funny.
Someone is both not humble and not patient.
John is not quiet.
Alice is both wise and not tall.
Lucy is both not quiet and not wise. | Mary is strong. | neutral | (![X]:((generous(X)|~kind(X))<=>(~curious(X)&wise(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(generous(X)|kind(X))))&
(![X]:((generous(X)|happy(X))=>(~strong(X)<~>~wise(X))))&
(((generous(mary)&~creative(mary)))<=>((~tall(paul)&~creative(paul))))&
(![X]:((~happy(X)&~humble(X))<=>(~brave(X)|rich(X))))&
(![X]:((strong(X)&~old(X))=>(~humble(X)&~kind(X))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:(~humble(X))))&
(![X]:((humble(X)<~>~strong(X))=>(~kind(X)<~>~curious(X))))&
(((~tall(paul)<~>funny(paul)))<=>(old(mary)))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
(![X]:(strong(X)=>~funny(X)))&
(![X]:((wise(X)|calm(X))<=>(~quiet(X)&creative(X))))&
(((~creative(john)<~>~kind(john)))<=>((humble(fred)<~>funny(fred))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~generous(X))))=>((happy(fred)&~creative(fred))))&
((?[X]:((~brave(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
(?[X]:((quiet(X)<~>brave(X))))&
(?[X]:(tall(X)))&
((~rich(fred)&~funny(fred)))&
(?[X]:((~humble(X)&~patient(X))))&
(~quiet(john))&
((wise(alice)&~tall(alice)))&
((~quiet(lucy)&~wise(lucy))) | strong(mary) | [] | null | 0 |
If someone is both quiet and not quiet then someone is either patient or not happy.
If mary is not funny then lucy is calm or not kind.
Everyone who is not quiet or not rich is both creative and generous and vice versa.
If someone is brave or not strong then susan is rich.
Everyone who is either calm or patient is quiet or not old.
If someone is either not tall or curious then lucy is generous or happy.
If lucy is creative then alice is both not creative and strong and vice versa.
Everyone who is both not happy and not curious is creative or rich and vice versa.
Everyone who is both not calm and happy is either tall or curious and vice versa.
Everyone who is wise or not rich is patient or not humble.
If someone is funny then someone is not quiet.
Everyone who is either not brave or rich is kind or calm and vice versa.
Everyone who is both strong and not rich is both not tall and not strong and vice versa.
Everyone who is both not curious and not kind is either old or not kind.
If someone is either not wise or not curious then john is both not patient and quiet and vice versa.
Lucy is humble or not quiet.
Alice is both not funny and quiet.
Someone is humble or not rich.
Lucy is not kind. | Lucy is quiet. | neutral | ((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
((~funny(mary))=>((calm(lucy)|~kind(lucy))))&
(![X]:((~quiet(X)|~rich(X))<=>(creative(X)&generous(X))))&
((?[X]:((brave(X)|~strong(X))))=>(rich(susan)))&
(![X]:((calm(X)<~>patient(X))=>(quiet(X)|~old(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>((generous(lucy)|happy(lucy))))&
((creative(lucy))<=>((~creative(alice)&strong(alice))))&
(![X]:((~happy(X)&~curious(X))<=>(creative(X)|rich(X))))&
(![X]:((~calm(X)&happy(X))<=>(tall(X)<~>curious(X))))&
(![X]:((wise(X)|~rich(X))=>(patient(X)|~humble(X))))&
((?[X]:(funny(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(kind(X)|calm(X))))&
(![X]:((strong(X)&~rich(X))<=>(~tall(X)&~strong(X))))&
(![X]:((~curious(X)&~kind(X))=>(old(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((~patient(john)&quiet(john))))&
((humble(lucy)|~quiet(lucy)))&
((~funny(alice)&quiet(alice)))&
(?[X]:((humble(X)|~rich(X))))&
(~kind(lucy)) | quiet(lucy) | [] | null | 0 |
If fred is either creative or not humble then someone is strong and vice versa. If paul is both kind and not strong then someone is both brave and not patient and vice versa. If someone is not old or funny then someone is both wise and creative and vice versa. If someone is not happy or not tall then fred is both kind and old and vice versa. If someone is not calm then someone is either not tall or not kind and vice versa. If someone is quiet then someone is patient. If someone is either not creative or not rich then someone is brave or humble and vice versa. Everyone who is not old or kind is both humble and not old and vice versa. Everyone who is both not calm and not happy is both not old and not strong and vice versa. If someone is curious then someone is both not curious and happy and vice versa. Everyone who is old is creative or brave and vice versa. Everyone who is not rich is both creative and brave and vice versa. If fred is both not rich and kind then john is not curious or humble. Everyone who is either strong or not humble is not brave. Everyone who is either generous or not tall is either calm or not creative. If someone is not quiet or generous then someone is either not wise or wise. Mary is not creative. Fred is generous or not funny. Fred is not humble or not generous. Someone is either strong or not strong. Someone is both not kind and wise. Alice is either not patient or not creative. John is both patient and not generous. | Alice is rich. | entailment | (((creative(fred)<~>~humble(fred)))<=>(?[X]:(strong(X))))&
(((kind(paul)&~strong(paul)))<=>(?[X]:((brave(X)&~patient(X)))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>((kind(fred)&old(fred))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(patient(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(humble(X)&~old(X))))&
(![X]:((~calm(X)&~happy(X))<=>(~old(X)&~strong(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(old(X)<=>(creative(X)|brave(X))))&
(![X]:(~rich(X)<=>(creative(X)&brave(X))))&
(((~rich(fred)&kind(fred)))=>((~curious(john)|humble(john))))&
(![X]:((strong(X)<~>~humble(X))=>~brave(X)))&
(![X]:((generous(X)<~>~tall(X))=>(calm(X)<~>~creative(X))))&
((?[X]:((~quiet(X)|generous(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(~creative(mary))&
((generous(fred)|~funny(fred)))&
((~humble(fred)|~generous(fred)))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((~kind(X)&wise(X))))&
((~patient(alice)<~>~creative(alice)))&
((patient(john)&~generous(john))) | rich(alice) | [
"p1",
"p3",
"p7",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4112484808636004403136548
% SZS output start Proof for 4112484808636004403136548
2. (~strong(paul) & kind(paul)) <=> ? [X0] : (~patient(X0) & brave(X0)) [input p1]
4. ? [X0] : (~tall(X0) | ~happy(X0)) <=> (old(fred) & kind(fred)) [input p3]
8. ! [X0] : ((kind(X0) | ~old(X0)) <=> (~old(X0) & humble(X0))) [input p7]
9. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~strong(X0) & ~old(X0))) [input p8]
12. ! [X0] : (~rich(X0) <=> (brave(X0) & creative(X0))) [input p11]
22. ~patient(alice) <~> ~creative(alice) [input p21]
24. ~rich(alice) [input hypothesis]
41. ((~strong(paul) & kind(paul)) | ! [X0] : (patient(X0) | ~brave(X0))) & (? [X0] : (~patient(X0) & brave(X0)) | (strong(paul) | ~kind(paul))) [nnf transformation 2]
42. ((~strong(paul) & kind(paul)) | ! [X0] : (patient(X0) | ~brave(X0))) & (? [X0] : (~patient(X0) & brave(X0)) | strong(paul) | ~kind(paul)) [flattening 41]
43. ((~strong(paul) & kind(paul)) | ! [X0] : (patient(X0) | ~brave(X0))) & (? [X1] : (~patient(X1) & brave(X1)) | strong(paul) | ~kind(paul)) [rectify 42]
44. ? [X1] : (~patient(X1) & brave(X1)) => (~patient(sK1) & brave(sK1)) [choice axiom]
45. ((~strong(paul) & kind(paul)) | ! [X0] : (patient(X0) | ~brave(X0))) & ((~patient(sK1) & brave(sK1)) | strong(paul) | ~kind(paul)) [skolemisation 43,44]
51. (? [X0] : (~tall(X0) | ~happy(X0)) | (~old(fred) | ~kind(fred))) & ((old(fred) & kind(fred)) | ! [X0] : (tall(X0) & happy(X0))) [nnf transformation 4]
52. (? [X0] : (~tall(X0) | ~happy(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X0] : (tall(X0) & happy(X0))) [flattening 51]
53. (? [X0] : (~tall(X0) | ~happy(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (tall(X1) & happy(X1))) [rectify 52]
54. ? [X0] : (~tall(X0) | ~happy(X0)) => (~tall(sK4) | ~happy(sK4)) [choice axiom]
55. ((~tall(sK4) | ~happy(sK4)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (tall(X1) & happy(X1))) [skolemisation 53,54]
69. ! [X0] : (((kind(X0) | ~old(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [nnf transformation 8]
70. ! [X0] : ((kind(X0) | ~old(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [flattening 69]
71. ! [X0] : (((~happy(X0) & ~calm(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 9]
72. ! [X0] : (((~happy(X0) & ~calm(X0)) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | happy(X0) | calm(X0))) [flattening 71]
80. ! [X0] : ((~rich(X0) | (~brave(X0) | ~creative(X0))) & ((brave(X0) & creative(X0)) | rich(X0))) [nnf transformation 12]
81. ! [X0] : ((~rich(X0) | ~brave(X0) | ~creative(X0)) & ((brave(X0) & creative(X0)) | rich(X0))) [flattening 80]
93. (creative(alice) | patient(alice)) & (~creative(alice) | ~patient(alice)) [nnf transformation 22]
100. kind(paul) | patient(X0) | ~brave(X0) [cnf transformation 45]
101. ~strong(paul) | patient(X0) | ~brave(X0) [cnf transformation 45]
107. kind(fred) | happy(X1) [cnf transformation 55]
109. old(fred) | happy(X1) [cnf transformation 55]
126. ~old(X0) | ~kind(X0) [cnf transformation 70]
131. ~happy(X0) | strong(X0) | old(X0) [cnf transformation 72]
138. rich(X0) | creative(X0) [cnf transformation 81]
139. rich(X0) | brave(X0) [cnf transformation 81]
159. ~creative(alice) | ~patient(alice) [cnf transformation 93]
163. ~rich(alice) [cnf transformation 24]
184. 5 <=> ! [X0] : (patient(X0) | ~brave(X0)) [avatar definition]
185. ~brave(X0) | patient(X0) <- (5) [avatar component clause 184]
187. 6 <=> strong(paul) [avatar definition]
189. ~strong(paul) <- (~6) [avatar component clause 187]
190. 5 | ~6 [avatar split clause 101,187,184]
192. 7 <=> kind(paul) [avatar definition]
194. kind(paul) <- (7) [avatar component clause 192]
195. 5 | 7 [avatar split clause 100,192,184]
237. 17 <=> kind(fred) [avatar definition]
241. 18 <=> old(fred) [avatar definition]
242. old(fred) <- (18) [avatar component clause 241]
258. 22 <=> ! [X1] : happy(X1) [avatar definition]
259. happy(X1) <- (22) [avatar component clause 258]
260. 22 | 18 [avatar split clause 109,241,258]
262. 22 | 17 [avatar split clause 107,237,258]
375. 49 <=> patient(alice) [avatar definition]
376. ~patient(alice) <- (~49) [avatar component clause 375]
379. 50 <=> creative(alice) [avatar definition]
383. ~49 | ~50 [avatar split clause 159,379,375]
405. ~kind(fred) <- (18) [resolution 126,242]
408. creative(alice) [resolution 138,163]
412. 50 [avatar split clause 408,379]
414. brave(alice) [resolution 139,163]
417. patient(alice) <- (5) [resolution 414,185]
419. $false <- (5, ~49) [subsumption resolution 417,376]
420. ~5 | 49 [avatar contradiction clause 419]
442. old(X0) | strong(X0) <- (22) [resolution 131,259]
539. ~kind(X2) | strong(X2) <- (22) [resolution 442,126]
549. strong(paul) <- (7, 22) [resolution 539,194]
550. $false <- (~6, 7, 22) [subsumption resolution 549,189]
551. 6 | ~7 | ~22 [avatar contradiction clause 550]
557. ~17 | ~18 [avatar split clause 405,241,237]
635. $false [avatar sat refutation 190,195,260,262,383,412,420,551,557]
% SZS output end Proof for 4112484808636004403136548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or rich is not funny. Everyone who is both quiet and not kind is not old or not generous and vice versa. Everyone who is either not wise or not old is not wise and vice versa. Everyone who is not generous or not old is not happy and vice versa. Everyone who is both happy and tall is happy and vice versa. Everyone who is patient is calm or tall and vice versa. If someone is calm or not curious then alice is funny or not brave and vice versa. If someone is both not quiet and not creative then someone is either generous or curious and vice versa. Everyone who is both not strong and not quiet is both patient and not quiet. Everyone who is not quiet is both not strong and funny and vice versa. If susan is rich then mary is not kind or not rich and vice versa. If someone is either rich or not quiet then someone is happy and vice versa. Everyone who is not curious is both not rich and not humble. Everyone who is either not wise or quiet is either not brave or strong. Everyone who is patient or not generous is wise. If fred is both not humble and curious then someone is generous or not brave and vice versa. Someone is either brave or not quiet. Susan is either tall or patient. Someone is rich or not happy. Someone is either tall or not generous. Mary is not funny. Someone is both happy and not rich. Someone is curious or not strong. | Fred is not wise. | contradiction | (![X]:((creative(X)<~>rich(X))=>~funny(X)))&
(![X]:((quiet(X)&~kind(X))<=>(~old(X)|~generous(X))))&
(![X]:((~wise(X)<~>~old(X))<=>~wise(X)))&
(![X]:((~generous(X)|~old(X))<=>~happy(X)))&
(![X]:((happy(X)&tall(X))<=>happy(X)))&
(![X]:(patient(X)<=>(calm(X)|tall(X))))&
((?[X]:((calm(X)|~curious(X))))<=>((funny(alice)|~brave(alice))))&
((?[X]:((~quiet(X)&~creative(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~strong(X)&~quiet(X))=>(patient(X)&~quiet(X))))&
(![X]:(~quiet(X)<=>(~strong(X)&funny(X))))&
((rich(susan))<=>((~kind(mary)|~rich(mary))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>(?[X]:(happy(X))))&
(![X]:(~curious(X)=>(~rich(X)&~humble(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~brave(X)<~>strong(X))))&
(![X]:((patient(X)|~generous(X))=>wise(X)))&
(((~humble(fred)&curious(fred)))<=>(?[X]:((generous(X)|~brave(X)))))&
(?[X]:((brave(X)<~>~quiet(X))))&
((tall(susan)<~>patient(susan)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
(~funny(mary))&
(?[X]:((happy(X)&~rich(X))))&
(?[X]:((curious(X)|~strong(X)))) | ~wise(fred) | [
"p2",
"p3",
"p4",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5497572006832232301145919
% SZS output start Proof for 5497572006832232301145919
3. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~old(X0) | ~generous(X0)) <=> ~happy(X0)) [input p3]
5. ! [X0] : ((tall(X0) & happy(X0)) <=> happy(X0)) [input p4]
6. ! [X0] : (patient(X0) <=> (tall(X0) | calm(X0))) [input p5]
15. ! [X0] : ((~generous(X0) | patient(X0)) => wise(X0)) [input p14]
24. ~wise(fred) [input hypothesis]
32. ! [X0] : (wise(X0) | (generous(X0) & ~patient(X0))) [ennf transformation 15]
36. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | wise(X0)) & (~wise(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 3]
37. ! [X0] : (((~old(X0) | ~generous(X0)) | happy(X0)) & (~happy(X0) | (old(X0) & generous(X0)))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | ~generous(X0) | happy(X0)) & (~happy(X0) | (old(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : (((tall(X0) & happy(X0)) | ~happy(X0)) & (happy(X0) | (~tall(X0) | ~happy(X0)))) [nnf transformation 5]
40. ! [X0] : (((tall(X0) & happy(X0)) | ~happy(X0)) & (happy(X0) | ~tall(X0) | ~happy(X0))) [flattening 39]
41. ! [X0] : ((patient(X0) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | ~patient(X0))) [nnf transformation 6]
42. ! [X0] : ((patient(X0) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | ~patient(X0))) [flattening 41]
89. ~wise(X0) | ~wise(X0) | old(X0) [cnf transformation 36]
91. old(X0) | wise(X0) | wise(X0) [cnf transformation 36]
94. ~old(X0) | ~generous(X0) | happy(X0) [cnf transformation 38]
97. ~happy(X0) | tall(X0) [cnf transformation 40]
100. ~tall(X0) | patient(X0) [cnf transformation 42]
129. ~patient(X0) | wise(X0) [cnf transformation 32]
130. wise(X0) | generous(X0) [cnf transformation 32]
147. ~wise(fred) [cnf transformation 24]
148. ~wise(X0) | old(X0) [duplicate literal removal 89]
149. wise(X0) | old(X0) [duplicate literal removal 91]
150. old(X0) [subsumption resolution 148,149]
151. ~generous(X0) | happy(X0) [subsumption resolution 94,150]
330. generous(fred) [resolution 130,147]
333. happy(fred) [resolution 151,330]
436. tall(fred) [resolution 333,97]
522. patient(fred) [resolution 436,100]
549. wise(fred) [resolution 522,129]
550. $false [subsumption resolution 549,147]
% SZS output end Proof for 5497572006832232301145919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is not generous or generous. If mary is either not tall or tall then someone is either patient or humble and vice versa. If someone is either not curious or generous then lucy is not kind or not happy and vice versa. If someone is both not kind and not patient then someone is both curious and quiet. If someone is not humble then john is either brave or rich and vice versa. If paul is not humble or old then someone is either not creative or not strong. If alice is both creative and tall then someone is funny and vice versa. If someone is both not curious and not tall then someone is either curious or not old and vice versa. Everyone who is not tall or not brave is both kind and curious. Everyone who is tall or happy is not brave or humble. If alice is not patient then mary is either not creative or brave and vice versa. Everyone who is not strong or not wise is both calm and not humble and vice versa. Everyone who is both not funny and patient is either wise or not wise and vice versa. Everyone who is both generous and brave is either wise or not calm. Everyone who is rich or not patient is old. Someone is either not funny or not humble. Someone is either brave or not old. Someone is not generous. John is calm. Mary is not quiet. Fred is not brave. Someone is both not old and quiet. | Alice is creative. | neutral | (![X]:(patient(X)=>(~generous(X)|generous(X))))&
(((~tall(mary)<~>tall(mary)))<=>(?[X]:((patient(X)<~>humble(X)))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~kind(lucy)|~happy(lucy))))&
((?[X]:((~kind(X)&~patient(X))))=>(?[X]:((curious(X)&quiet(X)))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(![X]:((~funny(X)&patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((generous(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:((rich(X)|~patient(X))=>old(X)))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:(~generous(X)))&
(calm(john))&
(~quiet(mary))&
(~brave(fred))&
(?[X]:((~old(X)&quiet(X)))) | creative(alice) | [] | null | 0 |
Everyone who is both not calm and tall is creative or not creative and vice versa.
If someone is both funny and quiet then someone is old or not tall.
Everyone who is both tall and not happy is both not humble and not happy and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is not calm or kind is strong and vice versa.
Everyone who is not funny is both humble and not wise and vice versa.
Everyone who is not kind or generous is old or not old.
If fred is both not creative and not quiet then susan is either not kind or wise and vice versa.
If someone is either not humble or not tall then someone is either not creative or funny.
Everyone who is humble is not wise and vice versa.
Everyone who is patient or generous is rich or not creative.
Everyone who is quiet or funny is either quiet or not quiet.
Everyone who is not kind is both calm and rich.
Everyone who is either rich or funny is not creative and vice versa.
If someone is either not generous or rich then someone is both creative and not tall.
Alice is both not patient and wise.
Someone is either creative or not patient.
Susan is curious or kind.
John is not rich.
Someone is not happy. | Susan is not patient. | neutral | (![X]:((~calm(X)&tall(X))<=>(creative(X)|~creative(X))))&
((?[X]:((funny(X)&quiet(X))))=>(?[X]:((old(X)|~tall(X)))))&
(![X]:((tall(X)&~happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:((~calm(X)|kind(X))<=>strong(X)))&
(![X]:(~funny(X)<=>(humble(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(old(X)|~old(X))))&
(((~creative(fred)&~quiet(fred)))<=>((~kind(susan)<~>wise(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((patient(X)|generous(X))=>(rich(X)|~creative(X))))&
(![X]:((quiet(X)|funny(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:(~kind(X)=>(calm(X)&rich(X))))&
(![X]:((rich(X)<~>funny(X))<=>~creative(X)))&
((?[X]:((~generous(X)<~>rich(X))))=>(?[X]:((creative(X)&~tall(X)))))&
((~patient(alice)&wise(alice)))&
(?[X]:((creative(X)<~>~patient(X))))&
((curious(susan)|kind(susan)))&
(~rich(john))&
(?[X]:(~happy(X))) | ~patient(susan) | [] | null | 0 |
Everyone who is either not kind or tall is creative and vice versa. Everyone who is both happy and not generous is either not calm or wise and vice versa. Everyone who is either not generous or curious is kind or brave. If someone is calm then someone is both not strong and curious. Everyone who is not brave is both tall and not creative and vice versa. Everyone who is both not wise and not funny is either strong or not humble and vice versa. Everyone who is either quiet or rich is not quiet or humble and vice versa. Everyone who is not quiet is not funny. If susan is wise then someone is tall or not old and vice versa. If paul is both not curious and kind then someone is both not wise and brave. Everyone who is tall is either not creative or not humble and vice versa. Everyone who is either not rich or happy is strong or not brave. If paul is either not creative or old then someone is kind. If someone is not patient then someone is either calm or not patient. If someone is not happy then someone is not brave or not strong and vice versa. Everyone who is not brave is either curious or calm and vice versa. Susan is both calm and not patient. John is quiet. Someone is not strong. Someone is both kind and funny. Someone is not quiet or wise. Alice is rich or not funny. John is either creative or not calm. Someone is both tall and not wise. | Susan is not curious. | contradiction | (![X]:((~kind(X)<~>tall(X))<=>creative(X)))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)<~>wise(X))))&
(![X]:((~generous(X)<~>curious(X))=>(kind(X)|brave(X))))&
((?[X]:(calm(X)))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(~brave(X)<=>(tall(X)&~creative(X))))&
(![X]:((~wise(X)&~funny(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>rich(X))<=>(~quiet(X)|humble(X))))&
(![X]:(~quiet(X)=>~funny(X)))&
((wise(susan))<=>(?[X]:((tall(X)|~old(X)))))&
(((~curious(paul)&kind(paul)))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(tall(X)<=>(~creative(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>happy(X))=>(strong(X)|~brave(X))))&
(((~creative(paul)<~>old(paul)))=>(?[X]:(kind(X))))&
((?[X]:(~patient(X)))=>(?[X]:((calm(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:(~brave(X)<=>(curious(X)<~>calm(X))))&
((calm(susan)&~patient(susan)))&
(quiet(john))&
(?[X]:(~strong(X)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((~quiet(X)|wise(X))))&
((rich(alice)|~funny(alice)))&
((creative(john)<~>~calm(john)))&
(?[X]:((tall(X)&~wise(X)))) | ~curious(susan) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p15",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 389762306244739863378175
% SZS output start Proof for 389762306244739863378175
1. ! [X0] : ((~kind(X0) <~> tall(X0)) <=> creative(X0)) [input p0]
2. ! [X0] : ((~generous(X0) & happy(X0)) <=> (~calm(X0) <~> wise(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> curious(X0)) => (brave(X0) | kind(X0))) [input p2]
5. ! [X0] : (~brave(X0) <=> (~creative(X0) & tall(X0))) [input p4]
9. wise(susan) <=> ? [X0] : (~old(X0) | tall(X0)) [input p8]
16. ! [X0] : (~brave(X0) <=> (curious(X0) <~> calm(X0))) [input p15]
17. ~patient(susan) & calm(susan) [input p16]
24. ? [X0] : (~wise(X0) & tall(X0)) [input p23]
25. ~curious(susan) [input hypothesis]
29. ! [X0] : ((brave(X0) | kind(X0)) | (~generous(X0) <=> curious(X0))) [ennf transformation 3]
30. ! [X0] : (brave(X0) | kind(X0) | (~generous(X0) <=> curious(X0))) [flattening 29]
39. ! [X0] : ((((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ~creative(X0)) & (creative(X0) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0))))) [nnf transformation 1]
40. ! [X0] : (((~generous(X0) & happy(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (generous(X0) | ~happy(X0)))) [nnf transformation 2]
41. ! [X0] : (((~generous(X0) & happy(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | generous(X0) | ~happy(X0))) [flattening 40]
42. ! [X0] : (brave(X0) | kind(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 30]
46. ! [X0] : ((~brave(X0) | (creative(X0) | ~tall(X0))) & ((~creative(X0) & tall(X0)) | brave(X0))) [nnf transformation 5]
47. ! [X0] : ((~brave(X0) | creative(X0) | ~tall(X0)) & ((~creative(X0) & tall(X0)) | brave(X0))) [flattening 46]
52. (wise(susan) | ! [X0] : (old(X0) & ~tall(X0))) & (? [X0] : (~old(X0) | tall(X0)) | ~wise(susan)) [nnf transformation 9]
53. (wise(susan) | ! [X0] : (old(X0) & ~tall(X0))) & (? [X1] : (~old(X1) | tall(X1)) | ~wise(susan)) [rectify 52]
54. ? [X1] : (~old(X1) | tall(X1)) => (~old(sK1) | tall(sK1)) [choice axiom]
55. (wise(susan) | ! [X0] : (old(X0) & ~tall(X0))) & ((~old(sK1) | tall(sK1)) | ~wise(susan)) [skolemisation 53,54]
72. ! [X0] : ((~brave(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | brave(X0))) [nnf transformation 16]
80. ? [X0] : (~wise(X0) & tall(X0)) => (~wise(sK10) & tall(sK10)) [choice axiom]
81. ~wise(sK10) & tall(sK10) [skolemisation 24,80]
83. ~tall(X0) | ~kind(X0) | creative(X0) [cnf transformation 39]
91. ~wise(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 41]
92. brave(X0) | kind(X0) | curious(X0) | generous(X0) [cnf transformation 42]
96. brave(X0) | tall(X0) [cnf transformation 47]
97. ~creative(X0) | brave(X0) [cnf transformation 47]
113. wise(susan) | ~tall(X0) [cnf transformation 55]
133. ~brave(X0) | curious(X0) | ~calm(X0) [cnf transformation 72]
134. calm(susan) [cnf transformation 17]
144. tall(sK10) [cnf transformation 81]
146. ~curious(susan) [cnf transformation 25]
167. 5 <=> wise(susan) [avatar definition]
169. wise(susan) <- (5) [avatar component clause 167]
172. 6 <=> ! [X0] : ~tall(X0) [avatar definition]
173. ~tall(X0) <- (6) [avatar component clause 172]
174. 6 | 5 [avatar split clause 113,167,172]
349. $false <- (6) [resolution 173,144]
352. ~6 [avatar contradiction clause 349]
354. ~calm(susan) | ~generous(susan) <- (5) [resolution 169,91]
356. ~generous(susan) <- (5) [subsumption resolution 354,134]
387. 43 <=> tall(susan) [avatar definition]
388. tall(susan) <- (43) [avatar component clause 387]
391. 44 <=> creative(susan) [avatar definition]
392. creative(susan) <- (44) [avatar component clause 391]
474. ~calm(X1) | curious(X1) | tall(X1) [resolution 133,96]
503. kind(X0) | curious(X0) | generous(X0) | curious(X0) | ~calm(X0) [resolution 92,133]
506. ~calm(X0) | curious(X0) | generous(X0) | kind(X0) [duplicate literal removal 503]
724. curious(susan) | tall(susan) [resolution 474,134]
726. tall(susan) [subsumption resolution 724,146]
729. 43 [avatar split clause 726,387]
731. 79 <=> kind(susan) [avatar definition]
736. ~kind(susan) | creative(susan) <- (43) [resolution 388,83]
739. 44 | ~79 | ~43 [avatar split clause 736,387,731,391]
775. curious(susan) | generous(susan) | kind(susan) [resolution 506,134]
777. generous(susan) | kind(susan) [subsumption resolution 775,146]
778. kind(susan) <- (5) [subsumption resolution 777,356]
781. 79 | ~5 [avatar split clause 778,167,731]
788. brave(susan) <- (44) [resolution 392,97]
900. curious(susan) | ~calm(susan) <- (44) [resolution 788,133]
903. ~calm(susan) <- (44) [subsumption resolution 900,146]
904. $false <- (44) [subsumption resolution 903,134]
905. ~44 [avatar contradiction clause 904]
906. $false [avatar sat refutation 174,352,729,739,781,905]
% SZS output end Proof for 389762306244739863378175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is both old and brave then someone is not rich.
Everyone who is either creative or quiet is both not strong and not quiet.
Everyone who is not generous is not rich.
Everyone who is either not old or humble is not old or calm and vice versa.
If someone is either funny or not patient then alice is patient or strong and vice versa.
Everyone who is both not strong and wise is either not brave or not curious and vice versa.
Everyone who is wise is both not strong and not calm.
Everyone who is both quiet and not humble is old and vice versa.
Everyone who is not brave is either not rich or wise.
If someone is happy or funny then someone is not happy and vice versa.
If john is not wise or not happy then susan is tall.
Everyone who is both not wise and rich is not calm.
Everyone who is either not funny or funny is both not kind and not tall.
If paul is not happy or old then someone is either not patient or not happy.
Everyone who is both humble and not quiet is both not funny and not calm and vice versa.
Everyone who is not humble is either not quiet or old and vice versa.
Someone is not kind.
Someone is happy or tall.
John is generous or not creative.
Lucy is either curious or generous.
Someone is either not quiet or not creative.
Someone is kind or not strong.
Someone is not rich.
Mary is both curious and rich. | Susan is tall. | contradiction | (((old(john)&brave(john)))=>(?[X]:(~rich(X))))&
(![X]:((creative(X)<~>quiet(X))=>(~strong(X)&~quiet(X))))&
(![X]:(~generous(X)=>~rich(X)))&
(![X]:((~old(X)<~>humble(X))<=>(~old(X)|calm(X))))&
((?[X]:((funny(X)<~>~patient(X))))<=>((patient(alice)|strong(alice))))&
(![X]:((~strong(X)&wise(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(wise(X)=>(~strong(X)&~calm(X))))&
(![X]:((quiet(X)&~humble(X))<=>old(X)))&
(![X]:(~brave(X)=>(~rich(X)<~>wise(X))))&
((?[X]:((happy(X)|funny(X))))<=>(?[X]:(~happy(X))))&
(((~wise(john)|~happy(john)))=>(tall(susan)))&
(![X]:((~wise(X)&rich(X))=>~calm(X)))&
(![X]:((~funny(X)<~>funny(X))=>(~kind(X)&~tall(X))))&
(((~happy(paul)|old(paul)))=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((humble(X)&~quiet(X))<=>(~funny(X)&~calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>old(X))))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)|tall(X))))&
((generous(john)|~creative(john)))&
((curious(lucy)<~>generous(lucy)))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:(~rich(X)))&
((curious(mary)&rich(mary))) | tall(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8241624687454267480458615
% SZS output start Proof for 8241624687454267480458615
13. ! [X0] : ((~funny(X0) <~> funny(X0)) => (~tall(X0) & ~kind(X0))) [input p12]
25. tall(susan) [input hypothesis]
36. ! [X0] : ((~tall(X0) & ~kind(X0)) | (~funny(X0) <=> funny(X0))) [ennf transformation 13]
58. ! [X0] : ((~tall(X0) & ~kind(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 36]
116. ~tall(X0) | funny(X0) | funny(X0) [cnf transformation 58]
117. ~tall(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 58]
141. tall(susan) [cnf transformation 25]
144. ~tall(X0) | funny(X0) [duplicate literal removal 116]
145. ~tall(X0) | ~funny(X0) [duplicate literal removal 117]
232. ~tall(X0) [subsumption resolution 144,145]
278. $false [subsumption resolution 141,232]
% SZS output end Proof for 8241624687454267480458615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either kind or happy then someone is either creative or not kind. If john is generous or quiet then susan is not patient or not creative. Everyone who is not strong is both wise and not patient and vice versa. If mary is both brave and strong then someone is strong or wise. Everyone who is funny is not quiet. If someone is either not old or not tall then susan is not humble or not strong and vice versa. Everyone who is either not wise or not kind is calm. Everyone who is both happy and old is not quiet or humble and vice versa. Everyone who is wise or happy is either not humble or not old and vice versa. If mary is either not tall or not rich then someone is not happy or happy and vice versa. If someone is not kind or strong then paul is not tall or not humble. If someone is either happy or not happy then someone is both curious and quiet and vice versa. Everyone who is either not curious or old is either calm or old and vice versa. If mary is both not tall and calm then john is tall or not old. Everyone who is rich or funny is not creative or wise and vice versa. Alice is either calm or funny. Someone is old. Fred is either not humble or happy. Someone is either not curious or not rich. Mary is both not old and curious. Someone is both brave and patient. Someone is not creative or not happy. | Susan is not kind. | neutral | (((kind(fred)<~>happy(fred)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(((generous(john)|quiet(john)))=>((~patient(susan)|~creative(susan))))&
(![X]:(~strong(X)<=>(wise(X)&~patient(X))))&
(((brave(mary)&strong(mary)))=>(?[X]:((strong(X)|wise(X)))))&
(![X]:(funny(X)=>~quiet(X)))&
((?[X]:((~old(X)<~>~tall(X))))<=>((~humble(susan)|~strong(susan))))&
(![X]:((~wise(X)<~>~kind(X))=>calm(X)))&
(![X]:((happy(X)&old(X))<=>(~quiet(X)|humble(X))))&
(![X]:((wise(X)|happy(X))<=>(~humble(X)<~>~old(X))))&
(((~tall(mary)<~>~rich(mary)))<=>(?[X]:((~happy(X)|happy(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((~tall(paul)|~humble(paul))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~curious(X)<~>old(X))<=>(calm(X)<~>old(X))))&
(((~tall(mary)&calm(mary)))=>((tall(john)|~old(john))))&
(![X]:((rich(X)|funny(X))<=>(~creative(X)|wise(X))))&
((calm(alice)<~>funny(alice)))&
(?[X]:(old(X)))&
((~humble(fred)<~>happy(fred)))&
(?[X]:((~curious(X)<~>~rich(X))))&
((~old(mary)&curious(mary)))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((~creative(X)|~happy(X)))) | ~kind(susan) | [] | null | 0 |
Everyone who is kind or not humble is either tall or strong.
If someone is happy then alice is both wise and not wise.
Everyone who is both not brave and rich is both not rich and kind and vice versa.
Everyone who is either not quiet or tall is either not funny or not patient.
If john is both not old and old then someone is both old and funny.
Everyone who is not wise or tall is not wise.
If alice is both not strong and humble then someone is either not calm or not old and vice versa.
If alice is both kind and not tall then alice is brave or not happy and vice versa.
Everyone who is not brave is either humble or not funny and vice versa.
Everyone who is calm is both tall and not curious.
If fred is either not patient or humble then someone is not tall.
Everyone who is either creative or calm is not creative or happy.
Everyone who is funny is either tall or creative and vice versa.
If john is not creative then someone is happy and vice versa.
If paul is not happy or kind then someone is either tall or not brave.
John is tall or not old.
Someone is not strong.
Susan is not tall or not brave.
Someone is not rich.
Susan is old.
Someone is curious or not generous.
Someone is either humble or funny.
Mary is both not creative and curious. | Alice is not humble. | contradiction | (![X]:((kind(X)|~humble(X))=>(tall(X)<~>strong(X))))&
((?[X]:(happy(X)))=>((wise(alice)&~wise(alice))))&
(![X]:((~brave(X)&rich(X))<=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~funny(X)<~>~patient(X))))&
(((~old(john)&old(john)))=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~wise(X)|tall(X))=>~wise(X)))&
(((~strong(alice)&humble(alice)))<=>(?[X]:((~calm(X)<~>~old(X)))))&
(((kind(alice)&~tall(alice)))<=>((brave(alice)|~happy(alice))))&
(![X]:(~brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(calm(X)=>(tall(X)&~curious(X))))&
(((~patient(fred)<~>humble(fred)))=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>calm(X))=>(~creative(X)|happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>creative(X))))&
((~creative(john))<=>(?[X]:(happy(X))))&
(((~happy(paul)|kind(paul)))=>(?[X]:((tall(X)<~>~brave(X)))))&
((tall(john)|~old(john)))&
(?[X]:(~strong(X)))&
((~tall(susan)|~brave(susan)))&
(?[X]:(~rich(X)))&
(old(susan))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((humble(X)<~>funny(X))))&
((~creative(mary)&curious(mary))) | ~humble(alice) | [
"p1",
"p2",
"p7",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8346986377955551379913056
% SZS output start Proof for 8346986377955551379913056
2. ? [X0] : happy(X0) => (~wise(alice) & wise(alice)) [input p1]
3. ! [X0] : ((rich(X0) & ~brave(X0)) <=> (kind(X0) & ~rich(X0))) [input p2]
8. (~tall(alice) & kind(alice)) <=> (~happy(alice) | brave(alice)) [input p7]
9. ! [X0] : (~brave(X0) <=> (humble(X0) <~> ~funny(X0))) [input p8]
10. ! [X0] : (calm(X0) => (~curious(X0) & tall(X0))) [input p9]
12. ! [X0] : ((creative(X0) <~> calm(X0)) => (happy(X0) | ~creative(X0))) [input p11]
13. ! [X0] : (funny(X0) <=> (tall(X0) <~> creative(X0))) [input p12]
24. ~humble(alice) [input hypothesis]
27. (~wise(alice) & wise(alice)) | ! [X0] : ~happy(X0) [ennf transformation 2]
32. ! [X0] : ((~curious(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 10]
34. ! [X0] : ((happy(X0) | ~creative(X0)) | (creative(X0) <=> calm(X0))) [ennf transformation 12]
35. ! [X0] : (happy(X0) | ~creative(X0) | (creative(X0) <=> calm(X0))) [flattening 34]
38. ! [X0] : (((rich(X0) & ~brave(X0)) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | (~rich(X0) | brave(X0)))) [nnf transformation 3]
39. ! [X0] : (((rich(X0) & ~brave(X0)) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | ~rich(X0) | brave(X0))) [flattening 38]
48. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & ((~happy(alice) | brave(alice)) | (tall(alice) | ~kind(alice))) [nnf transformation 8]
49. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & (~happy(alice) | brave(alice) | tall(alice) | ~kind(alice)) [flattening 48]
50. ! [X0] : ((~brave(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | brave(X0))) [nnf transformation 9]
54. ! [X0] : (happy(X0) | ~creative(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 35]
55. ! [X0] : ((funny(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | ~funny(X0))) [nnf transformation 13]
74. wise(alice) | ~happy(X0) [cnf transformation 27]
75. ~wise(alice) | ~happy(X0) [cnf transformation 27]
76. ~rich(X0) | ~rich(X0) | brave(X0) [cnf transformation 39]
79. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 39]
96. kind(alice) | happy(alice) [cnf transformation 49]
98. ~tall(alice) | happy(alice) [cnf transformation 49]
102. ~brave(X0) | humble(X0) | funny(X0) [cnf transformation 50]
103. ~calm(X0) | tall(X0) [cnf transformation 32]
107. happy(X0) | ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 54]
109. ~funny(X0) | tall(X0) | creative(X0) [cnf transformation 55]
128. ~humble(alice) [cnf transformation 24]
129. ~creative(X0) | happy(X0) | calm(X0) [duplicate literal removal 107]
130. ~rich(X0) | brave(X0) [duplicate literal removal 76]
131. ~kind(X0) | rich(X0) [duplicate literal removal 79]
133. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
134. ~happy(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(alice) [avatar definition]
139. 1 | ~2 [avatar split clause 75,136,133]
140. 1 | 2 [avatar split clause 74,136,133]
145. 4 <=> humble(alice) [avatar definition]
146. ~humble(alice) <- (~4) [avatar component clause 145]
170. 9 <=> happy(alice) [avatar definition]
171. ~happy(alice) <- (~9) [avatar component clause 170]
172. happy(alice) <- (9) [avatar component clause 170]
174. 10 <=> tall(alice) [avatar definition]
176. ~tall(alice) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 98,174,170]
179. 11 <=> brave(alice) [avatar definition]
180. brave(alice) <- (11) [avatar component clause 179]
184. 12 <=> kind(alice) [avatar definition]
186. kind(alice) <- (12) [avatar component clause 184]
187. 9 | 12 [avatar split clause 96,184,170]
262. ~4 [avatar split clause 128,145]
264. rich(alice) <- (12) [resolution 131,186]
265. brave(alice) <- (12) [resolution 264,130]
266. 11 | ~12 [avatar split clause 265,184,179]
305. humble(alice) | funny(alice) <- (11) [resolution 102,180]
307. funny(alice) <- (~4, 11) [subsumption resolution 305,146]
311. tall(alice) | creative(alice) <- (~4, 11) [resolution 109,307]
321. creative(alice) <- (~4, ~10, 11) [subsumption resolution 311,176]
369. happy(alice) | calm(alice) <- (~4, ~10, 11) [resolution 321,129]
372. calm(alice) <- (~4, ~9, ~10, 11) [subsumption resolution 369,171]
375. tall(alice) <- (~4, ~9, ~10, 11) [resolution 372,103]
376. $false <- (~4, ~9, ~10, 11) [subsumption resolution 375,176]
377. 4 | 9 | 10 | ~11 [avatar contradiction clause 376]
379. $false <- (1, 9) [subsumption resolution 172,134]
380. ~1 | ~9 [avatar contradiction clause 379]
381. $false [avatar sat refutation 139,140,177,187,262,266,377,380]
% SZS output end Proof for 8346986377955551379913056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or patient then john is strong.
If mary is both not humble and brave then john is both strong and not quiet.
Everyone who is not calm is tall.
Everyone who is quiet or curious is both not kind and not humble.
Everyone who is not tall is both not creative and not brave and vice versa.
Everyone who is both happy and patient is both old and brave.
Everyone who is both not patient and brave is not rich or not brave and vice versa.
Everyone who is not brave or not wise is both not happy and strong.
Everyone who is creative is both not generous and not curious and vice versa.
Everyone who is not rich is brave and vice versa.
Everyone who is strong or not creative is not calm or not wise.
If someone is not curious or humble then someone is both calm and not creative and vice versa.
If someone is wise then john is either patient or not patient.
If susan is not strong then someone is both funny and patient and vice versa.
If mary is not funny then john is humble or quiet.
If someone is humble or patient then someone is not strong or funny and vice versa.
Alice is either creative or happy.
Mary is both not kind and not patient.
John is either funny or rich.
John is strong or humble.
Someone is either happy or wise.
Someone is either wise or funny.
Someone is either creative or not old.
Someone is either not funny or not strong. | Mary is not humble. | neutral | ((?[X]:((kind(X)<~>patient(X))))=>(strong(john)))&
(((~humble(mary)&brave(mary)))=>((strong(john)&~quiet(john))))&
(![X]:(~calm(X)=>tall(X)))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))&
(![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))&
(![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~generous(X)&~curious(X))))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((strong(X)|~creative(X))=>(~calm(X)|~wise(X))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:(wise(X)))=>((patient(john)<~>~patient(john))))&
((~strong(susan))<=>(?[X]:((funny(X)&patient(X)))))&
((~funny(mary))=>((humble(john)|quiet(john))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
((creative(alice)<~>happy(alice)))&
((~kind(mary)&~patient(mary)))&
((funny(john)<~>rich(john)))&
((strong(john)|humble(john)))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((~funny(X)<~>~strong(X)))) | ~humble(mary) | [] | null | 0 |
If someone is either happy or not generous then mary is either not kind or not brave and vice versa. Everyone who is not humble is either strong or generous. Everyone who is either generous or funny is calm or not creative. If fred is wise then lucy is either funny or not brave and vice versa. Everyone who is calm is old and vice versa. If fred is not funny then fred is strong. If someone is funny then someone is not creative or old. Everyone who is both not wise and generous is wise. If someone is generous then someone is not old or old. If someone is either kind or brave then alice is either not old or brave and vice versa. If someone is tall then someone is both brave and funny and vice versa. If someone is both calm and not tall then someone is not wise or calm. If alice is both generous and calm then john is both not patient and happy. If someone is both not patient and wise then someone is either not brave or not funny and vice versa. Everyone who is not patient or strong is both wise and not quiet and vice versa. Everyone who is not tall is kind or not generous. John is not brave. Someone is both not patient and funny. Susan is either quiet or not rich. Someone is curious or strong. Fred is not strong or rich. Someone is either brave or not kind. Alice is both tall and strong. | John is not patient. | neutral | ((?[X]:((happy(X)<~>~generous(X))))<=>((~kind(mary)<~>~brave(mary))))&
(![X]:(~humble(X)=>(strong(X)<~>generous(X))))&
(![X]:((generous(X)<~>funny(X))=>(calm(X)|~creative(X))))&
((wise(fred))<=>((funny(lucy)<~>~brave(lucy))))&
(![X]:(calm(X)<=>old(X)))&
((~funny(fred))=>(strong(fred)))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~wise(X)&generous(X))=>wise(X)))&
((?[X]:(generous(X)))=>(?[X]:((~old(X)|old(X)))))&
((?[X]:((kind(X)<~>brave(X))))<=>((~old(alice)<~>brave(alice))))&
((?[X]:(tall(X)))<=>(?[X]:((brave(X)&funny(X)))))&
((?[X]:((calm(X)&~tall(X))))=>(?[X]:((~wise(X)|calm(X)))))&
(((generous(alice)&calm(alice)))=>((~patient(john)&happy(john))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:((~patient(X)|strong(X))<=>(wise(X)&~quiet(X))))&
(![X]:(~tall(X)=>(kind(X)|~generous(X))))&
(~brave(john))&
(?[X]:((~patient(X)&funny(X))))&
((quiet(susan)<~>~rich(susan)))&
(?[X]:((curious(X)|strong(X))))&
((~strong(fred)|rich(fred)))&
(?[X]:((brave(X)<~>~kind(X))))&
((tall(alice)&strong(alice))) | ~patient(john) | [] | null | 0 |
If someone is either old or calm then alice is not humble or creative and vice versa.
If someone is both not patient and creative then someone is wise and vice versa.
If lucy is both patient and not generous then someone is not curious or calm and vice versa.
Everyone who is not generous is either not kind or not quiet.
If someone is either not strong or rich then lucy is not happy or not kind.
Everyone who is both rich and not kind is brave or curious.
If someone is wise then alice is both not old and happy.
If alice is either patient or not tall then alice is not kind and vice versa.
If fred is funny then mary is both strong and not rich and vice versa.
Everyone who is both curious and not tall is both tall and not brave and vice versa.
If alice is not creative then mary is both rich and generous and vice versa.
If paul is not funny then someone is not quiet.
If someone is both not brave and wise then paul is both not calm and not tall.
Everyone who is not kind or not quiet is both not calm and old and vice versa.
Everyone who is either not strong or rich is happy or not creative and vice versa.
Everyone who is not humble is either strong or happy and vice versa.
Paul is either not happy or old.
Someone is funny.
Paul is either not curious or not creative.
Fred is either quiet or not generous.
Someone is either not strong or not curious.
Alice is wise.
Someone is either tall or not rich.
Someone is not happy. | Paul is creative. | neutral | ((?[X]:((old(X)<~>calm(X))))<=>((~humble(alice)|creative(alice))))&
((?[X]:((~patient(X)&creative(X))))<=>(?[X]:(wise(X))))&
(((patient(lucy)&~generous(lucy)))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~strong(X)<~>rich(X))))=>((~happy(lucy)|~kind(lucy))))&
(![X]:((rich(X)&~kind(X))=>(brave(X)|curious(X))))&
((?[X]:(wise(X)))=>((~old(alice)&happy(alice))))&
(((patient(alice)<~>~tall(alice)))<=>(~kind(alice)))&
((funny(fred))<=>((strong(mary)&~rich(mary))))&
(![X]:((curious(X)&~tall(X))<=>(tall(X)&~brave(X))))&
((~creative(alice))<=>((rich(mary)&generous(mary))))&
((~funny(paul))=>(?[X]:(~quiet(X))))&
((?[X]:((~brave(X)&wise(X))))=>((~calm(paul)&~tall(paul))))&
(![X]:((~kind(X)|~quiet(X))<=>(~calm(X)&old(X))))&
(![X]:((~strong(X)<~>rich(X))<=>(happy(X)|~creative(X))))&
(![X]:(~humble(X)<=>(strong(X)<~>happy(X))))&
((~happy(paul)<~>old(paul)))&
(?[X]:(funny(X)))&
((~curious(paul)<~>~creative(paul)))&
((quiet(fred)<~>~generous(fred)))&
(?[X]:((~strong(X)<~>~curious(X))))&
(wise(alice))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:(~happy(X))) | creative(paul) | [] | null | 0 |
If susan is generous or not tall then susan is both rich and wise and vice versa.
Everyone who is both not quiet and not creative is either calm or creative and vice versa.
If someone is happy then paul is calm or creative and vice versa.
If paul is patient then mary is either not humble or kind.
If paul is either not old or creative then someone is either not happy or not patient and vice versa.
Everyone who is not humble is not brave or creative and vice versa.
If someone is both curious and patient then someone is either not humble or not strong and vice versa.
Everyone who is either not patient or not old is not patient.
Everyone who is both curious and not quiet is both rich and not happy.
If someone is either calm or not old then someone is both happy and not happy.
Everyone who is happy or not patient is either not tall or not rich and vice versa.
Everyone who is both rich and humble is both not kind and not curious and vice versa.
Everyone who is not brave or strong is either not strong or happy.
Everyone who is either not wise or not old is tall or strong and vice versa.
If someone is not old then alice is old or not creative.
Everyone who is old or not quiet is both not curious and not wise and vice versa.
Someone is not humble.
Someone is both kind and not creative.
John is both not curious and wise.
Someone is both happy and not generous.
Susan is either not humble or curious.
Alice is both generous and not patient.
Someone is not happy or not kind.
Susan is both not patient and not strong. | Susan is quiet. | entailment | (((generous(susan)|~tall(susan)))<=>((rich(susan)&wise(susan))))&
(![X]:((~quiet(X)&~creative(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(happy(X)))<=>((calm(paul)|creative(paul))))&
((patient(paul))=>((~humble(mary)<~>kind(mary))))&
(((~old(paul)<~>creative(paul)))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:(~humble(X)<=>(~brave(X)|creative(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:((~patient(X)<~>~old(X))=>~patient(X)))&
(![X]:((curious(X)&~quiet(X))=>(rich(X)&~happy(X))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:((happy(X)|~patient(X))<=>(~tall(X)<~>~rich(X))))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&~curious(X))))&
(![X]:((~brave(X)|strong(X))=>(~strong(X)<~>happy(X))))&
(![X]:((~wise(X)<~>~old(X))<=>(tall(X)|strong(X))))&
((?[X]:(~old(X)))=>((old(alice)|~creative(alice))))&
(![X]:((old(X)|~quiet(X))<=>(~curious(X)&~wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)&~creative(X))))&
((~curious(john)&wise(john)))&
(?[X]:((happy(X)&~generous(X))))&
((~humble(susan)<~>curious(susan)))&
((generous(alice)&~patient(alice)))&
(?[X]:((~happy(X)|~kind(X))))&
((~patient(susan)&~strong(susan))) | quiet(susan) | [
"p0",
"p1",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6833554299818569985275763
% SZS output start Proof for 6833554299818569985275763
1. (~tall(susan) | generous(susan)) <=> (wise(susan) & rich(susan)) [input p0]
2. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (calm(X0) <~> creative(X0))) [input p1]
10. ? [X0] : (calm(X0) <~> ~old(X0)) => ? [X0] : (~happy(X0) & happy(X0)) [input p9]
14. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> (strong(X0) | tall(X0))) [input p13]
16. ! [X0] : ((~quiet(X0) | old(X0)) <=> (~wise(X0) & ~curious(X0))) [input p15]
25. ~quiet(susan) [input hypothesis]
27. ? [X0] : (calm(X0) <~> ~old(X0)) => ? [X1] : (~happy(X1) & happy(X1)) [rectify 10]
32. ? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : (calm(X0) <=> ~old(X0)) [ennf transformation 27]
36. ((~tall(susan) | generous(susan)) | (~wise(susan) | ~rich(susan))) & ((wise(susan) & rich(susan)) | (tall(susan) & ~generous(susan))) [nnf transformation 1]
37. (~tall(susan) | generous(susan) | ~wise(susan) | ~rich(susan)) & ((wise(susan) & rich(susan)) | (tall(susan) & ~generous(susan))) [flattening 36]
38. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (creative(X0) | quiet(X0)))) [nnf transformation 2]
39. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | creative(X0) | quiet(X0))) [flattening 38]
58. ? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))) [nnf transformation 32]
59. ? [X0] : (~happy(X0) & happy(X0)) | ! [X1] : ((calm(X1) | old(X1)) & (~old(X1) | ~calm(X1))) [rectify 58]
60. ? [X0] : (~happy(X0) & happy(X0)) => (~happy(sK4) & happy(sK4)) [choice axiom]
61. (~happy(sK4) & happy(sK4)) | ! [X1] : ((calm(X1) | old(X1)) & (~old(X1) | ~calm(X1))) [skolemisation 59,60]
67. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 14]
68. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [flattening 67]
69. ! [X0] : (((~quiet(X0) | old(X0)) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | (quiet(X0) & ~old(X0)))) [nnf transformation 16]
70. ! [X0] : ((~quiet(X0) | old(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | (quiet(X0) & ~old(X0)))) [flattening 69]
83. wise(susan) | tall(susan) [cnf transformation 37]
85. creative(X0) | calm(X0) | creative(X0) | quiet(X0) [cnf transformation 39]
90. ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 39]
117. happy(sK4) | ~old(X1) | ~calm(X1) [cnf transformation 61]
119. ~happy(sK4) | ~old(X1) | ~calm(X1) [cnf transformation 61]
139. ~tall(X0) | wise(X0) | old(X0) [cnf transformation 68]
145. ~wise(X0) | quiet(X0) [cnf transformation 70]
161. ~quiet(susan) [cnf transformation 25]
164. creative(X0) | calm(X0) | quiet(X0) [duplicate literal removal 85]
165. ~creative(X0) | calm(X0) [duplicate literal removal 90]
171. 2 <=> wise(susan) [avatar definition]
172. wise(susan) <- (2) [avatar component clause 171]
179. 4 <=> tall(susan) [avatar definition]
180. tall(susan) <- (4) [avatar component clause 179]
183. 4 | 2 [avatar split clause 83,171,179]
187. calm(X0) | quiet(X0) [subsumption resolution 164,165]
282. 25 <=> happy(sK4) [avatar definition]
287. 26 <=> ! [X1] : (~old(X1) | ~calm(X1)) [avatar definition]
288. ~old(X1) | ~calm(X1) <- (26) [avatar component clause 287]
289. 26 | ~25 [avatar split clause 119,282,287]
291. 26 | 25 [avatar split clause 117,282,287]
474. wise(susan) | old(susan) <- (4) [resolution 139,180]
477. 54 <=> old(susan) [avatar definition]
479. old(susan) <- (54) [avatar component clause 477]
480. 54 | 2 | ~4 [avatar split clause 474,179,171,477]
550. ~calm(susan) <- (26, 54) [resolution 479,288]
676. quiet(susan) <- (26, 54) [resolution 550,187]
677. $false <- (26, 54) [subsumption resolution 676,161]
678. ~26 | ~54 [avatar contradiction clause 677]
681. quiet(susan) <- (2) [resolution 172,145]
682. $false <- (2) [subsumption resolution 681,161]
683. ~2 [avatar contradiction clause 682]
684. $false [avatar sat refutation 183,289,291,480,678,683]
% SZS output end Proof for 6833554299818569985275763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is curious.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Everyone who is brave or not wise is happy or not humble and vice versa.
If john is either kind or not humble then someone is not curious and vice versa.
Everyone who is both not curious and happy is quiet or curious.
Someone is both not quiet and not calm.
Fred is either not kind or brave.
John is both not rich and not strong. | Susan is not kind. | contradiction | (![X]:(generous(X)=>curious(X)))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
(![X]:((brave(X)|~wise(X))<=>(happy(X)|~humble(X))))&
(((kind(john)<~>~humble(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)&happy(X))=>(quiet(X)|curious(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
((~kind(fred)<~>brave(fred)))&
((~rich(john)&~strong(john))) | ~kind(susan) | [
"p1",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 877621283877149676325905
% SZS output start Proof for 877621283877149676325905
2. ! [X0] : ((quiet(X0) <~> kind(X0)) <=> ~wise(X0)) [input p1]
7. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X0] : (~tall(X0) & ~old(X0)) [input p6]
12. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p11]
13. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p12]
20. ~kind(susan) [input hypothesis]
21. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X1] : (~tall(X1) & ~old(X1)) [rectify 7]
31. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [nnf transformation 2]
39. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 21]
40. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X2] : (~tall(X2) & ~old(X2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK1) | quiet(sK1)) [choice axiom]
42. ? [X2] : (~tall(X2) & ~old(X2)) => (~tall(sK2) & ~old(sK2)) [choice axiom]
43. ((~generous(sK1) | quiet(sK1)) | ! [X1] : (tall(X1) | old(X1))) & ((~tall(sK2) & ~old(sK2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [skolemisation 40,42,41]
48. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 12]
49. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 48]
50. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 13]
51. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 50]
64. wise(X0) | quiet(X0) | kind(X0) [cnf transformation 31]
77. ~tall(sK2) | ~quiet(X3) [cnf transformation 43]
91. ~wise(X0) | quiet(X0) [cnf transformation 49]
94. tall(X0) | tall(X0) [cnf transformation 51]
112. ~kind(susan) [cnf transformation 20]
115. tall(X0) [duplicate literal removal 94]
164. 12 <=> tall(sK2) [avatar definition]
166. ~tall(sK2) <- (~12) [avatar component clause 164]
169. 13 <=> ! [X3] : ~quiet(X3) [avatar definition]
170. ~quiet(X3) <- (13) [avatar component clause 169]
171. 13 | ~12 [avatar split clause 77,164,169]
236. $false <- (~12) [subsumption resolution 166,115]
237. 12 [avatar contradiction clause 236]
253. quiet(X2) | kind(X2) | quiet(X2) [resolution 64,91]
255. quiet(X2) | kind(X2) [duplicate literal removal 253]
258. kind(X2) <- (13) [subsumption resolution 255,170]
261. $false <- (13) [resolution 258,112]
265. ~13 [avatar contradiction clause 261]
266. $false [avatar sat refutation 171,237,265]
% SZS output end Proof for 877621283877149676325905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet or not strong then someone is not generous and vice versa.
Everyone who is brave is kind.
If john is not patient or kind then someone is either patient or creative and vice versa.
Everyone who is both not tall and old is rich or curious and vice versa.
If alice is tall then lucy is either not old or not curious.
Everyone who is quiet is either rich or creative and vice versa.
If lucy is not patient then someone is not kind or funny and vice versa.
Everyone who is not happy is wise.
Everyone who is either strong or not creative is both not generous and not humble and vice versa.
If someone is old or humble then paul is both wise and quiet.
If john is not wise then fred is either curious or wise and vice versa.
If someone is not brave or not patient then someone is both old and patient and vice versa.
If someone is both quiet and not old then john is either old or curious and vice versa.
If someone is old or kind then lucy is both not humble and not funny.
If someone is wise or not patient then paul is not brave.
Everyone who is both generous and calm is not brave and vice versa.
Someone is either not wise or not strong.
Someone is not humble or not creative.
John is either strong or brave.
Alice is not patient.
Susan is either not strong or brave.
Someone is patient or not humble.
Someone is wise or funny.
John is curious. | John is not curious. | contradiction | (((~quiet(paul)|~strong(paul)))<=>(?[X]:(~generous(X))))&
(![X]:(brave(X)=>kind(X)))&
(((~patient(john)|kind(john)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~tall(X)&old(X))<=>(rich(X)|curious(X))))&
((tall(alice))=>((~old(lucy)<~>~curious(lucy))))&
(![X]:(quiet(X)<=>(rich(X)<~>creative(X))))&
((~patient(lucy))<=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:(~happy(X)=>wise(X)))&
(![X]:((strong(X)<~>~creative(X))<=>(~generous(X)&~humble(X))))&
((?[X]:((old(X)|humble(X))))=>((wise(paul)&quiet(paul))))&
((~wise(john))<=>((curious(fred)<~>wise(fred))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((old(X)&patient(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>((old(john)<~>curious(john))))&
((?[X]:((old(X)|kind(X))))=>((~humble(lucy)&~funny(lucy))))&
((?[X]:((wise(X)|~patient(X))))=>(~brave(paul)))&
(![X]:((generous(X)&calm(X))<=>~brave(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:((~humble(X)|~creative(X))))&
((strong(john)<~>brave(john)))&
(~patient(alice))&
((~strong(susan)<~>brave(susan)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((wise(X)|funny(X))))&
(curious(john)) | ~curious(john) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8014454677524627605951644
% SZS output start Proof for 8014454677524627605951644
24. curious(john) [input p23]
25. ~curious(john) [input hypothesis]
144. curious(john) [cnf transformation 24]
145. ~curious(john) [cnf transformation 25]
294. 33 <=> curious(john) [avatar definition]
395. 33 [avatar split clause 144,294]
396. ~33 [avatar split clause 145,294]
397. $false [avatar sat refutation 395,396]
% SZS output end Proof for 8014454677524627605951644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is strong or quiet. Everyone who is tall is both not curious and old. If someone is both not tall and generous then someone is both not humble and happy. If fred is either not strong or rich then someone is either curious or tall. Everyone who is both humble and not old is both not generous and curious and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not generous and not brave is both patient and not old and vice versa. Everyone who is either old or not creative is either tall or not wise. Everyone who is either quiet or not calm is wise or not strong. If mary is either not wise or not tall then someone is creative. Everyone who is both not tall and tall is old and vice versa. Everyone who is both not generous and creative is not quiet and vice versa. Everyone who is not happy or not strong is both not tall and not generous. Everyone who is either not happy or not funny is curious. If john is either not funny or not strong then fred is not rich or wise and vice versa. If someone is either not tall or brave then john is both not kind and old and vice versa. Alice is not kind or generous. Someone is either strong or calm. Someone is brave. John is kind. Someone is either old or not strong. Mary is funny or curious. Someone is quiet. Alice is generous. | Alice is old. | contradiction | (![X]:(humble(X)=>(strong(X)|quiet(X))))&
(![X]:(tall(X)=>(~curious(X)&old(X))))&
((?[X]:((~tall(X)&generous(X))))=>(?[X]:((~humble(X)&happy(X)))))&
(((~strong(fred)<~>rich(fred)))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((humble(X)&~old(X))<=>(~generous(X)&curious(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~generous(X)&~brave(X))<=>(patient(X)&~old(X))))&
(![X]:((old(X)<~>~creative(X))=>(tall(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(wise(X)|~strong(X))))&
(((~wise(mary)<~>~tall(mary)))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)&tall(X))<=>old(X)))&
(![X]:((~generous(X)&creative(X))<=>~quiet(X)))&
(![X]:((~happy(X)|~strong(X))=>(~tall(X)&~generous(X))))&
(![X]:((~happy(X)<~>~funny(X))=>curious(X)))&
(((~funny(john)<~>~strong(john)))<=>((~rich(fred)|wise(fred))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((~kind(john)&old(john))))&
((~kind(alice)|generous(alice)))&
(?[X]:((strong(X)<~>calm(X))))&
(?[X]:(brave(X)))&
(kind(john))&
(?[X]:((old(X)<~>~strong(X))))&
((funny(mary)|curious(mary)))&
(?[X]:(quiet(X)))&
(generous(alice)) | old(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8666352982446539943119044
% SZS output start Proof for 8666352982446539943119044
11. ! [X0] : ((tall(X0) & ~tall(X0)) <=> old(X0)) [input p10]
25. old(alice) [input hypothesis]
54. ! [X0] : (((tall(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | ~tall(X0) | tall(X0))) [flattening 54]
104. ~tall(X0) | ~old(X0) [cnf transformation 55]
105. tall(X0) | ~old(X0) [cnf transformation 55]
137. old(alice) [cnf transformation 25]
185. ~old(X0) [subsumption resolution 104,105]
236. $false [subsumption resolution 137,185]
% SZS output end Proof for 8666352982446539943119044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is not quiet or humble and vice versa.
Everyone who is either not patient or wise is not happy or not quiet and vice versa.
If someone is either rich or not funny then someone is both happy and not kind and vice versa.
Everyone who is rich is both old and quiet.
Everyone who is humble is either not wise or not strong and vice versa.
If someone is either funny or not calm then someone is either not old or creative.
Everyone who is both happy and kind is not creative.
Everyone who is not quiet or not strong is not generous.
Everyone who is creative or not old is funny.
Everyone who is creative is either not happy or curious.
Everyone who is both strong and not patient is rich.
Everyone who is not humble or rich is either not quiet or not kind and vice versa.
Everyone who is not wise or not quiet is both kind and rich.
If alice is not creative or not generous then someone is not curious or not old.
If someone is not generous then lucy is both creative and patient.
Everyone who is both rich and kind is both strong and not patient and vice versa.
Someone is not tall or creative.
Someone is curious.
Someone is wise or kind.
Susan is brave.
Someone is either not happy or strong.
Someone is both calm and not kind.
Someone is not patient. | Lucy is creative. | entailment | ((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~patient(X)<~>wise(X))<=>(~happy(X)|~quiet(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:((happy(X)&~kind(X)))))&
(![X]:(rich(X)=>(old(X)&quiet(X))))&
(![X]:(humble(X)<=>(~wise(X)<~>~strong(X))))&
((?[X]:((funny(X)<~>~calm(X))))=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:((happy(X)&kind(X))=>~creative(X)))&
(![X]:((~quiet(X)|~strong(X))=>~generous(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
(![X]:(creative(X)=>(~happy(X)<~>curious(X))))&
(![X]:((strong(X)&~patient(X))=>rich(X)))&
(![X]:((~humble(X)|rich(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(kind(X)&rich(X))))&
(((~creative(alice)|~generous(alice)))=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:(~generous(X)))=>((creative(lucy)&patient(lucy))))&
(![X]:((rich(X)&kind(X))<=>(strong(X)&~patient(X))))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:(curious(X)))&
(?[X]:((wise(X)|kind(X))))&
(brave(susan))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((calm(X)&~kind(X))))&
(?[X]:(~patient(X))) | creative(lucy) | [
"p3",
"p4",
"p7",
"p11",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1406720030649379392987953
% SZS output start Proof for 1406720030649379392987953
4. ! [X0] : (rich(X0) => (quiet(X0) & old(X0))) [input p3]
5. ! [X0] : (humble(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p4]
8. ! [X0] : ((~strong(X0) | ~quiet(X0)) => ~generous(X0)) [input p7]
12. ! [X0] : ((rich(X0) | ~humble(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p11]
13. ! [X0] : ((~quiet(X0) | ~wise(X0)) => (rich(X0) & kind(X0))) [input p12]
15. ? [X0] : ~generous(X0) => (patient(lucy) & creative(lucy)) [input p14]
16. ! [X0] : ((kind(X0) & rich(X0)) <=> (~patient(X0) & strong(X0))) [input p15]
23. ? [X0] : ~patient(X0) [input p22]
24. ~creative(lucy) [input hypothesis]
30. ! [X0] : ((quiet(X0) & old(X0)) | ~rich(X0)) [ennf transformation 4]
34. ! [X0] : (~generous(X0) | (strong(X0) & quiet(X0))) [ennf transformation 8]
39. ! [X0] : ((rich(X0) & kind(X0)) | (quiet(X0) & wise(X0))) [ennf transformation 13]
41. (patient(lucy) & creative(lucy)) | ! [X0] : generous(X0) [ennf transformation 15]
54. ! [X0] : ((humble(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~humble(X0))) [nnf transformation 5]
60. ! [X0] : (((rich(X0) | ~humble(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~rich(X0) & humble(X0)))) [nnf transformation 12]
61. ! [X0] : ((rich(X0) | ~humble(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~rich(X0) & humble(X0)))) [flattening 60]
64. ! [X0] : (((kind(X0) & rich(X0)) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | (~kind(X0) | ~rich(X0)))) [nnf transformation 16]
65. ! [X0] : (((kind(X0) & rich(X0)) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ~kind(X0) | ~rich(X0))) [flattening 64]
75. ? [X0] : ~patient(X0) => ~patient(sK10) [choice axiom]
76. ~patient(sK10) [skolemisation 23,75]
93. ~rich(X0) | quiet(X0) [cnf transformation 30]
94. ~strong(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 54]
104. ~generous(X0) | strong(X0) [cnf transformation 34]
110. ~kind(X0) | ~quiet(X0) | humble(X0) [cnf transformation 61]
111. ~kind(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 61]
116. kind(X0) | wise(X0) [cnf transformation 39]
118. rich(X0) | wise(X0) [cnf transformation 39]
119. rich(X0) | quiet(X0) [cnf transformation 39]
122. creative(lucy) | generous(X0) [cnf transformation 41]
127. ~strong(X0) | patient(X0) | kind(X0) [cnf transformation 65]
134. ~patient(sK10) [cnf transformation 76]
135. ~creative(lucy) [cnf transformation 24]
137. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
138. ~humble(X1) <- (1) [avatar component clause 137]
145. 3 <=> ! [X1] : quiet(X1) [avatar definition]
146. quiet(X1) <- (3) [avatar component clause 145]
210. ~kind(X0) | ~rich(X0) [subsumption resolution 111,93]
211. quiet(X0) [subsumption resolution 119,93]
212. 3 [avatar split clause 211,145]
232. 22 <=> ! [X0] : generous(X0) [avatar definition]
233. generous(X0) <- (22) [avatar component clause 232]
240. 24 <=> creative(lucy) [avatar definition]
243. 22 | 24 [avatar split clause 122,240,232]
254. ~24 [avatar split clause 135,240]
258. strong(X0) <- (22) [resolution 104,233]
279. ~rich(X1) | wise(X1) [resolution 210,116]
281. wise(X1) [subsumption resolution 279,118]
300. ~wise(X0) | ~humble(X0) <- (22) [resolution 94,258]
301. ~humble(X0) <- (22) [subsumption resolution 300,281]
302. 1 | ~22 [avatar split clause 301,232,137]
344. kind(X0) | patient(X0) <- (22) [resolution 127,258]
354. patient(X1) | ~quiet(X1) | humble(X1) <- (22) [resolution 344,110]
357. patient(X1) | humble(X1) <- (3, 22) [subsumption resolution 354,146]
358. patient(X1) <- (1, 3, 22) [subsumption resolution 357,138]
363. $false <- (1, 3, 22) [resolution 358,134]
366. ~1 | ~3 | ~22 [avatar contradiction clause 363]
367. $false [avatar sat refutation 212,243,254,302,366]
% SZS output end Proof for 1406720030649379392987953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and tall is either not quiet or not happy. Everyone who is not strong or strong is either not wise or old and vice versa. Everyone who is calm or not calm is not creative or funny and vice versa. If someone is both not generous and not tall then someone is not humble or not calm. Everyone who is curious or generous is either not happy or calm and vice versa. If someone is both tall and not wise then fred is both not wise and brave and vice versa. If john is wise then alice is either not creative or humble. Everyone who is calm or not funny is kind or not humble and vice versa. If alice is both not generous and brave then fred is not brave. Everyone who is not curious or funny is either not patient or not humble. Everyone who is both not curious and not funny is not tall and vice versa. If someone is not rich or not kind then john is either not patient or not old and vice versa. If alice is either not brave or tall then someone is strong and vice versa. Everyone who is rich is brave or happy and vice versa. Everyone who is either not patient or not strong is happy or not kind. Everyone who is generous is calm or rich and vice versa. Alice is not happy. Someone is both not curious and not quiet. Susan is tall. Someone is brave. Someone is both not patient and wise. Lucy is both not tall and patient. John is not brave or not tall. Someone is both wise and funny. | Alice is not creative. | neutral | (![X]:((funny(X)&tall(X))=>(~quiet(X)<~>~happy(X))))&
(![X]:((~strong(X)|strong(X))<=>(~wise(X)<~>old(X))))&
(![X]:((calm(X)|~calm(X))<=>(~creative(X)|funny(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
((wise(john))=>((~creative(alice)<~>humble(alice))))&
(![X]:((calm(X)|~funny(X))<=>(kind(X)|~humble(X))))&
(((~generous(alice)&brave(alice)))=>(~brave(fred)))&
(![X]:((~curious(X)|funny(X))=>(~patient(X)<~>~humble(X))))&
(![X]:((~curious(X)&~funny(X))<=>~tall(X)))&
((?[X]:((~rich(X)|~kind(X))))<=>((~patient(john)<~>~old(john))))&
(((~brave(alice)<~>tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:(rich(X)<=>(brave(X)|happy(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(happy(X)|~kind(X))))&
(![X]:(generous(X)<=>(calm(X)|rich(X))))&
(~happy(alice))&
(?[X]:((~curious(X)&~quiet(X))))&
(tall(susan))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)&wise(X))))&
((~tall(lucy)&patient(lucy)))&
((~brave(john)|~tall(john)))&
(?[X]:((wise(X)&funny(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is wise is not funny or not generous.
Everyone who is not quiet or not humble is either not rich or not calm and vice versa.
If someone is not happy or wise then mary is either not rich or not happy and vice versa.
Everyone who is not old is not funny or not curious.
Everyone who is not quiet or not patient is brave.
Everyone who is both not humble and not rich is not rich or not humble and vice versa.
If someone is both not generous and old then fred is both not strong and not generous and vice versa.
If someone is funny or calm then someone is either generous or rich.
Everyone who is tall or not curious is not creative.
If someone is both calm and rich then alice is humble.
If susan is not calm or not creative then someone is not kind or not funny.
If someone is not wise then someone is brave.
Everyone who is calm or generous is both brave and calm and vice versa.
If john is either not quiet or not happy then lucy is either creative or funny and vice versa.
If someone is not funny then john is both not wise and not strong and vice versa.
If susan is not old then alice is either quiet or not tall.
Someone is patient.
Someone is not creative.
Fred is both tall and rich.
Someone is strong or not tall.
Someone is not wise or not calm.
Someone is creative or not creative.
Someone is not strong.
Someone is not calm or old. | John is brave. | entailment | (![X]:(wise(X)=>(~funny(X)|~generous(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~rich(X)<~>~calm(X))))&
((?[X]:((~happy(X)|wise(X))))<=>((~rich(mary)<~>~happy(mary))))&
(![X]:(~old(X)=>(~funny(X)|~curious(X))))&
(![X]:((~quiet(X)|~patient(X))=>brave(X)))&
(![X]:((~humble(X)&~rich(X))<=>(~rich(X)|~humble(X))))&
((?[X]:((~generous(X)&old(X))))<=>((~strong(fred)&~generous(fred))))&
((?[X]:((funny(X)|calm(X))))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~curious(X))=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))=>(humble(alice)))&
(((~calm(susan)|~creative(susan)))=>(?[X]:((~kind(X)|~funny(X)))))&
((?[X]:(~wise(X)))=>(?[X]:(brave(X))))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&calm(X))))&
(((~quiet(john)<~>~happy(john)))<=>((creative(lucy)<~>funny(lucy))))&
((?[X]:(~funny(X)))<=>((~wise(john)&~strong(john))))&
((~old(susan))=>((quiet(alice)<~>~tall(alice))))&
(?[X]:(patient(X)))&
(?[X]:(~creative(X)))&
((tall(fred)&rich(fred)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)|old(X)))) | brave(john) | [
"p1",
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7929156337583574393740945
% SZS output start Proof for 7929156337583574393740945
2. ! [X0] : ((~humble(X0) | ~quiet(X0)) <=> (~rich(X0) <~> ~calm(X0))) [input p1]
5. ! [X0] : ((~patient(X0) | ~quiet(X0)) => brave(X0)) [input p4]
6. ! [X0] : ((~rich(X0) & ~humble(X0)) <=> (~humble(X0) | ~rich(X0))) [input p5]
13. ! [X0] : ((generous(X0) | calm(X0)) <=> (calm(X0) & brave(X0))) [input p12]
25. ~brave(john) [input hypothesis]
30. ! [X0] : (~quiet(X0) => brave(X0)) [pure predicate removal 5]
35. ! [X0] : (brave(X0) | quiet(X0)) [ennf transformation 30]
41. ! [X0] : (((~humble(X0) | ~quiet(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0)))) & (((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (humble(X0) & quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((~humble(X0) | ~quiet(X0) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0)))) & (((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (humble(X0) & quiet(X0)))) [flattening 41]
47. ! [X0] : (((~rich(X0) & ~humble(X0)) | (humble(X0) & rich(X0))) & ((~humble(X0) | ~rich(X0)) | (rich(X0) | humble(X0)))) [nnf transformation 6]
48. ! [X0] : (((~rich(X0) & ~humble(X0)) | (humble(X0) & rich(X0))) & (~humble(X0) | ~rich(X0) | rich(X0) | humble(X0))) [flattening 47]
61. ! [X0] : (((generous(X0) | calm(X0)) | (~calm(X0) | ~brave(X0))) & ((calm(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 13]
62. ! [X0] : ((generous(X0) | calm(X0) | ~calm(X0) | ~brave(X0)) & ((calm(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 61]
86. calm(X0) | rich(X0) | humble(X0) [cnf transformation 42]
88. ~rich(X0) | ~quiet(X0) | ~humble(X0) | calm(X0) [cnf transformation 42]
96. brave(X0) | quiet(X0) [cnf transformation 35]
98. ~humble(X0) | rich(X0) [cnf transformation 48]
101. ~rich(X0) | humble(X0) [cnf transformation 48]
114. ~calm(X0) | brave(X0) [cnf transformation 62]
140. ~brave(john) [cnf transformation 25]
235. 22 <=> quiet(john) [avatar definition]
237. quiet(john) <- (22) [avatar component clause 235]
311. quiet(john) [resolution 96,140]
314. 22 [avatar split clause 311,235]
375. rich(X3) | humble(X3) | brave(X3) [resolution 86,114]
377. brave(X3) | rich(X3) [subsumption resolution 375,98]
407. rich(john) [resolution 377,140]
408. ~quiet(john) | ~humble(john) | calm(john) [resolution 407,88]
409. humble(john) [resolution 407,101]
410. ~humble(john) | calm(john) <- (22) [subsumption resolution 408,237]
412. 47 <=> calm(john) [avatar definition]
414. calm(john) <- (47) [avatar component clause 412]
416. 48 <=> humble(john) [avatar definition]
419. 47 | ~48 | ~22 [avatar split clause 410,235,416,412]
420. 48 [avatar split clause 409,416]
425. brave(john) <- (47) [resolution 414,114]
428. $false <- (47) [subsumption resolution 425,140]
429. ~47 [avatar contradiction clause 428]
430. $false [avatar sat refutation 314,419,420,429]
% SZS output end Proof for 7929156337583574393740945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not rich or creative then someone is both happy and old and vice versa.
Everyone who is wise is not generous or not funny and vice versa.
If someone is either creative or not tall then susan is both brave and old.
If someone is either brave or patient then john is either not generous or not old and vice versa.
If someone is both not tall and not curious then paul is not kind or not strong.
If alice is either not brave or tall then john is either not humble or quiet.
Everyone who is both patient and kind is not wise or not funny and vice versa.
If fred is funny or not curious then lucy is either not old or not quiet and vice versa.
Everyone who is either not creative or funny is either curious or not humble and vice versa.
If someone is either rich or not funny then someone is generous and vice versa.
Everyone who is either calm or rich is either not patient or not calm.
Everyone who is not brave or not old is not kind or not quiet and vice versa.
Everyone who is kind is rich or not happy.
If john is not curious then someone is strong.
If someone is kind then someone is happy or not funny.
Everyone who is happy is both not kind and not wise.
Susan is calm or kind.
Someone is either not brave or not generous.
Susan is both not tall and generous.
Paul is either happy or not creative.
Susan is either not strong or humble. | Fred is not creative. | neutral | (((~rich(paul)<~>creative(paul)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:(wise(X)<=>(~generous(X)|~funny(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>((brave(susan)&old(susan))))&
((?[X]:((brave(X)<~>patient(X))))<=>((~generous(john)<~>~old(john))))&
((?[X]:((~tall(X)&~curious(X))))=>((~kind(paul)|~strong(paul))))&
(((~brave(alice)<~>tall(alice)))=>((~humble(john)<~>quiet(john))))&
(![X]:((patient(X)&kind(X))<=>(~wise(X)|~funny(X))))&
(((funny(fred)|~curious(fred)))<=>((~old(lucy)<~>~quiet(lucy))))&
(![X]:((~creative(X)<~>funny(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>rich(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((~brave(X)|~old(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(kind(X)=>(rich(X)|~happy(X))))&
((~curious(john))=>(?[X]:(strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:(happy(X)=>(~kind(X)&~wise(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~tall(susan)&generous(susan)))&
((happy(paul)<~>~creative(paul)))&
((~strong(susan)<~>humble(susan))) | ~creative(fred) | [] | null | 0 |
If someone is both wise and rich then mary is both humble and rich. If someone is happy then alice is not brave. Everyone who is not wise or not brave is brave and vice versa. If someone is either happy or not tall then someone is both happy and calm. Everyone who is both not creative and not wise is strong or not kind and vice versa. If paul is humble or brave then alice is humble or wise. Everyone who is both kind and not curious is either not rich or not creative and vice versa. If someone is either patient or not strong then someone is either curious or not tall and vice versa. Everyone who is not rich or not generous is both funny and not creative. If someone is not quiet or not brave then paul is happy or not generous and vice versa. If alice is either quiet or not generous then someone is not rich or not curious. If someone is kind or not tall then someone is either not patient or patient and vice versa. Everyone who is calm is either not rich or not quiet and vice versa. Everyone who is both funny and not rich is not rich or not happy. Everyone who is either not rich or not funny is either not tall or not humble and vice versa. Everyone who is both generous and not patient is both quiet and patient. John is funny. John is not patient. Someone is either not tall or not wise. Lucy is generous. Mary is both funny and old. | Alice is not wise. | entailment | ((?[X]:((wise(X)&rich(X))))=>((humble(mary)&rich(mary))))&
((?[X]:(happy(X)))=>(~brave(alice)))&
(![X]:((~wise(X)|~brave(X))<=>brave(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(strong(X)|~kind(X))))&
(((humble(paul)|brave(paul)))=>((humble(alice)|wise(alice))))&
(![X]:((kind(X)&~curious(X))<=>(~rich(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~rich(X)|~generous(X))=>(funny(X)&~creative(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((happy(paul)|~generous(paul))))&
(((quiet(alice)<~>~generous(alice)))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((kind(X)|~tall(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(calm(X)<=>(~rich(X)<~>~quiet(X))))&
(![X]:((funny(X)&~rich(X))=>(~rich(X)|~happy(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((generous(X)&~patient(X))=>(quiet(X)&patient(X))))&
(funny(john))&
(~patient(john))&
(?[X]:((~tall(X)<~>~wise(X))))&
(generous(lucy))&
((funny(mary)&old(mary))) | ~wise(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1380071319598480756120648
% SZS output start Proof for 1380071319598480756120648
3. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> brave(X0)) [input p2]
22. wise(alice) [input hypothesis]
40. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) & wise(X0)))) [nnf transformation 3]
41. ! [X0] : ((~brave(X0) | ~wise(X0) | ~brave(X0)) & (brave(X0) | (brave(X0) & wise(X0)))) [flattening 40]
77. brave(X0) | brave(X0) [cnf transformation 41]
78. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 41]
139. wise(alice) [cnf transformation 22]
143. brave(X0) [duplicate literal removal 77]
144. ~brave(X0) | ~wise(X0) [duplicate literal removal 78]
190. 11 <=> wise(alice) [avatar definition]
192. wise(alice) <- (11) [avatar component clause 190]
305. 11 [avatar split clause 139,190]
310. ~wise(X0) [resolution 144,143]
320. $false <- (11) [resolution 310,192]
321. ~11 [avatar contradiction clause 320]
322. $false [avatar sat refutation 305,321]
% SZS output end Proof for 1380071319598480756120648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or generous then someone is not wise and vice versa.
If someone is either old or not strong then someone is tall and vice versa.
Everyone who is humble or quiet is both not humble and not brave and vice versa.
Everyone who is old is either not tall or not strong.
If fred is not wise or old then someone is not brave and vice versa.
Everyone who is wise or not funny is generous or not calm and vice versa.
If lucy is not rich or generous then lucy is kind and vice versa.
Everyone who is both not rich and not calm is not strong or tall.
If john is not wise or not brave then someone is creative or not happy and vice versa.
Everyone who is not brave is quiet or not wise.
Everyone who is quiet is either not brave or brave and vice versa.
Everyone who is either generous or not humble is either not tall or kind.
Everyone who is both tall and not kind is both not rich and calm.
Everyone who is either not calm or not brave is either quiet or not generous and vice versa.
Everyone who is rich is either not tall or not old and vice versa.
Everyone who is not old is funny or curious and vice versa.
Paul is curious or not tall.
Alice is wise or not patient.
Someone is not humble or rich.
Someone is not kind.
Someone is quiet.
Someone is both generous and not strong.
Someone is either humble or not patient. | Paul is wise. | entailment | (((calm(john)<~>generous(john)))<=>(?[X]:(~wise(X))))&
((?[X]:((old(X)<~>~strong(X))))<=>(?[X]:(tall(X))))&
(![X]:((humble(X)|quiet(X))<=>(~humble(X)&~brave(X))))&
(![X]:(old(X)=>(~tall(X)<~>~strong(X))))&
(((~wise(fred)|old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|~funny(X))<=>(generous(X)|~calm(X))))&
(((~rich(lucy)|generous(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(((~wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:(~brave(X)=>(quiet(X)|~wise(X))))&
(![X]:(quiet(X)<=>(~brave(X)<~>brave(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~tall(X)<~>kind(X))))&
(![X]:((tall(X)&~kind(X))=>(~rich(X)&calm(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(~tall(X)<~>~old(X))))&
(![X]:(~old(X)<=>(funny(X)|curious(X))))&
((curious(paul)|~tall(paul)))&
((wise(alice)|~patient(alice)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | wise(paul) | [
"p0",
"p2",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8031524457433278913708293
% SZS output start Proof for 8031524457433278913708293
1. (calm(john) <~> generous(john)) <=> ? [X0] : ~wise(X0) [input p0]
3. ! [X0] : ((quiet(X0) | humble(X0)) <=> (~brave(X0) & ~humble(X0))) [input p2]
11. ! [X0] : (quiet(X0) <=> (~brave(X0) <~> brave(X0))) [input p10]
14. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> (quiet(X0) <~> ~generous(X0))) [input p13]
24. ~wise(paul) [input hypothesis]
34. (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) [nnf transformation 1]
35. (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) [rectify 34]
36. ? [X1] : ~wise(X1) => ~wise(sK0) [choice axiom]
37. (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X0] : wise(X0)) & (~wise(sK0) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) [skolemisation 35,36]
43. ! [X0] : (((quiet(X0) | humble(X0)) | (brave(X0) | humble(X0))) & ((~brave(X0) & ~humble(X0)) | (~quiet(X0) & ~humble(X0)))) [nnf transformation 3]
44. ! [X0] : ((quiet(X0) | humble(X0) | brave(X0) | humble(X0)) & ((~brave(X0) & ~humble(X0)) | (~quiet(X0) & ~humble(X0)))) [flattening 43]
60. ! [X0] : ((quiet(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~quiet(X0))) [nnf transformation 11]
62. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 14]
79. generous(john) | calm(john) | wise(X0) [cnf transformation 37]
80. ~generous(john) | ~calm(john) | wise(X0) [cnf transformation 37]
88. ~brave(X0) | ~quiet(X0) [cnf transformation 44]
110. quiet(X0) | brave(X0) | brave(X0) [cnf transformation 60]
111. quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
121. generous(X0) | ~quiet(X0) | ~calm(X0) | brave(X0) [cnf transformation 62]
124. brave(X0) | calm(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 62]
142. ~wise(paul) [cnf transformation 24]
143. quiet(X0) | brave(X0) [duplicate literal removal 110]
144. quiet(X0) | ~brave(X0) [duplicate literal removal 111]
148. 1 <=> ! [X0] : wise(X0) [avatar definition]
149. wise(X0) <- (1) [avatar component clause 148]
151. 2 <=> calm(john) [avatar definition]
152. calm(john) <- (2) [avatar component clause 151]
153. ~calm(john) <- (~2) [avatar component clause 151]
155. 3 <=> generous(john) [avatar definition]
156. generous(john) <- (3) [avatar component clause 155]
158. 1 | ~2 | ~3 [avatar split clause 80,155,151,148]
159. 1 | 2 | 3 [avatar split clause 79,155,151,148]
250. ~brave(X0) [subsumption resolution 144,88]
251. quiet(X0) [subsumption resolution 143,250]
254. calm(X0) | ~generous(X0) | ~quiet(X0) [subsumption resolution 124,250]
255. ~generous(X0) | calm(X0) [subsumption resolution 254,251]
256. generous(X0) | ~calm(X0) | brave(X0) [subsumption resolution 121,251]
257. ~calm(X0) | generous(X0) [subsumption resolution 256,250]
279. generous(john) <- (2) [resolution 257,152]
282. 3 | ~2 [avatar split clause 279,151,155]
285. $false <- (1) [resolution 149,142]
288. ~1 [avatar contradiction clause 285]
291. calm(john) <- (3) [resolution 156,255]
292. $false <- (~2, 3) [subsumption resolution 291,153]
293. 2 | ~3 [avatar contradiction clause 292]
294. $false [avatar sat refutation 158,159,282,288,293]
% SZS output end Proof for 8031524457433278913708293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and rich then fred is both not funny and humble and vice versa. Everyone who is not old or not tall is both generous and not brave and vice versa. Everyone who is generous or not funny is not funny and vice versa. If someone is either not rich or not generous then mary is happy and vice versa. Everyone who is funny is either not rich or kind and vice versa. Everyone who is both funny and curious is both wise and not tall and vice versa. Everyone who is calm is not calm or not generous and vice versa. If someone is either not kind or not generous then fred is either not wise or not quiet and vice versa. Everyone who is both rich and not humble is both not creative and not brave. Everyone who is either curious or not tall is old. If john is happy or humble then paul is both happy and rich and vice versa. Everyone who is rich is old or wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. Everyone who is both humble and not wise is either not creative or not strong. Paul is either strong or not rich. Lucy is both not funny and old. Alice is either not humble or not quiet. John is not brave. John is both not strong and happy. Paul is both patient and humble. Someone is either not generous or curious. | Fred is wise. | neutral | ((?[X]:((curious(X)&rich(X))))<=>((~funny(fred)&humble(fred))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&~brave(X))))&
(![X]:((generous(X)|~funny(X))<=>~funny(X)))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(happy(mary)))&
(![X]:(funny(X)<=>(~rich(X)<~>kind(X))))&
(![X]:((funny(X)&curious(X))<=>(wise(X)&~tall(X))))&
(![X]:(calm(X)<=>(~calm(X)|~generous(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((rich(X)&~humble(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~tall(X))=>old(X)))&
(((happy(john)|humble(john)))<=>((happy(paul)&rich(paul))))&
(![X]:(rich(X)=>(old(X)|wise(X))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)<~>~strong(X))))&
((strong(paul)<~>~rich(paul)))&
((~funny(lucy)&old(lucy)))&
((~humble(alice)<~>~quiet(alice)))&
(~brave(john))&
((~strong(john)&happy(john)))&
((patient(paul)&humble(paul)))&
(?[X]:((~generous(X)<~>curious(X)))) | wise(fred) | [] | null | 0 |
If someone is creative then someone is either tall or quiet.
Everyone who is happy is either funny or patient and vice versa.
Everyone who is tall is rich.
If john is either not patient or kind then someone is not creative and vice versa.
Everyone who is patient is both not curious and strong and vice versa.
Everyone who is strong is happy and vice versa.
If paul is curious then someone is not happy.
If someone is both funny and not tall then mary is either not happy or wise and vice versa.
If john is both not funny and not calm then someone is either not rich or quiet and vice versa.
Everyone who is both old and humble is either wise or calm and vice versa.
If fred is either not strong or not humble then fred is tall or not calm and vice versa.
Everyone who is either not brave or rich is not rich or not old and vice versa.
Everyone who is humble is both rich and not creative.
Everyone who is patient is either not curious or not creative and vice versa.
If someone is either curious or not brave then someone is either not happy or not strong.
Someone is not rich.
Paul is generous or curious.
John is either tall or humble.
Fred is not brave.
Someone is tall or not tall.
Alice is not calm or funny. | Fred is happy. | neutral | ((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>patient(X))))&
(![X]:(tall(X)=>rich(X)))&
(((~patient(john)<~>kind(john)))<=>(?[X]:(~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)&strong(X))))&
(![X]:(strong(X)<=>happy(X)))&
((curious(paul))=>(?[X]:(~happy(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((~happy(mary)<~>wise(mary))))&
(((~funny(john)&~calm(john)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:((old(X)&humble(X))<=>(wise(X)<~>calm(X))))&
(((~strong(fred)<~>~humble(fred)))<=>((tall(fred)|~calm(fred))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|~old(X))))&
(![X]:(humble(X)=>(rich(X)&~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(?[X]:(~rich(X)))&
((generous(paul)|curious(paul)))&
((tall(john)<~>humble(john)))&
(~brave(fred))&
(?[X]:((tall(X)|~tall(X))))&
((~calm(alice)|funny(alice))) | happy(fred) | [] | null | 0 |
Everyone who is not brave is calm or old.
Everyone who is tall or not brave is both not quiet and not happy and vice versa.
Everyone who is either not curious or not wise is wise and vice versa.
Everyone who is either humble or calm is both patient and not creative.
If susan is not generous or funny then someone is not curious and vice versa.
Everyone who is patient or not happy is either quiet or not kind and vice versa.
If someone is either quiet or not strong then someone is both not generous and kind.
If paul is not strong or not calm then fred is kind and vice versa.
Everyone who is not generous is humble and vice versa.
If alice is quiet then someone is both not wise and brave and vice versa.
Everyone who is either brave or calm is not tall or not happy and vice versa.
Everyone who is not happy or kind is not calm or humble and vice versa.
If someone is rich or old then susan is patient.
If someone is humble then someone is both kind and calm.
If someone is both not creative and not generous then susan is both not patient and brave and vice versa.
If mary is both quiet and calm then someone is rich or happy and vice versa.
Someone is not creative.
Someone is patient.
Someone is not old or brave.
Alice is not old or not tall. | Susan is not funny. | contradiction | (![X]:(~brave(X)=>(calm(X)|old(X))))&
(![X]:((tall(X)|~brave(X))<=>(~quiet(X)&~happy(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>wise(X)))&
(![X]:((humble(X)<~>calm(X))=>(patient(X)&~creative(X))))&
(((~generous(susan)|funny(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((patient(X)|~happy(X))<=>(quiet(X)<~>~kind(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(((~strong(paul)|~calm(paul)))<=>(kind(fred)))&
(![X]:(~generous(X)<=>humble(X)))&
((quiet(alice))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~happy(X)|kind(X))<=>(~calm(X)|humble(X))))&
((?[X]:((rich(X)|old(X))))=>(patient(susan)))&
((?[X]:(humble(X)))=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~creative(X)&~generous(X))))<=>((~patient(susan)&brave(susan))))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((rich(X)|happy(X)))))&
(?[X]:(~creative(X)))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)|brave(X))))&
((~old(alice)|~tall(alice))) | ~funny(susan) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 198053926782800787345015
% SZS output start Proof for 198053926782800787345015
2. ! [X0] : ((~brave(X0) | tall(X0)) <=> (~happy(X0) & ~quiet(X0))) [input p1]
3. ! [X0] : ((~curious(X0) <~> ~wise(X0)) <=> wise(X0)) [input p2]
5. (funny(susan) | ~generous(susan)) <=> ? [X0] : ~curious(X0) [input p4]
6. ! [X0] : ((~happy(X0) | patient(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p5]
9. ! [X0] : (~generous(X0) <=> humble(X0)) [input p8]
11. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~happy(X0) | ~tall(X0))) [input p10]
14. ? [X0] : humble(X0) => ? [X0] : (calm(X0) & kind(X0)) [input p13]
16. (calm(mary) & quiet(mary)) <=> ? [X0] : (happy(X0) | rich(X0)) [input p15]
21. ~funny(susan) [input hypothesis]
23. ? [X0] : humble(X0) => ? [X1] : (calm(X1) & kind(X1)) [rectify 14]
29. ? [X1] : (calm(X1) & kind(X1)) | ! [X0] : ~humble(X0) [ennf transformation 23]
30. ! [X0] : (((~brave(X0) | tall(X0)) | (happy(X0) | quiet(X0))) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [nnf transformation 2]
31. ! [X0] : ((~brave(X0) | tall(X0) | happy(X0) | quiet(X0)) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [flattening 30]
32. ! [X0] : ((((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | ~wise(X0)) & (wise(X0) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0))))) [nnf transformation 3]
34. ((funny(susan) | ~generous(susan)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(susan) & generous(susan))) [nnf transformation 5]
35. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(susan) & generous(susan))) [flattening 34]
36. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | (~funny(susan) & generous(susan))) [rectify 35]
37. ? [X1] : ~curious(X1) => ~curious(sK0) [choice axiom]
38. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (~curious(sK0) | (~funny(susan) & generous(susan))) [skolemisation 36,37]
39. ! [X0] : (((~happy(X0) | patient(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [nnf transformation 6]
40. ! [X0] : ((~happy(X0) | patient(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [flattening 39]
47. ! [X0] : ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))) [nnf transformation 9]
52. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 11]
53. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [flattening 52]
56. ? [X0] : (calm(X0) & kind(X0)) | ! [X1] : ~humble(X1) [rectify 29]
57. ? [X0] : (calm(X0) & kind(X0)) => (calm(sK3) & kind(sK3)) [choice axiom]
58. (calm(sK3) & kind(sK3)) | ! [X1] : ~humble(X1) [skolemisation 56,57]
64. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | (~calm(mary) | ~quiet(mary))) [nnf transformation 16]
65. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | ~calm(mary) | ~quiet(mary)) [flattening 64]
66. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X1] : (happy(X1) | rich(X1)) | ~calm(mary) | ~quiet(mary)) [rectify 65]
67. ? [X1] : (happy(X1) | rich(X1)) => (happy(sK5) | rich(sK5)) [choice axiom]
68. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & ((happy(sK5) | rich(sK5)) | ~calm(mary) | ~quiet(mary)) [skolemisation 66,67]
76. ~quiet(X0) | ~tall(X0) [cnf transformation 31]
77. ~quiet(X0) | brave(X0) [cnf transformation 31]
82. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 32]
83. ~wise(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 32]
91. funny(susan) | ~generous(susan) | curious(X0) [cnf transformation 38]
93. ~kind(X0) | quiet(X0) | happy(X0) [cnf transformation 40]
105. generous(X0) | humble(X0) [cnf transformation 47]
114. ~calm(X0) | ~brave(X0) | tall(X0) [cnf transformation 53]
122. kind(sK3) | ~humble(X1) [cnf transformation 58]
123. calm(sK3) | ~humble(X1) [cnf transformation 58]
130. quiet(mary) | ~happy(X0) [cnf transformation 68]
132. calm(mary) | ~happy(X0) [cnf transformation 68]
137. ~funny(susan) [cnf transformation 21]
138. wise(X0) | ~curious(X0) [duplicate literal removal 82]
139. ~wise(X0) | ~curious(X0) [duplicate literal removal 83]
140. ~curious(X0) [subsumption resolution 138,139]
141. funny(susan) | ~generous(susan) [subsumption resolution 91,140]
143. 1 <=> generous(susan) [avatar definition]
145. ~generous(susan) <- (~1) [avatar component clause 143]
147. 2 <=> funny(susan) [avatar definition]
150. ~1 | 2 [avatar split clause 141,147,143]
216. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
217. ~humble(X1) <- (17) [avatar component clause 216]
219. 18 <=> calm(sK3) [avatar definition]
221. calm(sK3) <- (18) [avatar component clause 219]
222. 17 | 18 [avatar split clause 123,219,216]
224. 19 <=> kind(sK3) [avatar definition]
226. kind(sK3) <- (19) [avatar component clause 224]
227. 17 | 19 [avatar split clause 122,224,216]
248. 24 <=> ! [X0] : ~happy(X0) [avatar definition]
249. ~happy(X0) <- (24) [avatar component clause 248]
251. 25 <=> calm(mary) [avatar definition]
253. calm(mary) <- (25) [avatar component clause 251]
254. 24 | 25 [avatar split clause 132,251,248]
257. 26 <=> quiet(mary) [avatar definition]
259. quiet(mary) <- (26) [avatar component clause 257]
260. 24 | 26 [avatar split clause 130,257,248]
289. ~2 [avatar split clause 137,147]
290. humble(susan) <- (~1) [resolution 105,145]
293. $false <- (~1, 17) [subsumption resolution 290,217]
294. 1 | ~17 [avatar contradiction clause 293]
370. quiet(sK3) | happy(sK3) <- (19) [resolution 93,226]
391. ~brave(sK3) | tall(sK3) <- (18) [resolution 114,221]
397. 43 <=> tall(sK3) [avatar definition]
401. 44 <=> brave(sK3) [avatar definition]
403. ~brave(sK3) <- (~44) [avatar component clause 401]
404. 43 | ~44 | ~18 [avatar split clause 391,219,401,397]
405. quiet(sK3) <- (19, 24) [subsumption resolution 370,249]
425. brave(sK3) <- (19, 24) [resolution 405,77]
426. ~tall(sK3) <- (19, 24) [resolution 405,76]
427. $false <- (19, 24, ~44) [subsumption resolution 425,403]
428. ~19 | ~24 | 44 [avatar contradiction clause 427]
429. ~43 | ~19 | ~24 [avatar split clause 426,248,224,397]
444. ~brave(mary) | tall(mary) <- (25) [resolution 253,114]
456. 51 <=> brave(mary) [avatar definition]
458. ~brave(mary) <- (~51) [avatar component clause 456]
461. 52 <=> tall(mary) [avatar definition]
464. 52 | ~51 | ~25 [avatar split clause 444,251,456,461]
471. brave(mary) <- (26) [resolution 259,77]
472. ~tall(mary) <- (26) [resolution 259,76]
478. $false <- (26, ~51) [subsumption resolution 471,458]
479. ~26 | 51 [avatar contradiction clause 478]
480. ~52 | ~26 [avatar split clause 472,257,461]
481. $false [avatar sat refutation 150,222,227,254,260,289,294,404,428,429,464,479,480]
% SZS output end Proof for 198053926782800787345015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not calm then someone is not quiet or old.
If fred is not curious or not patient then susan is funny or not humble.
If mary is not brave then someone is both not brave and rich and vice versa.
If someone is not funny or not humble then fred is not old.
If paul is either rich or not strong then paul is not brave or strong and vice versa.
If alice is not strong then alice is both creative and curious and vice versa.
If fred is not quiet or not creative then mary is both happy and humble.
Everyone who is tall is both not calm and not tall and vice versa.
If someone is both not happy and strong then someone is not happy or not calm and vice versa.
If fred is not curious or patient then john is either not kind or not happy and vice versa.
Everyone who is not strong or tall is either funny or strong and vice versa.
If someone is not rich or not tall then someone is calm or patient and vice versa.
If alice is not brave then mary is not generous and vice versa.
If someone is both calm and rich then someone is not brave.
Everyone who is not patient is both not happy and old.
Everyone who is either strong or not old is either funny or not generous and vice versa.
Someone is not quiet or not strong.
John is wise or strong.
Mary is not funny or not happy.
Susan is not happy or not generous.
Someone is strong or tall.
Susan is not rich or not curious. | Mary is not tall. | entailment | ((?[X]:((happy(X)&~calm(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(((~curious(fred)|~patient(fred)))=>((funny(susan)|~humble(susan))))&
((~brave(mary))<=>(?[X]:((~brave(X)&rich(X)))))&
((?[X]:((~funny(X)|~humble(X))))=>(~old(fred)))&
(((rich(paul)<~>~strong(paul)))<=>((~brave(paul)|strong(paul))))&
((~strong(alice))<=>((creative(alice)&curious(alice))))&
(((~quiet(fred)|~creative(fred)))=>((happy(mary)&humble(mary))))&
(![X]:(tall(X)<=>(~calm(X)&~tall(X))))&
((?[X]:((~happy(X)&strong(X))))<=>(?[X]:((~happy(X)|~calm(X)))))&
(((~curious(fred)|patient(fred)))<=>((~kind(john)<~>~happy(john))))&
(![X]:((~strong(X)|tall(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((~brave(alice))<=>(~generous(mary)))&
((?[X]:((calm(X)&rich(X))))=>(?[X]:(~brave(X))))&
(![X]:(~patient(X)=>(~happy(X)&old(X))))&
(![X]:((strong(X)<~>~old(X))<=>(funny(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~strong(X))))&
((wise(john)|strong(john)))&
((~funny(mary)|~happy(mary)))&
((~happy(susan)|~generous(susan)))&
(?[X]:((strong(X)|tall(X))))&
((~rich(susan)|~curious(susan))) | ~tall(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2969109732891272601481251
% SZS output start Proof for 2969109732891272601481251
8. ! [X0] : (tall(X0) <=> (~tall(X0) & ~calm(X0))) [input p7]
23. tall(mary) [input hypothesis]
47. ! [X0] : ((tall(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [nnf transformation 8]
48. ! [X0] : ((tall(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [flattening 47]
94. ~tall(X0) | ~tall(X0) [cnf transformation 48]
135. tall(mary) [cnf transformation 23]
138. ~tall(X0) [duplicate literal removal 94]
369. $false [subsumption resolution 135,138]
% SZS output end Proof for 2969109732891272601481251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or generous is not old.
Everyone who is not old is funny.
If someone is either not kind or not brave then lucy is not patient or not calm and vice versa.
Everyone who is both not wise and strong is either not creative or not humble.
Everyone who is not calm is both curious and calm.
If someone is not old then someone is both not wise and tall and vice versa.
If fred is either not wise or not happy then someone is either funny or not quiet.
Everyone who is both strong and funny is not tall or happy and vice versa.
Everyone who is either not funny or old is both not calm and brave.
Everyone who is both not happy and not kind is either patient or tall and vice versa.
Everyone who is either not rich or quiet is either curious or calm.
If fred is both brave and happy then fred is not humble.
Everyone who is funny or wise is curious.
Everyone who is both not patient and not old is not kind and vice versa.
If someone is either rich or not old then someone is wise or humble and vice versa.
Everyone who is funny or creative is patient.
Someone is patient or tall.
Someone is not kind or wise.
Someone is both not wise and not generous.
Lucy is both humble and rich.
Fred is calm.
Alice is both humble and strong. | Lucy is quiet. | contradiction | (![X]:((~generous(X)<~>generous(X))=>~old(X)))&
(![X]:(~old(X)=>funny(X)))&
((?[X]:((~kind(X)<~>~brave(X))))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((~wise(X)&strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~calm(X)=>(curious(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(curious(X)<~>calm(X))))&
(((brave(fred)&happy(fred)))=>(~humble(fred)))&
(![X]:((funny(X)|wise(X))=>curious(X)))&
(![X]:((~patient(X)&~old(X))<=>~kind(X)))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((funny(X)|creative(X))=>patient(X)))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((humble(lucy)&rich(lucy)))&
(calm(fred))&
((humble(alice)&strong(alice))) | quiet(lucy) | [
"p0",
"p1",
"p4",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3570034697919125754811083
% SZS output start Proof for 3570034697919125754811083
1. ! [X0] : ((~generous(X0) <~> generous(X0)) => ~old(X0)) [input p0]
2. ! [X0] : (~old(X0) => funny(X0)) [input p1]
5. ! [X0] : (~calm(X0) => (calm(X0) & curious(X0))) [input p4]
11. ! [X0] : ((~rich(X0) <~> quiet(X0)) => (curious(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((wise(X0) | funny(X0)) => curious(X0)) [input p12]
20. rich(lucy) & humble(lucy) [input p19]
23. quiet(lucy) [input hypothesis]
26. ! [X0] : (~old(X0) | (~generous(X0) <=> generous(X0))) [ennf transformation 1]
27. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 2]
30. ! [X0] : ((calm(X0) & curious(X0)) | calm(X0)) [ennf transformation 5]
33. ! [X0] : ((curious(X0) <~> calm(X0)) | (~rich(X0) <=> quiet(X0))) [ennf transformation 11]
36. ! [X0] : (curious(X0) | (~wise(X0) & ~funny(X0))) [ennf transformation 13]
38. ! [X0] : (~old(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 26]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0)))) [nnf transformation 33]
72. ~old(X0) | generous(X0) | generous(X0) [cnf transformation 38]
73. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
74. funny(X0) | old(X0) [cnf transformation 27]
84. calm(X0) | calm(X0) [cnf transformation 30]
110. ~calm(X0) | ~curious(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 58]
112. curious(X0) | ~funny(X0) [cnf transformation 36]
130. rich(lucy) [cnf transformation 20]
134. quiet(lucy) [cnf transformation 23]
135. calm(X0) [duplicate literal removal 84]
136. ~old(X0) | generous(X0) [duplicate literal removal 72]
137. ~old(X0) | ~generous(X0) [duplicate literal removal 73]
138. ~old(X0) [subsumption resolution 136,137]
139. funny(X0) [subsumption resolution 74,138]
187. ~rich(X0) | ~curious(X0) | ~quiet(X0) [subsumption resolution 110,135]
198. curious(X0) [subsumption resolution 112,139]
278. ~curious(lucy) | ~quiet(lucy) [resolution 187,130]
279. ~quiet(lucy) [subsumption resolution 278,198]
280. $false [subsumption resolution 279,134]
% SZS output end Proof for 3570034697919125754811083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not generous or not patient then someone is either wise or not tall and vice versa.
Everyone who is brave or not patient is not generous.
Everyone who is not patient or not rich is both happy and not old and vice versa.
Everyone who is both not rich and not brave is not wise or rich.
If paul is kind then paul is either kind or not old.
Everyone who is not patient or rich is either not patient or not calm and vice versa.
If john is either not funny or not wise then someone is both not generous and not rich and vice versa.
Everyone who is not quiet or rich is either not patient or not rich and vice versa.
If someone is either not rich or not calm then someone is strong.
Everyone who is not kind or quiet is either tall or creative and vice versa.
Everyone who is not calm is both not old and not generous and vice versa.
Everyone who is both not old and quiet is both generous and not tall.
If someone is not rich or patient then susan is either not generous or not rich and vice versa.
Everyone who is both generous and brave is both wise and curious.
Everyone who is either humble or not old is both old and not quiet and vice versa.
Mary is not tall or curious.
Alice is old or humble.
Someone is both not rich and not curious.
Someone is either not quiet or strong.
Someone is both kind and not rich. | Mary is strong. | neutral | (((~generous(susan)<~>~patient(susan)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((brave(X)|~patient(X))=>~generous(X)))&
(![X]:((~patient(X)|~rich(X))<=>(happy(X)&~old(X))))&
(![X]:((~rich(X)&~brave(X))=>(~wise(X)|rich(X))))&
((kind(paul))=>((kind(paul)<~>~old(paul))))&
(![X]:((~patient(X)|rich(X))<=>(~patient(X)<~>~calm(X))))&
(((~funny(john)<~>~wise(john)))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~quiet(X)|rich(X))<=>(~patient(X)<~>~rich(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>(?[X]:(strong(X))))&
(![X]:((~kind(X)|quiet(X))<=>(tall(X)<~>creative(X))))&
(![X]:(~calm(X)<=>(~old(X)&~generous(X))))&
(![X]:((~old(X)&quiet(X))=>(generous(X)&~tall(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((~generous(susan)<~>~rich(susan))))&
(![X]:((generous(X)&brave(X))=>(wise(X)&curious(X))))&
(![X]:((humble(X)<~>~old(X))<=>(old(X)&~quiet(X))))&
((~tall(mary)|curious(mary)))&
((old(alice)|humble(alice)))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((kind(X)&~rich(X)))) | strong(mary) | [] | null | 0 |
Everyone who is creative or not generous is both rich and not patient.
If alice is both curious and not kind then someone is both calm and not generous.
If someone is tall then someone is either wise or creative.
If fred is not quiet or not kind then someone is not rich.
Everyone who is patient or happy is either not funny or not wise and vice versa.
Everyone who is both quiet and generous is not happy or kind and vice versa.
If mary is wise or not funny then mary is either not brave or funny and vice versa.
If someone is patient then someone is both not generous and brave.
If paul is not old or brave then someone is both not generous and not calm and vice versa.
If someone is either not rich or not wise then someone is not rich.
Everyone who is both funny and not patient is either not creative or not quiet.
Everyone who is both strong and not calm is both not humble and kind and vice versa.
Everyone who is patient or not strong is both happy and wise.
Everyone who is both not kind and calm is creative.
If paul is not curious or quiet then susan is calm and vice versa.
Everyone who is either not happy or strong is not creative or not patient and vice versa.
Susan is either brave or not curious.
John is both not curious and not calm.
Someone is not rich.
Someone is both strong and tall.
Someone is strong or brave.
Someone is creative or not curious.
Mary is not tall.
Someone is either curious or not generous. | John is kind. | entailment | (![X]:((creative(X)|~generous(X))=>(rich(X)&~patient(X))))&
(((curious(alice)&~kind(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
((?[X]:(tall(X)))=>(?[X]:((wise(X)<~>creative(X)))))&
(((~quiet(fred)|~kind(fred)))=>(?[X]:(~rich(X))))&
(![X]:((patient(X)|happy(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((quiet(X)&generous(X))<=>(~happy(X)|kind(X))))&
(((wise(mary)|~funny(mary)))<=>((~brave(mary)<~>funny(mary))))&
((?[X]:(patient(X)))=>(?[X]:((~generous(X)&brave(X)))))&
(((~old(paul)|brave(paul)))<=>(?[X]:((~generous(X)&~calm(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:((funny(X)&~patient(X))=>(~creative(X)<~>~quiet(X))))&
(![X]:((strong(X)&~calm(X))<=>(~humble(X)&kind(X))))&
(![X]:((patient(X)|~strong(X))=>(happy(X)&wise(X))))&
(![X]:((~kind(X)&calm(X))=>creative(X)))&
(((~curious(paul)|quiet(paul)))<=>(calm(susan)))&
(![X]:((~happy(X)<~>strong(X))<=>(~creative(X)|~patient(X))))&
((brave(susan)<~>~curious(susan)))&
((~curious(john)&~calm(john)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:((creative(X)|~curious(X))))&
(~tall(mary))&
(?[X]:((curious(X)<~>~generous(X)))) | kind(john) | [
"p0",
"p11",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 738156819401421869167615
% SZS output start Proof for 738156819401421869167615
1. ! [X0] : ((~generous(X0) | creative(X0)) => (~patient(X0) & rich(X0))) [input p0]
12. ! [X0] : ((~calm(X0) & strong(X0)) <=> (kind(X0) & ~humble(X0))) [input p11]
13. ! [X0] : ((~strong(X0) | patient(X0)) => (wise(X0) & happy(X0))) [input p12]
14. ! [X0] : ((calm(X0) & ~kind(X0)) => creative(X0)) [input p13]
16. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> (~patient(X0) | ~creative(X0))) [input p15]
18. ~calm(john) & ~curious(john) [input p17]
25. ~kind(john) [input hypothesis]
29. ! [X0] : ((~patient(X0) & rich(X0)) | (generous(X0) & ~creative(X0))) [ennf transformation 1]
38. ! [X0] : ((wise(X0) & happy(X0)) | (strong(X0) & ~patient(X0))) [ennf transformation 13]
39. ! [X0] : (creative(X0) | (~calm(X0) | kind(X0))) [ennf transformation 14]
40. ! [X0] : (creative(X0) | ~calm(X0) | kind(X0)) [flattening 39]
68. ! [X0] : (((~calm(X0) & strong(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 12]
69. ! [X0] : (((~calm(X0) & strong(X0)) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | calm(X0) | ~strong(X0))) [flattening 68]
72. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (patient(X0) & creative(X0))) & ((~patient(X0) | ~creative(X0)) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 16]
73. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (patient(X0) & creative(X0))) & (~patient(X0) | ~creative(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [flattening 72]
88. ~patient(X0) | ~creative(X0) [cnf transformation 29]
125. ~strong(X0) | calm(X0) | kind(X0) [cnf transformation 69]
128. ~patient(X0) | happy(X0) [cnf transformation 38]
129. strong(X0) | happy(X0) [cnf transformation 38]
132. ~calm(X0) | creative(X0) | kind(X0) [cnf transformation 40]
138. strong(X0) | ~happy(X0) | creative(X0) [cnf transformation 73]
139. strong(X0) | ~happy(X0) | patient(X0) [cnf transformation 73]
141. ~strong(X0) | happy(X0) | patient(X0) [cnf transformation 73]
145. ~calm(john) [cnf transformation 18]
154. ~kind(john) [cnf transformation 25]
283. ~strong(X0) | happy(X0) [subsumption resolution 141,128]
284. happy(X0) [subsumption resolution 283,129]
285. strong(X0) | patient(X0) [subsumption resolution 139,284]
286. strong(X0) | creative(X0) [subsumption resolution 138,284]
337. calm(X0) | kind(X0) | creative(X0) [resolution 125,286]
338. calm(X1) | kind(X1) | patient(X1) [resolution 125,285]
359. kind(X0) | creative(X0) [subsumption resolution 337,132]
402. creative(john) [resolution 359,154]
422. kind(john) | patient(john) [resolution 338,145]
427. patient(john) [subsumption resolution 422,154]
448. ~creative(john) [resolution 427,88]
449. $false [subsumption resolution 448,402]
% SZS output end Proof for 738156819401421869167615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not humble is either creative or wise. Everyone who is both strong and not patient is wise and vice versa. Everyone who is both creative and not old is both not creative and not quiet and vice versa. Everyone who is both not calm and not humble is not wise or funny and vice versa. If paul is either not funny or tall then someone is both not humble and humble. Everyone who is curious or old is either curious or kind. If john is both generous and kind then lucy is either curious or generous. Everyone who is both old and tall is both not kind and patient and vice versa. Everyone who is both wise and not kind is generous or happy and vice versa. Everyone who is either humble or quiet is either not creative or old and vice versa. Everyone who is not kind or not brave is not tall or humble. If someone is not humble then someone is not happy. Everyone who is funny or humble is curious. If someone is either generous or not creative then someone is both old and generous and vice versa. 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. Someone is not curious. Someone is both happy and curious. Alice is old. John is humble. Fred is curious. Someone is brave. Someone is both not patient and wise. Someone is either not funny or not quiet. | John is tall. | contradiction | (![X]:((generous(X)|~humble(X))=>(creative(X)<~>wise(X))))&
(![X]:((strong(X)&~patient(X))<=>wise(X)))&
(![X]:((creative(X)&~old(X))<=>(~creative(X)&~quiet(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~wise(X)|funny(X))))&
(((~funny(paul)<~>tall(paul)))=>(?[X]:((~humble(X)&humble(X)))))&
(![X]:((curious(X)|old(X))=>(curious(X)<~>kind(X))))&
(((generous(john)&kind(john)))=>((curious(lucy)<~>generous(lucy))))&
(![X]:((old(X)&tall(X))<=>(~kind(X)&patient(X))))&
(![X]:((wise(X)&~kind(X))<=>(generous(X)|happy(X))))&
(![X]:((humble(X)<~>quiet(X))<=>(~creative(X)<~>old(X))))&
(![X]:((~kind(X)|~brave(X))=>(~tall(X)|humble(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~happy(X))))&
(![X]:((funny(X)|humble(X))=>curious(X)))&
((?[X]:((generous(X)<~>~creative(X))))<=>(?[X]:((old(X)&generous(X)))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)&curious(X))))&
(old(alice))&
(humble(john))&
(curious(fred))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~funny(X)<~>~quiet(X)))) | tall(john) | [
"p1",
"p2",
"p3",
"p7",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8147956023251126339810261
% SZS output start Proof for 8147956023251126339810261
2. ! [X0] : ((~patient(X0) & strong(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : ((~old(X0) & creative(X0)) <=> (~quiet(X0) & ~creative(X0))) [input p2]
4. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> (funny(X0) | ~wise(X0))) [input p3]
8. ! [X0] : ((tall(X0) & old(X0)) <=> (patient(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> (~creative(X0) <~> old(X0))) [input p9]
20. humble(john) [input p19]
25. tall(john) [input hypothesis]
41. ! [X0] : (((~patient(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | (patient(X0) | ~strong(X0)))) [nnf transformation 2]
42. ! [X0] : (((~patient(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | patient(X0) | ~strong(X0))) [flattening 41]
43. ! [X0] : (((~old(X0) & creative(X0)) | (quiet(X0) | creative(X0))) & ((~quiet(X0) & ~creative(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((~old(X0) & creative(X0)) | quiet(X0) | creative(X0)) & ((~quiet(X0) & ~creative(X0)) | old(X0) | ~creative(X0))) [flattening 43]
45. ! [X0] : (((~humble(X0) & ~calm(X0)) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | (humble(X0) | calm(X0)))) [nnf transformation 4]
46. ! [X0] : (((~humble(X0) & ~calm(X0)) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | humble(X0) | calm(X0))) [flattening 45]
52. ! [X0] : (((tall(X0) & old(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (~tall(X0) | ~old(X0)))) [nnf transformation 8]
53. ! [X0] : (((tall(X0) & old(X0)) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | ~tall(X0) | ~old(X0))) [flattening 52]
56. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) & (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 10]
82. ~patient(X0) | ~wise(X0) [cnf transformation 42]
83. ~creative(X0) | old(X0) | ~creative(X0) [cnf transformation 44]
84. ~quiet(X0) | old(X0) | ~creative(X0) [cnf transformation 44]
85. creative(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
90. ~humble(X0) | wise(X0) [cnf transformation 46]
103. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 53]
117. ~quiet(X0) | ~humble(X0) | old(X0) | creative(X0) [cnf transformation 56]
139. humble(john) [cnf transformation 20]
145. tall(john) [cnf transformation 25]
147. ~creative(X0) | old(X0) [duplicate literal removal 83]
148. quiet(X0) | creative(X0) [duplicate literal removal 85]
184. ~quiet(X0) | ~humble(X0) | old(X0) [subsumption resolution 117,84]
266. wise(john) [resolution 90,139]
362. patient(john) | ~old(john) [resolution 103,145]
364. 30 <=> old(john) [avatar definition]
368. 31 <=> patient(john) [avatar definition]
370. patient(john) <- (31) [avatar component clause 368]
371. ~30 | 31 [avatar split clause 362,368,364]
444. ~humble(X1) | old(X1) | creative(X1) [resolution 184,148]
446. ~humble(X1) | old(X1) [subsumption resolution 444,147]
575. old(john) [resolution 446,139]
579. 30 [avatar split clause 575,364]
585. ~wise(john) <- (31) [resolution 370,82]
586. $false <- (31) [subsumption resolution 585,266]
587. ~31 [avatar contradiction clause 586]
588. $false [avatar sat refutation 371,579,587]
% SZS output end Proof for 8147956023251126339810261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and calm then someone is funny or brave and vice versa.
If someone is both not old and not wise then someone is not humble and vice versa.
Everyone who is either not wise or not patient is old.
Everyone who is patient is kind and vice versa.
Everyone who is both not old and kind is happy or quiet and vice versa.
If lucy is either humble or not tall then john is either not humble or not curious.
Everyone who is both creative and not calm is strong.
If someone is generous or tall then someone is patient or not generous.
Everyone who is either happy or brave is not calm or generous and vice versa.
Everyone who is both not kind and not generous is humble or not calm.
If mary is both not brave and quiet then john is not kind.
Everyone who is not rich is not brave or not wise and vice versa.
If mary is either not generous or not patient then someone is both quiet and not rich and vice versa.
Everyone who is happy or patient is humble or not funny and vice versa.
If someone is not tall or creative then someone is either brave or not old and vice versa.
Everyone who is curious is kind and vice versa.
Someone is not rich or not funny.
Someone is strong or not tall.
Someone is both not calm and not creative.
Lucy is wise or kind.
Someone is either not wise or not tall.
Alice is either not kind or patient.
Someone is either humble or calm.
Mary is both not old and generous. | Lucy is patient. | neutral | ((?[X]:((wise(X)&calm(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)<~>~patient(X))=>old(X)))&
(![X]:(patient(X)<=>kind(X)))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|quiet(X))))&
(((humble(lucy)<~>~tall(lucy)))=>((~humble(john)<~>~curious(john))))&
(![X]:((creative(X)&~calm(X))=>strong(X)))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~calm(X)|generous(X))))&
(![X]:((~kind(X)&~generous(X))=>(humble(X)|~calm(X))))&
(((~brave(mary)&quiet(mary)))=>(~kind(john)))&
(![X]:(~rich(X)<=>(~brave(X)|~wise(X))))&
(((~generous(mary)<~>~patient(mary)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)|~funny(X))))&
((?[X]:((~tall(X)|creative(X))))<=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(curious(X)<=>kind(X)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~calm(X)&~creative(X))))&
((wise(lucy)|kind(lucy)))&
(?[X]:((~wise(X)<~>~tall(X))))&
((~kind(alice)<~>patient(alice)))&
(?[X]:((humble(X)<~>calm(X))))&
((~old(mary)&generous(mary))) | patient(lucy) | [] | null | 0 |
Everyone who is old or funny is not old and vice versa. If someone is not humble or not generous then someone is both not humble and kind and vice versa. Everyone who is not quiet is both happy and humble. If someone is both not brave and not quiet then john is both not strong and kind and vice versa. If mary is not creative or not quiet then someone is both not wise and curious and vice versa. If lucy is either not generous or not calm then paul is patient. Everyone who is both not curious and not old is both creative and strong and vice versa. Everyone who is both humble and happy is either creative or old. Everyone who is either not creative or tall is not calm or not kind. Everyone who is not curious or quiet is not brave or not generous. If john is old then john is either not funny or not curious and vice versa. Everyone who is strong or rich is both funny and old and vice versa. If fred is both not calm and not curious then mary is not curious or tall and vice versa. Everyone who is either creative or not humble is both not curious and creative and vice versa. Everyone who is both creative and brave is brave or not old and vice versa. If fred is both patient and not generous then someone is either not kind or not generous and vice versa. Someone is not kind. Paul is happy. Mary is humble or not kind. Someone is wise or kind. Mary is wise or happy. Susan is either brave or calm. Someone is both not kind and funny. | Paul is not curious. | contradiction | (![X]:((old(X)|funny(X))<=>~old(X)))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:((~humble(X)&kind(X)))))&
(![X]:(~quiet(X)=>(happy(X)&humble(X))))&
((?[X]:((~brave(X)&~quiet(X))))<=>((~strong(john)&kind(john))))&
(((~creative(mary)|~quiet(mary)))<=>(?[X]:((~wise(X)&curious(X)))))&
(((~generous(lucy)<~>~calm(lucy)))=>(patient(paul)))&
(![X]:((~curious(X)&~old(X))<=>(creative(X)&strong(X))))&
(![X]:((humble(X)&happy(X))=>(creative(X)<~>old(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~calm(X)|~kind(X))))&
(![X]:((~curious(X)|quiet(X))=>(~brave(X)|~generous(X))))&
((old(john))<=>((~funny(john)<~>~curious(john))))&
(![X]:((strong(X)|rich(X))<=>(funny(X)&old(X))))&
(((~calm(fred)&~curious(fred)))<=>((~curious(mary)|tall(mary))))&
(![X]:((creative(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:((creative(X)&brave(X))<=>(brave(X)|~old(X))))&
(((patient(fred)&~generous(fred)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(?[X]:(~kind(X)))&
(happy(paul))&
((humble(mary)|~kind(mary)))&
(?[X]:((wise(X)|kind(X))))&
((wise(mary)|happy(mary)))&
((brave(susan)<~>calm(susan)))&
(?[X]:((~kind(X)&funny(X)))) | ~curious(paul) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3598590897920275682634450
% SZS output start Proof for 3598590897920275682634450
1. ! [X0] : ((funny(X0) | old(X0)) <=> ~old(X0)) [input p0]
7. ! [X0] : ((~old(X0) & ~curious(X0)) <=> (strong(X0) & creative(X0))) [input p6]
12. ! [X0] : ((rich(X0) | strong(X0)) <=> (old(X0) & funny(X0))) [input p11]
24. ~curious(paul) [input hypothesis]
34. ! [X0] : (((funny(X0) | old(X0)) | old(X0)) & (~old(X0) | (~funny(X0) & ~old(X0)))) [nnf transformation 1]
35. ! [X0] : ((funny(X0) | old(X0) | old(X0)) & (~old(X0) | (~funny(X0) & ~old(X0)))) [flattening 34]
52. ! [X0] : (((~old(X0) & ~curious(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (old(X0) | curious(X0)))) [nnf transformation 7]
53. ! [X0] : (((~old(X0) & ~curious(X0)) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | old(X0) | curious(X0))) [flattening 52]
57. ! [X0] : (((rich(X0) | strong(X0)) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 12]
58. ! [X0] : ((rich(X0) | strong(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | (~rich(X0) & ~strong(X0)))) [flattening 57]
77. ~old(X0) | ~old(X0) [cnf transformation 35]
99. strong(X0) | old(X0) | curious(X0) [cnf transformation 53]
114. old(X0) | ~strong(X0) [cnf transformation 58]
148. ~curious(paul) [cnf transformation 24]
151. ~old(X0) [duplicate literal removal 77]
244. curious(X0) | strong(X0) [subsumption resolution 99,151]
258. ~strong(X0) [subsumption resolution 114,151]
351. strong(paul) [resolution 244,148]
356. $false [subsumption resolution 351,258]
% SZS output end Proof for 3598590897920275682634450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not creative is happy and vice versa.
Everyone who is either not tall or not patient is both patient and not creative.
Everyone who is both not strong and quiet is wise and vice versa.
Everyone who is not creative or not brave is either creative or not brave and vice versa.
If fred is either not kind or patient then someone is either not curious or not kind.
If lucy is not tall then someone is curious.
If susan is both not tall and not old then fred is strong or curious and vice versa.
Everyone who is not creative or brave is either creative or not happy and vice versa.
Everyone who is old is both not wise and not curious.
If someone is both not quiet and not brave then mary is both not tall and not quiet and vice versa.
Everyone who is either not old or curious is either wise or not quiet and vice versa.
Everyone who is both not funny and old is both patient and funny.
Everyone who is both brave and funny is both not humble and curious.
If someone is not calm or not generous then mary is not rich or not creative and vice versa.
Everyone who is both rich and not calm is either generous or happy.
Everyone who is both not patient and funny is either rich or kind and vice versa.
Someone is both not funny and not curious.
Someone is either old or not calm.
Paul is wise or creative.
Fred is not funny or calm.
Fred is both not humble and not quiet.
Someone is not old.
Lucy is quiet.
Someone is not rich or not strong. | Fred is happy. | contradiction | (![X]:((happy(X)&~creative(X))<=>happy(X)))&
(![X]:((~tall(X)<~>~patient(X))=>(patient(X)&~creative(X))))&
(![X]:((~strong(X)&quiet(X))<=>wise(X)))&
(![X]:((~creative(X)|~brave(X))<=>(creative(X)<~>~brave(X))))&
(((~kind(fred)<~>patient(fred)))=>(?[X]:((~curious(X)<~>~kind(X)))))&
((~tall(lucy))=>(?[X]:(curious(X))))&
(((~tall(susan)&~old(susan)))<=>((strong(fred)|curious(fred))))&
(![X]:((~creative(X)|brave(X))<=>(creative(X)<~>~happy(X))))&
(![X]:(old(X)=>(~wise(X)&~curious(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>((~tall(mary)&~quiet(mary))))&
(![X]:((~old(X)<~>curious(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~funny(X)&old(X))=>(patient(X)&funny(X))))&
(![X]:((brave(X)&funny(X))=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~rich(mary)|~creative(mary))))&
(![X]:((rich(X)&~calm(X))=>(generous(X)<~>happy(X))))&
(![X]:((~patient(X)&funny(X))<=>(rich(X)<~>kind(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((old(X)<~>~calm(X))))&
((wise(paul)|creative(paul)))&
((~funny(fred)|calm(fred)))&
((~humble(fred)&~quiet(fred)))&
(?[X]:(~old(X)))&
(quiet(lucy))&
(?[X]:((~rich(X)|~strong(X)))) | happy(fred) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8074743979753037962651714
% SZS output start Proof for 8074743979753037962651714
4. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (creative(X0) <~> ~brave(X0))) [input p3]
8. ! [X0] : ((brave(X0) | ~creative(X0)) <=> (creative(X0) <~> ~happy(X0))) [input p7]
25. happy(fred) [input hypothesis]
43. ! [X0] : (((~brave(X0) | ~creative(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (brave(X0) & creative(X0)))) [nnf transformation 4]
44. ! [X0] : ((~brave(X0) | ~creative(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (brave(X0) & creative(X0)))) [flattening 43]
52. ! [X0] : (((brave(X0) | ~creative(X0)) | ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (~brave(X0) & creative(X0)))) [nnf transformation 8]
53. ! [X0] : ((brave(X0) | ~creative(X0) | ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (~brave(X0) & creative(X0)))) [flattening 52]
90. brave(X0) | ~creative(X0) | brave(X0) [cnf transformation 44]
91. ~brave(X0) | ~creative(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 44]
103. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 53]
148. happy(fred) [cnf transformation 25]
150. ~happy(X0) | creative(X0) [duplicate literal removal 103]
153. brave(X0) | ~creative(X0) [duplicate literal removal 90]
154. ~brave(X0) | ~creative(X0) [duplicate literal removal 91]
156. ~creative(X0) [subsumption resolution 153,154]
208. ~happy(X0) [subsumption resolution 150,156]
280. $false [subsumption resolution 148,208]
% SZS output end Proof for 8074743979753037962651714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not calm is strong or not creative and vice versa.
Everyone who is either not brave or brave is both not happy and not tall and vice versa.
If alice is either not generous or not curious then someone is not quiet or not old and vice versa.
Everyone who is not quiet or strong is not calm or calm.
If someone is humble or not creative then lucy is rich and vice versa.
If someone is both not funny and patient then someone is old and vice versa.
If someone is either not curious or tall then someone is either not patient or not rich and vice versa.
Everyone who is not curious is either old or humble.
Everyone who is either not quiet or not strong is not calm and vice versa.
If susan is tall or brave then someone is quiet and vice versa.
Everyone who is either not rich or patient is either happy or not curious.
If someone is either patient or rich then lucy is not generous.
Everyone who is either calm or not tall is not happy or not strong and vice versa.
Everyone who is both generous and strong is either old or not curious.
Someone is either old or not patient.
Fred is either humble or not generous.
Someone is both wise and not creative.
Someone is not patient.
Someone is patient or not old.
Lucy is kind or happy.
Someone is funny or not happy.
Mary is patient. | Fred is not kind. | neutral | (![X]:((strong(X)<~>~calm(X))<=>(strong(X)|~creative(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(~happy(X)&~tall(X))))&
(((~generous(alice)<~>~curious(alice)))<=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:((~quiet(X)|strong(X))=>(~calm(X)|calm(X))))&
((?[X]:((humble(X)|~creative(X))))<=>(rich(lucy)))&
((?[X]:((~funny(X)&patient(X))))<=>(?[X]:(old(X))))&
((?[X]:((~curious(X)<~>tall(X))))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(![X]:(~curious(X)=>(old(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~calm(X)))&
(((tall(susan)|brave(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((~rich(X)<~>patient(X))=>(happy(X)<~>~curious(X))))&
((?[X]:((patient(X)<~>rich(X))))=>(~generous(lucy)))&
(![X]:((calm(X)<~>~tall(X))<=>(~happy(X)|~strong(X))))&
(![X]:((generous(X)&strong(X))=>(old(X)<~>~curious(X))))&
(?[X]:((old(X)<~>~patient(X))))&
((humble(fred)<~>~generous(fred)))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)|~old(X))))&
((kind(lucy)|happy(lucy)))&
(?[X]:((funny(X)|~happy(X))))&
(patient(mary)) | ~kind(fred) | [] | null | 0 |
Everyone who is both happy and not kind is either not quiet or old.
If mary is both brave and wise then someone is either not happy or creative.
Everyone who is not curious is both patient and not calm and vice versa.
If someone is not calm then someone is both not funny and generous and vice versa.
If someone is either not curious or not calm then someone is not generous.
Everyone who is funny is both old and not curious and vice versa.
If someone is both not tall and not calm then someone is either humble or quiet and vice versa.
If john is either not patient or not curious then someone is not wise and vice versa.
Everyone who is both creative and happy is not creative and vice versa.
If someone is not wise or curious then someone is either strong or creative and vice versa.
Everyone who is not generous or not funny is not calm or brave.
If susan is not curious or not kind then paul is kind.
If someone is not kind then fred is not funny and vice versa.
Everyone who is both quiet and not calm is both quiet and brave.
Everyone who is patient or not quiet is both happy and not strong.
Susan is both rich and not kind.
Paul is creative or not creative.
Lucy is both curious and not strong.
Someone is both rich and not happy.
Someone is not patient or not wise.
Someone is not brave or not calm. | Mary is curious. | entailment | (![X]:((happy(X)&~kind(X))=>(~quiet(X)<~>old(X))))&
(((brave(mary)&wise(mary)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:(~curious(X)<=>(patient(X)&~calm(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:(~generous(X))))&
(![X]:(funny(X)<=>(old(X)&~curious(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:(~wise(X))))&
(![X]:((creative(X)&happy(X))<=>~creative(X)))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((~generous(X)|~funny(X))=>(~calm(X)|brave(X))))&
(((~curious(susan)|~kind(susan)))=>(kind(paul)))&
((?[X]:(~kind(X)))<=>(~funny(fred)))&
(![X]:((quiet(X)&~calm(X))=>(quiet(X)&brave(X))))&
(![X]:((patient(X)|~quiet(X))=>(happy(X)&~strong(X))))&
((rich(susan)&~kind(susan)))&
((creative(paul)|~creative(paul)))&
((curious(lucy)&~strong(lucy)))&
(?[X]:((rich(X)&~happy(X))))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:((~brave(X)|~calm(X)))) | curious(mary) | [
"p2",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6995691808391913114955950
% SZS output start Proof for 6995691808391913114955950
3. ! [X0] : (~curious(X0) <=> (~calm(X0) & patient(X0))) [input p2]
9. ! [X0] : ((happy(X0) & creative(X0)) <=> ~creative(X0)) [input p8]
15. ! [X0] : ((~quiet(X0) | patient(X0)) => (~strong(X0) & happy(X0))) [input p14]
22. ~curious(mary) [input hypothesis]
39. ! [X0] : ((~strong(X0) & happy(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 15]
44. ! [X0] : ((~curious(X0) | (calm(X0) | ~patient(X0))) & ((~calm(X0) & patient(X0)) | curious(X0))) [nnf transformation 3]
45. ! [X0] : ((~curious(X0) | calm(X0) | ~patient(X0)) & ((~calm(X0) & patient(X0)) | curious(X0))) [flattening 44]
66. ! [X0] : (((happy(X0) & creative(X0)) | creative(X0)) & (~creative(X0) | (~happy(X0) | ~creative(X0)))) [nnf transformation 9]
67. ! [X0] : (((happy(X0) & creative(X0)) | creative(X0)) & (~creative(X0) | ~happy(X0) | ~creative(X0))) [flattening 66]
87. patient(X0) | curious(X0) [cnf transformation 45]
108. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 67]
109. creative(X0) | creative(X0) [cnf transformation 67]
125. happy(X0) | ~patient(X0) [cnf transformation 39]
136. ~curious(mary) [cnf transformation 22]
137. ~creative(X0) | ~happy(X0) [duplicate literal removal 108]
138. creative(X0) [duplicate literal removal 109]
237. ~happy(X0) [subsumption resolution 137,138]
290. ~patient(X0) [subsumption resolution 125,237]
305. curious(X0) [resolution 87,290]
306. $false [resolution 305,136]
% SZS output end Proof for 6995691808391913114955950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and calm is not generous. If john is either not calm or not old then someone is both not patient and not quiet. If someone is both old and strong then someone is patient or not brave and vice versa. If someone is both not quiet and quiet then someone is either calm or happy and vice versa. Everyone who is both not strong and happy is not tall. If someone is both not quiet and quiet then john is funny and vice versa. Everyone who is either not wise or patient is either not kind or curious. Everyone who is either strong or not tall is either patient or old. Everyone who is either not wise or not tall is both tall and patient and vice versa. Everyone who is rich or not strong is both not funny and not brave. Everyone who is happy or not wise is either funny or not humble. Everyone who is both wise and not brave is not quiet or wise. Everyone who is generous is both not curious and not patient and vice versa. If fred is both not funny and kind then susan is both not creative and tall and vice versa. If fred is both not patient and calm then paul is old. Everyone who is both not generous and not quiet is both tall and curious and vice versa. Someone is both not rich and funny. Someone is either funny or wise. Fred is both rich and not calm. Someone is both rich and creative. Someone is both calm and rich. Someone is not quiet. Someone is either old or not old. Someone is either not generous or not happy. | John is not funny. | entailment | (![X]:((~calm(X)&calm(X))=>~generous(X)))&
(((~calm(john)<~>~old(john)))=>(?[X]:((~patient(X)&~quiet(X)))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((patient(X)|~brave(X)))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((~strong(X)&happy(X))=>~tall(X)))&
((?[X]:((~quiet(X)&quiet(X))))<=>(funny(john)))&
(![X]:((~wise(X)<~>patient(X))=>(~kind(X)<~>curious(X))))&
(![X]:((strong(X)<~>~tall(X))=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)<~>~tall(X))<=>(tall(X)&patient(X))))&
(![X]:((rich(X)|~strong(X))=>(~funny(X)&~brave(X))))&
(![X]:((happy(X)|~wise(X))=>(funny(X)<~>~humble(X))))&
(![X]:((wise(X)&~brave(X))=>(~quiet(X)|wise(X))))&
(![X]:(generous(X)<=>(~curious(X)&~patient(X))))&
(((~funny(fred)&kind(fred)))<=>((~creative(susan)&tall(susan))))&
(((~patient(fred)&calm(fred)))=>(old(paul)))&
(![X]:((~generous(X)&~quiet(X))<=>(tall(X)&curious(X))))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((funny(X)<~>wise(X))))&
((rich(fred)&~calm(fred)))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((~generous(X)<~>~happy(X)))) | ~funny(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7689639050945581734331532
% SZS output start Proof for 7689639050945581734331532
6. ? [X0] : (quiet(X0) & ~quiet(X0)) <=> funny(john) [input p5]
25. funny(john) [input hypothesis]
54. (? [X0] : (quiet(X0) & ~quiet(X0)) | ~funny(john)) & (funny(john) | ! [X0] : (~quiet(X0) | quiet(X0))) [nnf transformation 6]
55. (? [X0] : (quiet(X0) & ~quiet(X0)) | ~funny(john)) & (funny(john) | ! [X1] : (~quiet(X1) | quiet(X1))) [rectify 54]
56. ? [X0] : (quiet(X0) & ~quiet(X0)) => (quiet(sK5) & ~quiet(sK5)) [choice axiom]
57. ((quiet(sK5) & ~quiet(sK5)) | ~funny(john)) & (funny(john) | ! [X1] : (~quiet(X1) | quiet(X1))) [skolemisation 55,56]
104. ~quiet(sK5) | ~funny(john) [cnf transformation 57]
105. quiet(sK5) | ~funny(john) [cnf transformation 57]
156. funny(john) [cnf transformation 25]
224. 15 <=> funny(john) [avatar definition]
228. 16 <=> quiet(sK5) [avatar definition]
231. ~15 | 16 [avatar split clause 105,228,224]
232. ~15 | ~16 [avatar split clause 104,228,224]
287. 15 [avatar split clause 156,224]
288. $false [avatar sat refutation 231,232,287]
% SZS output end Proof for 7689639050945581734331532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either tall or not quiet then someone is not calm and vice versa.
Everyone who is both not old and creative is either not kind or strong and vice versa.
Everyone who is either not humble or not brave is both not curious and not kind.
If someone is both not curious and not brave then someone is not humble and vice versa.
If someone is quiet then someone is calm and vice versa.
If susan is funny then someone is either not wise or not humble and vice versa.
If someone is kind or rich then someone is both not funny and not creative.
Everyone who is strong is both curious and funny and vice versa.
Everyone who is not creative is both strong and not quiet and vice versa.
Everyone who is both strong and tall is both brave and tall and vice versa.
Everyone who is generous or strong is either happy or not brave and vice versa.
If alice is both not curious and humble then fred is not happy.
Everyone who is not strong or not calm is either tall or kind and vice versa.
Everyone who is wise is both not wise and not calm.
Everyone who is funny is quiet or not tall and vice versa.
If fred is not brave then mary is not brave and vice versa.
Susan is not wise.
Lucy is either creative or not brave.
Someone is both humble and not patient.
Fred is funny or not strong.
Someone is patient or not rich.
Mary is not generous or not happy.
Someone is not quiet or old.
Someone is generous. | Susan is not wise. | entailment | (((tall(lucy)<~>~quiet(lucy)))<=>(?[X]:(~calm(X))))&
(![X]:((~old(X)&creative(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(~curious(X)&~kind(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(calm(X))))&
((funny(susan))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(strong(X)<=>(curious(X)&funny(X))))&
(![X]:(~creative(X)<=>(strong(X)&~quiet(X))))&
(![X]:((strong(X)&tall(X))<=>(brave(X)&tall(X))))&
(![X]:((generous(X)|strong(X))<=>(happy(X)<~>~brave(X))))&
(((~curious(alice)&humble(alice)))=>(~happy(fred)))&
(![X]:((~strong(X)|~calm(X))<=>(tall(X)<~>kind(X))))&
(![X]:(wise(X)=>(~wise(X)&~calm(X))))&
(![X]:(funny(X)<=>(quiet(X)|~tall(X))))&
((~brave(fred))<=>(~brave(mary)))&
(~wise(susan))&
((creative(lucy)<~>~brave(lucy)))&
(?[X]:((humble(X)&~patient(X))))&
((funny(fred)|~strong(fred)))&
(?[X]:((patient(X)|~rich(X))))&
((~generous(mary)|~happy(mary)))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:(generous(X))) | ~wise(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 629878112514484984538244
% SZS output start Proof for 629878112514484984538244
14. ! [X0] : (wise(X0) => (~calm(X0) & ~wise(X0))) [input p13]
25. wise(susan) [input hypothesis]
36. ! [X0] : ((~calm(X0) & ~wise(X0)) | ~wise(X0)) [ennf transformation 14]
129. ~wise(X0) | ~wise(X0) [cnf transformation 36]
144. wise(susan) [cnf transformation 25]
145. ~wise(X0) [duplicate literal removal 129]
288. $false [subsumption resolution 144,145]
% SZS output end Proof for 629878112514484984538244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not strong then susan is kind. Everyone who is rich or not creative is both tall and not quiet. If someone is either not brave or creative then susan is not rich. If someone is not kind then someone is strong or curious and vice versa. Everyone who is curious is either patient or humble. Everyone who is either not happy or not curious is not humble and vice versa. Everyone who is either strong or humble is either brave or curious. If susan is both not tall and not brave then fred is not funny or strong and vice versa. If lucy is creative then lucy is funny and vice versa. Everyone who is rich or not wise is not kind and vice versa. Everyone who is generous is either rich or not tall. If lucy is both wise and quiet then someone is wise. Everyone who is not rich is either strong or not patient. Everyone who is not curious or not patient is either old or not happy. Everyone who is creative is both strong and not calm. Someone is kind. Someone is both patient and not curious. Someone is happy or not wise. Lucy is either funny or not brave. Alice is happy or creative. John is generous. Fred is kind or not patient. Fred is not strong. | Fred is patient. | contradiction | ((?[X]:((~calm(X)<~>~strong(X))))=>(kind(susan)))&
(![X]:((rich(X)|~creative(X))=>(tall(X)&~quiet(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(~rich(susan)))&
((?[X]:(~kind(X)))<=>(?[X]:((strong(X)|curious(X)))))&
(![X]:(curious(X)=>(patient(X)<~>humble(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>~humble(X)))&
(![X]:((strong(X)<~>humble(X))=>(brave(X)<~>curious(X))))&
(((~tall(susan)&~brave(susan)))<=>((~funny(fred)|strong(fred))))&
((creative(lucy))<=>(funny(lucy)))&
(![X]:((rich(X)|~wise(X))<=>~kind(X)))&
(![X]:(generous(X)=>(rich(X)<~>~tall(X))))&
(((wise(lucy)&quiet(lucy)))=>(?[X]:(wise(X))))&
(![X]:(~rich(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~curious(X)|~patient(X))=>(old(X)<~>~happy(X))))&
(![X]:(creative(X)=>(strong(X)&~calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((happy(X)|~wise(X))))&
((funny(lucy)<~>~brave(lucy)))&
((happy(alice)|creative(alice)))&
(generous(john))&
((kind(fred)|~patient(fred)))&
(~strong(fred)) | patient(fred) | [
"p9",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2917451132425934125849701
% SZS output start Proof for 2917451132425934125849701
10. ! [X0] : ((~wise(X0) | rich(X0)) <=> ~kind(X0)) [input p9]
13. ! [X0] : (~rich(X0) => (strong(X0) <~> ~patient(X0))) [input p12]
22. ~patient(fred) | kind(fred) [input p21]
23. ~strong(fred) [input p22]
24. patient(fred) [input hypothesis]
34. ! [X0] : ((strong(X0) <~> ~patient(X0)) | rich(X0)) [ennf transformation 13]
50. ! [X0] : (((~wise(X0) | rich(X0)) | kind(X0)) & (~kind(X0) | (wise(X0) & ~rich(X0)))) [nnf transformation 10]
51. ! [X0] : ((~wise(X0) | rich(X0) | kind(X0)) & (~kind(X0) | (wise(X0) & ~rich(X0)))) [flattening 50]
53. ! [X0] : (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | rich(X0)) [nnf transformation 34]
88. ~rich(X0) | ~kind(X0) [cnf transformation 51]
93. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 53]
109. ~patient(fred) | kind(fred) [cnf transformation 22]
110. ~strong(fred) [cnf transformation 23]
111. patient(fred) [cnf transformation 24]
161. 13 <=> strong(fred) [avatar definition]
163. ~strong(fred) <- (~13) [avatar component clause 161]
216. 24 <=> kind(fred) [avatar definition]
218. kind(fred) <- (24) [avatar component clause 216]
220. 25 <=> patient(fred) [avatar definition]
221. patient(fred) <- (25) [avatar component clause 220]
223. 24 | ~25 [avatar split clause 109,220,216]
224. ~13 [avatar split clause 110,161]
225. 25 [avatar split clause 111,220]
258. strong(fred) | rich(fred) <- (25) [resolution 93,221]
268. rich(fred) <- (~13, 25) [subsumption resolution 258,163]
289. ~kind(fred) <- (~13, 25) [resolution 268,88]
291. $false <- (~13, 24, 25) [subsumption resolution 289,218]
292. 13 | ~24 | ~25 [avatar contradiction clause 291]
293. $false [avatar sat refutation 223,224,225,292]
% SZS output end Proof for 2917451132425934125849701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not patient is both not generous and calm.
Everyone who is creative or not quiet is both happy and quiet and vice versa.
Everyone who is not generous is calm or not wise.
If susan is not wise then someone is not tall and vice versa.
If someone is either kind or humble then someone is not strong or humble and vice versa.
Everyone who is not creative is both generous and not creative and vice versa.
If someone is generous or not creative then someone is both not brave and quiet.
Everyone who is both generous and wise is either not generous or tall and vice versa.
Everyone who is both not funny and not creative is both generous and happy and vice versa.
If someone is not happy or not tall then someone is not humble or not calm.
Everyone who is both creative and not quiet is either not calm or not brave and vice versa.
If lucy is either patient or not strong then someone is not kind and vice versa.
Everyone who is both quiet and funny is both not patient and rich and vice versa.
Everyone who is kind or not curious is not brave or calm and vice versa.
If someone is quiet then paul is not generous.
Everyone who is both humble and wise is either not strong or curious.
Someone is either not old or not kind.
Someone is both quiet and patient.
Someone is curious.
John is either rich or wise.
Someone is not quiet or quiet.
Lucy is either brave or curious. | Susan is creative. | entailment | (![X]:((creative(X)|~patient(X))=>(~generous(X)&calm(X))))&
(![X]:((creative(X)|~quiet(X))<=>(happy(X)&quiet(X))))&
(![X]:(~generous(X)=>(calm(X)|~wise(X))))&
((~wise(susan))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:(~creative(X)<=>(generous(X)&~creative(X))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((generous(X)&wise(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~funny(X)&~creative(X))<=>(generous(X)&happy(X))))&
((?[X]:((~happy(X)|~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((creative(X)&~quiet(X))<=>(~calm(X)<~>~brave(X))))&
(((patient(lucy)<~>~strong(lucy)))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)&funny(X))<=>(~patient(X)&rich(X))))&
(![X]:((kind(X)|~curious(X))<=>(~brave(X)|calm(X))))&
((?[X]:(quiet(X)))=>(~generous(paul)))&
(![X]:((humble(X)&wise(X))=>(~strong(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:(curious(X)))&
((rich(john)<~>wise(john)))&
(?[X]:((~quiet(X)|quiet(X))))&
((brave(lucy)<~>curious(lucy))) | creative(susan) | [
"p0",
"p1",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5106099205007664439488316
% SZS output start Proof for 5106099205007664439488316
1. ! [X0] : ((~patient(X0) | creative(X0)) => (calm(X0) & ~generous(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (quiet(X0) & happy(X0))) [input p1]
6. ! [X0] : (~creative(X0) <=> (~creative(X0) & generous(X0))) [input p5]
9. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> (happy(X0) & generous(X0))) [input p8]
13. ! [X0] : ((funny(X0) & quiet(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
23. ~creative(susan) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~generous(X0)) | (patient(X0) & ~creative(X0))) [ennf transformation 1]
35. ! [X0] : (((~quiet(X0) | creative(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 2]
36. ! [X0] : ((~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 35]
46. ! [X0] : ((~creative(X0) | (creative(X0) | ~generous(X0))) & ((~creative(X0) & generous(X0)) | creative(X0))) [nnf transformation 6]
47. ! [X0] : ((~creative(X0) | creative(X0) | ~generous(X0)) & ((~creative(X0) & generous(X0)) | creative(X0))) [flattening 46]
53. ! [X0] : (((~creative(X0) & ~funny(X0)) | (~happy(X0) | ~generous(X0))) & ((happy(X0) & generous(X0)) | (creative(X0) | funny(X0)))) [nnf transformation 9]
54. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0) | ~generous(X0)) & ((happy(X0) & generous(X0)) | creative(X0) | funny(X0))) [flattening 53]
64. ! [X0] : (((funny(X0) & quiet(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 13]
65. ! [X0] : (((funny(X0) & quiet(X0)) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 64]
81. ~generous(X0) | patient(X0) [cnf transformation 27]
84. ~creative(X0) | happy(X0) [cnf transformation 36]
87. quiet(X0) | quiet(X0) [cnf transformation 36]
88. ~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 36]
98. generous(X0) | creative(X0) [cnf transformation 47]
112. happy(X0) | creative(X0) | funny(X0) [cnf transformation 54]
127. ~patient(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 65]
148. ~creative(susan) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 87]
152. ~happy(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 88]
201. 12 <=> ! [X1] : creative(X1) [avatar definition]
202. creative(X1) <- (12) [avatar component clause 201]
213. funny(X0) | happy(X0) [subsumption resolution 112,84]
224. 17 <=> ! [X1] : happy(X1) [avatar definition]
225. happy(X1) <- (17) [avatar component clause 224]
249. ~funny(X0) | ~patient(X0) [subsumption resolution 127,151]
283. patient(X0) | creative(X0) [resolution 98,81]
295. ~patient(X0) | happy(X0) [resolution 249,213]
361. happy(X0) | creative(X0) [resolution 295,283]
367. happy(X0) [subsumption resolution 361,84]
368. 17 [avatar split clause 367,224]
369. creative(X0) | ~quiet(X0) <- (17) [resolution 225,152]
370. creative(X0) <- (17) [subsumption resolution 369,151]
371. 12 | ~17 [avatar split clause 370,224,201]
372. $false <- (12) [resolution 202,148]
377. ~12 [avatar contradiction clause 372]
378. $false [avatar sat refutation 368,371,377]
% SZS output end Proof for 5106099205007664439488316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and brave then someone is either strong or not strong and vice versa.
If paul is either not happy or not calm then someone is both creative and calm.
If fred is both not wise and brave then john is not old or not wise.
If someone is either tall or not tall then someone is calm or not generous and vice versa.
Everyone who is not calm or not generous is not rich and vice versa.
Everyone who is not patient or strong is either creative or kind and vice versa.
Everyone who is not rich or not calm is funny and vice versa.
If someone is not curious or curious then john is wise and vice versa.
Everyone who is both not kind and not happy is both not generous and not quiet.
If someone is both not curious and old then someone is old or quiet.
If fred is both not strong and calm then someone is calm.
Everyone who is both not rich and generous is not strong or patient and vice versa.
If someone is both not rich and tall then paul is rich.
If someone is brave then someone is funny.
Everyone who is creative is both calm and not kind and vice versa.
Everyone who is not patient or not kind is both not old and quiet and vice versa.
Fred is strong or patient.
Paul is both not generous and funny.
Fred is funny or humble.
Fred is not funny or not rich.
Someone is happy.
Susan is not calm.
Mary is either quiet or strong.
Someone is both calm and brave. | Mary is not funny. | contradiction | ((?[X]:((~strong(X)&brave(X))))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(((~happy(paul)<~>~calm(paul)))=>(?[X]:((creative(X)&calm(X)))))&
(((~wise(fred)&brave(fred)))=>((~old(john)|~wise(john))))&
((?[X]:((tall(X)<~>~tall(X))))<=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((~calm(X)|~generous(X))<=>~rich(X)))&
(![X]:((~patient(X)|strong(X))<=>(creative(X)<~>kind(X))))&
(![X]:((~rich(X)|~calm(X))<=>funny(X)))&
((?[X]:((~curious(X)|curious(X))))<=>(wise(john)))&
(![X]:((~kind(X)&~happy(X))=>(~generous(X)&~quiet(X))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((old(X)|quiet(X)))))&
(((~strong(fred)&calm(fred)))=>(?[X]:(calm(X))))&
(![X]:((~rich(X)&generous(X))<=>(~strong(X)|patient(X))))&
((?[X]:((~rich(X)&tall(X))))=>(rich(paul)))&
((?[X]:(brave(X)))=>(?[X]:(funny(X))))&
(![X]:(creative(X)<=>(calm(X)&~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~old(X)&quiet(X))))&
((strong(fred)|patient(fred)))&
((~generous(paul)&funny(paul)))&
((funny(fred)|humble(fred)))&
((~funny(fred)|~rich(fred)))&
(?[X]:(happy(X)))&
(~calm(susan))&
((quiet(mary)<~>strong(mary)))&
(?[X]:((calm(X)&brave(X)))) | ~funny(mary) | [
"p6",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 352147725683244267529645
% SZS output start Proof for 352147725683244267529645
7. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> funny(X0)) [input p6]
12. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (patient(X0) | ~strong(X0))) [input p11]
16. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (quiet(X0) & ~old(X0))) [input p15]
23. quiet(mary) <~> strong(mary) [input p22]
25. ~funny(mary) [input hypothesis]
58. ! [X0] : (((~calm(X0) | ~rich(X0)) | ~funny(X0)) & (funny(X0) | (calm(X0) & rich(X0)))) [nnf transformation 7]
59. ! [X0] : ((~calm(X0) | ~rich(X0) | ~funny(X0)) & (funny(X0) | (calm(X0) & rich(X0)))) [flattening 58]
69. ! [X0] : (((generous(X0) & ~rich(X0)) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 12]
70. ! [X0] : (((generous(X0) & ~rich(X0)) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ~generous(X0) | rich(X0))) [flattening 69]
76. ! [X0] : (((~kind(X0) | ~patient(X0)) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 16]
77. ! [X0] : ((~kind(X0) | ~patient(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [flattening 76]
80. (~strong(mary) | ~quiet(mary)) & (strong(mary) | quiet(mary)) [nnf transformation 23]
109. funny(X0) | rich(X0) [cnf transformation 59]
120. ~rich(X0) | strong(X0) [cnf transformation 70]
121. ~patient(X0) | ~rich(X0) [cnf transformation 70]
131. quiet(X0) | patient(X0) [cnf transformation 77]
141. ~strong(mary) | ~quiet(mary) [cnf transformation 80]
144. ~funny(mary) [cnf transformation 25]
278. 30 <=> quiet(mary) [avatar definition]
280. ~quiet(mary) <- (~30) [avatar component clause 278]
282. 31 <=> strong(mary) [avatar definition]
285. ~30 | ~31 [avatar split clause 141,282,278]
289. rich(mary) [resolution 109,144]
293. strong(mary) [resolution 120,289]
296. 31 [avatar split clause 293,282]
299. patient(mary) <- (~30) [resolution 131,280]
301. ~rich(mary) <- (~30) [resolution 299,121]
302. $false <- (~30) [subsumption resolution 301,289]
303. 30 [avatar contradiction clause 302]
304. $false [avatar sat refutation 285,296,303]
% SZS output end Proof for 352147725683244267529645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or strong is not generous and vice versa.
If someone is either not curious or old then someone is both not old and generous and vice versa.
If someone is both generous and not curious then someone is not funny and vice versa.
If john is creative or rich then someone is not strong.
If someone is both tall and strong then someone is both not happy and rich.
Everyone who is either not patient or not brave is not quiet and vice versa.
Everyone who is both calm and kind is both wise and not curious and vice versa.
If paul is both strong and rich then someone is old or not creative and vice versa.
Everyone who is either not strong or quiet is both not kind and not rich.
If someone is not patient or not generous then someone is either kind or not happy.
Everyone who is both strong and kind is not calm or quiet and vice versa.
Everyone who is either not curious or calm is either not patient or not tall and vice versa.
Everyone who is either calm or old is not humble.
If someone is either not generous or creative then paul is tall.
Everyone who is not quiet or not generous is both not rich and happy.
Everyone who is happy is both not funny and not wise.
Someone is not patient.
Someone is happy.
Someone is creative.
Someone is not kind or not tall.
Paul is not curious. | Paul is happy. | entailment | (![X]:((tall(X)<~>strong(X))<=>~generous(X)))&
((?[X]:((~curious(X)<~>old(X))))<=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:(~funny(X))))&
(((creative(john)|rich(john)))=>(?[X]:(~strong(X))))&
((?[X]:((tall(X)&strong(X))))=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>~quiet(X)))&
(![X]:((calm(X)&kind(X))<=>(wise(X)&~curious(X))))&
(((strong(paul)&rich(paul)))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>(~kind(X)&~rich(X))))&
((?[X]:((~patient(X)|~generous(X))))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((strong(X)&kind(X))<=>(~calm(X)|quiet(X))))&
(![X]:((~curious(X)<~>calm(X))<=>(~patient(X)<~>~tall(X))))&
(![X]:((calm(X)<~>old(X))=>~humble(X)))&
((?[X]:((~generous(X)<~>creative(X))))=>(tall(paul)))&
(![X]:((~quiet(X)|~generous(X))=>(~rich(X)&happy(X))))&
(![X]:(happy(X)=>(~funny(X)&~wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:(happy(X)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|~tall(X))))&
(~curious(paul)) | happy(paul) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 730153847113622209692493
% SZS output start Proof for 730153847113622209692493
1. ! [X0] : ((tall(X0) <~> strong(X0)) <=> ~generous(X0)) [input p0]
5. ? [X0] : (strong(X0) & tall(X0)) => ? [X0] : (rich(X0) & ~happy(X0)) [input p4]
8. (rich(paul) & strong(paul)) <=> ? [X0] : (~creative(X0) | old(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~rich(X0) & ~kind(X0))) [input p8]
11. ! [X0] : ((kind(X0) & strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p10]
14. ? [X0] : (~generous(X0) <~> creative(X0)) => tall(paul) [input p13]
15. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (happy(X0) & ~rich(X0))) [input p14]
22. ~happy(paul) [input hypothesis]
25. ? [X0] : (strong(X0) & tall(X0)) => ? [X1] : (rich(X1) & ~happy(X1)) [rectify 5]
29. ? [X1] : (rich(X1) & ~happy(X1)) | ! [X0] : (~strong(X0) | ~tall(X0)) [ennf transformation 25]
30. ! [X0] : ((~rich(X0) & ~kind(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 9]
32. tall(paul) | ! [X0] : (~generous(X0) <=> creative(X0)) [ennf transformation 14]
33. ! [X0] : ((happy(X0) & ~rich(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 15]
35. ! [X0] : ((((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | generous(X0)) & (~generous(X0) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))))) [nnf transformation 1]
48. ? [X0] : (rich(X0) & ~happy(X0)) | ! [X1] : (~strong(X1) | ~tall(X1)) [rectify 29]
49. ? [X0] : (rich(X0) & ~happy(X0)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
50. (rich(sK5) & ~happy(sK5)) | ! [X1] : (~strong(X1) | ~tall(X1)) [skolemisation 48,49]
54. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X0] : (~creative(X0) | old(X0)) | (~rich(paul) | ~strong(paul))) [nnf transformation 8]
55. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X0] : (~creative(X0) | old(X0)) | ~rich(paul) | ~strong(paul)) [flattening 54]
56. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X1] : (~creative(X1) | old(X1)) | ~rich(paul) | ~strong(paul)) [rectify 55]
57. ? [X1] : (~creative(X1) | old(X1)) => (~creative(sK6) | old(sK6)) [choice axiom]
58. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & ((~creative(sK6) | old(sK6)) | ~rich(paul) | ~strong(paul)) [skolemisation 56,57]
59. ! [X0] : ((~rich(X0) & ~kind(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 30]
64. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~kind(X0) | ~strong(X0)))) [nnf transformation 11]
65. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~kind(X0) | ~strong(X0))) [flattening 64]
67. tall(paul) | ! [X0] : ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0))) [nnf transformation 32]
76. ~generous(X0) | strong(X0) | ~tall(X0) [cnf transformation 35]
77. ~generous(X0) | tall(X0) | ~strong(X0) [cnf transformation 35]
92. rich(sK5) | ~strong(X1) | ~tall(X1) [cnf transformation 50]
103. strong(paul) | creative(X0) [cnf transformation 58]
107. ~kind(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 59]
116. ~quiet(X0) | strong(X0) [cnf transformation 65]
118. ~quiet(X0) | kind(X0) [cnf transformation 65]
128. tall(paul) | ~generous(X0) | ~creative(X0) [cnf transformation 67]
129. ~rich(X0) | quiet(X0) [cnf transformation 33]
132. happy(X0) | generous(X0) [cnf transformation 33]
140. ~happy(paul) [cnf transformation 22]
208. 16 <=> ! [X1] : (~strong(X1) | ~tall(X1)) [avatar definition]
209. ~strong(X1) | ~tall(X1) <- (16) [avatar component clause 208]
211. 17 <=> rich(sK5) [avatar definition]
213. rich(sK5) <- (17) [avatar component clause 211]
214. 16 | 17 [avatar split clause 92,211,208]
221. 19 <=> ! [X0] : creative(X0) [avatar definition]
222. creative(X0) <- (19) [avatar component clause 221]
233. 22 <=> strong(paul) [avatar definition]
234. ~strong(paul) <- (~22) [avatar component clause 233]
235. strong(paul) <- (22) [avatar component clause 233]
236. 19 | 22 [avatar split clause 103,233,221]
267. 29 <=> ! [X0] : (~generous(X0) | ~creative(X0)) [avatar definition]
268. ~creative(X0) | ~generous(X0) <- (29) [avatar component clause 267]
270. 30 <=> tall(paul) [avatar definition]
272. tall(paul) <- (30) [avatar component clause 270]
273. 29 | 30 [avatar split clause 128,270,267]
299. generous(paul) [resolution 132,140]
303. ~tall(paul) <- (16, 22) [resolution 209,235]
304. $false <- (16, 22, 30) [subsumption resolution 303,272]
305. ~16 | ~22 | ~30 [avatar contradiction clause 304]
307. quiet(sK5) <- (17) [resolution 213,129]
346. 41 <=> strong(sK5) [avatar definition]
347. ~strong(sK5) <- (~41) [avatar component clause 346]
348. strong(sK5) <- (41) [avatar component clause 346]
364. strong(sK5) <- (17) [resolution 307,116]
365. $false <- (17, ~41) [subsumption resolution 364,347]
366. ~17 | 41 [avatar contradiction clause 365]
370. tall(paul) | ~strong(paul) [resolution 299,77]
371. strong(paul) | ~tall(paul) [resolution 299,76]
372. ~tall(paul) <- (~22) [subsumption resolution 371,234]
375. ~30 | 22 [avatar split clause 372,233,270]
376. ~generous(X0) <- (19, 29) [subsumption resolution 268,222]
377. $false <- (19, 29) [resolution 376,299]
384. ~19 | ~29 [avatar contradiction clause 377]
389. tall(paul) <- (22) [subsumption resolution 370,235]
390. 30 | ~22 [avatar split clause 389,233,270]
392. quiet(sK5) <- (17) [resolution 213,129]
407. kind(sK5) <- (17) [resolution 392,118]
486. ~strong(sK5) | ~quiet(sK5) <- (17) [resolution 107,407]
488. ~quiet(sK5) <- (17, 41) [subsumption resolution 486,348]
489. $false <- (17, 41) [subsumption resolution 488,392]
490. ~17 | ~41 [avatar contradiction clause 489]
491. $false [avatar sat refutation 214,236,273,305,366,375,384,390,490]
% SZS output end Proof for 730153847113622209692493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not tall or calm and vice versa.
If fred is either not generous or tall then someone is not creative.
Everyone who is either not kind or funny is not funny.
Everyone who is not patient or old is not brave or quiet and vice versa.
If someone is creative or generous then someone is either not strong or not creative and vice versa.
Everyone who is not happy or not curious is either generous or not old and vice versa.
Everyone who is old is not tall or not generous.
Everyone who is creative or not strong is either not curious or brave and vice versa.
If paul is not curious then john is both old and creative.
Everyone who is not strong is both not wise and tall and vice versa.
Everyone who is not kind is both not tall and not wise and vice versa.
Everyone who is either not happy or patient is not creative and vice versa.
If alice is not brave then john is either quiet or calm.
Everyone who is both happy and generous is wise or happy and vice versa.
Everyone who is both wise and curious is not patient or humble and vice versa.
Alice is either not patient or not wise.
Someone is either not old or rich.
Someone is creative.
Paul is not tall or curious.
Someone is humble or creative.
Susan is either kind or happy. | Susan is not calm. | contradiction | (![X]:(~old(X)<=>(~tall(X)|calm(X))))&
(((~generous(fred)<~>tall(fred)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>funny(X))=>~funny(X)))&
(![X]:((~patient(X)|old(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)=>(~tall(X)|~generous(X))))&
(![X]:((creative(X)|~strong(X))<=>(~curious(X)<~>brave(X))))&
((~curious(paul))=>((old(john)&creative(john))))&
(![X]:(~strong(X)<=>(~wise(X)&tall(X))))&
(![X]:(~kind(X)<=>(~tall(X)&~wise(X))))&
(![X]:((~happy(X)<~>patient(X))<=>~creative(X)))&
((~brave(alice))=>((quiet(john)<~>calm(john))))&
(![X]:((happy(X)&generous(X))<=>(wise(X)|happy(X))))&
(![X]:((wise(X)&curious(X))<=>(~patient(X)|humble(X))))&
((~patient(alice)<~>~wise(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(creative(X)))&
((~tall(paul)|curious(paul)))&
(?[X]:((humble(X)|creative(X))))&
((kind(susan)<~>happy(susan))) | ~calm(susan) | [
"p0",
"p3",
"p5",
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2037615990083691164599733
% SZS output start Proof for 2037615990083691164599733
1. ! [X0] : (~old(X0) <=> (calm(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((old(X0) | ~patient(X0)) <=> (quiet(X0) | ~brave(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (generous(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : (old(X0) => (~generous(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~curious(X0) <~> brave(X0))) [input p7]
10. ! [X0] : (~strong(X0) <=> (tall(X0) & ~wise(X0))) [input p9]
11. ! [X0] : (~kind(X0) <=> (~wise(X0) & ~tall(X0))) [input p10]
12. ! [X0] : ((~happy(X0) <~> patient(X0)) <=> ~creative(X0)) [input p11]
14. ! [X0] : ((generous(X0) & happy(X0)) <=> (happy(X0) | wise(X0))) [input p13]
15. ! [X0] : ((curious(X0) & wise(X0)) <=> (humble(X0) | ~patient(X0))) [input p14]
21. kind(susan) <~> happy(susan) [input p20]
22. ~calm(susan) [input hypothesis]
26. ! [X0] : ((~generous(X0) | ~tall(X0)) | ~old(X0)) [ennf transformation 7]
27. ! [X0] : (~generous(X0) | ~tall(X0) | ~old(X0)) [flattening 26]
30. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | old(X0))) [nnf transformation 1]
31. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | old(X0))) [flattening 30]
36. ! [X0] : (((old(X0) | ~patient(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (~old(X0) & patient(X0)))) [nnf transformation 4]
37. ! [X0] : ((old(X0) | ~patient(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (~old(X0) & patient(X0)))) [flattening 36]
43. ! [X0] : (((~curious(X0) | ~happy(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [nnf transformation 6]
44. ! [X0] : ((~curious(X0) | ~happy(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [flattening 43]
45. ! [X0] : (((~strong(X0) | creative(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [nnf transformation 8]
46. ! [X0] : ((~strong(X0) | creative(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (~tall(X0) | wise(X0))) & ((tall(X0) & ~wise(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | ~tall(X0) | wise(X0)) & ((tall(X0) & ~wise(X0)) | strong(X0))) [flattening 47]
49. ! [X0] : ((~kind(X0) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [flattening 49]
51. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [nnf transformation 12]
53. ! [X0] : (((generous(X0) & happy(X0)) | (~happy(X0) & ~wise(X0))) & ((happy(X0) | wise(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 14]
54. ! [X0] : (((generous(X0) & happy(X0)) | (~happy(X0) & ~wise(X0))) & (happy(X0) | wise(X0) | ~generous(X0) | ~happy(X0))) [flattening 53]
55. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~curious(X0) | ~wise(X0)))) [nnf transformation 15]
56. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~curious(X0) | ~wise(X0))) [flattening 55]
65. (~happy(susan) | ~kind(susan)) & (happy(susan) | kind(susan)) [nnf transformation 21]
66. ~tall(X0) | calm(X0) | old(X0) [cnf transformation 31]
67. ~old(X0) | tall(X0) [cnf transformation 31]
75. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 37]
83. ~old(X0) | generous(X0) | happy(X0) [cnf transformation 44]
86. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 44]
89. ~generous(X0) | ~tall(X0) | ~old(X0) [cnf transformation 27]
95. ~curious(X0) | creative(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 46]
99. strong(X0) | tall(X0) [cnf transformation 48]
102. ~wise(X0) | kind(X0) [cnf transformation 50]
103. ~kind(X0) | wise(X0) | tall(X0) [cnf transformation 50]
105. ~happy(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 51]
111. ~wise(X0) | happy(X0) [cnf transformation 54]
114. ~happy(X0) | generous(X0) [cnf transformation 54]
116. wise(X0) | patient(X0) [cnf transformation 56]
127. happy(susan) | kind(susan) [cnf transformation 65]
128. ~happy(susan) | ~kind(susan) [cnf transformation 65]
129. ~calm(susan) [cnf transformation 22]
179. ~generous(X0) | ~old(X0) [subsumption resolution 89,67]
242. 25 <=> kind(susan) [avatar definition]
243. kind(susan) <- (25) [avatar component clause 242]
244. ~kind(susan) <- (~25) [avatar component clause 242]
246. 26 <=> happy(susan) [avatar definition]
247. happy(susan) <- (26) [avatar component clause 246]
248. ~happy(susan) <- (~26) [avatar component clause 246]
249. ~25 | ~26 [avatar split clause 128,246,242]
250. 25 | 26 [avatar split clause 127,246,242]
253. patient(X2) | kind(X2) [resolution 116,102]
357. 38 <=> tall(susan) [avatar definition]
358. ~tall(susan) <- (~38) [avatar component clause 357]
359. tall(susan) <- (38) [avatar component clause 357]
361. 39 <=> wise(susan) [avatar definition]
363. wise(susan) <- (39) [avatar component clause 361]
365. generous(susan) <- (26) [resolution 247,114]
369. old(susan) | curious(susan) <- (26) [resolution 365,86]
371. ~old(susan) <- (26) [resolution 365,179]
373. 40 <=> curious(susan) [avatar definition]
375. curious(susan) <- (40) [avatar component clause 373]
377. 41 <=> old(susan) [avatar definition]
378. ~old(susan) <- (~41) [avatar component clause 377]
379. old(susan) <- (41) [avatar component clause 377]
380. 40 | 41 | ~26 [avatar split clause 369,246,377,373]
381. ~41 | ~26 [avatar split clause 371,246,377]
382. wise(susan) | tall(susan) <- (25) [resolution 243,103]
385. calm(susan) | old(susan) <- (38) [resolution 359,66]
387. old(susan) <- (38) [subsumption resolution 385,129]
388. 41 | ~38 [avatar split clause 387,357,377]
389. 38 | 39 | ~25 [avatar split clause 382,242,361,357]
397. happy(susan) <- (39) [resolution 363,111]
400. $false <- (~26, 39) [subsumption resolution 397,248]
401. 26 | ~39 [avatar contradiction clause 400]
403. ~creative(susan) | ~patient(susan) <- (26) [resolution 247,105]
406. 42 <=> creative(susan) [avatar definition]
407. ~creative(susan) <- (~42) [avatar component clause 406]
410. 43 <=> patient(susan) [avatar definition]
411. ~patient(susan) <- (~43) [avatar component clause 410]
412. patient(susan) <- (43) [avatar component clause 410]
414. ~43 | ~42 | ~26 [avatar split clause 403,246,406,410]
467. kind(susan) <- (~43) [resolution 253,411]
468. $false <- (~25, ~43) [subsumption resolution 467,244]
469. 25 | 43 [avatar contradiction clause 468]
471. old(susan) | brave(susan) <- (43) [resolution 412,75]
472. brave(susan) <- (~41, 43) [subsumption resolution 471,378]
473. creative(susan) | ~strong(susan) | ~brave(susan) <- (40) [resolution 375,95]
478. ~strong(susan) | ~brave(susan) <- (40, ~42) [subsumption resolution 473,407]
479. ~strong(susan) <- (40, ~41, ~42, 43) [subsumption resolution 478,472]
643. tall(susan) <- (40, ~41, ~42, 43) [resolution 479,99]
644. $false <- (~38, 40, ~41, ~42, 43) [subsumption resolution 643,358]
645. 38 | ~40 | 41 | 42 | ~43 [avatar contradiction clause 644]
663. generous(susan) | happy(susan) <- (41) [resolution 379,83]
818. generous(susan) <- (~26, 41) [subsumption resolution 663,248]
990. ~old(susan) <- (~26, 41) [resolution 818,179]
991. $false <- (~26, 41) [subsumption resolution 990,379]
992. 26 | ~41 [avatar contradiction clause 991]
993. $false [avatar sat refutation 249,250,380,381,388,389,401,414,469,645,992]
% SZS output end Proof for 2037615990083691164599733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then lucy is not patient or strong and vice versa.
Everyone who is not wise is either not tall or tall and vice versa.
Everyone who is not funny or creative is either wise or happy.
If someone is either not brave or not funny then someone is either generous or not tall.
If someone is not calm or not tall then someone is either humble or not humble.
Everyone who is not rich or not curious is both not tall and not kind and vice versa.
Everyone who is either wise or funny is calm and vice versa.
If john is not humble or brave then someone is not quiet.
If someone is either quiet or funny then alice is not quiet.
Everyone who is not tall or not humble is not tall.
If someone is curious then john is either humble or not funny and vice versa.
Everyone who is tall or not quiet is both not strong and quiet and vice versa.
Everyone who is either not tall or not wise is both not calm and curious and vice versa.
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
John is not kind or calm.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Someone is both happy and quiet.
Fred is either not calm or funny. | John is not strong. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))<=>((~patient(lucy)|strong(lucy))))&
(![X]:(~wise(X)<=>(~tall(X)<~>tall(X))))&
(![X]:((~funny(X)|creative(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>calm(X)))&
(((~humble(john)|brave(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>funny(X))))=>(~quiet(alice)))&
(![X]:((~tall(X)|~humble(X))=>~tall(X)))&
((?[X]:(curious(X)))<=>((humble(john)<~>~funny(john))))&
(![X]:((tall(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
((~kind(john)|calm(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
(?[X]:((happy(X)&quiet(X))))&
((~calm(fred)<~>funny(fred))) | ~strong(john) | [
"p1",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7875209320392970328345391
% SZS output start Proof for 7875209320392970328345391
2. ! [X0] : (~wise(X0) <=> (~tall(X0) <~> tall(X0))) [input p1]
7. ! [X0] : ((wise(X0) <~> funny(X0)) <=> calm(X0)) [input p6]
9. ? [X0] : (quiet(X0) <~> funny(X0)) => ~quiet(alice) [input p8]
12. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (quiet(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (curious(X0) & ~calm(X0))) [input p12]
23. ~strong(john) [input hypothesis]
32. ~quiet(alice) | ! [X0] : (quiet(X0) <=> funny(X0)) [ennf transformation 9]
39. ! [X0] : ((~wise(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | wise(X0))) [nnf transformation 2]
51. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~calm(X0)) & (calm(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 7]
54. ~quiet(alice) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0))) [nnf transformation 32]
59. ! [X0] : (((~quiet(X0) | tall(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~quiet(X0) | tall(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 59]
61. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~curious(X0) | calm(X0))) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 13]
62. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ~curious(X0) | calm(X0)) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [flattening 61]
89. ~wise(X0) | tall(X0) | tall(X0) [cnf transformation 39]
90. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 39]
107. calm(X0) | wise(X0) | ~funny(X0) [cnf transformation 51]
112. ~quiet(alice) | funny(X0) | ~quiet(X0) [cnf transformation 54]
123. quiet(X0) | quiet(X0) [cnf transformation 60]
124. ~quiet(X0) | tall(X0) | ~quiet(X0) | strong(X0) [cnf transformation 60]
126. ~calm(X0) | ~tall(X0) | wise(X0) [cnf transformation 62]
150. ~strong(john) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 123]
152. ~quiet(X0) | tall(X0) | strong(X0) [duplicate literal removal 124]
153. ~wise(X0) | tall(X0) [duplicate literal removal 89]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 90]
183. ~wise(X0) [subsumption resolution 153,154]
204. ~funny(X0) | calm(X0) [subsumption resolution 107,183]
223. 15 <=> quiet(alice) [avatar definition]
225. ~quiet(alice) <- (~15) [avatar component clause 223]
228. 16 <=> ! [X0] : (funny(X0) | ~quiet(X0)) [avatar definition]
229. funny(X0) | ~quiet(X0) <- (16) [avatar component clause 228]
230. 16 | ~15 [avatar split clause 112,223,228]
247. ~calm(X0) | ~tall(X0) [subsumption resolution 126,183]
294. $false <- (~15) [subsumption resolution 225,151]
295. 15 [avatar contradiction clause 294]
298. funny(X0) <- (16) [subsumption resolution 229,151]
302. calm(X0) <- (16) [resolution 204,298]
304. ~tall(X0) <- (16) [resolution 302,247]
318. tall(X0) | strong(X0) [resolution 152,151]
319. strong(X0) <- (16) [subsumption resolution 318,304]
329. $false <- (16) [resolution 319,150]
330. ~16 [avatar contradiction clause 329]
331. $false [avatar sat refutation 230,295,330]
% SZS output end Proof for 7875209320392970328345391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not happy and not humble then someone is funny or strong and vice versa.
Everyone who is tall or not wise is not generous and vice versa.
Everyone who is old is either not happy or old and vice versa.
If someone is funny then someone is both not creative and creative.
Everyone who is happy is both generous and patient and vice versa.
If someone is not happy or not calm then someone is strong or curious and vice versa.
If lucy is happy or not patient then mary is either creative or curious.
Everyone who is wise is both not calm and not creative and vice versa.
If john is either generous or calm then john is both wise and not curious and vice versa.
If mary is both not rich and not generous then someone is not tall or patient.
Everyone who is old or not calm is either not rich or not humble and vice versa.
Everyone who is wise or strong is not strong or not curious and vice versa.
Everyone who is either curious or not old is happy and vice versa.
If susan is humble then someone is either curious or brave and vice versa.
Everyone who is strong or not creative is not kind or strong and vice versa.
Everyone who is either not curious or funny is either not kind or not patient.
Mary is not strong.
Alice is not curious.
Mary is either not tall or kind.
Someone is either not funny or quiet.
Someone is either old or brave. | Susan is not tall. | entailment | ((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:((tall(X)|~wise(X))<=>~generous(X)))&
(![X]:(old(X)<=>(~happy(X)<~>old(X))))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:(happy(X)<=>(generous(X)&patient(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((strong(X)|curious(X)))))&
(((happy(lucy)|~patient(lucy)))=>((creative(mary)<~>curious(mary))))&
(![X]:(wise(X)<=>(~calm(X)&~creative(X))))&
(((generous(john)<~>calm(john)))<=>((wise(john)&~curious(john))))&
(((~rich(mary)&~generous(mary)))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:((old(X)|~calm(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((wise(X)|strong(X))<=>(~strong(X)|~curious(X))))&
(![X]:((curious(X)<~>~old(X))<=>happy(X)))&
((humble(susan))<=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((strong(X)|~creative(X))<=>(~kind(X)|strong(X))))&
(![X]:((~curious(X)<~>funny(X))=>(~kind(X)<~>~patient(X))))&
(~strong(mary))&
(~curious(alice))&
((~tall(mary)<~>kind(mary)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:((old(X)<~>brave(X)))) | ~tall(susan) | [
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2446925082323453626619865
% SZS output start Proof for 2446925082323453626619865
2. ! [X0] : ((~wise(X0) | tall(X0)) <=> ~generous(X0)) [input p1]
3. ! [X0] : (old(X0) <=> (~happy(X0) <~> old(X0))) [input p2]
5. ! [X0] : (happy(X0) <=> (patient(X0) & generous(X0))) [input p4]
22. tall(susan) [input hypothesis]
36. ! [X0] : (((~wise(X0) | tall(X0)) | generous(X0)) & (~generous(X0) | (wise(X0) & ~tall(X0)))) [nnf transformation 2]
37. ! [X0] : ((~wise(X0) | tall(X0) | generous(X0)) & (~generous(X0) | (wise(X0) & ~tall(X0)))) [flattening 36]
38. ! [X0] : ((old(X0) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0)))) & (((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | ~old(X0))) [nnf transformation 3]
42. ! [X0] : ((happy(X0) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | ~happy(X0))) [nnf transformation 5]
43. ! [X0] : ((happy(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | ~happy(X0))) [flattening 42]
80. ~generous(X0) | ~tall(X0) [cnf transformation 37]
84. ~old(X0) | happy(X0) | ~old(X0) [cnf transformation 38]
85. old(X0) | old(X0) | happy(X0) [cnf transformation 38]
89. generous(X0) | ~happy(X0) [cnf transformation 43]
144. tall(susan) [cnf transformation 22]
147. ~old(X0) | happy(X0) [duplicate literal removal 84]
148. old(X0) | happy(X0) [duplicate literal removal 85]
179. happy(X0) [subsumption resolution 147,148]
187. generous(X0) [subsumption resolution 89,179]
295. ~tall(X0) [resolution 80,187]
296. $false [resolution 295,144]
% SZS output end Proof for 2446925082323453626619865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is either calm or funny and vice versa.
If mary is not kind then someone is both calm and old.
If someone is either not calm or not tall then someone is either tall or not rich.
Everyone who is old or not calm is either not brave or creative and vice versa.
Everyone who is either not wise or strong is kind or not brave.
Everyone who is both not patient and rich is old or not strong.
If someone is both not patient and not brave then someone is both not curious and brave and vice versa.
If someone is both not quiet and creative then fred is generous or tall and vice versa.
Everyone who is not wise or not old is either not creative or calm.
Everyone who is both not patient and not quiet is rich.
If someone is both not patient and curious then someone is happy and vice versa.
Everyone who is either not tall or kind is not funny.
Everyone who is both not calm and not patient is both not happy and not kind.
If fred is funny or humble then someone is either not creative or old and vice versa.
Everyone who is either generous or not tall is not old or not creative.
If alice is curious then paul is both rich and creative and vice versa.
Lucy is both funny and not quiet.
Someone is both rich and not old.
Someone is not funny.
Someone is both not humble and calm.
Someone is both generous and rich.
Someone is both tall and not brave.
Someone is generous.
Mary is creative or happy. | Alice is not curious. | neutral | (![X]:(~wise(X)<=>(calm(X)<~>funny(X))))&
((~kind(mary))=>(?[X]:((calm(X)&old(X)))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((old(X)|~calm(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((~wise(X)<~>strong(X))=>(kind(X)|~brave(X))))&
(![X]:((~patient(X)&rich(X))=>(old(X)|~strong(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:((~quiet(X)&creative(X))))<=>((generous(fred)|tall(fred))))&
(![X]:((~wise(X)|~old(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~patient(X)&~quiet(X))=>rich(X)))&
((?[X]:((~patient(X)&curious(X))))<=>(?[X]:(happy(X))))&
(![X]:((~tall(X)<~>kind(X))=>~funny(X)))&
(![X]:((~calm(X)&~patient(X))=>(~happy(X)&~kind(X))))&
(((funny(fred)|humble(fred)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~old(X)|~creative(X))))&
((curious(alice))<=>((rich(paul)&creative(paul))))&
((funny(lucy)&~quiet(lucy)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&calm(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:(generous(X)))&
((creative(mary)|happy(mary))) | ~curious(alice) | [] | null | 0 |
Everyone who is not humble is not generous or strong.
Everyone who is not curious is kind.
Everyone who is both not funny and patient is both not wise and not brave.
Everyone who is not creative or not funny is both not quiet and not patient and vice versa.
If someone is not patient or quiet then someone is rich and vice versa.
Everyone who is both not old and calm is patient or not tall and vice versa.
If someone is not kind or not happy then someone is both not old and brave.
If susan is both curious and funny then someone is either brave or not strong and vice versa.
If susan is both not calm and curious then someone is both not creative and curious.
If someone is both not kind and happy then alice is brave.
If someone is either calm or tall then alice is both not humble and not calm and vice versa.
If susan is either quiet or creative then alice is funny.
Everyone who is happy or not curious is both not calm and funny and vice versa.
Everyone who is either wise or strong is both not funny and funny.
Everyone who is wise or not quiet is both not curious and strong and vice versa.
If someone is both tall and not brave then someone is not strong or happy and vice versa.
Paul is either not strong or not quiet.
Someone is old.
Someone is either not happy or quiet.
Someone is humble.
Lucy is both kind and quiet.
John is either funny or quiet.
Someone is either old or creative.
Someone is both not wise and not patient. | John is strong. | entailment | (![X]:(~humble(X)=>(~generous(X)|strong(X))))&
(![X]:(~curious(X)=>kind(X)))&
(![X]:((~funny(X)&patient(X))=>(~wise(X)&~brave(X))))&
(![X]:((~creative(X)|~funny(X))<=>(~quiet(X)&~patient(X))))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)&calm(X))<=>(patient(X)|~tall(X))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:((~old(X)&brave(X)))))&
(((curious(susan)&funny(susan)))<=>(?[X]:((brave(X)<~>~strong(X)))))&
(((~calm(susan)&curious(susan)))=>(?[X]:((~creative(X)&curious(X)))))&
((?[X]:((~kind(X)&happy(X))))=>(brave(alice)))&
((?[X]:((calm(X)<~>tall(X))))<=>((~humble(alice)&~calm(alice))))&
(((quiet(susan)<~>creative(susan)))=>(funny(alice)))&
(![X]:((happy(X)|~curious(X))<=>(~calm(X)&funny(X))))&
(![X]:((wise(X)<~>strong(X))=>(~funny(X)&funny(X))))&
(![X]:((wise(X)|~quiet(X))<=>(~curious(X)&strong(X))))&
((?[X]:((tall(X)&~brave(X))))<=>(?[X]:((~strong(X)|happy(X)))))&
((~strong(paul)<~>~quiet(paul)))&
(?[X]:(old(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:(humble(X)))&
((kind(lucy)&quiet(lucy)))&
((funny(john)<~>quiet(john)))&
(?[X]:((old(X)<~>creative(X))))&
(?[X]:((~wise(X)&~patient(X)))) | strong(john) | [
"p3",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 310129172383790034624918
% SZS output start Proof for 310129172383790034624918
4. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> (~patient(X0) & ~quiet(X0))) [input p3]
15. ! [X0] : ((~quiet(X0) | wise(X0)) <=> (strong(X0) & ~curious(X0))) [input p14]
22. funny(john) <~> quiet(john) [input p21]
25. ~strong(john) [input hypothesis]
41. ! [X0] : (((~funny(X0) | ~creative(X0)) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | (funny(X0) & creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | ~creative(X0) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | (funny(X0) & creative(X0)))) [flattening 41]
69. ! [X0] : (((~quiet(X0) | wise(X0)) | (~strong(X0) | curious(X0))) & ((strong(X0) & ~curious(X0)) | (quiet(X0) & ~wise(X0)))) [nnf transformation 15]
70. ! [X0] : ((~quiet(X0) | wise(X0) | ~strong(X0) | curious(X0)) & ((strong(X0) & ~curious(X0)) | (quiet(X0) & ~wise(X0)))) [flattening 69]
84. (~quiet(john) | ~funny(john)) & (quiet(john) | funny(john)) [nnf transformation 22]
93. ~quiet(X0) | funny(X0) [cnf transformation 42]
135. quiet(X0) | strong(X0) [cnf transformation 70]
150. ~quiet(john) | ~funny(john) [cnf transformation 84]
155. ~strong(john) [cnf transformation 25]
330. ~quiet(john) [subsumption resolution 150,93]
366. strong(john) [resolution 135,330]
369. $false [subsumption resolution 366,155]
% SZS output end Proof for 310129172383790034624918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not calm and vice versa.
If someone is not curious then someone is not brave or not happy and vice versa.
Everyone who is not strong or kind is either old or not generous.
Everyone who is wise is either not rich or old and vice versa.
Everyone who is either brave or patient is either not kind or not patient and vice versa.
Everyone who is wise or not brave is not strong or funny and vice versa.
If fred is not old then paul is both kind and rich and vice versa.
Everyone who is calm or not happy is happy or generous.
Everyone who is quiet or not curious is not happy and vice versa.
Everyone who is either not patient or happy is either tall or strong and vice versa.
If someone is not funny or not patient then someone is not creative.
Everyone who is tall or not rich is both not funny and funny and vice versa.
If lucy is not creative then fred is not old and vice versa.
If susan is both not patient and patient then someone is either not wise or generous and vice versa.
If lucy is not quiet then someone is quiet.
If fred is either not rich or old then someone is both not happy and rich and vice versa.
Someone is not kind.
Paul is either kind or not humble.
Someone is either funny or wise.
Someone is either not quiet or brave.
Paul is either not wise or funny.
Paul is not tall.
Susan is curious or not happy.
Someone is not generous or not humble. | Fred is patient. | entailment | (![X]:(~old(X)<=>~calm(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~strong(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(~rich(X)<~>old(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~strong(X)|funny(X))))&
((~old(fred))<=>((kind(paul)&rich(paul))))&
(![X]:((calm(X)|~happy(X))=>(happy(X)|generous(X))))&
(![X]:((quiet(X)|~curious(X))<=>~happy(X)))&
(![X]:((~patient(X)<~>happy(X))<=>(tall(X)<~>strong(X))))&
((?[X]:((~funny(X)|~patient(X))))=>(?[X]:(~creative(X))))&
(![X]:((tall(X)|~rich(X))<=>(~funny(X)&funny(X))))&
((~creative(lucy))<=>(~old(fred)))&
(((~patient(susan)&patient(susan)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
((~quiet(lucy))=>(?[X]:(quiet(X))))&
(((~rich(fred)<~>old(fred)))<=>(?[X]:((~happy(X)&rich(X)))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((~wise(paul)<~>funny(paul)))&
(~tall(paul))&
((curious(susan)|~happy(susan)))&
(?[X]:((~generous(X)|~humble(X)))) | patient(fred) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8524052374379481132284110
% SZS output start Proof for 8524052374379481132284110
3. ! [X0] : ((kind(X0) | ~strong(X0)) => (old(X0) <~> ~generous(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> (~rich(X0) <~> old(X0))) [input p3]
8. ! [X0] : ((~happy(X0) | calm(X0)) => (generous(X0) | happy(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | quiet(X0)) <=> ~happy(X0)) [input p8]
10. ! [X0] : ((~patient(X0) <~> happy(X0)) <=> (tall(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((~rich(X0) | tall(X0)) <=> (funny(X0) & ~funny(X0))) [input p11]
14. (patient(susan) & ~patient(susan)) <=> ? [X0] : (~wise(X0) <~> generous(X0)) [input p13]
15. ~quiet(lucy) => ? [X0] : quiet(X0) [input p14]
16. (~rich(fred) <~> old(fred)) <=> ? [X0] : (rich(X0) & ~happy(X0)) [input p15]
25. ~patient(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~generous(X0)) | (~kind(X0) & strong(X0))) [ennf transformation 3]
29. ! [X0] : ((generous(X0) | happy(X0)) | (happy(X0) & ~calm(X0))) [ennf transformation 8]
30. ! [X0] : (generous(X0) | happy(X0) | (happy(X0) & ~calm(X0))) [flattening 29]
32. ? [X0] : quiet(X0) | quiet(lucy) [ennf transformation 15]
39. ! [X0] : (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (~kind(X0) & strong(X0))) [nnf transformation 28]
40. ! [X0] : ((wise(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | ~wise(X0))) [nnf transformation 4]
46. ! [X0] : (((~curious(X0) | quiet(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | quiet(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [flattening 46]
48. ! [X0] : ((((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0)))) & (((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))))) [nnf transformation 10]
52. ! [X0] : (((~rich(X0) | tall(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [nnf transformation 12]
53. ! [X0] : ((~rich(X0) | tall(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [flattening 52]
55. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X0] : ((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~patient(susan) | patient(susan))) [nnf transformation 14]
56. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X0] : ((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ~patient(susan) | patient(susan)) [flattening 55]
57. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X1] : ((~generous(X1) | wise(X1)) & (generous(X1) | ~wise(X1))) | ~patient(susan) | patient(susan)) [rectify 56]
58. ? [X1] : ((~generous(X1) | wise(X1)) & (generous(X1) | ~wise(X1))) => ((~generous(sK3) | wise(sK3)) & (generous(sK3) | ~wise(sK3))) [choice axiom]
59. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(sK3) | wise(sK3)) & (generous(sK3) | ~wise(sK3))) | ~patient(susan) | patient(susan)) [skolemisation 57,58]
60. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
61. quiet(sK4) | quiet(lucy) [skolemisation 32,60]
62. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X0] : (rich(X0) & ~happy(X0)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [nnf transformation 16]
63. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X1] : (rich(X1) & ~happy(X1)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [rectify 62]
64. ? [X1] : (rich(X1) & ~happy(X1)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
65. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & ((rich(sK5) & ~happy(sK5)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [skolemisation 63,64]
85. ~old(X0) | generous(X0) | strong(X0) [cnf transformation 39]
90. ~rich(X0) | wise(X0) | ~old(X0) [cnf transformation 40]
107. generous(X0) | happy(X0) | happy(X0) [cnf transformation 30]
108. ~quiet(X0) | ~happy(X0) [cnf transformation 47]
118. ~strong(X0) | patient(X0) | tall(X0) | ~happy(X0) [cnf transformation 48]
121. ~funny(X0) | ~tall(X0) [cnf transformation 53]
122. ~funny(X0) | rich(X0) [cnf transformation 53]
123. ~tall(X0) | funny(X0) [cnf transformation 53]
124. funny(X0) | rich(X0) [cnf transformation 53]
131. ~patient(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 59]
133. patient(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 59]
134. quiet(sK4) | quiet(lucy) [cnf transformation 61]
139. old(fred) | ~rich(fred) | ~rich(X0) | happy(X0) [cnf transformation 65]
153. ~patient(fred) [cnf transformation 25]
154. generous(X0) | happy(X0) [duplicate literal removal 107]
160. 1 <=> ! [X1] : happy(X1) [avatar definition]
161. happy(X1) <- (1) [avatar component clause 160]
194. 9 <=> old(fred) [avatar definition]
195. old(fred) <- (9) [avatar component clause 194]
212. rich(X0) [subsumption resolution 122,124]
213. ~tall(X0) [subsumption resolution 121,123]
221. 14 <=> ! [X0] : (~wise(X0) | ~generous(X0)) [avatar definition]
222. ~wise(X0) | ~generous(X0) <- (14) [avatar component clause 221]
224. 15 <=> patient(susan) [avatar definition]
227. 14 | 15 [avatar split clause 133,224,221]
232. 14 | ~15 [avatar split clause 131,224,221]
235. 17 <=> quiet(lucy) [avatar definition]
237. quiet(lucy) <- (17) [avatar component clause 235]
239. 18 <=> quiet(sK4) [avatar definition]
241. quiet(sK4) <- (18) [avatar component clause 239]
242. 17 | 18 [avatar split clause 134,239,235]
243. old(fred) | ~rich(X0) | happy(X0) [subsumption resolution 139,212]
244. old(fred) | happy(X0) [subsumption resolution 243,212]
245. 1 | 9 [avatar split clause 244,194,160]
299. ~happy(lucy) <- (17) [resolution 108,237]
332. generous(fred) | strong(fred) <- (9) [resolution 85,195]
334. 33 <=> strong(fred) [avatar definition]
336. strong(fred) <- (33) [avatar component clause 334]
338. 34 <=> generous(fred) [avatar definition]
339. ~generous(fred) <- (~34) [avatar component clause 338]
341. 33 | 34 | ~9 [avatar split clause 332,194,338,334]
343. $false <- (1, 17) [resolution 161,299]
345. ~1 | ~17 [avatar contradiction clause 343]
356. ~happy(sK4) <- (18) [resolution 241,108]
357. $false <- (1, 18) [subsumption resolution 356,161]
358. ~1 | ~18 [avatar contradiction clause 357]
388. ~old(X1) | wise(X1) [resolution 90,212]
464. patient(fred) | tall(fred) | ~happy(fred) <- (33) [resolution 118,336]
466. tall(fred) | ~happy(fred) <- (33) [subsumption resolution 464,153]
467. ~happy(fred) <- (33) [subsumption resolution 466,213]
477. wise(fred) <- (9) [resolution 388,195]
553. ~generous(fred) <- (9, 14) [resolution 477,222]
558. ~34 | ~9 | ~14 [avatar split clause 553,221,194,338]
560. happy(fred) <- (~34) [resolution 339,154]
561. $false <- (33, ~34) [subsumption resolution 560,467]
562. ~33 | 34 [avatar contradiction clause 561]
563. $false [avatar sat refutation 227,232,242,245,341,345,358,558,562]
% SZS output end Proof for 8524052374379481132284110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not tall or tall then mary is not wise or strong. If susan is either strong or not generous then mary is wise. If someone is kind then fred is patient or creative. Everyone who is calm is both old and not calm and vice versa. Everyone who is both strong and not generous is strong or brave. Everyone who is either generous or rich is both creative and rich. Everyone who is not wise or wise is not old or calm. If someone is either strong or not kind then john is not quiet and vice versa. Everyone who is wise is rich. Everyone who is either funny or wise is both creative and not patient. If someone is either rich or creative then fred is strong or not tall and vice versa. Everyone who is not generous or not happy is both not tall and not brave. If someone is wise or not old then john is either not creative or strong and vice versa. Everyone who is either wise or rich is happy or rich and vice versa. If someone is patient or quiet then mary is either not tall or strong and vice versa. Everyone who is not old is not generous or not rich. Someone is not kind. Alice is either calm or not rich. Someone is strong or not happy. Someone is either happy or humble. Susan is happy. Fred is either not old or not funny. | Paul is tall. | contradiction | (((~tall(paul)|tall(paul)))=>((~wise(mary)|strong(mary))))&
(((strong(susan)<~>~generous(susan)))=>(wise(mary)))&
((?[X]:(kind(X)))=>((patient(fred)|creative(fred))))&
(![X]:(calm(X)<=>(old(X)&~calm(X))))&
(![X]:((strong(X)&~generous(X))=>(strong(X)|brave(X))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)&rich(X))))&
(![X]:((~wise(X)|wise(X))=>(~old(X)|calm(X))))&
((?[X]:((strong(X)<~>~kind(X))))<=>(~quiet(john)))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((funny(X)<~>wise(X))=>(creative(X)&~patient(X))))&
((?[X]:((rich(X)<~>creative(X))))<=>((strong(fred)|~tall(fred))))&
(![X]:((~generous(X)|~happy(X))=>(~tall(X)&~brave(X))))&
((?[X]:((wise(X)|~old(X))))<=>((~creative(john)<~>strong(john))))&
(![X]:((wise(X)<~>rich(X))<=>(happy(X)|rich(X))))&
((?[X]:((patient(X)|quiet(X))))<=>((~tall(mary)<~>strong(mary))))&
(![X]:(~old(X)=>(~generous(X)|~rich(X))))&
(?[X]:(~kind(X)))&
((calm(alice)<~>~rich(alice)))&
(?[X]:((strong(X)|~happy(X))))&
(?[X]:((happy(X)<~>humble(X))))&
(happy(susan))&
((~old(fred)<~>~funny(fred))) | tall(paul) | [
"p3",
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6472957495424777430454294
% SZS output start Proof for 6472957495424777430454294
4. ! [X0] : (calm(X0) <=> (~calm(X0) & old(X0))) [input p3]
6. ! [X0] : ((generous(X0) <~> rich(X0)) => (rich(X0) & creative(X0))) [input p5]
12. ! [X0] : ((~happy(X0) | ~generous(X0)) => (~brave(X0) & ~tall(X0))) [input p11]
16. ! [X0] : (~old(X0) => (~rich(X0) | ~generous(X0))) [input p15]
23. tall(paul) [input hypothesis]
31. ! [X0] : ((rich(X0) & creative(X0)) | (generous(X0) <=> rich(X0))) [ennf transformation 6]
36. ! [X0] : ((~brave(X0) & ~tall(X0)) | (happy(X0) & generous(X0))) [ennf transformation 12]
37. ! [X0] : ((~rich(X0) | ~generous(X0)) | old(X0)) [ennf transformation 16]
38. ! [X0] : (~rich(X0) | ~generous(X0) | old(X0)) [flattening 37]
40. ! [X0] : ((calm(X0) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | ~calm(X0))) [nnf transformation 4]
41. ! [X0] : ((calm(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | ~calm(X0))) [flattening 40]
42. ! [X0] : ((rich(X0) & creative(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0)))) [nnf transformation 31]
78. ~calm(X0) | ~calm(X0) [cnf transformation 41]
79. calm(X0) | calm(X0) | ~old(X0) [cnf transformation 41]
83. rich(X0) | rich(X0) | ~generous(X0) [cnf transformation 42]
102. ~tall(X0) | generous(X0) [cnf transformation 36]
124. ~rich(X0) | ~generous(X0) | old(X0) [cnf transformation 38]
134. tall(paul) [cnf transformation 23]
137. ~generous(X0) | rich(X0) [duplicate literal removal 83]
138. ~calm(X0) [duplicate literal removal 78]
139. ~old(X0) | calm(X0) [duplicate literal removal 79]
141. 1 <=> tall(paul) [avatar definition]
142. tall(paul) <- (1) [avatar component clause 141]
282. ~generous(X0) | old(X0) [subsumption resolution 124,137]
313. 1 [avatar split clause 134,141]
314. generous(paul) <- (1) [resolution 102,142]
326. old(paul) <- (1) [resolution 282,314]
345. calm(paul) <- (1) [resolution 326,139]
346. $false <- (1) [subsumption resolution 345,138]
347. ~1 [avatar contradiction clause 346]
348. $false [avatar sat refutation 313,347]
% SZS output end Proof for 6472957495424777430454294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not rich then susan is generous and vice versa. Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. Mary is not patient or humble. Someone is not kind. Someone is not wise. Someone is either old or not rich. Alice is both not curious and happy. Someone is kind. Someone is not funny. | Susan is not happy. | neutral | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((~patient(mary)|humble(mary)))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)<~>~rich(X))))&
((~curious(alice)&happy(alice)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X))) | ~happy(susan) | [] | null | 0 |
If someone is both curious and not wise then john is not patient.
Everyone who is curious or not kind is old.
If fred is not brave then fred is either tall or not old.
Everyone who is curious or rich is either humble or patient and vice versa.
Everyone who is kind is not curious or not tall.
Everyone who is not humble or not quiet is both brave and strong.
If lucy is either not creative or wise then mary is both not old and curious and vice versa.
Everyone who is either rich or not quiet is either kind or calm and vice versa.
If john is either calm or strong then susan is not kind or not curious and vice versa.
Everyone who is calm or not patient is either funny or quiet and vice versa.
Everyone who is both brave and curious is quiet or not funny.
If someone is not creative then paul is not kind or not happy and vice versa.
If john is either kind or humble then someone is either not brave or funny.
Everyone who is strong is either funny or brave.
Everyone who is not calm or not curious is not quiet or not humble.
If someone is brave or creative then someone is both not strong and quiet.
Someone is not quiet.
Someone is either not tall or not happy.
Mary is either happy or not curious.
John is both generous and humble.
Fred is either not funny or rich.
Someone is generous or not funny.
Susan is either generous or quiet.
Someone is wise. | John is funny. | contradiction | ((?[X]:((curious(X)&~wise(X))))=>(~patient(john)))&
(![X]:((curious(X)|~kind(X))=>old(X)))&
((~brave(fred))=>((tall(fred)<~>~old(fred))))&
(![X]:((curious(X)|rich(X))<=>(humble(X)<~>patient(X))))&
(![X]:(kind(X)=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)|~quiet(X))=>(brave(X)&strong(X))))&
(((~creative(lucy)<~>wise(lucy)))<=>((~old(mary)&curious(mary))))&
(![X]:((rich(X)<~>~quiet(X))<=>(kind(X)<~>calm(X))))&
(((calm(john)<~>strong(john)))<=>((~kind(susan)|~curious(susan))))&
(![X]:((calm(X)|~patient(X))<=>(funny(X)<~>quiet(X))))&
(![X]:((brave(X)&curious(X))=>(quiet(X)|~funny(X))))&
((?[X]:(~creative(X)))<=>((~kind(paul)|~happy(paul))))&
(((kind(john)<~>humble(john)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:(strong(X)=>(funny(X)<~>brave(X))))&
(![X]:((~calm(X)|~curious(X))=>(~quiet(X)|~humble(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~strong(X)&quiet(X)))))&
(?[X]:(~quiet(X)))&
(?[X]:((~tall(X)<~>~happy(X))))&
((happy(mary)<~>~curious(mary)))&
((generous(john)&humble(john)))&
((~funny(fred)<~>rich(fred)))&
(?[X]:((generous(X)|~funny(X))))&
((generous(susan)<~>quiet(susan)))&
(?[X]:(wise(X))) | funny(john) | [
"p5",
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8432954507486544111140843
% SZS output start Proof for 8432954507486544111140843
6. ! [X0] : ((~quiet(X0) | ~humble(X0)) => (strong(X0) & brave(X0))) [input p5]
10. ! [X0] : ((~patient(X0) | calm(X0)) <=> (funny(X0) <~> quiet(X0))) [input p9]
14. ! [X0] : (strong(X0) => (funny(X0) <~> brave(X0))) [input p13]
15. ! [X0] : ((~curious(X0) | ~calm(X0)) => (~humble(X0) | ~quiet(X0))) [input p14]
20. humble(john) & generous(john) [input p19]
25. funny(john) [input hypothesis]
32. ! [X0] : ((strong(X0) & brave(X0)) | (quiet(X0) & humble(X0))) [ennf transformation 6]
36. ! [X0] : ((funny(X0) <~> brave(X0)) | ~strong(X0)) [ennf transformation 14]
37. ! [X0] : ((~humble(X0) | ~quiet(X0)) | (curious(X0) & calm(X0))) [ennf transformation 15]
38. ! [X0] : (~humble(X0) | ~quiet(X0) | (curious(X0) & calm(X0))) [flattening 37]
48. ! [X0] : (((~patient(X0) | calm(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (patient(X0) & ~calm(X0)))) [nnf transformation 10]
49. ! [X0] : ((~patient(X0) | calm(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (patient(X0) & ~calm(X0)))) [flattening 48]
58. ! [X0] : (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ~strong(X0)) [nnf transformation 36]
87. quiet(X0) | brave(X0) [cnf transformation 32]
89. strong(X0) | quiet(X0) [cnf transformation 32]
112. ~funny(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 49]
125. ~funny(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 58]
126. ~quiet(X0) | ~humble(X0) | calm(X0) [cnf transformation 38]
138. humble(john) [cnf transformation 20]
145. funny(john) [cnf transformation 25]
193. 11 <=> calm(john) [avatar definition]
195. ~calm(john) <- (~11) [avatar component clause 193]
197. 12 <=> strong(john) [avatar definition]
198. strong(john) <- (12) [avatar component clause 197]
199. ~strong(john) <- (~12) [avatar component clause 197]
230. 18 <=> humble(john) [avatar definition]
231. humble(john) <- (18) [avatar component clause 230]
283. 18 [avatar split clause 138,230]
389. ~quiet(john) | ~calm(john) [resolution 112,145]
406. 49 <=> quiet(john) [avatar definition]
407. quiet(john) <- (49) [avatar component clause 406]
408. ~quiet(john) <- (~49) [avatar component clause 406]
409. ~11 | ~49 [avatar split clause 389,406,193]
427. ~brave(john) | ~strong(john) [resolution 125,145]
432. ~brave(john) <- (12) [subsumption resolution 427,198]
435. brave(john) <- (~49) [resolution 408,87]
436. $false <- (12, ~49) [subsumption resolution 435,432]
437. ~12 | 49 [avatar contradiction clause 436]
452. ~humble(john) | calm(john) <- (49) [resolution 126,407]
455. calm(john) <- (18, 49) [subsumption resolution 452,231]
456. $false <- (~11, 18, 49) [subsumption resolution 455,195]
457. 11 | ~18 | ~49 [avatar contradiction clause 456]
475. quiet(john) <- (~12) [resolution 199,89]
477. $false <- (~12, ~49) [subsumption resolution 475,408]
478. 12 | 49 [avatar contradiction clause 477]
479. $false [avatar sat refutation 283,409,437,457,478]
% SZS output end Proof for 8432954507486544111140843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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