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
|
|---|---|---|---|---|---|---|---|
Everyone who is not strong or not funny is curious or not creative.
If someone is wise then someone is quiet or not calm.
Everyone who is generous is not old or funny and vice versa.
If john is either kind or quiet then susan is either not wise or humble.
If someone is not brave then someone is not calm.
If someone is not calm or not wise then someone is not funny or not patient.
Everyone who is not funny is either quiet or not funny and vice versa.
Everyone who is both wise and not rich is both wise and not humble and vice versa.
Everyone who is both not quiet and not strong is either generous or not curious.
Everyone who is not kind is patient or not wise and vice versa.
Everyone who is not humble is not old.
Everyone who is not happy or calm is both not funny and not curious and vice versa.
Everyone who is calm is not funny and vice versa.
Everyone who is either curious or not funny is both not funny and happy.
If someone is not old then someone is both not humble and rich.
Someone is both tall and not curious.
Someone is not curious.
Someone is not quiet or not old.
Paul is both rich and not quiet.
Someone is rich or curious.
Someone is tall or not calm.
Someone is not old. | Paul is happy. | entailment | (![X]:((~strong(X)|~funny(X))=>(curious(X)|~creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:(generous(X)<=>(~old(X)|funny(X))))&
(((kind(john)<~>quiet(john)))=>((~wise(susan)<~>humble(susan))))&
((?[X]:(~brave(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~calm(X)|~wise(X))))=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:(~funny(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((wise(X)&~rich(X))<=>(wise(X)&~humble(X))))&
(![X]:((~quiet(X)&~strong(X))=>(generous(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(patient(X)|~wise(X))))&
(![X]:(~humble(X)=>~old(X)))&
(![X]:((~happy(X)|calm(X))<=>(~funny(X)&~curious(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(![X]:((curious(X)<~>~funny(X))=>(~funny(X)&happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~humble(X)&rich(X)))))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)|~old(X))))&
((rich(paul)&~quiet(paul)))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:((tall(X)|~calm(X))))&
(?[X]:(~old(X))) | happy(paul) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1628561464469330627795438
% SZS output start Proof for 1628561464469330627795438
12. ! [X0] : ((calm(X0) | ~happy(X0)) <=> (~curious(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((curious(X0) <~> ~funny(X0)) => (happy(X0) & ~funny(X0))) [input p13]
23. ~happy(paul) [input hypothesis]
37. ! [X0] : ((happy(X0) & ~funny(X0)) | (curious(X0) <=> ~funny(X0))) [ennf transformation 14]
51. ! [X0] : (((calm(X0) | ~happy(X0)) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | (~calm(X0) & happy(X0)))) [nnf transformation 12]
52. ! [X0] : ((calm(X0) | ~happy(X0) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | (~calm(X0) & happy(X0)))) [flattening 51]
54. ! [X0] : ((happy(X0) & ~funny(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) [nnf transformation 37]
87. ~funny(X0) | happy(X0) [cnf transformation 52]
89. ~curious(X0) | happy(X0) [cnf transformation 52]
97. happy(X0) | curious(X0) | funny(X0) [cnf transformation 54]
107. ~happy(paul) [cnf transformation 23]
160. happy(X0) | funny(X0) [subsumption resolution 97,89]
161. happy(X0) [subsumption resolution 160,87]
184. $false [subsumption resolution 107,161]
% SZS output end Proof for 1628561464469330627795438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either patient or strong then someone is old or not wise and vice versa.
Everyone who is kind or not generous is humble or kind and vice versa.
If mary is not creative or not funny then paul is either not curious or not patient.
Everyone who is not humble is either patient or wise.
Everyone who is either humble or generous is both rich and not rich and vice versa.
If someone is both not quiet and not creative then john is not strong and vice versa.
Everyone who is either quiet or creative is both calm and not rich.
If someone is tall or happy then alice is not creative or humble.
Everyone who is both not kind and not creative is generous or calm and vice versa.
Everyone who is humble or not kind is either not funny or brave and vice versa.
Everyone who is funny or happy is both not wise and calm and vice versa.
If lucy is not creative then susan is not curious or kind and vice versa.
Everyone who is both patient and rich is patient or not old.
Everyone who is either wise or calm is both kind and not kind.
If john is either tall or not generous then john is either not kind or curious.
Someone is either not quiet or patient.
Someone is patient.
Paul is strong or not wise.
Susan is both quiet and not old.
Fred is curious or not quiet. | Mary is not curious. | neutral | (((patient(mary)<~>strong(mary)))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:((kind(X)|~generous(X))<=>(humble(X)|kind(X))))&
(((~creative(mary)|~funny(mary)))=>((~curious(paul)<~>~patient(paul))))&
(![X]:(~humble(X)=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>generous(X))<=>(rich(X)&~rich(X))))&
((?[X]:((~quiet(X)&~creative(X))))<=>(~strong(john)))&
(![X]:((quiet(X)<~>creative(X))=>(calm(X)&~rich(X))))&
((?[X]:((tall(X)|happy(X))))=>((~creative(alice)|humble(alice))))&
(![X]:((~kind(X)&~creative(X))<=>(generous(X)|calm(X))))&
(![X]:((humble(X)|~kind(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)|happy(X))<=>(~wise(X)&calm(X))))&
((~creative(lucy))<=>((~curious(susan)|kind(susan))))&
(![X]:((patient(X)&rich(X))=>(patient(X)|~old(X))))&
(![X]:((wise(X)<~>calm(X))=>(kind(X)&~kind(X))))&
(((tall(john)<~>~generous(john)))=>((~kind(john)<~>curious(john))))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:(patient(X)))&
((strong(paul)|~wise(paul)))&
((quiet(susan)&~old(susan)))&
((curious(fred)|~quiet(fred))) | ~curious(mary) | [] | null | 0 |
If mary is creative or kind then paul is rich.
Everyone who is both happy and old is either old or quiet and vice versa.
If fred is both strong and not rich then lucy is both not humble and tall and vice versa.
Everyone who is not humble or strong is both not happy and not curious and vice versa.
If paul is not old or funny then someone is not wise and vice versa.
Everyone who is not funny or curious is patient and vice versa.
If someone is either humble or not curious then someone is not kind and vice versa.
If someone is both funny and not curious then susan is either not strong or not old and vice versa.
If someone is brave or patient then someone is both funny and wise and vice versa.
Everyone who is creative is rich.
Everyone who is not strong is generous.
If alice is not patient then paul is either not rich or not kind and vice versa.
If someone is not wise then paul is patient or not funny and vice versa.
If john is not rich or quiet then lucy is either not brave or not tall and vice versa.
Everyone who is not patient or happy is calm or not quiet and vice versa.
Paul is either not curious or rich.
Paul is wise or not wise.
Someone is both not humble and not kind.
Lucy is either calm or not funny.
Fred is either tall or not old.
Someone is both kind and not happy.
Alice is not strong. | Susan is wise. | neutral | (((creative(mary)|kind(mary)))=>(rich(paul)))&
(![X]:((happy(X)&old(X))<=>(old(X)<~>quiet(X))))&
(((strong(fred)&~rich(fred)))<=>((~humble(lucy)&tall(lucy))))&
(![X]:((~humble(X)|strong(X))<=>(~happy(X)&~curious(X))))&
(((~old(paul)|funny(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|curious(X))<=>patient(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((funny(X)&~curious(X))))<=>((~strong(susan)<~>~old(susan))))&
((?[X]:((brave(X)|patient(X))))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(~strong(X)=>generous(X)))&
((~patient(alice))<=>((~rich(paul)<~>~kind(paul))))&
((?[X]:(~wise(X)))<=>((patient(paul)|~funny(paul))))&
(((~rich(john)|quiet(john)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:((~patient(X)|happy(X))<=>(calm(X)|~quiet(X))))&
((~curious(paul)<~>rich(paul)))&
((wise(paul)|~wise(paul)))&
(?[X]:((~humble(X)&~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~strong(alice)) | wise(susan) | [] | null | 0 |
If someone is either brave or happy then mary is not strong.
Everyone who is creative or not old is brave or patient and vice versa.
If someone is both not funny and happy then someone is both not creative and not humble.
If someone is either not old or not funny then alice is either not rich or not wise and vice versa.
Everyone who is creative or calm is brave and vice versa.
If susan is rich then mary is not funny and vice versa.
If paul is not kind or not funny then someone is both strong and not generous and vice versa.
Everyone who is not humble or not creative is both funny and creative.
Everyone who is not old or not kind is both tall and not creative and vice versa.
Everyone who is either brave or curious is not funny or curious and vice versa.
Everyone who is not humble is wise or tall.
Everyone who is tall is both not curious and not strong and vice versa.
Everyone who is both quiet and generous is wise and vice versa.
Everyone who is either not kind or not old is humble.
If alice is either quiet or not funny then someone is both not tall and not wise and vice versa.
John is both quiet and not wise.
Someone is rich.
Fred is creative.
Mary is not rich or quiet.
Someone is either strong or funny. | Alice is rich. | entailment | ((?[X]:((brave(X)<~>happy(X))))=>(~strong(mary)))&
(![X]:((creative(X)|~old(X))<=>(brave(X)|patient(X))))&
((?[X]:((~funny(X)&happy(X))))=>(?[X]:((~creative(X)&~humble(X)))))&
((?[X]:((~old(X)<~>~funny(X))))<=>((~rich(alice)<~>~wise(alice))))&
(![X]:((creative(X)|calm(X))<=>brave(X)))&
((rich(susan))<=>(~funny(mary)))&
(((~kind(paul)|~funny(paul)))<=>(?[X]:((strong(X)&~generous(X)))))&
(![X]:((~humble(X)|~creative(X))=>(funny(X)&creative(X))))&
(![X]:((~old(X)|~kind(X))<=>(tall(X)&~creative(X))))&
(![X]:((brave(X)<~>curious(X))<=>(~funny(X)|curious(X))))&
(![X]:(~humble(X)=>(wise(X)|tall(X))))&
(![X]:(tall(X)<=>(~curious(X)&~strong(X))))&
(![X]:((quiet(X)&generous(X))<=>wise(X)))&
(![X]:((~kind(X)<~>~old(X))=>humble(X)))&
(((quiet(alice)<~>~funny(alice)))<=>(?[X]:((~tall(X)&~wise(X)))))&
((quiet(john)&~wise(john)))&
(?[X]:(rich(X)))&
(creative(fred))&
((~rich(mary)|quiet(mary)))&
(?[X]:((strong(X)<~>funny(X)))) | rich(alice) | [
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7291126957604781798717835
% SZS output start Proof for 7291126957604781798717835
4. ? [X0] : (~old(X0) <~> ~funny(X0)) <=> (~rich(alice) <~> ~wise(alice)) [input p3]
5. ! [X0] : ((calm(X0) | creative(X0)) <=> brave(X0)) [input p4]
7. (~funny(paul) | ~kind(paul)) <=> ? [X0] : (~generous(X0) & strong(X0)) [input p6]
8. ! [X0] : ((~creative(X0) | ~humble(X0)) => (creative(X0) & funny(X0))) [input p7]
9. ! [X0] : ((~kind(X0) | ~old(X0)) <=> (~creative(X0) & tall(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (curious(X0) | ~funny(X0))) [input p9]
12. ! [X0] : (tall(X0) <=> (~strong(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((generous(X0) & quiet(X0)) <=> wise(X0)) [input p12]
15. (quiet(alice) <~> ~funny(alice)) <=> ? [X0] : (~wise(X0) & ~tall(X0)) [input p14]
21. ~rich(alice) [input hypothesis]
25. ! [X0] : ((creative(X0) & funny(X0)) | (creative(X0) & humble(X0))) [ennf transformation 8]
35. (? [X0] : ((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ((~rich(alice) | wise(alice)) & (~wise(alice) | rich(alice)))) & (((wise(alice) | rich(alice)) & (~wise(alice) | ~rich(alice))) | ! [X0] : ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0)))) [nnf transformation 4]
36. (? [X0] : ((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ((~rich(alice) | wise(alice)) & (~wise(alice) | rich(alice)))) & (((wise(alice) | rich(alice)) & (~wise(alice) | ~rich(alice))) | ! [X1] : ((~old(X1) | funny(X1)) & (~funny(X1) | old(X1)))) [rectify 35]
37. ? [X0] : ((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) => ((funny(sK1) | old(sK1)) & (~funny(sK1) | ~old(sK1))) [choice axiom]
38. (((funny(sK1) | old(sK1)) & (~funny(sK1) | ~old(sK1))) | ((~rich(alice) | wise(alice)) & (~wise(alice) | rich(alice)))) & (((wise(alice) | rich(alice)) & (~wise(alice) | ~rich(alice))) | ! [X1] : ((~old(X1) | funny(X1)) & (~funny(X1) | old(X1)))) [skolemisation 36,37]
39. ! [X0] : (((calm(X0) | creative(X0)) | ~brave(X0)) & (brave(X0) | (~calm(X0) & ~creative(X0)))) [nnf transformation 5]
40. ! [X0] : ((calm(X0) | creative(X0) | ~brave(X0)) & (brave(X0) | (~calm(X0) & ~creative(X0)))) [flattening 39]
42. ((~funny(paul) | ~kind(paul)) | ! [X0] : (generous(X0) | ~strong(X0))) & (? [X0] : (~generous(X0) & strong(X0)) | (funny(paul) & kind(paul))) [nnf transformation 7]
43. (~funny(paul) | ~kind(paul) | ! [X0] : (generous(X0) | ~strong(X0))) & (? [X0] : (~generous(X0) & strong(X0)) | (funny(paul) & kind(paul))) [flattening 42]
44. (~funny(paul) | ~kind(paul) | ! [X0] : (generous(X0) | ~strong(X0))) & (? [X1] : (~generous(X1) & strong(X1)) | (funny(paul) & kind(paul))) [rectify 43]
45. ? [X1] : (~generous(X1) & strong(X1)) => (~generous(sK2) & strong(sK2)) [choice axiom]
46. (~funny(paul) | ~kind(paul) | ! [X0] : (generous(X0) | ~strong(X0))) & ((~generous(sK2) & strong(sK2)) | (funny(paul) & kind(paul))) [skolemisation 44,45]
47. ! [X0] : (((~kind(X0) | ~old(X0)) | (creative(X0) | ~tall(X0))) & ((~creative(X0) & tall(X0)) | (kind(X0) & old(X0)))) [nnf transformation 9]
48. ! [X0] : ((~kind(X0) | ~old(X0) | creative(X0) | ~tall(X0)) & ((~creative(X0) & tall(X0)) | (kind(X0) & old(X0)))) [flattening 47]
49. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 10]
50. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [flattening 49]
51. ! [X0] : ((tall(X0) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | ~tall(X0))) [nnf transformation 12]
52. ! [X0] : ((tall(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~tall(X0))) [flattening 51]
53. ! [X0] : (((generous(X0) & quiet(X0)) | ~wise(X0)) & (wise(X0) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 13]
54. ! [X0] : (((generous(X0) & quiet(X0)) | ~wise(X0)) & (wise(X0) | ~generous(X0) | ~quiet(X0))) [flattening 53]
56. (((funny(alice) | ~quiet(alice)) & (~funny(alice) | quiet(alice))) | ! [X0] : (wise(X0) | tall(X0))) & (? [X0] : (~wise(X0) & ~tall(X0)) | ((quiet(alice) | funny(alice)) & (~funny(alice) | ~quiet(alice)))) [nnf transformation 15]
57. (((funny(alice) | ~quiet(alice)) & (~funny(alice) | quiet(alice))) | ! [X0] : (wise(X0) | tall(X0))) & (? [X1] : (~wise(X1) & ~tall(X1)) | ((quiet(alice) | funny(alice)) & (~funny(alice) | ~quiet(alice)))) [rectify 56]
58. ? [X1] : (~wise(X1) & ~tall(X1)) => (~wise(sK3) & ~tall(sK3)) [choice axiom]
59. (((funny(alice) | ~quiet(alice)) & (~funny(alice) | quiet(alice))) | ! [X0] : (wise(X0) | tall(X0))) & ((~wise(sK3) & ~tall(sK3)) | ((quiet(alice) | funny(alice)) & (~funny(alice) | ~quiet(alice)))) [skolemisation 57,58]
76. wise(alice) | rich(alice) | ~old(X1) | funny(X1) [cnf transformation 38]
81. ~creative(X0) | brave(X0) [cnf transformation 40]
87. strong(sK2) | funny(paul) [cnf transformation 46]
89. ~generous(sK2) | funny(paul) [cnf transformation 46]
94. creative(X0) | creative(X0) [cnf transformation 25]
97. ~creative(X0) | old(X0) [cnf transformation 48]
100. curious(X0) | ~funny(X0) | curious(X0) | ~brave(X0) [cnf transformation 50]
105. ~curious(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 50]
108. ~tall(X0) | ~strong(X0) [cnf transformation 52]
111. ~wise(X0) | quiet(X0) [cnf transformation 54]
112. ~wise(X0) | generous(X0) [cnf transformation 54]
120. funny(alice) | ~quiet(alice) | wise(X0) | tall(X0) [cnf transformation 59]
128. ~rich(alice) [cnf transformation 21]
129. curious(X0) | ~funny(X0) | ~brave(X0) [duplicate literal removal 100]
130. ~curious(X0) | ~brave(X0) [duplicate literal removal 105]
131. creative(X0) [duplicate literal removal 94]
158. 7 <=> wise(alice) [avatar definition]
160. wise(alice) <- (7) [avatar component clause 158]
162. 8 <=> rich(alice) [avatar definition]
178. 11 <=> ! [X1] : (~old(X1) | funny(X1)) [avatar definition]
179. ~old(X1) | funny(X1) <- (11) [avatar component clause 178]
180. 11 | 8 | 7 [avatar split clause 76,158,162,178]
205. 17 <=> funny(paul) [avatar definition]
206. funny(paul) <- (17) [avatar component clause 205]
210. 18 <=> generous(sK2) [avatar definition]
212. ~generous(sK2) <- (~18) [avatar component clause 210]
213. 17 | ~18 [avatar split clause 89,210,205]
216. 19 <=> strong(sK2) [avatar definition]
218. strong(sK2) <- (19) [avatar component clause 216]
219. 17 | 19 [avatar split clause 87,216,205]
222. old(X0) [subsumption resolution 97,131]
223. ~funny(X0) | ~brave(X0) [subsumption resolution 129,130]
225. 20 <=> ! [X0] : (wise(X0) | tall(X0)) [avatar definition]
226. tall(X0) | wise(X0) <- (20) [avatar component clause 225]
228. 21 <=> quiet(alice) [avatar definition]
230. ~quiet(alice) <- (~21) [avatar component clause 228]
232. 22 <=> funny(alice) [avatar definition]
233. ~funny(alice) <- (~22) [avatar component clause 232]
234. funny(alice) <- (22) [avatar component clause 232]
235. 20 | ~21 | 22 [avatar split clause 120,232,228,225]
268. ~8 [avatar split clause 128,162]
271. brave(X0) [resolution 81,131]
273. quiet(alice) <- (7) [resolution 111,160]
274. $false <- (7, ~21) [subsumption resolution 273,230]
275. ~7 | 21 [avatar contradiction clause 274]
276. funny(X1) <- (11) [subsumption resolution 179,222]
278. $false <- (11, ~22) [resolution 276,233]
281. ~11 | 22 [avatar contradiction clause 278]
287. ~brave(paul) <- (17) [resolution 223,206]
291. $false <- (17) [subsumption resolution 287,271]
292. ~17 [avatar contradiction clause 291]
302. ~brave(alice) <- (22) [resolution 234,223]
303. $false <- (22) [subsumption resolution 302,271]
304. ~22 [avatar contradiction clause 303]
308. ~strong(X0) | wise(X0) <- (20) [resolution 226,108]
311. wise(sK2) <- (19, 20) [resolution 308,218]
315. generous(sK2) <- (19, 20) [resolution 311,112]
317. $false <- (~18, 19, 20) [subsumption resolution 315,212]
318. 18 | ~19 | ~20 [avatar contradiction clause 317]
319. $false [avatar sat refutation 180,213,219,235,268,275,281,292,304,318]
% SZS output end Proof for 7291126957604781798717835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then john is not tall or old and vice versa.
If susan is tall then susan is either happy or not old and vice versa.
Everyone who is either happy or not humble is not happy or quiet and vice versa.
If someone is both not rich and not humble then lucy is curious.
If john is not rich or calm then someone is not quiet.
Everyone who is both not happy and not humble is curious or not generous.
Everyone who is either not strong or funny is both tall and not rich and vice versa.
Everyone who is both not curious and not humble is either old or kind.
If paul is either not humble or not calm then fred is either tall or not patient.
Everyone who is either wise or happy is creative or not humble and vice versa.
If susan is either generous or old then someone is not quiet or not generous.
Everyone who is curious or not calm is both strong and patient and vice versa.
Everyone who is either not old or not tall is calm and vice versa.
If lucy is both not strong and not rich then someone is quiet or not generous and vice versa.
Everyone who is tall is not quiet or rich.
If fred is either not rich or not strong then someone is both quiet and rich.
Someone is not funny.
Susan is patient.
Someone is either quiet or not old.
Alice is not rich.
Someone is either not funny or tall.
Someone is either not curious or creative.
Someone is either not strong or not happy. | Fred is strong. | neutral | ((~old(alice))<=>((~tall(john)|old(john))))&
((tall(susan))<=>((happy(susan)<~>~old(susan))))&
(![X]:((happy(X)<~>~humble(X))<=>(~happy(X)|quiet(X))))&
((?[X]:((~rich(X)&~humble(X))))=>(curious(lucy)))&
(((~rich(john)|calm(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&~humble(X))=>(curious(X)|~generous(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(tall(X)&~rich(X))))&
(![X]:((~curious(X)&~humble(X))=>(old(X)<~>kind(X))))&
(((~humble(paul)<~>~calm(paul)))=>((tall(fred)<~>~patient(fred))))&
(![X]:((wise(X)<~>happy(X))<=>(creative(X)|~humble(X))))&
(((generous(susan)<~>old(susan)))=>(?[X]:((~quiet(X)|~generous(X)))))&
(![X]:((curious(X)|~calm(X))<=>(strong(X)&patient(X))))&
(![X]:((~old(X)<~>~tall(X))<=>calm(X)))&
(((~strong(lucy)&~rich(lucy)))<=>(?[X]:((quiet(X)|~generous(X)))))&
(![X]:(tall(X)=>(~quiet(X)|rich(X))))&
(((~rich(fred)<~>~strong(fred)))=>(?[X]:((quiet(X)&rich(X)))))&
(?[X]:(~funny(X)))&
(patient(susan))&
(?[X]:((quiet(X)<~>~old(X))))&
(~rich(alice))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((~curious(X)<~>creative(X))))&
(?[X]:((~strong(X)<~>~happy(X)))) | strong(fred) | [] | null | 0 |
If mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not happy or not calm is either not tall or not brave.
If susan is both not humble and generous then someone is both rich and not humble.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
John is both not quiet and not wise.
Someone is brave.
Alice is both not wise and not generous.
Susan is not patient or strong.
Someone is not quiet or generous. | Paul is not creative. | entailment | ((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((~happy(X)|~calm(X))=>(~tall(X)<~>~brave(X))))&
(((~humble(susan)&generous(susan)))=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
((~quiet(john)&~wise(john)))&
(?[X]:(brave(X)))&
((~wise(alice)&~generous(alice)))&
((~patient(susan)|strong(susan)))&
(?[X]:((~quiet(X)|generous(X)))) | ~creative(paul) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1809324495436794675941658
% SZS output start Proof for 1809324495436794675941658
4. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p3]
5. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p4]
6. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> wise(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p7]
11. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p10]
12. ! [X0] : (~rich(X0) <=> humble(X0)) [input p11]
22. creative(paul) [input hypothesis]
38. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 38]
40. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 5]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 40]
42. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
43. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 41,42]
44. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 6]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 44]
46. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK2) | calm(sK2)) [choice axiom]
47. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK2) | calm(sK2)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 7]
49. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 8]
50. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 49]
59. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 11]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 59]
61. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 12]
74. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
75. ~humble(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
76. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
77. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
84. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
86. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
91. strong(paul) | ~quiet(paul) | rich(X0) [cnf transformation 47]
93. ~strong(paul) | quiet(paul) | rich(X0) [cnf transformation 47]
94. old(X0) | wise(X0) [cnf transformation 48]
95. ~old(X0) | ~wise(X0) [cnf transformation 48]
96. old(X0) | creative(X0) [cnf transformation 50]
98. ~old(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 50]
107. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 60]
109. ~old(X0) | ~humble(X0) [cnf transformation 60]
110. rich(X0) | humble(X0) [cnf transformation 61]
111. ~rich(X0) | ~humble(X0) [cnf transformation 61]
125. creative(paul) [cnf transformation 22]
157. 8 <=> humble(mary) [avatar definition]
158. humble(mary) <- (8) [avatar component clause 157]
159. ~humble(mary) <- (~8) [avatar component clause 157]
161. 9 <=> wise(mary) [avatar definition]
162. wise(mary) <- (9) [avatar component clause 161]
163. ~wise(mary) <- (~9) [avatar component clause 161]
166. 10 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
167. ~rich(X0) | happy(X0) <- (10) [avatar component clause 166]
168. 10 | ~8 | ~9 [avatar split clause 86,161,157,166]
170. 10 | 8 | 9 [avatar split clause 84,161,157,166]
184. 13 <=> ! [X0] : rich(X0) [avatar definition]
185. rich(X0) <- (13) [avatar component clause 184]
187. 14 <=> quiet(paul) [avatar definition]
188. ~quiet(paul) <- (~14) [avatar component clause 187]
189. quiet(paul) <- (14) [avatar component clause 187]
191. 15 <=> strong(paul) [avatar definition]
192. strong(paul) <- (15) [avatar component clause 191]
193. ~strong(paul) <- (~15) [avatar component clause 191]
194. 13 | 14 | ~15 [avatar split clause 93,191,187,184]
199. 13 | ~14 | 15 [avatar split clause 91,191,187,184]
236. 24 <=> ! [X1] : (~wise(X1) | humble(X1)) [avatar definition]
237. ~wise(X1) | humble(X1) <- (24) [avatar component clause 236]
244. 26 <=> ! [X1] : (~humble(X1) | wise(X1)) [avatar definition]
245. ~humble(X1) | wise(X1) <- (26) [avatar component clause 244]
247. old(X0) | humble(X0) [subsumption resolution 107,96]
289. ~humble(X1) | wise(X1) [resolution 109,94]
290. 26 [avatar split clause 289,244]
295. humble(X0) | happy(X0) <- (10) [resolution 167,110]
299. humble(X1) | ~wise(X1) [resolution 247,95]
300. 24 [avatar split clause 299,236]
348. ~rich(X0) | ~creative(X0) | humble(X0) [resolution 98,247]
351. ~rich(X0) | ~creative(X0) [subsumption resolution 348,111]
396. happy(X0) | ~strong(X0) | ~quiet(X0) <- (10) [resolution 295,75]
397. happy(X1) | quiet(X1) | strong(X1) <- (10) [resolution 295,74]
400. ~quiet(X0) | ~strong(X0) <- (10) [subsumption resolution 396,77]
401. quiet(X1) | strong(X1) <- (10) [subsumption resolution 397,76]
428. strong(paul) <- (10, ~14) [resolution 401,188]
434. $false <- (10, ~14, ~15) [subsumption resolution 428,193]
435. ~10 | 14 | 15 [avatar contradiction clause 434]
441. ~strong(paul) <- (10, 14) [resolution 189,400]
443. $false <- (10, 14, 15) [subsumption resolution 441,192]
444. ~10 | ~14 | ~15 [avatar contradiction clause 443]
445. ~creative(X0) <- (13) [resolution 185,351]
460. $false <- (13) [resolution 445,125]
461. ~13 [avatar contradiction clause 460]
500. wise(mary) <- (8, 26) [resolution 158,245]
503. $false <- (8, ~9, 26) [subsumption resolution 500,163]
504. ~8 | 9 | ~26 [avatar contradiction clause 503]
506. humble(mary) <- (9, 24) [resolution 162,237]
507. $false <- (~8, 9, 24) [subsumption resolution 506,159]
508. 8 | ~9 | ~24 [avatar contradiction clause 507]
509. $false [avatar sat refutation 168,170,194,199,290,300,435,444,461,504,508]
% SZS output end Proof for 1809324495436794675941658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not strong is both not wise and not happy.
If someone is either funny or strong then alice is not generous or calm.
If paul is either patient or not brave then someone is not strong.
Everyone who is calm or old is either strong or quiet and vice versa.
Everyone who is creative is both brave and not quiet and vice versa.
Everyone who is not wise is either not creative or not tall and vice versa.
If mary is either patient or not kind then lucy is happy or old and vice versa.
If susan is both not curious and not wise then john is either happy or not funny.
Everyone who is both not creative and curious is either brave or not brave and vice versa.
If fred is not generous then lucy is either tall or not calm.
If someone is not rich or not patient then someone is both funny and not quiet and vice versa.
Everyone who is both not kind and not generous is not wise or not funny.
If someone is not funny or calm then someone is kind or not creative and vice versa.
If someone is both not wise and generous then john is both not curious and strong.
Everyone who is both calm and not kind is both calm and curious.
Everyone who is both not kind and brave is not old or not quiet and vice versa.
Susan is either brave or creative.
Paul is either not quiet or quiet.
Someone is not happy or not calm.
Susan is either creative or not old.
Paul is either not quiet or not strong.
Lucy is both curious and funny.
Someone is either old or not generous. | Paul is not wise. | entailment | (![X]:((~funny(X)|~strong(X))=>(~wise(X)&~happy(X))))&
((?[X]:((funny(X)<~>strong(X))))=>((~generous(alice)|calm(alice))))&
(((patient(paul)<~>~brave(paul)))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|old(X))<=>(strong(X)<~>quiet(X))))&
(![X]:(creative(X)<=>(brave(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(~creative(X)<~>~tall(X))))&
(((patient(mary)<~>~kind(mary)))<=>((happy(lucy)|old(lucy))))&
(((~curious(susan)&~wise(susan)))=>((happy(john)<~>~funny(john))))&
(![X]:((~creative(X)&curious(X))<=>(brave(X)<~>~brave(X))))&
((~generous(fred))=>((tall(lucy)<~>~calm(lucy))))&
((?[X]:((~rich(X)|~patient(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(![X]:((~kind(X)&~generous(X))=>(~wise(X)|~funny(X))))&
((?[X]:((~funny(X)|calm(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((~wise(X)&generous(X))))=>((~curious(john)&strong(john))))&
(![X]:((calm(X)&~kind(X))=>(calm(X)&curious(X))))&
(![X]:((~kind(X)&brave(X))<=>(~old(X)|~quiet(X))))&
((brave(susan)<~>creative(susan)))&
((~quiet(paul)<~>quiet(paul)))&
(?[X]:((~happy(X)|~calm(X))))&
((creative(susan)<~>~old(susan)))&
((~quiet(paul)<~>~strong(paul)))&
((curious(lucy)&funny(lucy)))&
(?[X]:((old(X)<~>~generous(X)))) | ~wise(paul) | [
"p0",
"p4",
"p8",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7399155150448192440835091
% SZS output start Proof for 7399155150448192440835091
1. ! [X0] : ((~strong(X0) | ~funny(X0)) => (~happy(X0) & ~wise(X0))) [input p0]
5. ! [X0] : (creative(X0) <=> (~quiet(X0) & brave(X0))) [input p4]
9. ! [X0] : ((curious(X0) & ~creative(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p8]
16. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (~quiet(X0) | ~old(X0))) [input p15]
21. ~quiet(paul) <~> ~strong(paul) [input p20]
24. wise(paul) [input hypothesis]
27. ! [X0] : ((~happy(X0) & ~wise(X0)) | (strong(X0) & funny(X0))) [ennf transformation 1]
45. ! [X0] : ((creative(X0) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | ~creative(X0))) [nnf transformation 5]
46. ! [X0] : ((creative(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~creative(X0))) [flattening 45]
51. ! [X0] : (((curious(X0) & ~creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~curious(X0) | creative(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~curious(X0) | creative(X0))) [flattening 51]
64. ! [X0] : (((brave(X0) & ~kind(X0)) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 16]
65. ! [X0] : (((brave(X0) & ~kind(X0)) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ~brave(X0) | kind(X0))) [flattening 64]
71. (strong(paul) | quiet(paul)) & (~strong(paul) | ~quiet(paul)) [nnf transformation 21]
76. ~wise(X0) | strong(X0) [cnf transformation 27]
89. ~creative(X0) | brave(X0) [cnf transformation 46]
91. ~brave(X0) | quiet(X0) | creative(X0) [cnf transformation 46]
106. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
130. quiet(X0) | brave(X0) [cnf transformation 65]
138. ~strong(paul) | ~quiet(paul) [cnf transformation 71]
144. wise(paul) [cnf transformation 24]
145. ~creative(X0) | ~brave(X0) [duplicate literal removal 106]
166. 5 <=> brave(paul) [avatar definition]
168. brave(paul) <- (5) [avatar component clause 166]
219. ~creative(X0) [subsumption resolution 145,89]
301. 33 <=> quiet(paul) [avatar definition]
302. ~quiet(paul) <- (~33) [avatar component clause 301]
305. 34 <=> strong(paul) [avatar definition]
309. ~33 | ~34 [avatar split clause 138,305,301]
327. strong(paul) [resolution 76,144]
330. 34 [avatar split clause 327,305]
334. brave(paul) <- (~33) [resolution 130,302]
335. 5 | 33 [avatar split clause 334,301,166]
346. quiet(paul) | creative(paul) <- (5) [resolution 91,168]
351. creative(paul) <- (5, ~33) [subsumption resolution 346,302]
352. $false <- (5, ~33) [subsumption resolution 351,219]
353. ~5 | 33 [avatar contradiction clause 352]
360. $false [avatar sat refutation 309,330,335,353]
% SZS output end Proof for 7399155150448192440835091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not creative is either creative or humble.
If someone is either quiet or calm then mary is humble or funny and vice versa.
Everyone who is both humble and strong is generous or funny and vice versa.
Everyone who is not tall or kind is either funny or kind.
If someone is not curious then someone is either wise or not kind and vice versa.
If someone is both kind and funny then susan is calm and vice versa.
If someone is calm or kind then someone is not brave.
If someone is either tall or old then paul is calm.
If mary is not patient or rich then someone is old or not old and vice versa.
Everyone who is either kind or not kind is both not creative and not wise and vice versa.
Everyone who is creative or kind is not happy or generous and vice versa.
If someone is either not curious or strong then someone is not happy or not tall and vice versa.
Everyone who is both not funny and tall is not calm or not creative.
If someone is both not generous and patient then someone is not patient or not generous and vice versa.
Everyone who is both not patient and rich is both generous and happy.
Everyone who is both not tall and tall is either not humble or not generous and vice versa.
Fred is either kind or funny.
Someone is not quiet.
Susan is both not tall and patient.
Alice is generous.
Lucy is kind or not happy.
Someone is curious.
Someone is either not quiet or not strong.
Someone is not funny or not strong. | Susan is patient. | entailment | (![X]:((creative(X)&~creative(X))=>(creative(X)<~>humble(X))))&
((?[X]:((quiet(X)<~>calm(X))))<=>((humble(mary)|funny(mary))))&
(![X]:((humble(X)&strong(X))<=>(generous(X)|funny(X))))&
(![X]:((~tall(X)|kind(X))=>(funny(X)<~>kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
((?[X]:((kind(X)&funny(X))))<=>(calm(susan)))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)<~>old(X))))=>(calm(paul)))&
(((~patient(mary)|rich(mary)))<=>(?[X]:((old(X)|~old(X)))))&
(![X]:((kind(X)<~>~kind(X))<=>(~creative(X)&~wise(X))))&
(![X]:((creative(X)|kind(X))<=>(~happy(X)|generous(X))))&
((?[X]:((~curious(X)<~>strong(X))))<=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~funny(X)&tall(X))=>(~calm(X)|~creative(X))))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~patient(X)&rich(X))=>(generous(X)&happy(X))))&
(![X]:((~tall(X)&tall(X))<=>(~humble(X)<~>~generous(X))))&
((kind(fred)<~>funny(fred)))&
(?[X]:(~quiet(X)))&
((~tall(susan)&patient(susan)))&
(generous(alice))&
((kind(lucy)|~happy(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~funny(X)|~strong(X)))) | patient(susan) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5327643108930577181317760
% SZS output start Proof for 5327643108930577181317760
19. patient(susan) & ~tall(susan) [input p18]
25. ~patient(susan) [input hypothesis]
153. patient(susan) [cnf transformation 19]
160. ~patient(susan) [cnf transformation 25]
353. $false [subsumption resolution 160,153]
% SZS output end Proof for 5327643108930577181317760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and not brave.
If someone is both strong and not humble then paul is both not creative and not old and vice versa.
Everyone who is not creative or strong is either kind or not humble.
Everyone who is both humble and brave is not creative and vice versa.
Everyone who is either brave or humble is rich.
Everyone who is not happy or not old is either not curious or brave.
Everyone who is both not generous and calm is humble and vice versa.
If someone is either patient or not patient then susan is not quiet or not old.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
Mary is both wise and creative.
Someone is not humble.
Fred is either not brave or not patient.
John is not curious or brave.
Mary is both not curious and tall.
Fred is not creative or curious.
John is both not strong and not kind. | Paul is not calm. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:((strong(X)&~humble(X))))<=>((~creative(paul)&~old(paul))))&
(![X]:((~creative(X)|strong(X))=>(kind(X)<~>~humble(X))))&
(![X]:((humble(X)&brave(X))<=>~creative(X)))&
(![X]:((brave(X)<~>humble(X))=>rich(X)))&
(![X]:((~happy(X)|~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((wise(mary)&creative(mary)))&
(?[X]:(~humble(X)))&
((~brave(fred)<~>~patient(fred)))&
((~curious(john)|brave(john)))&
((~curious(mary)&tall(mary)))&
((~creative(fred)|curious(fred)))&
((~strong(john)&~kind(john))) | ~calm(paul) | [] | null | 0 |
Everyone who is not quiet is either brave or not creative.
If alice is not patient then someone is either not rich or rich and vice versa.
If john is both funny and not wise then someone is quiet or not creative and vice versa.
If someone is either not funny or curious then paul is both strong and not curious and vice versa.
Everyone who is either quiet or humble is happy.
Everyone who is both not funny and curious is not old or not curious.
If fred is both not quiet and not tall then someone is either tall or not wise and vice versa.
If someone is brave then susan is both curious and funny and vice versa.
Everyone who is not rich is both curious and kind and vice versa.
Everyone who is both not rich and funny is happy and vice versa.
Everyone who is not funny is not calm or not creative.
If someone is not strong or wise then someone is patient or not wise and vice versa.
Everyone who is either not quiet or not patient is either happy or tall and vice versa.
If someone is both calm and wise then someone is either not strong or happy.
Everyone who is either brave or curious is either not curious or kind and vice versa.
If someone is either strong or calm then someone is either not strong or not brave and vice versa.
Someone is not rich.
Paul is not strong.
Someone is wise or rich.
Lucy is not wise or humble.
Fred is calm.
Mary is either old or not tall.
Someone is wise. | John is not brave. | entailment | (![X]:(~quiet(X)=>(brave(X)<~>~creative(X))))&
((~patient(alice))<=>(?[X]:((~rich(X)<~>rich(X)))))&
(((funny(john)&~wise(john)))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((~funny(X)<~>curious(X))))<=>((strong(paul)&~curious(paul))))&
(![X]:((quiet(X)<~>humble(X))=>happy(X)))&
(![X]:((~funny(X)&curious(X))=>(~old(X)|~curious(X))))&
(((~quiet(fred)&~tall(fred)))<=>(?[X]:((tall(X)<~>~wise(X)))))&
((?[X]:(brave(X)))<=>((curious(susan)&funny(susan))))&
(![X]:(~rich(X)<=>(curious(X)&kind(X))))&
(![X]:((~rich(X)&funny(X))<=>happy(X)))&
(![X]:(~funny(X)=>(~calm(X)|~creative(X))))&
((?[X]:((~strong(X)|wise(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(happy(X)<~>tall(X))))&
((?[X]:((calm(X)&wise(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((brave(X)<~>curious(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(?[X]:(~rich(X)))&
(~strong(paul))&
(?[X]:((wise(X)|rich(X))))&
((~wise(lucy)|humble(lucy)))&
(calm(fred))&
((old(mary)<~>~tall(mary)))&
(?[X]:(wise(X))) | ~brave(john) | [
"p3",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2518367919786185226576979
% SZS output start Proof for 2518367919786185226576979
4. ? [X0] : (~funny(X0) <~> curious(X0)) <=> (~curious(paul) & strong(paul)) [input p3]
8. ? [X0] : brave(X0) <=> (funny(susan) & curious(susan)) [input p7]
18. ~strong(paul) [input p17]
24. brave(john) [input hypothesis]
45. (? [X0] : ((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | (curious(paul) | ~strong(paul))) & ((~curious(paul) & strong(paul)) | ! [X0] : ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [nnf transformation 4]
46. (? [X0] : ((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | curious(paul) | ~strong(paul)) & ((~curious(paul) & strong(paul)) | ! [X0] : ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [flattening 45]
47. (? [X0] : ((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | curious(paul) | ~strong(paul)) & ((~curious(paul) & strong(paul)) | ! [X1] : ((~funny(X1) | ~curious(X1)) & (curious(X1) | funny(X1)))) [rectify 46]
48. ? [X0] : ((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) => ((~curious(sK2) | funny(sK2)) & (curious(sK2) | ~funny(sK2))) [choice axiom]
49. (((~curious(sK2) | funny(sK2)) & (curious(sK2) | ~funny(sK2))) | curious(paul) | ~strong(paul)) & ((~curious(paul) & strong(paul)) | ! [X1] : ((~funny(X1) | ~curious(X1)) & (curious(X1) | funny(X1)))) [skolemisation 47,48]
56. (? [X0] : brave(X0) | (~funny(susan) | ~curious(susan))) & ((funny(susan) & curious(susan)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
57. (? [X0] : brave(X0) | ~funny(susan) | ~curious(susan)) & ((funny(susan) & curious(susan)) | ! [X0] : ~brave(X0)) [flattening 56]
58. (? [X0] : brave(X0) | ~funny(susan) | ~curious(susan)) & ((funny(susan) & curious(susan)) | ! [X1] : ~brave(X1)) [rectify 57]
59. ? [X0] : brave(X0) => brave(sK4) [choice axiom]
60. (brave(sK4) | ~funny(susan) | ~curious(susan)) & ((funny(susan) & curious(susan)) | ! [X1] : ~brave(X1)) [skolemisation 58,59]
100. strong(paul) | ~funny(X1) | ~curious(X1) [cnf transformation 49]
114. curious(susan) | ~brave(X1) [cnf transformation 60]
115. funny(susan) | ~brave(X1) [cnf transformation 60]
155. ~strong(paul) [cnf transformation 18]
162. brave(john) [cnf transformation 24]
210. 10 <=> strong(paul) [avatar definition]
228. 14 <=> ! [X1] : (~funny(X1) | ~curious(X1)) [avatar definition]
229. ~curious(X1) | ~funny(X1) <- (14) [avatar component clause 228]
235. 14 | 10 [avatar split clause 100,210,228]
266. 22 <=> curious(susan) [avatar definition]
267. curious(susan) <- (22) [avatar component clause 266]
270. 23 <=> funny(susan) [avatar definition]
279. 25 <=> ! [X1] : ~brave(X1) [avatar definition]
280. ~brave(X1) <- (25) [avatar component clause 279]
281. 25 | 23 [avatar split clause 115,270,279]
282. 25 | 22 [avatar split clause 114,266,279]
366. ~10 [avatar split clause 155,210]
395. ~funny(susan) <- (14, 22) [resolution 229,267]
399. ~23 | ~14 | ~22 [avatar split clause 395,266,228,270]
400. $false <- (25) [resolution 280,162]
403. ~25 [avatar contradiction clause 400]
404. $false [avatar sat refutation 235,281,282,366,399,403]
% SZS output end Proof for 2518367919786185226576979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not curious is either rich or not happy.
Everyone who is wise or not generous is either not brave or not tall.
If someone is either curious or not strong then someone is either rich or not funny.
If alice is either strong or not rich then paul is not wise and vice versa.
If fred is not rich or not strong then mary is not patient.
Everyone who is both generous and strong is both humble and rich and vice versa.
Everyone who is curious is both generous and wise.
Everyone who is not rich or not creative is both patient and brave.
If john is calm or creative then paul is both kind and not generous.
If john is kind then john is rich or not patient.
Everyone who is either humble or kind is both not brave and wise and vice versa.
If susan is brave or kind then someone is quiet.
If lucy is either not quiet or funny then alice is generous and vice versa.
If someone is calm or not tall then john is patient and vice versa.
Everyone who is not kind is wise or generous.
If someone is either patient or not strong then someone is either not funny or calm and vice versa.
Lucy is not calm.
Someone is both curious and creative.
Paul is both brave and not curious.
Someone is either not creative or kind.
Fred is either not patient or rich.
Lucy is both patient and not happy.
Someone is old.
Paul is both rich and calm. | John is not creative. | entailment | (![X]:((brave(X)&~curious(X))=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|~generous(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:((curious(X)<~>~strong(X))))=>(?[X]:((rich(X)<~>~funny(X)))))&
(((strong(alice)<~>~rich(alice)))<=>(~wise(paul)))&
(((~rich(fred)|~strong(fred)))=>(~patient(mary)))&
(![X]:((generous(X)&strong(X))<=>(humble(X)&rich(X))))&
(![X]:(curious(X)=>(generous(X)&wise(X))))&
(![X]:((~rich(X)|~creative(X))=>(patient(X)&brave(X))))&
(((calm(john)|creative(john)))=>((kind(paul)&~generous(paul))))&
((kind(john))=>((rich(john)|~patient(john))))&
(![X]:((humble(X)<~>kind(X))<=>(~brave(X)&wise(X))))&
(((brave(susan)|kind(susan)))=>(?[X]:(quiet(X))))&
(((~quiet(lucy)<~>funny(lucy)))<=>(generous(alice)))&
((?[X]:((calm(X)|~tall(X))))<=>(patient(john)))&
(![X]:(~kind(X)=>(wise(X)|generous(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(~calm(lucy))&
(?[X]:((curious(X)&creative(X))))&
((brave(paul)&~curious(paul)))&
(?[X]:((~creative(X)<~>kind(X))))&
((~patient(fred)<~>rich(fred)))&
((patient(lucy)&~happy(lucy)))&
(?[X]:(old(X)))&
((rich(paul)&calm(paul))) | ~creative(john) | [
"p5",
"p8",
"p10",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4108755348954190282279435
% SZS output start Proof for 4108755348954190282279435
6. ! [X0] : ((strong(X0) & generous(X0)) <=> (rich(X0) & humble(X0))) [input p5]
9. (creative(john) | calm(john)) => (~generous(paul) & kind(paul)) [input p8]
11. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (wise(X0) & ~brave(X0))) [input p10]
19. ~curious(paul) & brave(paul) [input p18]
24. calm(paul) & rich(paul) [input p23]
25. creative(john) [input hypothesis]
36. (~generous(paul) & kind(paul)) | (~creative(john) & ~calm(john)) [ennf transformation 9]
49. ! [X0] : (((strong(X0) & generous(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 6]
50. ! [X0] : (((strong(X0) & generous(X0)) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | ~strong(X0) | ~generous(X0))) [flattening 49]
51. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [flattening 51]
89. ~humble(X0) | ~rich(X0) | generous(X0) [cnf transformation 50]
98. kind(paul) | ~creative(john) [cnf transformation 36]
100. ~generous(paul) | ~creative(john) [cnf transformation 36]
103. ~kind(X0) | humble(X0) | ~brave(X0) [cnf transformation 52]
129. brave(paul) [cnf transformation 19]
137. rich(paul) [cnf transformation 24]
139. creative(john) [cnf transformation 25]
189. 11 <=> creative(john) [avatar definition]
193. 12 <=> generous(paul) [avatar definition]
195. ~generous(paul) <- (~12) [avatar component clause 193]
196. ~11 | ~12 [avatar split clause 100,193,189]
203. 14 <=> kind(paul) [avatar definition]
205. kind(paul) <- (14) [avatar component clause 203]
206. ~11 | 14 [avatar split clause 98,203,189]
318. 11 [avatar split clause 139,189]
362. humble(paul) | ~brave(paul) <- (14) [resolution 103,205]
363. humble(paul) <- (14) [subsumption resolution 362,129]
367. ~rich(paul) | generous(paul) <- (14) [resolution 363,89]
369. generous(paul) <- (14) [subsumption resolution 367,137]
370. $false <- (~12, 14) [subsumption resolution 369,195]
371. 12 | ~14 [avatar contradiction clause 370]
372. $false [avatar sat refutation 196,206,318,371]
% SZS output end Proof for 4108755348954190282279435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not rich is not brave and vice versa.
If someone is either not patient or not funny then lucy is either not wise or strong.
Everyone who is both not curious and not calm is either not rich or not old.
If susan is rich or patient then alice is not old or not creative and vice versa.
Everyone who is both not patient and not strong is either curious or not rich and vice versa.
Everyone who is kind or tall is either not rich or not happy and vice versa.
Everyone who is either patient or not calm is both brave and not old and vice versa.
If lucy is both not humble and not quiet then someone is not generous or not happy and vice versa.
Everyone who is not old or not tall is funny and vice versa.
If alice is not happy then alice is both not quiet and not funny.
If someone is not rich then someone is happy or not strong.
If susan is rich or not happy then someone is patient or not funny and vice versa.
If someone is both not old and curious then someone is wise or not tall.
Everyone who is both not strong and quiet is quiet.
If fred is either creative or calm then someone is either not wise or not generous.
If someone is either brave or tall then someone is not curious.
Someone is patient.
Paul is either tall or not rich.
Paul is not brave or not kind.
Someone is either funny or not patient.
Paul is either not patient or kind.
Someone is both kind and not quiet.
Someone is either tall or rich.
Someone is both not generous and humble. | Fred is rich. | entailment | (![X]:((~brave(X)<~>~rich(X))<=>~brave(X)))&
((?[X]:((~patient(X)<~>~funny(X))))=>((~wise(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)&~calm(X))=>(~rich(X)<~>~old(X))))&
(((rich(susan)|patient(susan)))<=>((~old(alice)|~creative(alice))))&
(![X]:((~patient(X)&~strong(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((kind(X)|tall(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(brave(X)&~old(X))))&
(((~humble(lucy)&~quiet(lucy)))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:((~old(X)|~tall(X))<=>funny(X)))&
((~happy(alice))=>((~quiet(alice)&~funny(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((happy(X)|~strong(X)))))&
(((rich(susan)|~happy(susan)))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:((~strong(X)&quiet(X))=>quiet(X)))&
(((creative(fred)<~>calm(fred)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
((?[X]:((brave(X)<~>tall(X))))=>(?[X]:(~curious(X))))&
(?[X]:(patient(X)))&
((tall(paul)<~>~rich(paul)))&
((~brave(paul)|~kind(paul)))&
(?[X]:((funny(X)<~>~patient(X))))&
((~patient(paul)<~>kind(paul)))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:((tall(X)<~>rich(X))))&
(?[X]:((~generous(X)&humble(X)))) | rich(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1943871143022704582837790
% SZS output start Proof for 1943871143022704582837790
1. ! [X0] : ((~brave(X0) <~> ~rich(X0)) <=> ~brave(X0)) [input p0]
25. ~rich(fred) [input hypothesis]
39. ! [X0] : ((((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0))))) [nnf transformation 1]
90. ~brave(X0) | ~brave(X0) | rich(X0) [cnf transformation 39]
92. rich(X0) | brave(X0) | brave(X0) [cnf transformation 39]
158. ~rich(fred) [cnf transformation 25]
159. ~brave(X0) | rich(X0) [duplicate literal removal 90]
160. rich(X0) | brave(X0) [duplicate literal removal 92]
161. rich(X0) [subsumption resolution 159,160]
329. $false [subsumption resolution 158,161]
% SZS output end Proof for 1943871143022704582837790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is kind or calm and vice versa.
Everyone who is kind or not calm is both wise and funny.
Everyone who is not kind is generous.
Everyone who is either brave or happy is not old or funny and vice versa.
If lucy is either not creative or calm then susan is not creative or not generous.
Everyone who is wise is not funny and vice versa.
If john is generous or not happy then fred is not quiet and vice versa.
If someone is both not kind and not tall then alice is not calm or not humble and vice versa.
Everyone who is either tall or generous is either wise or kind and vice versa.
Everyone who is not kind or creative is not patient or funny.
If someone is generous or curious then mary is wise.
If lucy is not tall then someone is either not happy or not curious.
If someone is not calm or not funny then someone is either not quiet or creative and vice versa.
Everyone who is both not calm and kind is wise.
Someone is both creative and brave.
Lucy is both not strong and not creative.
Someone is curious or funny.
Susan is either funny or not strong.
Paul is rich or tall.
Lucy is either humble or not creative. | Mary is not tall. | entailment | (![X]:(~humble(X)<=>(kind(X)|calm(X))))&
(![X]:((kind(X)|~calm(X))=>(wise(X)&funny(X))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((brave(X)<~>happy(X))<=>(~old(X)|funny(X))))&
(((~creative(lucy)<~>calm(lucy)))=>((~creative(susan)|~generous(susan))))&
(![X]:(wise(X)<=>~funny(X)))&
(((generous(john)|~happy(john)))<=>(~quiet(fred)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul)))&
((humble(lucy)<~>~creative(lucy))) | ~tall(mary) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1547147243366329547302138
% SZS output start Proof for 1547147243366329547302138
1. ! [X0] : (~humble(X0) <=> (calm(X0) | kind(X0))) [input p0]
2. ! [X0] : ((~calm(X0) | kind(X0)) => (funny(X0) & wise(X0))) [input p1]
3. ! [X0] : (~kind(X0) => generous(X0)) [input p2]
6. ! [X0] : (wise(X0) <=> ~funny(X0)) [input p5]
8. ? [X0] : (~tall(X0) & ~kind(X0)) <=> (~humble(alice) | ~calm(alice)) [input p7]
9. ! [X0] : ((tall(X0) <~> generous(X0)) <=> (wise(X0) <~> kind(X0))) [input p8]
11. ? [X0] : (curious(X0) | generous(X0)) => wise(mary) [input p10]
21. tall(mary) [input hypothesis]
25. ! [X0] : ((funny(X0) & wise(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 2]
26. ! [X0] : (generous(X0) | kind(X0)) [ennf transformation 3]
29. wise(mary) | ! [X0] : (~curious(X0) & ~generous(X0)) [ennf transformation 11]
33. ! [X0] : ((~humble(X0) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | humble(X0))) [nnf transformation 1]
34. ! [X0] : ((~humble(X0) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | humble(X0))) [flattening 33]
38. ! [X0] : ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))) [nnf transformation 6]
41. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & ((~humble(alice) | ~calm(alice)) | ! [X0] : (tall(X0) | kind(X0))) [nnf transformation 8]
42. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X0] : (tall(X0) | kind(X0))) [flattening 41]
43. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X1] : (tall(X1) | kind(X1))) [rectify 42]
44. ? [X0] : (~tall(X0) & ~kind(X0)) => (~tall(sK0) & ~kind(sK0)) [choice axiom]
45. ((~tall(sK0) & ~kind(sK0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X1] : (tall(X1) | kind(X1))) [skolemisation 43,44]
46. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 9]
63. ~calm(X0) | ~humble(X0) [cnf transformation 34]
65. wise(X0) | calm(X0) [cnf transformation 25]
66. ~kind(X0) | funny(X0) [cnf transformation 25]
67. funny(X0) | calm(X0) [cnf transformation 25]
68. generous(X0) | kind(X0) [cnf transformation 26]
77. ~funny(X0) | ~wise(X0) [cnf transformation 38]
84. ~kind(sK0) | humble(alice) [cnf transformation 45]
93. ~generous(X0) | ~tall(X0) | kind(X0) | ~wise(X0) [cnf transformation 46]
95. wise(mary) | ~generous(X0) [cnf transformation 29]
115. tall(mary) [cnf transformation 21]
150. 8 <=> humble(alice) [avatar definition]
152. humble(alice) <- (8) [avatar component clause 150]
164. 11 <=> kind(sK0) [avatar definition]
166. ~kind(sK0) <- (~11) [avatar component clause 164]
167. 8 | ~11 [avatar split clause 84,164,150]
169. ~tall(X0) | kind(X0) | ~wise(X0) [subsumption resolution 93,68]
177. 13 <=> wise(mary) [avatar definition]
179. wise(mary) <- (13) [avatar component clause 177]
182. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
183. ~generous(X0) <- (14) [avatar component clause 182]
184. 14 | 13 [avatar split clause 95,177,182]
228. 25 <=> ! [X3] : calm(X3) [avatar definition]
229. calm(X3) <- (25) [avatar component clause 228]
261. ~wise(X0) | calm(X0) [resolution 77,67]
262. calm(X0) [subsumption resolution 261,65]
263. 25 [avatar split clause 262,228]
265. ~humble(X0) <- (25) [resolution 229,63]
274. kind(mary) | ~wise(mary) [resolution 169,115]
276. kind(mary) <- (13) [subsumption resolution 274,179]
287. funny(mary) <- (13) [resolution 276,66]
301. ~wise(mary) <- (13) [resolution 287,77]
311. $false <- (13) [subsumption resolution 301,179]
312. ~13 [avatar contradiction clause 311]
326. kind(X0) <- (14) [resolution 183,68]
340. $false <- (~11, 14) [resolution 326,166]
344. 11 | ~14 [avatar contradiction clause 340]
346. $false <- (8, 25) [subsumption resolution 152,265]
347. ~8 | ~25 [avatar contradiction clause 346]
348. $false [avatar sat refutation 167,184,263,312,344,347]
% SZS output end Proof for 1547147243366329547302138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either patient or tall. Everyone who is either creative or not funny is not old or not humble and vice versa. If fred is either old or not quiet then someone is either not strong or generous and vice versa. If someone is either not humble or funny then mary is not strong or tall and vice versa. Everyone who is funny or creative is both not strong and tall. Everyone who is not brave or not patient is not funny. Everyone who is happy or not tall is either not generous or generous and vice versa. Everyone who is happy or brave is rich and vice versa. Everyone who is curious or kind is both not old and not curious. If paul is either strong or humble then lucy is not rich or curious. If paul is generous or not kind then susan is creative and vice versa. If someone is calm or kind then someone is patient or old and vice versa. Everyone who is quiet or not funny is either not calm or curious. If alice is both curious and not old then someone is not strong or happy and vice versa. Everyone who is rich is not quiet or funny. If someone is not rich then someone is either not old or calm and vice versa. Paul is both not creative and not calm. Someone is either curious or quiet. Someone is either patient or rich. Someone is not creative. Lucy is old or rich. Someone is either not curious or wise. Susan is not quiet. Someone is either patient or not strong. | Alice is not happy. | entailment | (![X]:(~patient(X)=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~old(X)|~humble(X))))&
(((old(fred)<~>~quiet(fred)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((~strong(mary)|tall(mary))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(((curious(alice)&~old(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
((~creative(paul)&~calm(paul)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
((old(lucy)|rich(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~quiet(susan))&
(?[X]:((patient(X)<~>~strong(X)))) | ~happy(alice) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7380164660988008516625714
% SZS output start Proof for 7380164660988008516625714
9. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p8]
14. (~old(alice) & curious(alice)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p13]
25. happy(alice) [input hypothesis]
31. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 9]
62. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | (old(alice) | ~curious(alice))) [nnf transformation 14]
63. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | old(alice) | ~curious(alice)) [flattening 62]
64. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X1] : (happy(X1) | ~strong(X1)) | old(alice) | ~curious(alice)) [rectify 63]
65. ? [X1] : (happy(X1) | ~strong(X1)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
66. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & ((happy(sK4) | ~strong(sK4)) | old(alice) | ~curious(alice)) [skolemisation 64,65]
125. ~curious(X0) | ~curious(X0) [cnf transformation 31]
142. curious(alice) | ~happy(X0) [cnf transformation 66]
163. happy(alice) [cnf transformation 25]
164. ~curious(X0) [duplicate literal removal 125]
293. 27 <=> ! [X0] : ~happy(X0) [avatar definition]
294. ~happy(X0) <- (27) [avatar component clause 293]
304. ~happy(X0) [subsumption resolution 142,164]
305. 27 [avatar split clause 304,293]
366. $false <- (27) [resolution 294,163]
367. ~27 [avatar contradiction clause 366]
368. $false [avatar sat refutation 305,367]
% SZS output end Proof for 7380164660988008516625714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not quiet is both not patient and not tall.
If lucy is curious then someone is not old and vice versa.
Everyone who is both patient and old is either not wise or not old and vice versa.
If lucy is either not calm or funny then john is not curious or not patient.
Everyone who is both not generous and quiet is either not calm or not creative.
If someone is either old or patient then someone is both not calm and quiet and vice versa.
Everyone who is either old or not quiet is patient or not old and vice versa.
If lucy is not rich or not creative then lucy is both not curious and tall and vice versa.
If susan is not quiet or not funny then someone is not patient and vice versa.
Everyone who is either patient or rich is not strong or not happy.
Everyone who is either not kind or kind is generous or not curious and vice versa.
Everyone who is either not creative or not quiet is not funny.
If john is quiet then someone is humble.
Everyone who is either strong or curious is not humble.
If someone is either calm or quiet then lucy is not patient.
Everyone who is either funny or not kind is either not creative or not quiet and vice versa.
Alice is either not curious or calm.
Alice is both not calm and quiet.
Someone is both not generous and not funny.
Paul is tall.
Someone is not rich.
Someone is not calm or kind.
Someone is quiet or creative.
Someone is both not funny and generous. | Paul is not happy. | neutral | (![X]:((~funny(X)&~quiet(X))=>(~patient(X)&~tall(X))))&
((curious(lucy))<=>(?[X]:(~old(X))))&
(![X]:((patient(X)&old(X))<=>(~wise(X)<~>~old(X))))&
(((~calm(lucy)<~>funny(lucy)))=>((~curious(john)|~patient(john))))&
(![X]:((~generous(X)&quiet(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:((old(X)<~>patient(X))))<=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((old(X)<~>~quiet(X))<=>(patient(X)|~old(X))))&
(((~rich(lucy)|~creative(lucy)))<=>((~curious(lucy)&tall(lucy))))&
(((~quiet(susan)|~funny(susan)))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)<~>rich(X))=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>~funny(X)))&
((quiet(john))=>(?[X]:(humble(X))))&
(![X]:((strong(X)<~>curious(X))=>~humble(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(~patient(lucy)))&
(![X]:((funny(X)<~>~kind(X))<=>(~creative(X)<~>~quiet(X))))&
((~curious(alice)<~>calm(alice)))&
((~calm(alice)&quiet(alice)))&
(?[X]:((~generous(X)&~funny(X))))&
(tall(paul))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~funny(X)&generous(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is wise or not old is not strong or generous and vice versa.
If fred is both kind and not wise then fred is either not brave or generous.
Everyone who is both not strong and tall is either brave or not quiet.
Everyone who is both creative and not wise is quiet.
Everyone who is both not quiet and calm is either not humble or generous and vice versa.
If someone is either wise or not wise then someone is both happy and not rich and vice versa.
If mary is brave then someone is either not brave or not kind and vice versa.
If susan is not brave then someone is tall or not old and vice versa.
Everyone who is either not quiet or wise is either strong or not funny.
Everyone who is not rich or old is kind and vice versa.
Everyone who is both not humble and quiet is brave and vice versa.
If john is happy or not funny then john is not patient and vice versa.
Everyone who is either not rich or funny is either not kind or humble.
Everyone who is old or not generous is happy and vice versa.
If someone is both not strong and not curious then alice is curious or calm and vice versa.
If someone is either old or not wise then paul is both old and rich.
Someone is not generous or generous.
Alice is both generous and not patient.
Someone is both not curious and not creative.
Susan is both funny and humble.
Someone is both not kind and funny.
Susan is humble.
Susan is either not strong or happy.
Fred is not humble. | Susan is not humble. | contradiction | (![X]:((wise(X)|~old(X))<=>(~strong(X)|generous(X))))&
(((kind(fred)&~wise(fred)))=>((~brave(fred)<~>generous(fred))))&
(![X]:((~strong(X)&tall(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((creative(X)&~wise(X))=>quiet(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~humble(X)<~>generous(X))))&
((?[X]:((wise(X)<~>~wise(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
((brave(mary))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
((~brave(susan))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~quiet(X)<~>wise(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~rich(X)|old(X))<=>kind(X)))&
(![X]:((~humble(X)&quiet(X))<=>brave(X)))&
(((happy(john)|~funny(john)))<=>(~patient(john)))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>humble(X))))&
(![X]:((old(X)|~generous(X))<=>happy(X)))&
((?[X]:((~strong(X)&~curious(X))))<=>((curious(alice)|calm(alice))))&
((?[X]:((old(X)<~>~wise(X))))=>((old(paul)&rich(paul))))&
(?[X]:((~generous(X)|generous(X))))&
((generous(alice)&~patient(alice)))&
(?[X]:((~curious(X)&~creative(X))))&
((funny(susan)&humble(susan)))&
(?[X]:((~kind(X)&funny(X))))&
(humble(susan))&
((~strong(susan)<~>happy(susan)))&
(~humble(fred)) | ~humble(susan) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 584488916362030255539954
% SZS output start Proof for 584488916362030255539954
20. humble(susan) & funny(susan) [input p19]
25. ~humble(susan) [input hypothesis]
139. humble(susan) [cnf transformation 20]
146. ~humble(susan) [cnf transformation 25]
299. $false [subsumption resolution 146,139]
% SZS output end Proof for 584488916362030255539954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and brave is both humble and wise and vice versa. Everyone who is strong is humble or quiet. If fred is either not generous or not humble then paul is either rich or not tall. Everyone who is both creative and not brave is not generous. If susan is not old then someone is not old and vice versa. Everyone who is either not funny or not creative is not humble and vice versa. If someone is either not strong or brave then someone is either not patient or patient and vice versa. If someone is either not strong or not old then susan is both not quiet and not tall. If john is either not tall or patient then someone is not generous or curious and vice versa. If someone is either not brave or not wise then someone is both not humble and old. If someone is patient or funny then fred is both not quiet and not creative and vice versa. If alice is both not calm and not funny then lucy is either tall or not brave and vice versa. Everyone who is either not creative or not tall is calm or not funny and vice versa. If alice is not calm or creative then mary is both humble and kind. Everyone who is both strong and not brave is either kind or calm and vice versa. If fred is happy then someone is either patient or generous and vice versa. Susan is not funny. Someone is not quiet or kind. Someone is either rich or happy. Someone is not tall. Lucy is not wise or rich. Someone is not curious or curious. Someone is either strong or not brave. | Susan is not curious. | neutral | (![X]:((creative(X)&brave(X))<=>(humble(X)&wise(X))))&
(![X]:(strong(X)=>(humble(X)|quiet(X))))&
(((~generous(fred)<~>~humble(fred)))=>((rich(paul)<~>~tall(paul))))&
(![X]:((creative(X)&~brave(X))=>~generous(X)))&
((~old(susan))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)<~>~creative(X))<=>~humble(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((~strong(X)<~>~old(X))))=>((~quiet(susan)&~tall(susan))))&
(((~tall(john)<~>patient(john)))<=>(?[X]:((~generous(X)|curious(X)))))&
((?[X]:((~brave(X)<~>~wise(X))))=>(?[X]:((~humble(X)&old(X)))))&
((?[X]:((patient(X)|funny(X))))<=>((~quiet(fred)&~creative(fred))))&
(((~calm(alice)&~funny(alice)))<=>((tall(lucy)<~>~brave(lucy))))&
(![X]:((~creative(X)<~>~tall(X))<=>(calm(X)|~funny(X))))&
(((~calm(alice)|creative(alice)))=>((humble(mary)&kind(mary))))&
(![X]:((strong(X)&~brave(X))<=>(kind(X)<~>calm(X))))&
((happy(fred))<=>(?[X]:((patient(X)<~>generous(X)))))&
(~funny(susan))&
(?[X]:((~quiet(X)|kind(X))))&
(?[X]:((rich(X)<~>happy(X))))&
(?[X]:(~tall(X)))&
((~wise(lucy)|rich(lucy)))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((strong(X)<~>~brave(X)))) | ~curious(susan) | [] | null | 0 |
If mary is either not old or not kind then someone is either old or quiet and vice versa. Everyone who is both not humble and not patient is both not happy and old. Everyone who is not humble or old is strong or generous and vice versa. If susan is both not strong and not kind then someone is happy and vice versa. Everyone who is either not humble or wise is either kind or patient. Everyone who is not creative or curious is creative or happy. If someone is not strong then mary is both calm and not creative and vice versa. If lucy is either strong or not kind then someone is rich or not strong. Everyone who is not brave or brave is not humble or creative. Everyone who is either creative or quiet is either rich or quiet and vice versa. If mary is both humble and quiet then someone is either not tall or not quiet and vice versa. If someone is not old then someone is wise or humble. If mary is not old or funny then lucy is both generous and not patient and vice versa. If paul is both not strong and calm then someone is either not strong or not creative. Everyone who is not generous is not tall. Everyone who is both curious and not calm is calm and vice versa. Lucy is both not brave and tall. John is both not old and not tall. Susan is either not tall or strong. | John is not humble. | entailment | (((~old(mary)<~>~kind(mary)))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((~humble(X)&~patient(X))=>(~happy(X)&old(X))))&
(![X]:((~humble(X)|old(X))<=>(strong(X)|generous(X))))&
(((~strong(susan)&~kind(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~humble(X)<~>wise(X))=>(kind(X)<~>patient(X))))&
(![X]:((~creative(X)|curious(X))=>(creative(X)|happy(X))))&
((?[X]:(~strong(X)))<=>((calm(mary)&~creative(mary))))&
(((strong(lucy)<~>~kind(lucy)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:((~brave(X)|brave(X))=>(~humble(X)|creative(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(rich(X)<~>quiet(X))))&
(((humble(mary)&quiet(mary)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:(~old(X)))=>(?[X]:((wise(X)|humble(X)))))&
(((~old(mary)|funny(mary)))<=>((generous(lucy)&~patient(lucy))))&
(((~strong(paul)&calm(paul)))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:(~generous(X)=>~tall(X)))&
(![X]:((curious(X)&~calm(X))<=>calm(X)))&
((~brave(lucy)&tall(lucy)))&
((~old(john)&~tall(john)))&
((~tall(susan)<~>strong(susan))) | ~humble(john) | [
"p2",
"p6",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7602369314424434031154136
% SZS output start Proof for 7602369314424434031154136
3. ! [X0] : ((old(X0) | ~humble(X0)) <=> (generous(X0) | strong(X0))) [input p2]
7. ? [X0] : ~strong(X0) <=> (~creative(mary) & calm(mary)) [input p6]
16. ! [X0] : ((~calm(X0) & curious(X0)) <=> calm(X0)) [input p15]
18. ~tall(john) & ~old(john) [input p17]
20. humble(john) [input hypothesis]
38. ! [X0] : (((old(X0) | ~humble(X0)) | (~generous(X0) & ~strong(X0))) & ((generous(X0) | strong(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 3]
39. ! [X0] : ((old(X0) | ~humble(X0) | (~generous(X0) & ~strong(X0))) & (generous(X0) | strong(X0) | (~old(X0) & humble(X0)))) [flattening 38]
46. (? [X0] : ~strong(X0) | (creative(mary) | ~calm(mary))) & ((~creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [nnf transformation 7]
47. (? [X0] : ~strong(X0) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [flattening 46]
48. (? [X0] : ~strong(X0) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [rectify 47]
49. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
50. (~strong(sK2) | creative(mary) | ~calm(mary)) & ((~creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [skolemisation 48,49]
68. ! [X0] : (((~calm(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | ~curious(X0)))) [nnf transformation 16]
69. ! [X0] : (((~calm(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | ~curious(X0))) [flattening 68]
83. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 39]
94. calm(mary) | strong(X1) [cnf transformation 50]
126. ~calm(X0) | ~calm(X0) [cnf transformation 69]
129. ~old(john) [cnf transformation 18]
133. humble(john) [cnf transformation 20]
135. ~calm(X0) [duplicate literal removal 126]
190. 11 <=> calm(mary) [avatar definition]
191. calm(mary) <- (11) [avatar component clause 190]
203. 14 <=> ! [X1] : strong(X1) [avatar definition]
204. strong(X1) <- (14) [avatar component clause 203]
206. 14 | 11 [avatar split clause 94,190,203]
310. $false <- (11) [subsumption resolution 191,135]
311. ~11 [avatar contradiction clause 310]
353. ~humble(X0) | old(X0) <- (14) [resolution 83,204]
357. old(john) <- (14) [resolution 353,133]
358. $false <- (14) [subsumption resolution 357,129]
359. ~14 [avatar contradiction clause 358]
360. $false [avatar sat refutation 206,311,359]
% SZS output end Proof for 7602369314424434031154136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either rich or not curious and vice versa.
Everyone who is either brave or funny is not kind.
Everyone who is not funny or generous is both not happy and happy and vice versa.
Everyone who is quiet or wise is rich or not curious and vice versa.
Everyone who is quiet is either quiet or happy and vice versa.
Everyone who is either not wise or not strong is either rich or not patient.
Everyone who is generous is both funny and strong and vice versa.
Everyone who is both brave and not rich is not old and vice versa.
Everyone who is both not old and not calm is not creative.
Everyone who is not funny or kind is creative or tall and vice versa.
If someone is both tall and not tall then fred is either generous or old.
If someone is generous or calm then someone is not funny or not quiet and vice versa.
Everyone who is not tall or rich is both not tall and not calm and vice versa.
If fred is humble or kind then someone is either not generous or not calm and vice versa.
If someone is both curious and not old then alice is tall or humble and vice versa.
Alice is both not tall and not kind.
Someone is either not calm or not happy.
Susan is both old and kind.
Someone is either not funny or not patient.
Someone is wise or not quiet.
Susan is funny or humble. | Fred is not wise. | neutral | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>funny(X))=>~kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)|wise(X))<=>(rich(X)|~curious(X))))&
(![X]:(quiet(X)<=>(quiet(X)<~>happy(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(rich(X)<~>~patient(X))))&
(![X]:(generous(X)<=>(funny(X)&strong(X))))&
(![X]:((brave(X)&~rich(X))<=>~old(X)))&
(![X]:((~old(X)&~calm(X))=>~creative(X)))&
(![X]:((~funny(X)|kind(X))<=>(creative(X)|tall(X))))&
((?[X]:((tall(X)&~tall(X))))=>((generous(fred)<~>old(fred))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:((~funny(X)|~quiet(X)))))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)&~calm(X))))&
(((humble(fred)|kind(fred)))<=>(?[X]:((~generous(X)<~>~calm(X)))))&
((?[X]:((curious(X)&~old(X))))<=>((tall(alice)|humble(alice))))&
((~tall(alice)&~kind(alice)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((old(susan)&kind(susan)))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((wise(X)|~quiet(X))))&
((funny(susan)|humble(susan))) | ~wise(fred) | [] | null | 0 |
If mary is either strong or not old then someone is both not old and brave and vice versa.
Everyone who is both not wise and happy is both not funny and not generous.
If someone is either humble or brave then someone is either not kind or quiet.
If someone is not kind then fred is both not brave and funny and vice versa.
Everyone who is both not creative and funny is wise or not old and vice versa.
If someone is quiet or not humble then alice is both kind and not quiet.
Everyone who is tall or not kind is either humble or brave and vice versa.
If mary is either not happy or rich then someone is old.
If someone is both rich and not happy then susan is either kind or humble.
Everyone who is either not quiet or not curious is both brave and wise.
Everyone who is not wise or not rich is both not funny and not rich and vice versa.
Everyone who is not generous or funny is both not funny and not wise and vice versa.
Everyone who is not tall is either calm or not old.
If mary is both happy and not patient then someone is either not rich or not generous.
Everyone who is not calm or kind is brave and vice versa.
If someone is both not generous and not patient then paul is either quiet or funny and vice versa.
Mary is both not creative and kind.
Someone is not rich.
Someone is either funny or strong.
Someone is creative.
John is either not strong or calm.
Someone is kind or not happy.
Paul is funny or not funny.
Lucy is curious. | John is brave. | entailment | (((strong(mary)<~>~old(mary)))<=>(?[X]:((~old(X)&brave(X)))))&
(![X]:((~wise(X)&happy(X))=>(~funny(X)&~generous(X))))&
((?[X]:((humble(X)<~>brave(X))))=>(?[X]:((~kind(X)<~>quiet(X)))))&
((?[X]:(~kind(X)))<=>((~brave(fred)&funny(fred))))&
(![X]:((~creative(X)&funny(X))<=>(wise(X)|~old(X))))&
((?[X]:((quiet(X)|~humble(X))))=>((kind(alice)&~quiet(alice))))&
(![X]:((tall(X)|~kind(X))<=>(humble(X)<~>brave(X))))&
(((~happy(mary)<~>rich(mary)))=>(?[X]:(old(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(susan)<~>humble(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(brave(X)&wise(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~generous(X)|funny(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~tall(X)=>(calm(X)<~>~old(X))))&
(((happy(mary)&~patient(mary)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~calm(X)|kind(X))<=>brave(X)))&
((?[X]:((~generous(X)&~patient(X))))<=>((quiet(paul)<~>funny(paul))))&
((~creative(mary)&kind(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:(creative(X)))&
((~strong(john)<~>calm(john)))&
(?[X]:((kind(X)|~happy(X))))&
((funny(paul)|~funny(paul)))&
(curious(lucy)) | brave(john) | [
"p3",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7753358091153598428840215
% SZS output start Proof for 7753358091153598428840215
4. ? [X0] : ~kind(X0) <=> (funny(fred) & ~brave(fred)) [input p3]
11. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (~rich(X0) & ~funny(X0))) [input p10]
12. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~wise(X0) & ~funny(X0))) [input p11]
15. ! [X0] : ((kind(X0) | ~calm(X0)) <=> brave(X0)) [input p14]
25. ~brave(john) [input hypothesis]
45. (? [X0] : ~kind(X0) | (~funny(fred) | brave(fred))) & ((funny(fred) & ~brave(fred)) | ! [X0] : kind(X0)) [nnf transformation 4]
46. (? [X0] : ~kind(X0) | ~funny(fred) | brave(fred)) & ((funny(fred) & ~brave(fred)) | ! [X0] : kind(X0)) [flattening 45]
47. (? [X0] : ~kind(X0) | ~funny(fred) | brave(fred)) & ((funny(fred) & ~brave(fred)) | ! [X1] : kind(X1)) [rectify 46]
48. ? [X0] : ~kind(X0) => ~kind(sK2) [choice axiom]
49. (~kind(sK2) | ~funny(fred) | brave(fred)) & ((funny(fred) & ~brave(fred)) | ! [X1] : kind(X1)) [skolemisation 47,48]
59. ! [X0] : (((~rich(X0) | ~wise(X0)) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 11]
60. ! [X0] : ((~rich(X0) | ~wise(X0) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | (rich(X0) & wise(X0)))) [flattening 59]
61. ! [X0] : (((funny(X0) | ~generous(X0)) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 12]
62. ! [X0] : ((funny(X0) | ~generous(X0) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | (~funny(X0) & generous(X0)))) [flattening 61]
67. ! [X0] : (((kind(X0) | ~calm(X0)) | ~brave(X0)) & (brave(X0) | (~kind(X0) & calm(X0)))) [nnf transformation 15]
68. ! [X0] : ((kind(X0) | ~calm(X0) | ~brave(X0)) & (brave(X0) | (~kind(X0) & calm(X0)))) [flattening 67]
96. funny(fred) | kind(X1) [cnf transformation 49]
121. ~funny(X0) | wise(X0) [cnf transformation 60]
129. ~wise(X0) | ~funny(X0) [cnf transformation 62]
136. ~kind(X0) | brave(X0) [cnf transformation 68]
155. ~brave(john) [cnf transformation 25]
206. 11 <=> funny(fred) [avatar definition]
207. funny(fred) <- (11) [avatar component clause 206]
215. 13 <=> ! [X1] : kind(X1) [avatar definition]
216. kind(X1) <- (13) [avatar component clause 215]
217. 13 | 11 [avatar split clause 96,206,215]
265. ~funny(X0) [subsumption resolution 129,121]
321. $false <- (11) [subsumption resolution 207,265]
322. ~11 [avatar contradiction clause 321]
354. brave(X0) <- (13) [resolution 136,216]
357. $false <- (13) [resolution 354,155]
361. ~13 [avatar contradiction clause 357]
363. $false [avatar sat refutation 217,322,361]
% SZS output end Proof for 7753358091153598428840215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both creative and curious is not funny or not tall and vice versa. If john is either not quiet or calm then someone is creative and vice versa. Everyone who is both not calm and not kind is not wise or generous and vice versa. If someone is not kind or not strong then paul is generous. Everyone who is either not old or old is generous and vice versa. Everyone who is calm or not strong is creative and vice versa. If alice is not kind or generous then someone is brave and vice versa. Everyone who is both not tall and not funny is either funny or not calm. Everyone who is either generous or not old is not creative. If john is both not happy and quiet then lucy is not funny or happy. If someone is either not funny or patient then fred is not curious and vice versa. If john is either happy or tall then someone is both not humble and not strong and vice versa. Everyone who is both not tall and not creative is either rich or strong. Everyone who is both curious and not old is either not old or strong. If someone is not humble then someone is not creative. If someone is either not wise or old then lucy is both not kind and not funny. Alice is both not wise and not calm. Someone is both not tall and not kind. Someone is both not quiet and humble. Fred is quiet. Someone is not tall or not rich. Someone is curious or patient. Paul is rich. | John is quiet. | contradiction | (![X]:((creative(X)&curious(X))<=>(~funny(X)|~tall(X))))&
(((~quiet(john)<~>calm(john)))<=>(?[X]:(creative(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(generous(paul)))&
(![X]:((~old(X)<~>old(X))<=>generous(X)))&
(![X]:((calm(X)|~strong(X))<=>creative(X)))&
(((~kind(alice)|generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((~tall(X)&~funny(X))=>(funny(X)<~>~calm(X))))&
(![X]:((generous(X)<~>~old(X))=>~creative(X)))&
(((~happy(john)&quiet(john)))=>((~funny(lucy)|happy(lucy))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
((~wise(alice)&~calm(alice)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(quiet(fred))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul)) | quiet(john) | [
"p0",
"p1",
"p2",
"p4",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3297812662956241979445878
% SZS output start Proof for 3297812662956241979445878
1. ! [X0] : ((curious(X0) & creative(X0)) <=> (~tall(X0) | ~funny(X0))) [input p0]
2. (~quiet(john) <~> calm(john)) <=> ? [X0] : creative(X0) [input p1]
3. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> (generous(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> old(X0)) <=> generous(X0)) [input p4]
18. ? [X0] : (~kind(X0) & ~tall(X0)) [input p17]
24. quiet(john) [input hypothesis]
38. ! [X0] : (((curious(X0) & creative(X0)) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | (~curious(X0) | ~creative(X0)))) [nnf transformation 1]
39. ! [X0] : (((curious(X0) & creative(X0)) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ~curious(X0) | ~creative(X0))) [flattening 38]
40. (((~calm(john) | quiet(john)) & (calm(john) | ~quiet(john))) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | ((~quiet(john) | ~calm(john)) & (calm(john) | quiet(john)))) [nnf transformation 2]
41. (((~calm(john) | quiet(john)) & (calm(john) | ~quiet(john))) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | ((~quiet(john) | ~calm(john)) & (calm(john) | quiet(john)))) [rectify 40]
42. ? [X1] : creative(X1) => creative(sK0) [choice axiom]
43. (((~calm(john) | quiet(john)) & (calm(john) | ~quiet(john))) | ! [X0] : ~creative(X0)) & (creative(sK0) | ((~quiet(john) | ~calm(john)) & (calm(john) | quiet(john)))) [skolemisation 41,42]
44. ! [X0] : (((~kind(X0) & ~calm(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (kind(X0) | calm(X0)))) [nnf transformation 3]
45. ! [X0] : (((~kind(X0) & ~calm(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | kind(X0) | calm(X0))) [flattening 44]
46. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~generous(X0)) & (generous(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 5]
70. ? [X0] : (~kind(X0) & ~tall(X0)) => (~kind(sK5) & ~tall(sK5)) [choice axiom]
71. ~kind(sK5) & ~tall(sK5) [skolemisation 18,70]
80. tall(X0) | creative(X0) [cnf transformation 39]
85. calm(john) | ~quiet(john) | ~creative(X0) [cnf transformation 43]
89. ~generous(X0) | ~calm(X0) [cnf transformation 45]
94. generous(X0) | old(X0) | old(X0) [cnf transformation 46]
95. generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 46]
130. ~tall(sK5) [cnf transformation 71]
138. quiet(john) [cnf transformation 24]
141. generous(X0) | old(X0) [duplicate literal removal 94]
142. ~old(X0) | generous(X0) [duplicate literal removal 95]
144. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
145. ~creative(X0) <- (1) [avatar component clause 144]
147. 2 <=> quiet(john) [avatar definition]
151. 3 <=> calm(john) [avatar definition]
152. calm(john) <- (3) [avatar component clause 151]
155. 1 | ~2 | 3 [avatar split clause 85,151,147,144]
174. generous(X0) [subsumption resolution 141,142]
273. 2 [avatar split clause 138,147]
276. creative(sK5) [resolution 80,130]
285. ~calm(X0) [resolution 89,174]
289. $false <- (3) [resolution 285,152]
290. ~3 [avatar contradiction clause 289]
295. $false <- (1) [resolution 145,276]
298. ~1 [avatar contradiction clause 295]
303. $false [avatar sat refutation 155,273,290,298]
% SZS output end Proof for 3297812662956241979445878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either not strong or funny then someone is not humble.
Everyone who is both old and tall is both old and not curious.
If fred is creative or generous then alice is not happy.
If someone is either humble or not brave then mary is both brave and patient.
Everyone who is quiet is not happy.
If paul is old then susan is rich or kind and vice versa.
Everyone who is both not brave and not quiet is not brave or not generous.
If someone is either generous or brave then lucy is either creative or not brave and vice versa.
Everyone who is patient is both happy and funny and vice versa.
If someone is not curious or funny then someone is both tall and not old.
If alice is either strong or not funny then mary is creative or not creative.
Everyone who is either not quiet or not curious is either calm or quiet and vice versa.
Everyone who is either not strong or curious is both not old and not tall.
If mary is not funny then mary is either not rich or creative and vice versa.
If someone is not generous then someone is either not old or calm.
Everyone who is either patient or not funny is either not brave or not rich.
Alice is calm.
Someone is not patient.
Fred is creative.
John is happy.
Lucy is both rich and not humble.
Someone is strong.
Paul is either not generous or brave.
Fred is either not funny or not old. | John is not quiet. | entailment | (((~strong(john)<~>funny(john)))=>(?[X]:(~humble(X))))&
(![X]:((old(X)&tall(X))=>(old(X)&~curious(X))))&
(((creative(fred)|generous(fred)))=>(~happy(alice)))&
((?[X]:((humble(X)<~>~brave(X))))=>((brave(mary)&patient(mary))))&
(![X]:(quiet(X)=>~happy(X)))&
((old(paul))<=>((rich(susan)|kind(susan))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((creative(lucy)<~>~brave(lucy))))&
(![X]:(patient(X)<=>(happy(X)&funny(X))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:((tall(X)&~old(X)))))&
(((strong(alice)<~>~funny(alice)))=>((creative(mary)|~creative(mary))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((~strong(X)<~>curious(X))=>(~old(X)&~tall(X))))&
((~funny(mary))<=>((~rich(mary)<~>creative(mary))))&
((?[X]:(~generous(X)))=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((patient(X)<~>~funny(X))=>(~brave(X)<~>~rich(X))))&
(calm(alice))&
(?[X]:(~patient(X)))&
(creative(fred))&
(happy(john))&
((rich(lucy)&~humble(lucy)))&
(?[X]:(strong(X)))&
((~generous(paul)<~>brave(paul)))&
((~funny(fred)<~>~old(fred))) | ~quiet(john) | [
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6857626450531476566892894
% SZS output start Proof for 6857626450531476566892894
5. ! [X0] : (quiet(X0) => ~happy(X0)) [input p4]
20. happy(john) [input p19]
25. quiet(john) [input hypothesis]
33. ! [X0] : (~happy(X0) | ~quiet(X0)) [ennf transformation 5]
82. ~quiet(X0) | ~happy(X0) [cnf transformation 33]
129. happy(john) [cnf transformation 20]
137. quiet(john) [cnf transformation 25]
309. ~happy(john) [resolution 82,137]
310. $false [subsumption resolution 309,129]
% SZS output end Proof for 6857626450531476566892894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or not generous then fred is happy and vice versa.
Everyone who is not patient is either not strong or funny.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious.
Someone is old.
Someone is not humble. | Lucy is not patient. | neutral | ((?[X]:((~patient(X)<~>~generous(X))))<=>(happy(fred)))&
(![X]:(~patient(X)=>(~strong(X)<~>funny(X))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X)))&
(?[X]:(~humble(X))) | ~patient(lucy) | [] | null | 0 |
Everyone who is both not patient and not brave is either not humble or calm and vice versa.
Everyone who is rich or creative is humble and vice versa.
If susan is both not brave and patient then mary is not humble or not calm.
If someone is both not quiet and old then someone is not quiet and vice versa.
Everyone who is brave is not funny.
If lucy is both happy and not tall then someone is both not humble and not patient.
Everyone who is not calm is either rich or humble.
If someone is not funny or happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
If mary is both patient and rich then someone is not patient or happy.
If john is not strong or brave then someone is not tall or not generous.
If john is both not wise and not humble then john is both happy and old and vice versa.
Everyone who is not curious or not patient is both quiet and curious and vice versa.
Everyone who is not tall is not rich.
Someone is both happy and quiet.
John is not rich or generous.
Someone is quiet.
Mary is either patient or tall.
Lucy is either not generous or strong.
Someone is either not old or not humble.
Susan is either creative or not brave.
Paul is not wise or tall. | Mary is creative. | neutral | (![X]:((~patient(X)&~brave(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((rich(X)|creative(X))<=>humble(X)))&
(((~brave(susan)&patient(susan)))=>((~humble(mary)|~calm(mary))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>~funny(X)))&
(((happy(lucy)&~tall(lucy)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:(~calm(X)=>(rich(X)<~>humble(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
(((patient(mary)&rich(mary)))=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(john)|brave(john)))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~wise(john)&~humble(john)))<=>((happy(john)&old(john))))&
(![X]:((~curious(X)|~patient(X))<=>(quiet(X)&curious(X))))&
(![X]:(~tall(X)=>~rich(X)))&
(?[X]:((happy(X)&quiet(X))))&
((~rich(john)|generous(john)))&
(?[X]:(quiet(X)))&
((patient(mary)<~>tall(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((~old(X)<~>~humble(X))))&
((creative(susan)<~>~brave(susan)))&
((~wise(paul)|tall(paul))) | creative(mary) | [] | null | 0 |
If someone is both quiet and not old then someone is not strong.
If alice is not generous or humble then someone is both tall and not quiet and vice versa.
Everyone who is both not funny and not quiet is not kind or not tall.
Everyone who is both not funny and strong is either old or funny.
If someone is both not generous and happy then fred is either not humble or not happy and vice versa.
Everyone who is both not strong and patient is kind and vice versa.
Everyone who is either tall or brave is either not generous or calm and vice versa.
If mary is both generous and not calm then mary is either not generous or not happy.
If john is either funny or humble then someone is either not quiet or not creative and vice versa.
If someone is rich then someone is not generous or not rich.
If someone is either not old or not humble then someone is both not humble and not tall and vice versa.
Everyone who is both not quiet and patient is humble.
Everyone who is both not humble and brave is either old or not tall.
If someone is curious or funny then john is patient.
Everyone who is both humble and strong is not curious or curious and vice versa.
Everyone who is kind or humble is both not patient and calm.
Someone is not rich.
Someone is either not generous or old.
Lucy is not generous.
Someone is either not brave or not old.
Someone is quiet.
Someone is generous.
Susan is not happy. | Alice is not generous. | neutral | ((?[X]:((quiet(X)&~old(X))))=>(?[X]:(~strong(X))))&
(((~generous(alice)|humble(alice)))<=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))=>(~kind(X)|~tall(X))))&
(![X]:((~funny(X)&strong(X))=>(old(X)<~>funny(X))))&
((?[X]:((~generous(X)&happy(X))))<=>((~humble(fred)<~>~happy(fred))))&
(![X]:((~strong(X)&patient(X))<=>kind(X)))&
(![X]:((tall(X)<~>brave(X))<=>(~generous(X)<~>calm(X))))&
(((generous(mary)&~calm(mary)))=>((~generous(mary)<~>~happy(mary))))&
(((funny(john)<~>humble(john)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
((?[X]:(rich(X)))=>(?[X]:((~generous(X)|~rich(X)))))&
((?[X]:((~old(X)<~>~humble(X))))<=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((~quiet(X)&patient(X))=>humble(X)))&
(![X]:((~humble(X)&brave(X))=>(old(X)<~>~tall(X))))&
((?[X]:((curious(X)|funny(X))))=>(patient(john)))&
(![X]:((humble(X)&strong(X))<=>(~curious(X)|curious(X))))&
(![X]:((kind(X)|humble(X))=>(~patient(X)&calm(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)<~>old(X))))&
(~generous(lucy))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:(quiet(X)))&
(?[X]:(generous(X)))&
(~happy(susan)) | ~generous(alice) | [] | null | 0 |
If lucy is not tall or curious then fred is both wise and patient and vice versa.
If alice is not funny then someone is both not happy and funny.
Everyone who is not funny is not tall.
If susan is not funny or tall then paul is not humble or strong and vice versa.
Everyone who is either not humble or not funny is not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
If john is both curious and not creative then someone is either creative or not kind.
Someone is either wise or not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is not creative or curious.
Someone is not tall or patient.
Mary is either not strong or generous. | Alice is not wise. | contradiction | (((~tall(lucy)|curious(lucy)))<=>((wise(fred)&patient(fred))))&
((~funny(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~funny(X)=>~tall(X)))&
(((~funny(susan)|tall(susan)))<=>((~humble(paul)|strong(paul))))&
(![X]:((~humble(X)<~>~funny(X))<=>~tall(X)))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:((~tall(X)|patient(X))))&
((~strong(mary)<~>generous(mary))) | ~wise(alice) | [
"p2",
"p4",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7351680226842150820663327
% SZS output start Proof for 7351680226842150820663327
3. ! [X0] : (~funny(X0) => ~tall(X0)) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p4]
13. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & ~calm(X0))) [input p12]
15. ! [X0] : (~wise(X0) => (~humble(X0) & ~wise(X0))) [input p14]
23. ~wise(alice) [input hypothesis]
27. ! [X0] : (~tall(X0) | funny(X0)) [ennf transformation 3]
33. ! [X0] : ((tall(X0) & ~calm(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 13]
34. ! [X0] : ((~humble(X0) & ~wise(X0)) | wise(X0)) [ennf transformation 15]
43. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | tall(X0)) & (~tall(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 5]
57. ! [X0] : ((tall(X0) & ~calm(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 33]
82. ~tall(X0) | funny(X0) [cnf transformation 27]
87. ~tall(X0) | ~funny(X0) | humble(X0) [cnf transformation 43]
90. funny(X0) | humble(X0) | tall(X0) [cnf transformation 43]
111. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
112. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
118. ~humble(X0) | wise(X0) [cnf transformation 34]
131. ~wise(alice) [cnf transformation 23]
134. tall(X0) | quiet(X0) [duplicate literal removal 111]
135. ~quiet(X0) | tall(X0) [duplicate literal removal 112]
191. humble(X0) | funny(X0) [subsumption resolution 90,82]
192. ~tall(X0) | humble(X0) [subsumption resolution 87,191]
267. tall(X0) [subsumption resolution 134,135]
316. humble(X0) [resolution 192,267]
318. wise(X0) [resolution 316,118]
320. $false [resolution 318,131]
% SZS output end Proof for 7351680226842150820663327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or quiet is either not curious or not kind and vice versa.
Everyone who is either curious or old is rich and vice versa.
If susan is either not funny or not patient then someone is not generous.
If paul is both not creative and wise then fred is not calm.
If someone is creative then fred is either generous or not creative and vice versa.
Everyone who is not old is both kind and patient.
Everyone who is old or curious is happy or not patient and vice versa.
If someone is either strong or tall then someone is not creative or old and vice versa.
Everyone who is not kind is calm or happy and vice versa.
If someone is either wise or funny then alice is both not strong and not humble.
If susan is not quiet or patient then someone is either not generous or not old.
Everyone who is both patient and creative is not calm and vice versa.
If paul is strong or quiet then john is either rich or tall and vice versa.
If someone is both kind and not kind then susan is either kind or generous.
Everyone who is both rich and not wise is creative.
Lucy is both not curious and not patient.
Someone is not rich or quiet.
Paul is both wise and not brave.
Someone is curious or humble.
Someone is not wise or not patient.
Someone is not tall.
Lucy is either rich or funny. | Fred is not creative. | neutral | (![X]:((wise(X)<~>quiet(X))<=>(~curious(X)<~>~kind(X))))&
(![X]:((curious(X)<~>old(X))<=>rich(X)))&
(((~funny(susan)<~>~patient(susan)))=>(?[X]:(~generous(X))))&
(((~creative(paul)&wise(paul)))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>((generous(fred)<~>~creative(fred))))&
(![X]:(~old(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|curious(X))<=>(happy(X)|~patient(X))))&
((?[X]:((strong(X)<~>tall(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:(~kind(X)<=>(calm(X)|happy(X))))&
((?[X]:((wise(X)<~>funny(X))))=>((~strong(alice)&~humble(alice))))&
(((~quiet(susan)|patient(susan)))=>(?[X]:((~generous(X)<~>~old(X)))))&
(![X]:((patient(X)&creative(X))<=>~calm(X)))&
(((strong(paul)|quiet(paul)))<=>((rich(john)<~>tall(john))))&
((?[X]:((kind(X)&~kind(X))))=>((kind(susan)<~>generous(susan))))&
(![X]:((rich(X)&~wise(X))=>creative(X)))&
((~curious(lucy)&~patient(lucy)))&
(?[X]:((~rich(X)|quiet(X))))&
((wise(paul)&~brave(paul)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((~wise(X)|~patient(X))))&
(?[X]:(~tall(X)))&
((rich(lucy)<~>funny(lucy))) | ~creative(fred) | [] | null | 0 |
Everyone who is humble is strong or quiet and vice versa. Everyone who is not funny or calm is brave or patient. If paul is both quiet and tall then fred is either not kind or not curious. Everyone who is not calm or not quiet is both not kind and not generous. If someone is both not funny and curious then someone is creative and vice versa. If lucy is either humble or strong then john is not curious or not generous and vice versa. If lucy is strong or patient then susan is calm and vice versa. If fred is not rich or quiet then someone is either not generous or wise. If someone is both not old and not patient then someone is both not generous and generous and vice versa. If mary is wise then someone is either quiet or rich and vice versa. Everyone who is not kind or not humble is either patient or brave. Everyone who is both humble and rich is not kind or not brave and vice versa. If someone is not quiet or quiet then someone is both quiet and happy. If someone is not funny then susan is funny or tall. Everyone who is patient is curious and vice versa. If someone is either not humble or calm then someone is calm or not humble. Someone is both strong and kind. Someone is not creative. Susan is either not brave or rich. Mary is either not patient or not funny. Someone is brave. Someone is both humble and not kind. Someone is not quiet or quiet. | Susan is curious. | contradiction | (![X]:(humble(X)<=>(strong(X)|quiet(X))))&
(![X]:((~funny(X)|calm(X))=>(brave(X)|patient(X))))&
(((quiet(paul)&tall(paul)))=>((~kind(fred)<~>~curious(fred))))&
(![X]:((~calm(X)|~quiet(X))=>(~kind(X)&~generous(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:(creative(X))))&
(((humble(lucy)<~>strong(lucy)))<=>((~curious(john)|~generous(john))))&
(((strong(lucy)|patient(lucy)))<=>(calm(susan)))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~generous(X)<~>wise(X)))))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~generous(X)&generous(X)))))&
((wise(mary))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((~kind(X)|~humble(X))=>(patient(X)<~>brave(X))))&
(![X]:((humble(X)&rich(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:(~funny(X)))=>((funny(susan)|tall(susan))))&
(![X]:(patient(X)<=>curious(X)))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((calm(X)|~humble(X)))))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:(~creative(X)))&
((~brave(susan)<~>rich(susan)))&
((~patient(mary)<~>~funny(mary)))&
(?[X]:(brave(X)))&
(?[X]:((humble(X)&~kind(X))))&
(?[X]:((~quiet(X)|quiet(X)))) | curious(susan) | [
"p0",
"p3",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8582459689823121216663172
% SZS output start Proof for 8582459689823121216663172
1. ! [X0] : (humble(X0) <=> (quiet(X0) | strong(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (~generous(X0) & ~kind(X0))) [input p3]
11. ! [X0] : ((~humble(X0) | ~kind(X0)) => (patient(X0) <~> brave(X0))) [input p10]
12. ! [X0] : ((rich(X0) & humble(X0)) <=> (~brave(X0) | ~kind(X0))) [input p11]
15. ! [X0] : (patient(X0) <=> curious(X0)) [input p14]
19. ~brave(susan) <~> rich(susan) [input p18]
24. curious(susan) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~kind(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 4]
36. ! [X0] : ((patient(X0) <~> brave(X0)) | (humble(X0) & kind(X0))) [ennf transformation 11]
41. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | ~humble(X0))) [nnf transformation 1]
42. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | ~humble(X0))) [flattening 41]
65. ! [X0] : (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (humble(X0) & kind(X0))) [nnf transformation 36]
66. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 12]
67. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~rich(X0) | ~humble(X0))) [flattening 66]
71. ! [X0] : ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))) [nnf transformation 15]
80. (~rich(susan) | brave(susan)) & (rich(susan) | ~brave(susan)) [nnf transformation 19]
90. ~quiet(X0) | humble(X0) [cnf transformation 42]
96. ~kind(X0) | quiet(X0) [cnf transformation 34]
125. ~patient(X0) | ~brave(X0) | kind(X0) [cnf transformation 65]
127. ~rich(X0) | ~kind(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 67]
128. kind(X0) | humble(X0) [cnf transformation 67]
131. rich(X0) | brave(X0) [cnf transformation 67]
136. ~curious(X0) | patient(X0) [cnf transformation 71]
142. rich(susan) | ~brave(susan) [cnf transformation 80]
143. ~rich(susan) | brave(susan) [cnf transformation 80]
150. curious(susan) [cnf transformation 24]
317. brave(susan) [subsumption resolution 143,131]
318. rich(susan) [subsumption resolution 142,317]
339. humble(X0) | quiet(X0) [resolution 128,96]
341. humble(X0) [subsumption resolution 339,90]
348. patient(susan) [resolution 136,150]
440. ~brave(susan) | kind(susan) [resolution 125,348]
458. kind(susan) [subsumption resolution 440,317]
493. ~kind(susan) | ~brave(susan) | ~humble(susan) [resolution 127,318]
496. ~brave(susan) | ~humble(susan) [subsumption resolution 493,458]
497. ~humble(susan) [subsumption resolution 496,317]
498. $false [subsumption resolution 497,341]
% SZS output end Proof for 8582459689823121216663172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not happy then paul is not generous or kind.
If someone is quiet then john is not humble or not tall.
Everyone who is not rich or rich is either not old or not happy.
If lucy is brave or quiet then lucy is either not kind or not old and vice versa.
Everyone who is not patient is curious or not wise and vice versa.
Everyone who is either curious or generous is generous and vice versa.
If someone is strong then paul is not patient and vice versa.
Everyone who is not calm or not generous is either tall or not quiet and vice versa.
Everyone who is either wise or funny is either humble or not patient and vice versa.
If someone is either not strong or not happy then someone is either creative or rich and vice versa.
If someone is not wise then someone is not strong and vice versa.
If susan is either not wise or not rich then lucy is not generous and vice versa.
If someone is either calm or strong then john is either not old or not strong and vice versa.
Everyone who is either calm or not calm is both not rich and not happy and vice versa.
Everyone who is either not humble or old is not brave.
Everyone who is either funny or not humble is both not old and humble and vice versa.
Fred is not happy or not curious.
Someone is not funny.
Susan is not creative or not tall. | Fred is generous. | neutral | ((~happy(john))=>((~generous(paul)|kind(paul))))&
((?[X]:(quiet(X)))=>((~humble(john)|~tall(john))))&
(![X]:((~rich(X)|rich(X))=>(~old(X)<~>~happy(X))))&
(((brave(lucy)|quiet(lucy)))<=>((~kind(lucy)<~>~old(lucy))))&
(![X]:(~patient(X)<=>(curious(X)|~wise(X))))&
(![X]:((curious(X)<~>generous(X))<=>generous(X)))&
((?[X]:(strong(X)))<=>(~patient(paul)))&
(![X]:((~calm(X)|~generous(X))<=>(tall(X)<~>~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(humble(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>~happy(X))))<=>(?[X]:((creative(X)<~>rich(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:(~strong(X))))&
(((~wise(susan)<~>~rich(susan)))<=>(~generous(lucy)))&
((?[X]:((calm(X)<~>strong(X))))<=>((~old(john)<~>~strong(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~rich(X)&~happy(X))))&
(![X]:((~humble(X)<~>old(X))=>~brave(X)))&
(![X]:((funny(X)<~>~humble(X))<=>(~old(X)&humble(X))))&
((~happy(fred)|~curious(fred)))&
(?[X]:(~funny(X)))&
((~creative(susan)|~tall(susan))) | generous(fred) | [] | null | 0 |
Everyone who is both not funny and calm is both humble and not humble and vice versa. Everyone who is either not brave or kind is both not wise and not strong and vice versa. If john is not wise or not quiet then someone is wise and vice versa. If someone is both not wise and generous then lucy is old. If john is either not old or strong then lucy is both wise and calm. If someone is not tall or tall then someone is happy or humble and vice versa. Everyone who is both not wise and creative is either curious or rich and vice versa. Everyone who is either not tall or quiet is either not tall or not wise and vice versa. Everyone who is both funny and not rich is either not funny or rich and vice versa. Everyone who is creative or funny is not quiet or not happy. Everyone who is tall is both not strong and quiet and vice versa. If susan is quiet then someone is calm and vice versa. If someone is both not kind and curious then someone is either generous or not curious. If someone is not rich then paul is either creative or not patient. Everyone who is either not happy or generous is curious or strong. Everyone who is both not patient and generous is not creative. John is funny or strong. Lucy is either old or funny. Someone is either not brave or not funny. Someone is both not patient and happy. Someone is brave or not strong. Fred is wise. Alice is not kind or wise. | John is funny. | contradiction | (![X]:((~funny(X)&calm(X))<=>(humble(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~wise(X)&~strong(X))))&
(((~wise(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
((?[X]:((~wise(X)&generous(X))))=>(old(lucy)))&
(((~old(john)<~>strong(john)))=>((wise(lucy)&calm(lucy))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~wise(X)&creative(X))<=>(curious(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>~wise(X))))&
(![X]:((funny(X)&~rich(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((creative(X)|funny(X))=>(~quiet(X)|~happy(X))))&
(![X]:(tall(X)<=>(~strong(X)&quiet(X))))&
((quiet(susan))<=>(?[X]:(calm(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:(~rich(X)))=>((creative(paul)<~>~patient(paul))))&
(![X]:((~happy(X)<~>generous(X))=>(curious(X)|strong(X))))&
(![X]:((~patient(X)&generous(X))=>~creative(X)))&
((funny(john)|strong(john)))&
((old(lucy)<~>funny(lucy)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((brave(X)|~strong(X))))&
(wise(fred))&
((~kind(alice)|wise(alice))) | funny(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6716244545220802856828710
% SZS output start Proof for 6716244545220802856828710
9. ! [X0] : ((~rich(X0) & funny(X0)) <=> (~funny(X0) <~> rich(X0))) [input p8]
24. funny(john) [input hypothesis]
55. ! [X0] : (((~rich(X0) & funny(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (rich(X0) | ~funny(X0)))) [nnf transformation 9]
56. ! [X0] : (((~rich(X0) & funny(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | rich(X0) | ~funny(X0))) [flattening 55]
113. rich(X0) | ~funny(X0) | rich(X0) | ~funny(X0) [cnf transformation 56]
115. funny(X0) | rich(X0) | funny(X0) [cnf transformation 56]
118. ~rich(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 56]
143. funny(john) [cnf transformation 24]
144. rich(X0) | ~funny(X0) [duplicate literal removal 113]
145. rich(X0) | funny(X0) [duplicate literal removal 115]
146. ~rich(X0) | ~funny(X0) [duplicate literal removal 118]
216. rich(X0) [subsumption resolution 144,145]
244. 21 <=> funny(john) [avatar definition]
246. funny(john) <- (21) [avatar component clause 244]
282. 21 [avatar split clause 143,244]
284. ~funny(X1) [resolution 146,216]
285. $false <- (21) [resolution 284,246]
286. ~21 [avatar contradiction clause 285]
287. $false [avatar sat refutation 282,286]
% SZS output end Proof for 6716244545220802856828710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and calm then someone is generous. If susan is not brave then lucy is both not wise and not kind and vice versa. If susan is both not rich and not calm then someone is both not calm and quiet. If someone is kind or not patient then john is not curious or not tall and vice versa. Everyone who is both quiet and not creative is both not rich and not wise and vice versa. Everyone who is not generous is either not generous or curious and vice versa. If someone is tall then john is rich. Everyone who is both curious and rich is old. Everyone who is strong or kind is either generous or not creative. Everyone who is not humble or not old is both generous and not tall. Everyone who is both curious and funny is either not funny or curious and vice versa. Everyone who is both not funny and not tall is not kind or humble. Everyone who is both generous and funny is both not kind and creative. If paul is not humble then fred is both not curious and not tall. Everyone who is both brave and not quiet is funny or not tall. Everyone who is either not humble or humble is not generous and vice versa. John is both not wise and happy. Someone is either not strong or not patient. Paul is both not generous and patient. Someone is either wise or calm. Someone is not kind. Fred is either kind or humble. | Fred is old. | entailment | ((?[X]:((~old(X)&calm(X))))=>(?[X]:(generous(X))))&
((~brave(susan))<=>((~wise(lucy)&~kind(lucy))))&
(((~rich(susan)&~calm(susan)))=>(?[X]:((~calm(X)&quiet(X)))))&
((?[X]:((kind(X)|~patient(X))))<=>((~curious(john)|~tall(john))))&
(![X]:((quiet(X)&~creative(X))<=>(~rich(X)&~wise(X))))&
(![X]:(~generous(X)<=>(~generous(X)<~>curious(X))))&
((?[X]:(tall(X)))=>(rich(john)))&
(![X]:((curious(X)&rich(X))=>old(X)))&
(![X]:((strong(X)|kind(X))=>(generous(X)<~>~creative(X))))&
(![X]:((~humble(X)|~old(X))=>(generous(X)&~tall(X))))&
(![X]:((curious(X)&funny(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~funny(X)&~tall(X))=>(~kind(X)|humble(X))))&
(![X]:((generous(X)&funny(X))=>(~kind(X)&creative(X))))&
((~humble(paul))=>((~curious(fred)&~tall(fred))))&
(![X]:((brave(X)&~quiet(X))=>(funny(X)|~tall(X))))&
(![X]:((~humble(X)<~>humble(X))<=>~generous(X)))&
((~wise(john)&happy(john)))&
(?[X]:((~strong(X)<~>~patient(X))))&
((~generous(paul)&patient(paul)))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:(~kind(X)))&
((kind(fred)<~>humble(fred))) | old(fred) | [
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 864618019120292801286580
% SZS output start Proof for 864618019120292801286580
10. ! [X0] : ((~old(X0) | ~humble(X0)) => (~tall(X0) & generous(X0))) [input p9]
16. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~generous(X0)) [input p15]
23. ~old(fred) [input hypothesis]
33. ! [X0] : ((~tall(X0) & generous(X0)) | (old(X0) & humble(X0))) [ennf transformation 10]
59. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | generous(X0)) & (~generous(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 16]
93. humble(X0) | generous(X0) [cnf transformation 33]
94. generous(X0) | old(X0) [cnf transformation 33]
109. ~generous(X0) | humble(X0) | humble(X0) [cnf transformation 59]
110. ~generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 59]
123. ~old(fred) [cnf transformation 23]
124. ~generous(X0) | humble(X0) [duplicate literal removal 109]
125. ~humble(X0) | ~generous(X0) [duplicate literal removal 110]
220. humble(X0) [subsumption resolution 124,93]
244. ~generous(X1) [resolution 125,220]
246. old(X0) [resolution 244,94]
249. $false [resolution 246,123]
% SZS output end Proof for 864618019120292801286580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is not creative or not strong and vice versa.
Everyone who is rich or not calm is both not humble and not curious.
If susan is wise then someone is not tall.
If john is either not quiet or creative then someone is strong and vice versa.
Everyone who is either not generous or not wise is patient and vice versa.
Everyone who is not happy is either patient or not strong and vice versa.
If someone is not old or tall then alice is not humble and vice versa.
Everyone who is both not humble and brave is either rich or not tall and vice versa.
Everyone who is both not strong and old is calm or quiet and vice versa.
If someone is either not patient or old then someone is not brave.
If someone is tall or rich then someone is calm and vice versa.
Everyone who is both not calm and funny is patient or brave and vice versa.
Everyone who is both rich and not humble is both old and not strong.
If alice is both quiet and rich then alice is not calm and vice versa.
If someone is not calm then someone is wise or calm.
Everyone who is old is not humble.
Someone is both tall and quiet.
Someone is both not patient and not brave.
Someone is calm or not old.
Someone is wise or funny.
Someone is not creative.
Mary is not humble.
Someone is either strong or calm. | Mary is brave. | neutral | ((?[X]:(~brave(X)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((rich(X)|~calm(X))=>(~humble(X)&~curious(X))))&
((wise(susan))=>(?[X]:(~tall(X))))&
(((~quiet(john)<~>creative(john)))<=>(?[X]:(strong(X))))&
(![X]:((~generous(X)<~>~wise(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:((~old(X)|tall(X))))<=>(~humble(alice)))&
(![X]:((~humble(X)&brave(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~strong(X)&old(X))<=>(calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(patient(X)|brave(X))))&
(![X]:((rich(X)&~humble(X))=>(old(X)&~strong(X))))&
(((quiet(alice)&rich(alice)))<=>(~calm(alice)))&
((?[X]:(~calm(X)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(old(X)=>~humble(X)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~patient(X)&~brave(X))))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:(~creative(X)))&
(~humble(mary))&
(?[X]:((strong(X)<~>calm(X)))) | brave(mary) | [] | null | 0 |
If someone is not happy or not quiet then someone is calm or not calm.
Everyone who is not humble is not wise and vice versa.
Everyone who is either creative or not kind is either curious or wise.
If someone is either not rich or not wise then lucy is patient or not humble and vice versa.
If mary is brave then john is both not kind and not brave.
Everyone who is both not tall and not brave is not creative or rich and vice versa.
Everyone who is not wise is not patient and vice versa.
Everyone who is not old is both not funny and patient.
Everyone who is calm or funny is patient.
Everyone who is both wise and not kind is rich and vice versa.
Everyone who is both funny and not wise is tall or brave and vice versa.
If someone is both happy and not happy then paul is either not quiet or humble and vice versa.
If someone is wise or not creative then someone is not strong or generous.
If fred is kind then john is both humble and not brave.
Everyone who is not wise is not kind and vice versa.
Everyone who is both calm and wise is kind or rich.
Susan is either rich or funny.
Susan is both not tall and old.
Someone is both calm and quiet.
Someone is both old and curious.
Lucy is either quiet or generous.
Fred is either not wise or brave.
Someone is either wise or tall. | Fred is not old. | contradiction | ((?[X]:((~happy(X)|~quiet(X))))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((patient(lucy)|~humble(lucy))))&
((brave(mary))=>((~kind(john)&~brave(john))))&
(![X]:((~tall(X)&~brave(X))<=>(~creative(X)|rich(X))))&
(![X]:(~wise(X)<=>~patient(X)))&
(![X]:(~old(X)=>(~funny(X)&patient(X))))&
(![X]:((calm(X)|funny(X))=>patient(X)))&
(![X]:((wise(X)&~kind(X))<=>rich(X)))&
(![X]:((funny(X)&~wise(X))<=>(tall(X)|brave(X))))&
((?[X]:((happy(X)&~happy(X))))<=>((~quiet(paul)<~>humble(paul))))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~strong(X)|generous(X)))))&
((kind(fred))=>((humble(john)&~brave(john))))&
(![X]:(~wise(X)<=>~kind(X)))&
(![X]:((calm(X)&wise(X))=>(kind(X)|rich(X))))&
((rich(susan)<~>funny(susan)))&
((~tall(susan)&old(susan)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((old(X)&curious(X))))&
((quiet(lucy)<~>generous(lucy)))&
((~wise(fred)<~>brave(fred)))&
(?[X]:((wise(X)<~>tall(X)))) | ~old(fred) | [
"p6",
"p7",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1157327748981693196576152
% SZS output start Proof for 1157327748981693196576152
7. ! [X0] : (~wise(X0) <=> ~patient(X0)) [input p6]
8. ! [X0] : (~old(X0) => (patient(X0) & ~funny(X0))) [input p7]
11. ! [X0] : ((~wise(X0) & funny(X0)) <=> (brave(X0) | tall(X0))) [input p10]
22. ~wise(fred) <~> brave(fred) [input p21]
24. ~old(fred) [input hypothesis]
31. ! [X0] : ((patient(X0) & ~funny(X0)) | old(X0)) [ennf transformation 8]
48. ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))) [nnf transformation 7]
51. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 11]
52. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | wise(X0) | ~funny(X0))) [flattening 51]
64. (~brave(fred) | wise(fred)) & (brave(fred) | ~wise(fred)) [nnf transformation 22]
89. ~patient(X0) | wise(X0) [cnf transformation 48]
92. old(X0) | patient(X0) [cnf transformation 31]
102. ~wise(X0) | ~brave(X0) [cnf transformation 52]
124. brave(fred) | ~wise(fred) [cnf transformation 64]
125. ~brave(fred) | wise(fred) [cnf transformation 64]
128. ~old(fred) [cnf transformation 24]
218. ~brave(fred) [subsumption resolution 125,102]
219. ~wise(fred) [subsumption resolution 124,218]
236. patient(fred) [resolution 92,128]
237. wise(fred) [resolution 236,89]
238. $false [subsumption resolution 237,219]
% SZS output end Proof for 1157327748981693196576152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is not old or not rich and vice versa. If someone is not quiet then someone is either not quiet or rich. If someone is not kind or tall then someone is not calm or patient. Everyone who is not funny or calm is either happy or strong and vice versa. Everyone who is creative or not old is either not brave or not calm and vice versa. Everyone who is not tall is not funny or not curious and vice versa. Everyone who is happy or humble is both not calm and calm. Everyone who is wise or tall is either quiet or not rich. If fred is brave then alice is curious or not wise. Everyone who is both not kind and creative is not happy or quiet. If mary is both humble and strong then someone is both calm and not happy and vice versa. If someone is not old or not creative then mary is both not happy and quiet. Everyone who is either brave or patient is both creative and quiet. If paul is both kind and not curious then someone is curious or funny and vice versa. Everyone who is either not creative or not wise is not kind and vice versa. Everyone who is not rich or happy is either not funny or not strong and vice versa. Someone is both wise and curious. Someone is not quiet or curious. John is either not creative or not rich. Someone is both not happy and funny. Someone is not rich. Someone is both tall and funny. Fred is both not funny and curious. | Fred is not rich. | entailment | ((?[X]:(~kind(X)))<=>(?[X]:((~old(X)|~rich(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((~quiet(X)<~>rich(X)))))&
((?[X]:((~kind(X)|tall(X))))=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~funny(X)|calm(X))<=>(happy(X)<~>strong(X))))&
(![X]:((creative(X)|~old(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:(~tall(X)<=>(~funny(X)|~curious(X))))&
(![X]:((happy(X)|humble(X))=>(~calm(X)&calm(X))))&
(![X]:((wise(X)|tall(X))=>(quiet(X)<~>~rich(X))))&
((brave(fred))=>((curious(alice)|~wise(alice))))&
(![X]:((~kind(X)&creative(X))=>(~happy(X)|quiet(X))))&
(((humble(mary)&strong(mary)))<=>(?[X]:((calm(X)&~happy(X)))))&
((?[X]:((~old(X)|~creative(X))))=>((~happy(mary)&quiet(mary))))&
(![X]:((brave(X)<~>patient(X))=>(creative(X)&quiet(X))))&
(((kind(paul)&~curious(paul)))<=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~creative(X)<~>~wise(X))<=>~kind(X)))&
(![X]:((~rich(X)|happy(X))<=>(~funny(X)<~>~strong(X))))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:((~quiet(X)|curious(X))))&
((~creative(john)<~>~rich(john)))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)&funny(X))))&
((~funny(fred)&curious(fred))) | ~rich(fred) | [
"p3",
"p6",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 234161443387594349386129
% SZS output start Proof for 234161443387594349386129
4. ! [X0] : ((calm(X0) | ~funny(X0)) <=> (happy(X0) <~> strong(X0))) [input p3]
7. ! [X0] : ((humble(X0) | happy(X0)) => (calm(X0) & ~calm(X0))) [input p6]
16. ! [X0] : ((happy(X0) | ~rich(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p15]
23. curious(fred) & ~funny(fred) [input p22]
24. rich(fred) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~calm(X0)) | (~humble(X0) & ~happy(X0))) [ennf transformation 7]
50. ! [X0] : (((calm(X0) | ~funny(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~calm(X0) & funny(X0)))) [nnf transformation 4]
51. ! [X0] : ((calm(X0) | ~funny(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~calm(X0) & funny(X0)))) [flattening 50]
69. ! [X0] : (((happy(X0) | ~rich(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [nnf transformation 16]
70. ! [X0] : ((happy(X0) | ~rich(X0) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [flattening 69]
89. strong(X0) | happy(X0) | funny(X0) [cnf transformation 51]
104. ~calm(X0) | ~happy(X0) [cnf transformation 30]
106. ~happy(X0) | calm(X0) [cnf transformation 30]
139. happy(X0) | ~rich(X0) | ~strong(X0) | funny(X0) [cnf transformation 70]
151. ~funny(fred) [cnf transformation 23]
153. rich(fred) [cnf transformation 24]
205. ~happy(X0) [subsumption resolution 104,106]
268. ~strong(X0) | ~rich(X0) | funny(X0) [subsumption resolution 139,205]
409. ~rich(X1) | funny(X1) | happy(X1) | funny(X1) [resolution 268,89]
410. ~rich(X1) | funny(X1) | happy(X1) [duplicate literal removal 409]
412. ~rich(X1) | funny(X1) [subsumption resolution 410,205]
413. funny(fred) [resolution 412,153]
414. $false [subsumption resolution 413,151]
% SZS output end Proof for 234161443387594349386129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not patient is either not old or happy and vice versa.
If someone is both not happy and generous then john is either not kind or not quiet.
If someone is both not kind and curious then someone is creative or not quiet and vice versa.
Everyone who is both calm and funny is generous or not brave and vice versa.
If alice is not wise or kind then lucy is both not rich and kind.
If someone is generous then someone is either kind or not old.
Everyone who is old is either patient or happy and vice versa.
Everyone who is not humble or not strong is quiet or old and vice versa.
If someone is funny or quiet then susan is not brave.
If someone is not curious or rich then someone is either not generous or not strong and vice versa.
Everyone who is either creative or old is not calm or not curious and vice versa.
Everyone who is either wise or not quiet is brave.
Everyone who is not patient is either old or not funny.
If someone is both not strong and not tall then lucy is not generous or not creative and vice versa.
If mary is both not old and not humble then someone is wise and vice versa.
If someone is both not humble and not curious then someone is both kind and not wise and vice versa.
Fred is either not wise or wise.
Someone is either not curious or creative.
John is both generous and not quiet.
Someone is both kind and quiet.
Mary is humble or calm.
Someone is either patient or calm.
Someone is not humble.
Someone is either not happy or not strong. | Susan is calm. | entailment | (![X]:((~strong(X)<~>~patient(X))<=>(~old(X)<~>happy(X))))&
((?[X]:((~happy(X)&generous(X))))=>((~kind(john)<~>~quiet(john))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((calm(X)&funny(X))<=>(generous(X)|~brave(X))))&
(((~wise(alice)|kind(alice)))=>((~rich(lucy)&kind(lucy))))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:(old(X)<=>(patient(X)<~>happy(X))))&
(![X]:((~humble(X)|~strong(X))<=>(quiet(X)|old(X))))&
((?[X]:((funny(X)|quiet(X))))=>(~brave(susan)))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~calm(X)|~curious(X))))&
(![X]:((wise(X)<~>~quiet(X))=>brave(X)))&
(![X]:(~patient(X)=>(old(X)<~>~funny(X))))&
((?[X]:((~strong(X)&~tall(X))))<=>((~generous(lucy)|~creative(lucy))))&
(((~old(mary)&~humble(mary)))<=>(?[X]:(wise(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((~curious(X)<~>creative(X))))&
((generous(john)&~quiet(john)))&
(?[X]:((kind(X)&quiet(X))))&
((humble(mary)|calm(mary)))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)<~>~strong(X)))) | calm(susan) | [
"p3",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2636727787783608770934797
% SZS output start Proof for 2636727787783608770934797
4. ! [X0] : ((funny(X0) & calm(X0)) <=> (~brave(X0) | generous(X0))) [input p3]
9. ? [X0] : (quiet(X0) | funny(X0)) => ~brave(susan) [input p8]
20. ? [X0] : (quiet(X0) & kind(X0)) [input p19]
25. ~calm(susan) [input hypothesis]
33. ~brave(susan) | ! [X0] : (~quiet(X0) & ~funny(X0)) [ennf transformation 9]
43. ! [X0] : (((funny(X0) & calm(X0)) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : (((funny(X0) & calm(X0)) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~funny(X0) | ~calm(X0))) [flattening 43]
80. ? [X0] : (quiet(X0) & kind(X0)) => (quiet(sK10) & kind(sK10)) [choice axiom]
81. quiet(sK10) & kind(sK10) [skolemisation 20,80]
107. brave(X0) | calm(X0) [cnf transformation 44]
125. ~brave(susan) | ~quiet(X0) [cnf transformation 33]
161. quiet(sK10) [cnf transformation 81]
168. ~calm(susan) [cnf transformation 25]
246. 18 <=> ! [X0] : ~quiet(X0) [avatar definition]
247. ~quiet(X0) <- (18) [avatar component clause 246]
249. 19 <=> brave(susan) [avatar definition]
251. ~brave(susan) <- (~19) [avatar component clause 249]
252. 18 | ~19 [avatar split clause 125,249,246]
397. calm(susan) <- (~19) [resolution 107,251]
398. $false <- (~19) [subsumption resolution 397,168]
399. 19 [avatar contradiction clause 398]
400. $false <- (18) [resolution 247,161]
401. ~18 [avatar contradiction clause 400]
402. $false [avatar sat refutation 252,399,401]
% SZS output end Proof for 2636727787783608770934797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and kind then someone is tall or calm. Everyone who is old or tall is humble. Everyone who is either generous or not happy is curious or rich. Everyone who is both patient and not generous is not quiet and vice versa. Everyone who is not strong is not generous and vice versa. Everyone who is not humble is either happy or creative and vice versa. If susan is not kind or not rich then susan is either not curious or not patient and vice versa. Everyone who is not old is either not happy or patient. Everyone who is kind or not rich is either not happy or not generous and vice versa. Everyone who is either not creative or not quiet is both creative and strong and vice versa. If lucy is either humble or rich then paul is humble or not calm. Everyone who is both not generous and not curious is either wise or not happy and vice versa. Everyone who is not patient or quiet is both wise and not humble and vice versa. If someone is tall or not funny then someone is not humble and vice versa. If alice is either creative or rich then paul is not generous. Everyone who is curious or humble is both not wise and not quiet. Lucy is not rich or calm. Someone is humble. Someone is calm. Paul is both happy and curious. Fred is patient or not curious. | Fred is not strong. | entailment | ((?[X]:((curious(X)&kind(X))))=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((old(X)|tall(X))=>humble(X)))&
(![X]:((generous(X)<~>~happy(X))=>(curious(X)|rich(X))))&
(![X]:((patient(X)&~generous(X))<=>~quiet(X)))&
(![X]:(~strong(X)<=>~generous(X)))&
(![X]:(~humble(X)<=>(happy(X)<~>creative(X))))&
(((~kind(susan)|~rich(susan)))<=>((~curious(susan)<~>~patient(susan))))&
(![X]:(~old(X)=>(~happy(X)<~>patient(X))))&
(![X]:((kind(X)|~rich(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(creative(X)&strong(X))))&
(((humble(lucy)<~>rich(lucy)))=>((humble(paul)|~calm(paul))))&
(![X]:((~generous(X)&~curious(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~patient(X)|quiet(X))<=>(wise(X)&~humble(X))))&
((?[X]:((tall(X)|~funny(X))))<=>(?[X]:(~humble(X))))&
(((creative(alice)<~>rich(alice)))=>(~generous(paul)))&
(![X]:((curious(X)|humble(X))=>(~wise(X)&~quiet(X))))&
((~rich(lucy)|calm(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
((happy(paul)&curious(paul)))&
((patient(fred)|~curious(fred))) | ~strong(fred) | [
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6172890326787383723669498
% SZS output start Proof for 6172890326787383723669498
4. ! [X0] : ((~generous(X0) & patient(X0)) <=> ~quiet(X0)) [input p3]
5. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p4]
10. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (strong(X0) & creative(X0))) [input p9]
22. strong(fred) [input hypothesis]
38. ! [X0] : (((~generous(X0) & patient(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) | ~patient(X0)))) [nnf transformation 4]
39. ! [X0] : (((~generous(X0) & patient(X0)) | quiet(X0)) & (~quiet(X0) | generous(X0) | ~patient(X0))) [flattening 38]
40. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 5]
47. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 10]
48. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 47]
71. ~generous(X0) | quiet(X0) [cnf transformation 39]
73. ~strong(X0) | generous(X0) [cnf transformation 40]
92. creative(X0) | ~quiet(X0) | creative(X0) [cnf transformation 48]
96. ~quiet(X0) | ~creative(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 48]
126. strong(fred) [cnf transformation 22]
127. ~quiet(X0) | creative(X0) [duplicate literal removal 92]
128. ~creative(X0) | ~quiet(X0) | ~strong(X0) [duplicate literal removal 96]
235. generous(fred) [resolution 73,126]
237. quiet(fred) [resolution 235,71]
251. creative(fred) [resolution 127,237]
360. ~quiet(fred) | ~strong(fred) [resolution 128,251]
364. ~strong(fred) [subsumption resolution 360,237]
365. $false [subsumption resolution 364,126]
% SZS output end Proof for 6172890326787383723669498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not rich or tall then someone is both funny and creative and vice versa. Everyone who is both not funny and not wise is either not funny or creative and vice versa. If paul is either not calm or tall then fred is both creative and quiet. If lucy is either humble or not curious then susan is either not brave or rich and vice versa. Everyone who is both not patient and old is both tall and humble. Everyone who is strong is not quiet. Everyone who is either creative or not kind is both calm and not happy and vice versa. Everyone who is brave is not humble. Everyone who is either not old or not patient is both not calm and not quiet and vice versa. If susan is both happy and not brave then someone is either not funny or not wise and vice versa. Everyone who is quiet is rich and vice versa. If fred is happy or not happy then susan is not patient or not rich and vice versa. If someone is either patient or not tall then alice is curious or not old. Everyone who is either old or not old is old or not old and vice versa. Everyone who is humble is both not humble and not happy and vice versa. Someone is both not calm and not strong. Susan is not curious or not creative. John is not rich. Fred is not humble or not tall. Paul is not tall. Alice is either not creative or not tall. Lucy is both not calm and strong. Mary is kind. | Lucy is funny. | neutral | (((~rich(alice)<~>tall(alice)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~funny(X)&~wise(X))<=>(~funny(X)<~>creative(X))))&
(((~calm(paul)<~>tall(paul)))=>((creative(fred)&quiet(fred))))&
(((humble(lucy)<~>~curious(lucy)))<=>((~brave(susan)<~>rich(susan))))&
(![X]:((~patient(X)&old(X))=>(tall(X)&humble(X))))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((creative(X)<~>~kind(X))<=>(calm(X)&~happy(X))))&
(![X]:(brave(X)=>~humble(X)))&
(![X]:((~old(X)<~>~patient(X))<=>(~calm(X)&~quiet(X))))&
(((happy(susan)&~brave(susan)))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:(quiet(X)<=>rich(X)))&
(((happy(fred)|~happy(fred)))<=>((~patient(susan)|~rich(susan))))&
((?[X]:((patient(X)<~>~tall(X))))=>((curious(alice)|~old(alice))))&
(![X]:((old(X)<~>~old(X))<=>(old(X)|~old(X))))&
(![X]:(humble(X)<=>(~humble(X)&~happy(X))))&
(?[X]:((~calm(X)&~strong(X))))&
((~curious(susan)|~creative(susan)))&
(~rich(john))&
((~humble(fred)|~tall(fred)))&
(~tall(paul))&
((~creative(alice)<~>~tall(alice)))&
((~calm(lucy)&strong(lucy)))&
(kind(mary)) | funny(lucy) | [] | null | 0 |
Everyone who is both patient and not happy is either not generous or brave. If someone is curious then someone is both brave and generous and vice versa. If paul is funny then someone is either not humble or calm. If someone is both rich and wise then john is old and vice versa. Everyone who is not old is not wise or not funny and vice versa. Everyone who is not wise or strong is brave. If someone is both not wise and rich then john is brave or not brave. If paul is quiet then someone is either curious or not rich and vice versa. If someone is either not generous or kind then paul is both rich and kind. Everyone who is rich or kind is not wise or rich. If someone is wise then someone is not happy or not humble. If paul is strong or not brave then someone is either not funny or wise and vice versa. If someone is not funny then lucy is old and vice versa. Everyone who is quiet or rich is both not rich and funny and vice versa. If someone is strong or curious then mary is not kind. Everyone who is not generous or patient is not quiet or rich and vice versa. John is both not old and quiet. Susan is both funny and not brave. Fred is either not funny or not old. Someone is either humble or brave. Someone is not strong. Mary is either wise or generous. Someone is both not strong and happy. | Susan is wise. | entailment | (![X]:((patient(X)&~happy(X))=>(~generous(X)<~>brave(X))))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)&generous(X)))))&
((funny(paul))=>(?[X]:((~humble(X)<~>calm(X)))))&
((?[X]:((rich(X)&wise(X))))<=>(old(john)))&
(![X]:(~old(X)<=>(~wise(X)|~funny(X))))&
(![X]:((~wise(X)|strong(X))=>brave(X)))&
((?[X]:((~wise(X)&rich(X))))=>((brave(john)|~brave(john))))&
((quiet(paul))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~generous(X)<~>kind(X))))=>((rich(paul)&kind(paul))))&
(![X]:((rich(X)|kind(X))=>(~wise(X)|rich(X))))&
((?[X]:(wise(X)))=>(?[X]:((~happy(X)|~humble(X)))))&
(((strong(paul)|~brave(paul)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:(~funny(X)))<=>(old(lucy)))&
(![X]:((quiet(X)|rich(X))<=>(~rich(X)&funny(X))))&
((?[X]:((strong(X)|curious(X))))=>(~kind(mary)))&
(![X]:((~generous(X)|patient(X))<=>(~quiet(X)|rich(X))))&
((~old(john)&quiet(john)))&
((funny(susan)&~brave(susan)))&
((~funny(fred)<~>~old(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~strong(X)))&
((wise(mary)<~>generous(mary)))&
(?[X]:((~strong(X)&happy(X)))) | wise(susan) | [
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1759518463409780290610337
% SZS output start Proof for 1759518463409780290610337
6. ! [X0] : ((strong(X0) | ~wise(X0)) => brave(X0)) [input p5]
18. ~brave(susan) & funny(susan) [input p17]
24. ~wise(susan) [input hypothesis]
30. ! [X0] : (brave(X0) | (~strong(X0) & wise(X0))) [ennf transformation 6]
96. wise(X0) | brave(X0) [cnf transformation 30]
132. ~brave(susan) [cnf transformation 18]
142. ~wise(susan) [cnf transformation 24]
329. brave(susan) [resolution 96,142]
331. $false [subsumption resolution 329,132]
% SZS output end Proof for 1759518463409780290610337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and tall is not curious.
If someone is creative then someone is wise.
Everyone who is either funny or not patient is quiet or creative.
Everyone who is not quiet is not tall and vice versa.
If someone is both quiet and not curious then someone is both creative and curious.
Everyone who is both not funny and creative is not curious and vice versa.
If someone is both not strong and not old then paul is either happy or not strong and vice versa.
Everyone who is both generous and strong is patient and vice versa.
If alice is not happy then someone is either happy or strong.
If someone is both not quiet and not tall then john is either patient or funny and vice versa.
Everyone who is either curious or not funny is both patient and not brave and vice versa.
If someone is not quiet then mary is strong and vice versa.
Everyone who is both funny and tall is calm or happy.
Everyone who is kind or old is both not humble and rich and vice versa.
If john is either old or not strong then paul is either patient or not happy.
Everyone who is both not creative and not strong is both not happy and old.
Alice is wise.
Someone is not brave or strong.
John is either not creative or not happy.
Lucy is both not humble and not tall.
Paul is quiet or not wise.
Mary is both not old and quiet. | Paul is not happy. | entailment | (![X]:((quiet(X)&tall(X))=>~curious(X)))&
((?[X]:(creative(X)))=>(?[X]:(wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(quiet(X)|creative(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((quiet(X)&~curious(X))))=>(?[X]:((creative(X)&curious(X)))))&
(![X]:((~funny(X)&creative(X))<=>~curious(X)))&
((?[X]:((~strong(X)&~old(X))))<=>((happy(paul)<~>~strong(paul))))&
(![X]:((generous(X)&strong(X))<=>patient(X)))&
((~happy(alice))=>(?[X]:((happy(X)<~>strong(X)))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((patient(john)<~>funny(john))))&
(![X]:((curious(X)<~>~funny(X))<=>(patient(X)&~brave(X))))&
((?[X]:(~quiet(X)))<=>(strong(mary)))&
(![X]:((funny(X)&tall(X))=>(calm(X)|happy(X))))&
(![X]:((kind(X)|old(X))<=>(~humble(X)&rich(X))))&
(((old(john)<~>~strong(john)))=>((patient(paul)<~>~happy(paul))))&
(![X]:((~creative(X)&~strong(X))=>(~happy(X)&old(X))))&
(wise(alice))&
(?[X]:((~brave(X)|strong(X))))&
((~creative(john)<~>~happy(john)))&
((~humble(lucy)&~tall(lucy)))&
((quiet(paul)|~wise(paul)))&
((~old(mary)&quiet(mary))) | ~happy(paul) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6879673074095628893208879
% SZS output start Proof for 6879673074095628893208879
1. ! [X0] : ((tall(X0) & quiet(X0)) => ~curious(X0)) [input p0]
3. ! [X0] : ((funny(X0) <~> ~patient(X0)) => (creative(X0) | quiet(X0))) [input p2]
4. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p3]
6. ! [X0] : ((creative(X0) & ~funny(X0)) <=> ~curious(X0)) [input p5]
7. ? [X0] : (~old(X0) & ~strong(X0)) <=> (happy(paul) <~> ~strong(paul)) [input p6]
8. ! [X0] : ((strong(X0) & generous(X0)) <=> patient(X0)) [input p7]
11. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (~brave(X0) & patient(X0))) [input p10]
16. ! [X0] : ((~strong(X0) & ~creative(X0)) => (old(X0) & ~happy(X0))) [input p15]
23. happy(paul) [input hypothesis]
27. ! [X0] : (~curious(X0) | (~tall(X0) | ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~curious(X0) | ~tall(X0) | ~quiet(X0)) [flattening 27]
30. ! [X0] : ((creative(X0) | quiet(X0)) | (funny(X0) <=> ~patient(X0))) [ennf transformation 3]
31. ! [X0] : (creative(X0) | quiet(X0) | (funny(X0) <=> ~patient(X0))) [flattening 30]
35. ! [X0] : ((old(X0) & ~happy(X0)) | (strong(X0) | creative(X0))) [ennf transformation 16]
36. ! [X0] : ((old(X0) & ~happy(X0)) | strong(X0) | creative(X0)) [flattening 35]
40. ! [X0] : (creative(X0) | quiet(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) [nnf transformation 31]
41. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 4]
45. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | funny(X0)))) [nnf transformation 6]
46. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | funny(X0))) [flattening 45]
47. (? [X0] : (~old(X0) & ~strong(X0)) | ((happy(paul) | strong(paul)) & (~strong(paul) | ~happy(paul)))) & (((strong(paul) | ~happy(paul)) & (~strong(paul) | happy(paul))) | ! [X0] : (old(X0) | strong(X0))) [nnf transformation 7]
48. (? [X0] : (~old(X0) & ~strong(X0)) | ((happy(paul) | strong(paul)) & (~strong(paul) | ~happy(paul)))) & (((strong(paul) | ~happy(paul)) & (~strong(paul) | happy(paul))) | ! [X1] : (old(X1) | strong(X1))) [rectify 47]
49. ? [X0] : (~old(X0) & ~strong(X0)) => (~old(sK2) & ~strong(sK2)) [choice axiom]
50. ((~old(sK2) & ~strong(sK2)) | ((happy(paul) | strong(paul)) & (~strong(paul) | ~happy(paul)))) & (((strong(paul) | ~happy(paul)) & (~strong(paul) | happy(paul))) | ! [X1] : (old(X1) | strong(X1))) [skolemisation 48,49]
51. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) | ~generous(X0)))) [nnf transformation 8]
52. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | ~strong(X0) | ~generous(X0))) [flattening 51]
60. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 11]
61. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 60]
72. ~curious(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 28]
75. patient(X0) | quiet(X0) | funny(X0) | creative(X0) [cnf transformation 40]
77. ~quiet(X0) | tall(X0) [cnf transformation 41]
80. ~creative(X0) | ~curious(X0) | funny(X0) [cnf transformation 46]
81. ~funny(X0) | curious(X0) [cnf transformation 46]
85. ~strong(sK2) | ~strong(paul) | ~happy(paul) [cnf transformation 50]
91. ~patient(X0) | strong(X0) [cnf transformation 52]
100. patient(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 61]
101. patient(X0) | curious(X0) | funny(X0) [cnf transformation 61]
117. ~happy(X0) | strong(X0) | creative(X0) [cnf transformation 36]
128. happy(paul) [cnf transformation 23]
151. 6 <=> strong(paul) [avatar definition]
152. ~strong(paul) <- (~6) [avatar component clause 151]
155. 7 <=> happy(paul) [avatar definition]
157. happy(paul) <- (7) [avatar component clause 155]
165. 9 <=> strong(sK2) [avatar definition]
167. ~strong(sK2) <- (~9) [avatar component clause 165]
169. ~7 | ~6 | ~9 [avatar split clause 85,165,151,155]
218. patient(X0) | curious(X0) [subsumption resolution 101,81]
219. ~funny(X0) | patient(X0) [subsumption resolution 100,81]
239. 23 <=> patient(paul) [avatar definition]
240. patient(paul) <- (23) [avatar component clause 239]
274. 7 [avatar split clause 128,155]
283. strong(X0) | curious(X0) [resolution 218,91]
302. strong(paul) | creative(paul) <- (7) [resolution 117,157]
334. 34 <=> funny(sK2) [avatar definition]
335. ~funny(sK2) <- (~34) [avatar component clause 334]
336. funny(sK2) <- (34) [avatar component clause 334]
338. 35 <=> curious(sK2) [avatar definition]
339. curious(sK2) <- (35) [avatar component clause 338]
343. strong(X1) | funny(X1) | creative(X1) | quiet(X1) [resolution 75,91]
355. curious(sK2) <- (~9) [resolution 283,167]
358. 35 | 9 [avatar split clause 355,165,338]
359. patient(sK2) <- (34) [resolution 336,219]
362. ~tall(sK2) | ~quiet(sK2) <- (35) [resolution 339,72]
363. ~quiet(sK2) <- (35) [subsumption resolution 362,77]
365. funny(sK2) | creative(sK2) | quiet(sK2) <- (~9) [resolution 343,167]
370. strong(sK2) <- (34) [resolution 359,91]
372. $false <- (~9, 34) [subsumption resolution 370,167]
373. 9 | ~34 [avatar contradiction clause 372]
375. 36 <=> creative(paul) [avatar definition]
377. creative(paul) <- (36) [avatar component clause 375]
378. 36 | 6 | ~7 [avatar split clause 302,155,151,375]
379. funny(sK2) | creative(sK2) <- (~9, 35) [subsumption resolution 365,363]
381. 37 <=> creative(sK2) [avatar definition]
383. creative(sK2) <- (37) [avatar component clause 381]
384. 37 | 34 | 9 | ~35 [avatar split clause 379,338,165,334,381]
386. curious(paul) <- (~6) [resolution 152,283]
391. ~curious(paul) | funny(paul) <- (36) [resolution 377,80]
392. funny(paul) <- (~6, 36) [subsumption resolution 391,386]
395. ~curious(sK2) | funny(sK2) <- (37) [resolution 383,80]
396. funny(sK2) <- (35, 37) [subsumption resolution 395,339]
397. $false <- (~34, 35, 37) [subsumption resolution 396,335]
398. 34 | ~35 | ~37 [avatar contradiction clause 397]
419. patient(paul) <- (~6, 36) [resolution 392,219]
421. 23 | 6 | ~36 [avatar split clause 419,375,151,239]
424. strong(paul) <- (23) [resolution 240,91]
426. $false <- (~6, 23) [subsumption resolution 424,152]
427. 6 | ~23 [avatar contradiction clause 426]
428. $false [avatar sat refutation 169,274,358,373,378,384,398,421,427]
% SZS output end Proof for 6879673074095628893208879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not funny or not curious then someone is both generous and not kind.
Everyone who is kind or rich is not strong or not rich and vice versa.
If someone is not kind then someone is both rich and funny.
Everyone who is either not kind or not wise is not tall.
Everyone who is both creative and rich is not humble and vice versa.
Everyone who is quiet or not kind is not patient or happy and vice versa.
If john is calm then john is generous and vice versa.
Everyone who is either old or not humble is rich or not happy and vice versa.
If john is tall or not funny then someone is not generous.
Everyone who is not happy is curious or not old.
Everyone who is brave is not generous.
If mary is not humble then someone is old or curious.
If someone is either not generous or not happy then susan is quiet or not curious and vice versa.
If fred is both not calm and not tall then susan is creative or humble.
Everyone who is either creative or calm is both kind and not tall and vice versa.
Everyone who is both strong and brave is either not strong or old and vice versa.
Someone is not wise or humble.
Someone is either patient or not strong.
Susan is either patient or funny.
Someone is both not kind and quiet.
Fred is either patient or brave.
Someone is generous.
Someone is both not happy and not patient.
Someone is kind or humble. | Fred is humble. | entailment | (((~funny(alice)|~curious(alice)))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((kind(X)|rich(X))<=>(~strong(X)|~rich(X))))&
((?[X]:(~kind(X)))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((~kind(X)<~>~wise(X))=>~tall(X)))&
(![X]:((creative(X)&rich(X))<=>~humble(X)))&
(![X]:((quiet(X)|~kind(X))<=>(~patient(X)|happy(X))))&
((calm(john))<=>(generous(john)))&
(![X]:((old(X)<~>~humble(X))<=>(rich(X)|~happy(X))))&
(((tall(john)|~funny(john)))=>(?[X]:(~generous(X))))&
(![X]:(~happy(X)=>(curious(X)|~old(X))))&
(![X]:(brave(X)=>~generous(X)))&
((~humble(mary))=>(?[X]:((old(X)|curious(X)))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>((quiet(susan)|~curious(susan))))&
(((~calm(fred)&~tall(fred)))=>((creative(susan)|humble(susan))))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)&~tall(X))))&
(![X]:((strong(X)&brave(X))<=>(~strong(X)<~>old(X))))&
(?[X]:((~wise(X)|humble(X))))&
(?[X]:((patient(X)<~>~strong(X))))&
((patient(susan)<~>funny(susan)))&
(?[X]:((~kind(X)&quiet(X))))&
((patient(fred)<~>brave(fred)))&
(?[X]:(generous(X)))&
(?[X]:((~happy(X)&~patient(X))))&
(?[X]:((kind(X)|humble(X)))) | humble(fred) | [
"p1",
"p4",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 955116495816845934181547
% SZS output start Proof for 955116495816845934181547
2. ! [X0] : ((rich(X0) | kind(X0)) <=> (~rich(X0) | ~strong(X0))) [input p1]
5. ! [X0] : ((rich(X0) & creative(X0)) <=> ~humble(X0)) [input p4]
8. ! [X0] : ((old(X0) <~> ~humble(X0)) <=> (~happy(X0) | rich(X0))) [input p7]
16. ! [X0] : ((brave(X0) & strong(X0)) <=> (~strong(X0) <~> old(X0))) [input p15]
25. ~humble(fred) [input hypothesis]
39. ! [X0] : (((rich(X0) | kind(X0)) | (rich(X0) & strong(X0))) & ((~rich(X0) | ~strong(X0)) | (~rich(X0) & ~kind(X0)))) [nnf transformation 2]
40. ! [X0] : ((rich(X0) | kind(X0) | (rich(X0) & strong(X0))) & (~rich(X0) | ~strong(X0) | (~rich(X0) & ~kind(X0)))) [flattening 39]
45. ! [X0] : (((rich(X0) & creative(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) | ~creative(X0)))) [nnf transformation 5]
46. ! [X0] : (((rich(X0) & creative(X0)) | humble(X0)) & (~humble(X0) | ~rich(X0) | ~creative(X0))) [flattening 45]
50. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [nnf transformation 8]
51. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [flattening 50]
63. ! [X0] : (((brave(X0) & strong(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (~brave(X0) | ~strong(X0)))) [nnf transformation 16]
64. ! [X0] : (((brave(X0) & strong(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ~brave(X0) | ~strong(X0))) [flattening 63]
85. ~rich(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 40]
94. humble(X0) | rich(X0) [cnf transformation 46]
105. humble(X0) | ~old(X0) | ~rich(X0) [cnf transformation 51]
127. strong(X0) | old(X0) | strong(X0) [cnf transformation 64]
144. ~humble(fred) [cnf transformation 25]
146. old(X0) | strong(X0) [duplicate literal removal 127]
147. ~strong(X0) | ~rich(X0) [duplicate literal removal 85]
192. ~old(X0) | humble(X0) [subsumption resolution 105,94]
301. rich(fred) [resolution 94,144]
302. humble(X0) | strong(X0) [resolution 192,146]
303. strong(fred) [resolution 302,144]
304. ~rich(fred) [resolution 303,147]
305. $false [subsumption resolution 304,301]
% SZS output end Proof for 955116495816845934181547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and tall is both creative and not strong and vice versa. Everyone who is not creative is funny. Everyone who is kind is not curious. If susan is old then someone is both brave and old. Everyone who is brave or kind is either not kind or quiet. Everyone who is both not quiet and not happy is creative or not brave. Everyone who is either not tall or calm is both not happy and not rich and vice versa. Everyone who is either not quiet or wise is both rich and calm and vice versa. If someone is old then fred is both humble and not rich and vice versa. If someone is either not generous or strong then mary is not humble. If lucy is either tall or not funny then someone is tall and vice versa. Everyone who is rich is not funny or not humble. Everyone who is not generous is humble or tall. If paul is humble or strong then someone is either wise or creative and vice versa. If someone is both funny and strong then someone is funny or wise. If someone is calm then john is either not generous or generous. Someone is humble or brave. Susan is strong. Someone is not happy or not wise. Someone is either curious or old. Fred is either not wise or not rich. Someone is not brave. Someone is not brave or not creative. Paul is both calm and rich. | Paul is not tall. | entailment | (![X]:((old(X)&tall(X))<=>(creative(X)&~strong(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:(kind(X)=>~curious(X)))&
((old(susan))=>(?[X]:((brave(X)&old(X)))))&
(![X]:((brave(X)|kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~brave(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>(rich(X)&calm(X))))&
((?[X]:(old(X)))<=>((humble(fred)&~rich(fred))))&
((?[X]:((~generous(X)<~>strong(X))))=>(~humble(mary)))&
(((tall(lucy)<~>~funny(lucy)))<=>(?[X]:(tall(X))))&
(![X]:(rich(X)=>(~funny(X)|~humble(X))))&
(![X]:(~generous(X)=>(humble(X)|tall(X))))&
(((humble(paul)|strong(paul)))<=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((funny(X)|wise(X)))))&
((?[X]:(calm(X)))=>((~generous(john)<~>generous(john))))&
(?[X]:((humble(X)|brave(X))))&
(strong(susan))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~wise(fred)<~>~rich(fred)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|~creative(X))))&
((calm(paul)&rich(paul))) | ~tall(paul) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 911330109886277952179222
% SZS output start Proof for 911330109886277952179222
7. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> (~rich(X0) & ~happy(X0))) [input p6]
24. rich(paul) & calm(paul) [input p23]
25. tall(paul) [input hypothesis]
45. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (rich(X0) | happy(X0))) & ((~rich(X0) & ~happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | rich(X0) | happy(X0)) & ((~rich(X0) & ~happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [flattening 45]
96. ~rich(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 46]
134. calm(paul) [cnf transformation 24]
135. rich(paul) [cnf transformation 24]
136. tall(paul) [cnf transformation 25]
323. ~tall(paul) | ~calm(paul) [resolution 96,135]
325. ~calm(paul) [subsumption resolution 323,136]
326. $false [subsumption resolution 325,134]
% SZS output end Proof for 911330109886277952179222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is quiet then susan is either old or wise and vice versa.
Everyone who is both not old and not strong is both patient and not quiet and vice versa.
If someone is either not calm or brave then someone is curious.
Everyone who is both calm and patient is both not generous and old.
Everyone who is either creative or humble is not kind or not tall and vice versa.
If lucy is both not strong and not kind then fred is both not patient and tall and vice versa.
If someone is not strong or creative then someone is both brave and not calm and vice versa.
Everyone who is both funny and brave is both happy and wise.
Everyone who is not generous is calm and vice versa.
If someone is rich then lucy is both not generous and not strong.
If someone is either not funny or curious then paul is not funny or not calm.
If fred is funny or tall then paul is both not generous and strong and vice versa.
Everyone who is both not creative and kind is not kind and vice versa.
Everyone who is not rich is tall or not happy and vice versa.
If someone is both not generous and not humble then someone is both not funny and not old and vice versa.
If alice is not quiet then lucy is generous or funny and vice versa.
Paul is either not happy or old.
Alice is both calm and old.
Someone is either not happy or not brave.
Someone is both not rich and tall.
Someone is humble or not tall.
Someone is wise or old.
Someone is either happy or kind.
Susan is either creative or calm. | Paul is not kind. | contradiction | ((quiet(paul))<=>((old(susan)<~>wise(susan))))&
(![X]:((~old(X)&~strong(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((~calm(X)<~>brave(X))))=>(?[X]:(curious(X))))&
(![X]:((calm(X)&patient(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)<~>humble(X))<=>(~kind(X)|~tall(X))))&
(((~strong(lucy)&~kind(lucy)))<=>((~patient(fred)&tall(fred))))&
((?[X]:((~strong(X)|creative(X))))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((funny(X)&brave(X))=>(happy(X)&wise(X))))&
(![X]:(~generous(X)<=>calm(X)))&
((?[X]:(rich(X)))=>((~generous(lucy)&~strong(lucy))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~funny(paul)|~calm(paul))))&
(((funny(fred)|tall(fred)))<=>((~generous(paul)&strong(paul))))&
(![X]:((~creative(X)&kind(X))<=>~kind(X)))&
(![X]:(~rich(X)<=>(tall(X)|~happy(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((~funny(X)&~old(X)))))&
((~quiet(alice))<=>((generous(lucy)|funny(lucy))))&
((~happy(paul)<~>old(paul)))&
((calm(alice)&old(alice)))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((wise(X)|old(X))))&
(?[X]:((happy(X)<~>kind(X))))&
((creative(susan)<~>calm(susan))) | ~kind(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6615323144111807587244494
% SZS output start Proof for 6615323144111807587244494
13. ! [X0] : ((kind(X0) & ~creative(X0)) <=> ~kind(X0)) [input p12]
25. ~kind(paul) [input hypothesis]
60. ! [X0] : (((kind(X0) & ~creative(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) | creative(X0)))) [nnf transformation 13]
61. ! [X0] : (((kind(X0) & ~creative(X0)) | kind(X0)) & (~kind(X0) | ~kind(X0) | creative(X0))) [flattening 60]
125. kind(X0) | kind(X0) [cnf transformation 61]
148. ~kind(paul) [cnf transformation 25]
150. kind(X0) [duplicate literal removal 125]
349. $false [subsumption resolution 148,150]
% SZS output end Proof for 6615323144111807587244494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and patient is not patient or calm and vice versa. If alice is not quiet or curious then someone is both patient and humble and vice versa. Everyone who is wise or not strong is not kind or not old and vice versa. Everyone who is either not creative or not calm is not calm. Everyone who is rich is not wise or happy and vice versa. Everyone who is either not strong or not wise is both not tall and not curious and vice versa. Everyone who is patient or old is both happy and wise and vice versa. If someone is not calm or humble then someone is tall. If mary is not strong then someone is not brave and vice versa. Everyone who is not quiet is both not old and not calm and vice versa. If someone is wise or not humble then someone is either not wise or generous. Everyone who is either strong or not funny is creative or funny and vice versa. Everyone who is generous or curious is patient. Everyone who is both not old and not quiet is not generous or not quiet and vice versa. Everyone who is either not patient or not humble is both not generous and not old. Someone is not old. Someone is both brave and happy. Paul is not kind or not patient. Mary is either not generous or not funny. Someone is tall or funny. Someone is both strong and quiet. | Paul is quiet. | neutral | (![X]:((funny(X)&patient(X))<=>(~patient(X)|calm(X))))&
(((~quiet(alice)|curious(alice)))<=>(?[X]:((patient(X)&humble(X)))))&
(![X]:((wise(X)|~strong(X))<=>(~kind(X)|~old(X))))&
(![X]:((~creative(X)<~>~calm(X))=>~calm(X)))&
(![X]:(rich(X)<=>(~wise(X)|happy(X))))&
(![X]:((~strong(X)<~>~wise(X))<=>(~tall(X)&~curious(X))))&
(![X]:((patient(X)|old(X))<=>(happy(X)&wise(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:(tall(X))))&
((~strong(mary))<=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>(~old(X)&~calm(X))))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>(creative(X)|funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(![X]:((~old(X)&~quiet(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~patient(X)<~>~humble(X))=>(~generous(X)&~old(X))))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)&happy(X))))&
((~kind(paul)|~patient(paul)))&
((~generous(mary)<~>~funny(mary)))&
(?[X]:((tall(X)|funny(X))))&
(?[X]:((strong(X)&quiet(X)))) | quiet(paul) | [] | null | 0 |
Everyone who is either not patient or humble is generous.
Everyone who is not quiet or strong is either wise or not rich.
Everyone who is happy or old is strong and vice versa.
If someone is not rich or not creative then alice is quiet or not strong.
Everyone who is both not strong and not wise is both not tall and patient and vice versa.
If mary is rich or not humble then mary is either calm or wise.
Everyone who is either tall or not rich is both not strong and funny.
If paul is wise or not funny then fred is either not kind or humble.
Everyone who is either not patient or not funny is brave and vice versa.
Everyone who is either not old or not creative is not creative and vice versa.
Everyone who is not wise or humble is both rich and calm.
Everyone who is either not old or funny is old.
If fred is both curious and not creative then fred is not quiet or creative.
If fred is both not brave and calm then mary is not patient or rich and vice versa.
Everyone who is generous or humble is kind or quiet and vice versa.
If someone is happy then lucy is either not patient or generous.
Someone is either creative or not strong.
Paul is either not old or not funny.
Paul is either quiet or not humble.
Lucy is not kind or wise.
Someone is either wise or curious.
Someone is either not humble or tall. | Alice is not wise. | contradiction | (![X]:((~patient(X)<~>humble(X))=>generous(X)))&
(![X]:((~quiet(X)|strong(X))=>(wise(X)<~>~rich(X))))&
(![X]:((happy(X)|old(X))<=>strong(X)))&
((?[X]:((~rich(X)|~creative(X))))=>((quiet(alice)|~strong(alice))))&
(![X]:((~strong(X)&~wise(X))<=>(~tall(X)&patient(X))))&
(((rich(mary)|~humble(mary)))=>((calm(mary)<~>wise(mary))))&
(![X]:((tall(X)<~>~rich(X))=>(~strong(X)&funny(X))))&
(((wise(paul)|~funny(paul)))=>((~kind(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>~funny(X))<=>brave(X)))&
(![X]:((~old(X)<~>~creative(X))<=>~creative(X)))&
(![X]:((~wise(X)|humble(X))=>(rich(X)&calm(X))))&
(![X]:((~old(X)<~>funny(X))=>old(X)))&
(((curious(fred)&~creative(fred)))=>((~quiet(fred)|creative(fred))))&
(((~brave(fred)&calm(fred)))<=>((~patient(mary)|rich(mary))))&
(![X]:((generous(X)|humble(X))<=>(kind(X)|quiet(X))))&
((?[X]:(happy(X)))=>((~patient(lucy)<~>generous(lucy))))&
(?[X]:((creative(X)<~>~strong(X))))&
((~old(paul)<~>~funny(paul)))&
((quiet(paul)<~>~humble(paul)))&
((~kind(lucy)|wise(lucy)))&
(?[X]:((wise(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>tall(X)))) | ~wise(alice) | [
"p1",
"p2",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3400050558238494904362877
% SZS output start Proof for 3400050558238494904362877
2. ! [X0] : ((strong(X0) | ~quiet(X0)) => (wise(X0) <~> ~rich(X0))) [input p1]
3. ! [X0] : ((old(X0) | happy(X0)) <=> strong(X0)) [input p2]
10. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p9]
11. ! [X0] : ((humble(X0) | ~wise(X0)) => (calm(X0) & rich(X0))) [input p10]
23. ~wise(alice) [input hypothesis]
25. ! [X0] : ((wise(X0) <~> ~rich(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 2]
31. ! [X0] : ((calm(X0) & rich(X0)) | (~humble(X0) & wise(X0))) [ennf transformation 11]
37. ! [X0] : (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~strong(X0) & quiet(X0))) [nnf transformation 25]
38. ! [X0] : (((old(X0) | happy(X0)) | ~strong(X0)) & (strong(X0) | (~old(X0) & ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : ((old(X0) | happy(X0) | ~strong(X0)) & (strong(X0) | (~old(X0) & ~happy(X0)))) [flattening 38]
46. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | creative(X0)) & (~creative(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 10]
67. ~rich(X0) | wise(X0) | ~strong(X0) [cnf transformation 37]
71. ~old(X0) | strong(X0) [cnf transformation 39]
95. ~creative(X0) | ~creative(X0) | old(X0) [cnf transformation 46]
98. creative(X0) | old(X0) | creative(X0) [cnf transformation 46]
99. rich(X0) | wise(X0) [cnf transformation 31]
128. ~wise(alice) [cnf transformation 23]
131. ~creative(X0) | old(X0) [duplicate literal removal 95]
132. creative(X0) | old(X0) [duplicate literal removal 98]
189. old(X0) [subsumption resolution 131,132]
284. strong(X0) [resolution 71,189]
308. wise(X0) | ~strong(X0) | wise(X0) [resolution 67,99]
310. wise(X0) | ~strong(X0) [duplicate literal removal 308]
311. wise(X0) [subsumption resolution 310,284]
312. $false [resolution 311,128]
% SZS output end Proof for 3400050558238494904362877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not quiet then someone is wise and vice versa. Everyone who is kind or not strong is either generous or not kind. Everyone who is not quiet or not rich is both not happy and not patient. Everyone who is not old or not wise is either rich or not tall and vice versa. If someone is both brave and tall then someone is both not wise and not creative and vice versa. Everyone who is curious is not happy and vice versa. Everyone who is both not generous and quiet is not generous or not kind. Everyone who is either not kind or happy is both not curious and creative. Everyone who is not generous is not kind or not tall and vice versa. Everyone who is both patient and curious is either not calm or happy and vice versa. Everyone who is not happy or curious is either old or not wise and vice versa. If mary is either not strong or humble then someone is not wise or tall. Everyone who is both not creative and not kind is humble or generous and vice versa. If someone is either wise or quiet then someone is tall and vice versa. Everyone who is kind or not creative is both not quiet and generous and vice versa. John is not wise. Paul is either happy or not happy. Someone is generous or happy. Susan is wise or not funny. Someone is both happy and quiet. Someone is not old. Fred is either not strong or not curious. | John is brave. | contradiction | ((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~curious(X)&creative(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~tall(X))))&
(![X]:((patient(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~happy(X)|curious(X))<=>(old(X)<~>~wise(X))))&
(((~strong(mary)<~>humble(mary)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(humble(X)|generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)|~creative(X))<=>(~quiet(X)&generous(X))))&
(~wise(john))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((generous(X)|happy(X))))&
((wise(susan)|~funny(susan)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:(~old(X)))&
((~strong(fred)<~>~curious(fred))) | brave(john) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 434280802924458274340775
% SZS output start Proof for 434280802924458274340775
2. ! [X0] : ((~strong(X0) | kind(X0)) => (generous(X0) <~> ~kind(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | ~quiet(X0)) => (~patient(X0) & ~happy(X0))) [input p2]
4. ! [X0] : ((~wise(X0) | ~old(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p3]
5. ? [X0] : (tall(X0) & brave(X0)) <=> ? [X0] : (~creative(X0) & ~wise(X0)) [input p4]
6. ! [X0] : (curious(X0) <=> ~happy(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> happy(X0)) => (creative(X0) & ~curious(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (~tall(X0) | ~kind(X0))) [input p8]
13. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (generous(X0) | humble(X0))) [input p12]
15. ! [X0] : ((~creative(X0) | kind(X0)) <=> (generous(X0) & ~quiet(X0))) [input p14]
16. ~wise(john) [input p15]
23. brave(john) [input hypothesis]
25. ? [X0] : (tall(X0) & brave(X0)) <=> ? [X1] : (~creative(X1) & ~wise(X1)) [rectify 5]
28. ! [X0] : ((generous(X0) <~> ~kind(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 2]
29. ! [X0] : ((~patient(X0) & ~happy(X0)) | (rich(X0) & quiet(X0))) [ennf transformation 3]
32. ! [X0] : ((creative(X0) & ~curious(X0)) | (~kind(X0) <=> happy(X0))) [ennf transformation 8]
39. ! [X0] : (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (strong(X0) & ~kind(X0))) [nnf transformation 28]
40. ! [X0] : (((~wise(X0) | ~old(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (wise(X0) & old(X0)))) [nnf transformation 4]
41. ! [X0] : ((~wise(X0) | ~old(X0) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (wise(X0) & old(X0)))) [flattening 40]
42. (? [X0] : (tall(X0) & brave(X0)) | ! [X1] : (creative(X1) | wise(X1))) & (? [X1] : (~creative(X1) & ~wise(X1)) | ! [X0] : (~tall(X0) | ~brave(X0))) [nnf transformation 25]
43. (? [X0] : (tall(X0) & brave(X0)) | ! [X1] : (creative(X1) | wise(X1))) & (? [X2] : (~creative(X2) & ~wise(X2)) | ! [X3] : (~tall(X3) | ~brave(X3))) [rectify 42]
44. ? [X0] : (tall(X0) & brave(X0)) => (tall(sK2) & brave(sK2)) [choice axiom]
45. ? [X2] : (~creative(X2) & ~wise(X2)) => (~creative(sK3) & ~wise(sK3)) [choice axiom]
46. ((tall(sK2) & brave(sK2)) | ! [X1] : (creative(X1) | wise(X1))) & ((~creative(sK3) & ~wise(sK3)) | ! [X3] : (~tall(X3) | ~brave(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))) [nnf transformation 6]
48. ! [X0] : ((creative(X0) & ~curious(X0)) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 32]
49. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 9]
50. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | generous(X0))) [flattening 49]
58. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 13]
59. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | kind(X0) | creative(X0))) [flattening 58]
65. ! [X0] : (((~creative(X0) | kind(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (creative(X0) & ~kind(X0)))) [nnf transformation 15]
66. ! [X0] : ((~creative(X0) | kind(X0) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | (creative(X0) & ~kind(X0)))) [flattening 65]
78. ~kind(X0) | generous(X0) | ~kind(X0) [cnf transformation 39]
83. ~happy(X0) | rich(X0) [cnf transformation 29]
89. ~rich(X0) | tall(X0) | wise(X0) [cnf transformation 41]
93. ~creative(sK3) | ~tall(X3) | ~brave(X3) [cnf transformation 46]
96. ~curious(X0) | ~happy(X0) [cnf transformation 47]
97. curious(X0) | happy(X0) [cnf transformation 47]
99. ~curious(X0) | happy(X0) | kind(X0) [cnf transformation 48]
104. ~generous(X0) | kind(X0) [cnf transformation 50]
124. ~kind(X0) | ~generous(X0) [cnf transformation 59]
132. generous(X0) | creative(X0) [cnf transformation 66]
134. ~wise(john) [cnf transformation 16]
143. brave(john) [cnf transformation 23]
144. ~kind(X0) | generous(X0) [duplicate literal removal 78]
183. 10 <=> ! [X3] : (~tall(X3) | ~brave(X3)) [avatar definition]
184. ~brave(X3) | ~tall(X3) <- (10) [avatar component clause 183]
186. 11 <=> creative(sK3) [avatar definition]
188. ~creative(sK3) <- (~11) [avatar component clause 186]
189. 10 | ~11 [avatar split clause 93,186,183]
195. ~curious(X0) | kind(X0) [subsumption resolution 99,96]
219. ~generous(X0) [subsumption resolution 124,104]
246. creative(X0) [subsumption resolution 132,219]
258. $false <- (~11) [subsumption resolution 188,246]
259. 11 [avatar contradiction clause 258]
270. ~tall(john) <- (10) [resolution 184,143]
271. happy(X0) | kind(X0) [resolution 195,97]
272. rich(X0) | kind(X0) [resolution 271,83]
335. tall(X0) | wise(X0) | kind(X0) [resolution 89,272]
563. 46 <=> kind(john) [avatar definition]
564. ~kind(john) <- (~46) [avatar component clause 563]
565. kind(john) <- (46) [avatar component clause 563]
572. generous(john) <- (46) [resolution 565,144]
575. $false <- (46) [subsumption resolution 572,219]
576. ~46 [avatar contradiction clause 575]
579. wise(john) | kind(john) <- (10) [resolution 335,270]
584. kind(john) <- (10) [subsumption resolution 579,134]
585. $false <- (10, ~46) [subsumption resolution 584,564]
586. ~10 | 46 [avatar contradiction clause 585]
587. $false [avatar sat refutation 189,259,576,586]
% SZS output end Proof for 434280802924458274340775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not brave then alice is not patient. If someone is both not generous and not kind then someone is old or happy and vice versa. If someone is either not happy or calm then fred is both rich and not brave. Everyone who is generous is not tall or humble and vice versa. If mary is happy then someone is both not rich and brave and vice versa. Everyone who is both not humble and wise is both creative and quiet and vice versa. If someone is either brave or not rich then susan is both calm and not funny and vice versa. Everyone who is not funny is curious. If someone is either calm or patient then someone is not funny. Everyone who is not tall or old is not curious and vice versa. If someone is wise or not creative then someone is either not quiet or kind. If alice is both tall and generous then someone is either not happy or strong and vice versa. Everyone who is not happy is both not curious and not old. Everyone who is both not kind and rich is either not kind or patient and vice versa. If alice is either generous or not curious then someone is patient and vice versa. Everyone who is not old or not happy is wise. John is either not creative or curious. Someone is both humble and not brave. Someone is generous. Someone is brave or not calm. Someone is strong. Susan is generous or strong. Mary is generous. Mary is both not tall and calm. | Mary is not curious. | entailment | ((?[X]:((patient(X)<~>~brave(X))))=>(~patient(alice)))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((~happy(X)<~>calm(X))))=>((rich(fred)&~brave(fred))))&
(![X]:(generous(X)<=>(~tall(X)|humble(X))))&
((happy(mary))<=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:((~humble(X)&wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((brave(X)<~>~rich(X))))<=>((calm(susan)&~funny(susan))))&
(![X]:(~funny(X)=>curious(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|old(X))<=>~curious(X)))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((tall(alice)&generous(alice)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~happy(X)=>(~curious(X)&~old(X))))&
(![X]:((~kind(X)&rich(X))<=>(~kind(X)<~>patient(X))))&
(((generous(alice)<~>~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~old(X)|~happy(X))=>wise(X)))&
((~creative(john)<~>curious(john)))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:(strong(X)))&
((generous(susan)|strong(susan)))&
(generous(mary))&
((~tall(mary)&calm(mary))) | ~curious(mary) | [
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 618754280561822776386290
% SZS output start Proof for 618754280561822776386290
10. ! [X0] : ((old(X0) | ~tall(X0)) <=> ~curious(X0)) [input p9]
24. calm(mary) & ~tall(mary) [input p23]
25. curious(mary) [input hypothesis]
60. ! [X0] : (((old(X0) | ~tall(X0)) | curious(X0)) & (~curious(X0) | (~old(X0) & tall(X0)))) [nnf transformation 10]
61. ! [X0] : ((old(X0) | ~tall(X0) | curious(X0)) & (~curious(X0) | (~old(X0) & tall(X0)))) [flattening 60]
116. ~curious(X0) | tall(X0) [cnf transformation 61]
152. ~tall(mary) [cnf transformation 24]
154. curious(mary) [cnf transformation 25]
370. tall(mary) [resolution 116,154]
372. $false [subsumption resolution 370,152]
% SZS output end Proof for 618754280561822776386290
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not wise or not kind and vice versa.
Everyone who is either not wise or not curious is both kind and strong and vice versa.
Everyone who is calm is both wise and brave.
If someone is not wise or not funny then john is either not brave or funny and vice versa.
If susan is either not generous or strong then someone is either patient or not funny and vice versa.
If someone is not curious or brave then john is either not happy or not generous.
If john is not old or generous then paul is patient or old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Alice is either wise or not generous.
Paul is either not funny or old.
Mary is wise.
Alice is not curious or funny.
Paul is both not generous and not creative.
Alice is not creative. | Alice is not quiet. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(kind(X)&strong(X))))&
(![X]:(calm(X)=>(wise(X)&brave(X))))&
((?[X]:((~wise(X)|~funny(X))))<=>((~brave(john)<~>funny(john))))&
(((~generous(susan)<~>strong(susan)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((~curious(X)|brave(X))))=>((~happy(john)<~>~generous(john))))&
(((~old(john)|generous(john)))=>((patient(paul)|old(paul))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
((wise(alice)<~>~generous(alice)))&
((~funny(paul)<~>old(paul)))&
(wise(mary))&
((~curious(alice)|funny(alice)))&
((~generous(paul)&~creative(paul)))&
(~creative(alice)) | ~quiet(alice) | [
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8110791923236447625393639
% SZS output start Proof for 8110791923236447625393639
13. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p12]
22. ~creative(alice) [input p21]
23. ~quiet(alice) [input hypothesis]
61. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 13]
62. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 61]
113. creative(X0) | quiet(X0) [cnf transformation 62]
128. ~creative(alice) [cnf transformation 22]
129. ~quiet(alice) [cnf transformation 23]
302. quiet(alice) [resolution 113,128]
303. $false [subsumption resolution 302,129]
% SZS output end Proof for 8110791923236447625393639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not calm is either not funny or tall and vice versa.
Everyone who is happy is either not creative or generous and vice versa.
Everyone who is both not creative and not generous is curious.
If someone is both not funny and quiet then someone is both funny and creative and vice versa.
Everyone who is generous is either not tall or quiet.
Everyone who is both kind and not funny is not humble or rich and vice versa.
If someone is kind or not kind then mary is either not humble or quiet and vice versa.
If lucy is old then alice is not funny.
Everyone who is not strong or humble is either not curious or not kind and vice versa.
Everyone who is quiet is generous or not humble and vice versa.
Everyone who is not old or not rich is not quiet and vice versa.
If someone is kind or not kind then mary is not tall or brave and vice versa.
If lucy is either not quiet or funny then mary is not funny.
Everyone who is either happy or brave is both not quiet and not rich.
Everyone who is both humble and not humble is both kind and creative.
Alice is not brave or funny.
Lucy is not kind or not brave.
Paul is both calm and not old.
Someone is creative or not generous.
Someone is humble or not calm.
Susan is strong. | Alice is strong. | neutral | (![X]:((~curious(X)<~>~calm(X))<=>(~funny(X)<~>tall(X))))&
(![X]:(happy(X)<=>(~creative(X)<~>generous(X))))&
(![X]:((~creative(X)&~generous(X))=>curious(X)))&
((?[X]:((~funny(X)&quiet(X))))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:(generous(X)=>(~tall(X)<~>quiet(X))))&
(![X]:((kind(X)&~funny(X))<=>(~humble(X)|rich(X))))&
((?[X]:((kind(X)|~kind(X))))<=>((~humble(mary)<~>quiet(mary))))&
((old(lucy))=>(~funny(alice)))&
(![X]:((~strong(X)|humble(X))<=>(~curious(X)<~>~kind(X))))&
(![X]:(quiet(X)<=>(generous(X)|~humble(X))))&
(![X]:((~old(X)|~rich(X))<=>~quiet(X)))&
((?[X]:((kind(X)|~kind(X))))<=>((~tall(mary)|brave(mary))))&
(((~quiet(lucy)<~>funny(lucy)))=>(~funny(mary)))&
(![X]:((happy(X)<~>brave(X))=>(~quiet(X)&~rich(X))))&
(![X]:((humble(X)&~humble(X))=>(kind(X)&creative(X))))&
((~brave(alice)|funny(alice)))&
((~kind(lucy)|~brave(lucy)))&
((calm(paul)&~old(paul)))&
(?[X]:((creative(X)|~generous(X))))&
(?[X]:((humble(X)|~calm(X))))&
(strong(susan)) | strong(alice) | [] | null | 0 |
If someone is either not kind or not generous then alice is either wise or not patient. If someone is funny then someone is not quiet or quiet. Everyone who is either not kind or rich is not happy and vice versa. Everyone who is not patient is not happy and vice versa. Everyone who is either wise or not tall is not generous and vice versa. If someone is not generous then susan is both not curious and not strong and vice versa. Everyone who is both tall and curious is tall and vice versa. If mary is both calm and not humble then someone is not patient or not wise. Everyone who is not calm or kind is both not old and happy. Everyone who is either old or not humble is not calm or not strong. If someone is both not quiet and happy then john is rich. Everyone who is either rich or not creative is not creative. If paul is calm then paul is both not old and strong. Everyone who is either not funny or curious is generous or old. If lucy is not wise or not humble then john is either strong or not funny. Everyone who is either not quiet or creative is either not happy or curious and vice versa. Lucy is not creative. Someone is both brave and humble. Paul is curious or not creative. Someone is not humble. Someone is both humble and not generous. John is kind. Someone is either not brave or tall. Someone is both curious and generous. | John is not rich. | entailment | ((?[X]:((~kind(X)<~>~generous(X))))=>((wise(alice)<~>~patient(alice))))&
((?[X]:(funny(X)))=>(?[X]:((~quiet(X)|quiet(X)))))&
(![X]:((~kind(X)<~>rich(X))<=>~happy(X)))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((wise(X)<~>~tall(X))<=>~generous(X)))&
((?[X]:(~generous(X)))<=>((~curious(susan)&~strong(susan))))&
(![X]:((tall(X)&curious(X))<=>tall(X)))&
(((calm(mary)&~humble(mary)))=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((~calm(X)|kind(X))=>(~old(X)&happy(X))))&
(![X]:((old(X)<~>~humble(X))=>(~calm(X)|~strong(X))))&
((?[X]:((~quiet(X)&happy(X))))=>(rich(john)))&
(![X]:((rich(X)<~>~creative(X))=>~creative(X)))&
((calm(paul))=>((~old(paul)&strong(paul))))&
(![X]:((~funny(X)<~>curious(X))=>(generous(X)|old(X))))&
(((~wise(lucy)|~humble(lucy)))=>((strong(john)<~>~funny(john))))&
(![X]:((~quiet(X)<~>creative(X))<=>(~happy(X)<~>curious(X))))&
(~creative(lucy))&
(?[X]:((brave(X)&humble(X))))&
((curious(paul)|~creative(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)&~generous(X))))&
(kind(john))&
(?[X]:((~brave(X)<~>tall(X))))&
(?[X]:((curious(X)&generous(X)))) | ~rich(john) | [
"p2",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7612876386505519304913137
% SZS output start Proof for 7612876386505519304913137
3. ! [X0] : ((~kind(X0) <~> rich(X0)) <=> ~happy(X0)) [input p2]
9. ! [X0] : ((kind(X0) | ~calm(X0)) => (happy(X0) & ~old(X0))) [input p8]
22. kind(john) [input p21]
25. rich(john) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~old(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 9]
44. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | happy(X0)) & (~happy(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [nnf transformation 3]
78. ~happy(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 44]
97. ~kind(X0) | happy(X0) [cnf transformation 31]
126. kind(john) [cnf transformation 22]
131. rich(john) [cnf transformation 25]
191. 14 <=> rich(john) [avatar definition]
193. rich(john) <- (14) [avatar component clause 191]
244. 14 [avatar split clause 131,191]
246. happy(john) [resolution 97,126]
261. ~kind(john) | ~rich(john) [resolution 78,246]
262. ~rich(john) [subsumption resolution 261,126]
263. $false <- (14) [subsumption resolution 262,193]
264. ~14 [avatar contradiction clause 263]
265. $false [avatar sat refutation 244,264]
% SZS output end Proof for 7612876386505519304913137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not creative is both rich and kind and vice versa.
Everyone who is both generous and not brave is not wise and vice versa.
If lucy is both rich and brave then someone is either calm or not brave and vice versa.
Everyone who is funny is both old and not creative.
Everyone who is both not old and wise is humble or wise and vice versa.
If john is both old and wise then fred is both rich and not tall.
Everyone who is either not brave or not calm is not strong or not curious and vice versa.
Everyone who is either kind or old is both happy and not strong and vice versa.
Everyone who is patient is either not humble or not brave.
Everyone who is either not tall or kind is either humble or curious and vice versa.
Everyone who is either calm or curious is curious or generous and vice versa.
If paul is either kind or not wise then someone is both tall and not quiet.
Everyone who is wise is either creative or brave and vice versa.
If alice is happy or generous then someone is not strong or patient and vice versa.
Everyone who is both not rich and creative is not curious and vice versa.
Everyone who is rich is humble and vice versa.
Lucy is not kind.
Someone is either creative or quiet.
Paul is either not old or not strong.
Lucy is creative or curious.
Fred is both not happy and tall.
Someone is either not wise or not generous.
Someone is either not humble or not curious.
Alice is both happy and brave. | Alice is humble. | contradiction | (![X]:((~calm(X)<~>~creative(X))<=>(rich(X)&kind(X))))&
(![X]:((generous(X)&~brave(X))<=>~wise(X)))&
(((rich(lucy)&brave(lucy)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(old(X)&~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(humble(X)|wise(X))))&
(((old(john)&wise(john)))=>((rich(fred)&~tall(fred))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~strong(X)|~curious(X))))&
(![X]:((kind(X)<~>old(X))<=>(happy(X)&~strong(X))))&
(![X]:(patient(X)=>(~humble(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>kind(X))<=>(humble(X)<~>curious(X))))&
(![X]:((calm(X)<~>curious(X))<=>(curious(X)|generous(X))))&
(((kind(paul)<~>~wise(paul)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:(wise(X)<=>(creative(X)<~>brave(X))))&
(((happy(alice)|generous(alice)))<=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:((~rich(X)&creative(X))<=>~curious(X)))&
(![X]:(rich(X)<=>humble(X)))&
(~kind(lucy))&
(?[X]:((creative(X)<~>quiet(X))))&
((~old(paul)<~>~strong(paul)))&
((creative(lucy)|curious(lucy)))&
((~happy(fred)&tall(fred)))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
((happy(alice)&brave(alice))) | humble(alice) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p10",
"p12",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4998600650089033236678975
% SZS output start Proof for 4998600650089033236678975
1. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (kind(X0) & rich(X0))) [input p0]
2. ! [X0] : ((~brave(X0) & generous(X0)) <=> ~wise(X0)) [input p1]
5. ! [X0] : ((wise(X0) & ~old(X0)) <=> (wise(X0) | humble(X0))) [input p4]
7. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (~curious(X0) | ~strong(X0))) [input p6]
8. ! [X0] : ((kind(X0) <~> old(X0)) <=> (~strong(X0) & happy(X0))) [input p7]
11. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (generous(X0) | curious(X0))) [input p10]
13. ! [X0] : (wise(X0) <=> (creative(X0) <~> brave(X0))) [input p12]
15. ! [X0] : ((creative(X0) & ~rich(X0)) <=> ~curious(X0)) [input p14]
16. ! [X0] : (rich(X0) <=> humble(X0)) [input p15]
24. brave(alice) & happy(alice) [input p23]
25. humble(alice) [input hypothesis]
31. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 1]
32. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 31]
33. ! [X0] : (((~brave(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | (brave(X0) | ~generous(X0)))) [nnf transformation 2]
34. ! [X0] : (((~brave(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | brave(X0) | ~generous(X0))) [flattening 33]
40. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~wise(X0) | old(X0))) [flattening 40]
42. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 7]
43. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [flattening 42]
44. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [flattening 44]
48. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 11]
49. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [flattening 48]
53. ! [X0] : ((wise(X0) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0)))) & (((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | ~wise(X0))) [nnf transformation 13]
59. ! [X0] : (((creative(X0) & ~rich(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | rich(X0)))) [nnf transformation 15]
60. ! [X0] : (((creative(X0) & ~rich(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | rich(X0))) [flattening 59]
61. ! [X0] : ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))) [nnf transformation 16]
77. ~kind(X0) | calm(X0) | creative(X0) | ~rich(X0) [cnf transformation 32]
80. ~brave(X0) | wise(X0) [cnf transformation 34]
88. ~humble(X0) | ~old(X0) [cnf transformation 41]
95. ~curious(X0) | ~strong(X0) | ~brave(X0) | calm(X0) [cnf transformation 43]
96. ~brave(X0) | ~calm(X0) | strong(X0) [cnf transformation 43]
104. ~happy(X0) | kind(X0) | strong(X0) | old(X0) [cnf transformation 45]
120. ~curious(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 49]
127. ~brave(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 53]
128. wise(X0) | brave(X0) | ~creative(X0) [cnf transformation 53]
136. curious(X0) | creative(X0) [cnf transformation 60]
138. ~humble(X0) | rich(X0) [cnf transformation 61]
151. happy(alice) [cnf transformation 24]
152. brave(alice) [cnf transformation 24]
153. humble(alice) [cnf transformation 25]
155. ~curious(X0) | ~calm(X0) [duplicate literal removal 120]
205. ~creative(X0) | wise(X0) [subsumption resolution 128,80]
206. ~brave(X0) | ~creative(X0) [subsumption resolution 127,205]
211. 12 <=> happy(alice) [avatar definition]
213. happy(alice) <- (12) [avatar component clause 211]
272. 12 [avatar split clause 151,211]
275. ~old(alice) [resolution 88,153]
287. rich(alice) [resolution 138,153]
289. ~calm(X0) | creative(X0) [resolution 155,136]
303. ~creative(alice) [resolution 206,152]
318. ~calm(alice) | strong(alice) [resolution 96,152]
321. 27 <=> strong(alice) [avatar definition]
323. strong(alice) <- (27) [avatar component clause 321]
325. 28 <=> calm(alice) [avatar definition]
327. ~calm(alice) <- (~28) [avatar component clause 325]
328. 27 | ~28 [avatar split clause 318,325,321]
459. ~strong(X1) | ~brave(X1) | calm(X1) | creative(X1) [resolution 95,136]
464. ~strong(X1) | ~brave(X1) | creative(X1) [subsumption resolution 459,289]
465. ~strong(X1) | ~brave(X1) [subsumption resolution 464,206]
475. kind(alice) | strong(alice) | old(alice) <- (12) [resolution 104,213]
476. kind(alice) | strong(alice) <- (12) [subsumption resolution 475,275]
478. 42 <=> kind(alice) [avatar definition]
480. kind(alice) <- (42) [avatar component clause 478]
481. 27 | 42 | ~12 [avatar split clause 476,211,478,321]
483. calm(alice) | creative(alice) | ~rich(alice) <- (42) [resolution 480,77]
486. creative(alice) | ~rich(alice) <- (~28, 42) [subsumption resolution 483,327]
487. ~rich(alice) <- (~28, 42) [subsumption resolution 486,303]
488. $false <- (~28, 42) [subsumption resolution 487,287]
489. 28 | ~42 [avatar contradiction clause 488]
582. ~brave(alice) <- (27) [resolution 465,323]
584. $false <- (27) [subsumption resolution 582,152]
585. ~27 [avatar contradiction clause 584]
588. $false [avatar sat refutation 272,328,481,489,585]
% SZS output end Proof for 4998600650089033236678975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not quiet or old and vice versa.
Everyone who is both patient and kind is not rich and vice versa.
Everyone who is patient is both not happy and not old.
If john is wise or old then someone is either not brave or old and vice versa.
Everyone who is not creative or funny is both generous and not happy and vice versa.
If someone is either quiet or curious then susan is either kind or not rich.
If someone is funny then someone is both not curious and not funny and vice versa.
Everyone who is both rich and not curious is not happy and vice versa.
If someone is not quiet then someone is both tall and quiet.
Everyone who is not happy or not wise is rich or tall and vice versa.
If someone is either tall or not strong then mary is both not tall and funny.
If someone is not wise or not kind then someone is not rich.
If someone is brave or curious then fred is either not happy or not brave.
If john is both patient and not funny then someone is not old or not tall and vice versa.
Everyone who is both not brave and happy is humble or not tall and vice versa.
If john is both brave and generous then susan is not funny.
Susan is not rich or tall.
Someone is quiet or old.
Paul is both quiet and old.
Mary is both not happy and brave.
Someone is either not wise or not curious.
Someone is not tall or funny.
Susan is not strong. | Susan is curious. | contradiction | (![X]:(~patient(X)<=>(~quiet(X)|old(X))))&
(![X]:((patient(X)&kind(X))<=>~rich(X)))&
(![X]:(patient(X)=>(~happy(X)&~old(X))))&
(((wise(john)|old(john)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~creative(X)|funny(X))<=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((kind(susan)<~>~rich(susan))))&
((?[X]:(funny(X)))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((rich(X)&~curious(X))<=>~happy(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~happy(X)|~wise(X))<=>(rich(X)|tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~tall(mary)&funny(mary))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
((~rich(susan)|tall(susan)))&
(?[X]:((quiet(X)|old(X))))&
((quiet(paul)&old(paul)))&
((~happy(mary)&brave(mary)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((~tall(X)|funny(X))))&
(~strong(susan)) | curious(susan) | [
"p1",
"p2",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 43225379368591825878327
% SZS output start Proof for 43225379368591825878327
2. ! [X0] : ((kind(X0) & patient(X0)) <=> ~rich(X0)) [input p1]
3. ! [X0] : (patient(X0) => (~old(X0) & ~happy(X0))) [input p2]
8. ! [X0] : ((~curious(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
10. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (tall(X0) | rich(X0))) [input p9]
12. ? [X0] : (~kind(X0) | ~wise(X0)) => ? [X0] : ~rich(X0) [input p11]
24. curious(susan) [input hypothesis]
27. ? [X0] : (~kind(X0) | ~wise(X0)) => ? [X1] : ~rich(X1) [rectify 12]
28. ! [X0] : ((~old(X0) & ~happy(X0)) | ~patient(X0)) [ennf transformation 3]
32. ? [X1] : ~rich(X1) | ! [X0] : (kind(X0) & wise(X0)) [ennf transformation 27]
38. ! [X0] : (((kind(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : (((kind(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | ~kind(X0) | ~patient(X0))) [flattening 38]
53. ! [X0] : (((~curious(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) | ~rich(X0)))) [nnf transformation 8]
54. ! [X0] : (((~curious(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | curious(X0) | ~rich(X0))) [flattening 53]
58. ! [X0] : (((~wise(X0) | ~happy(X0)) | (~tall(X0) & ~rich(X0))) & ((tall(X0) | rich(X0)) | (wise(X0) & happy(X0)))) [nnf transformation 10]
59. ! [X0] : ((~wise(X0) | ~happy(X0) | (~tall(X0) & ~rich(X0))) & (tall(X0) | rich(X0) | (wise(X0) & happy(X0)))) [flattening 58]
61. ? [X0] : ~rich(X0) | ! [X1] : (kind(X1) & wise(X1)) [rectify 32]
62. ? [X0] : ~rich(X0) => ~rich(sK4) [choice axiom]
63. ~rich(sK4) | ! [X1] : (kind(X1) & wise(X1)) [skolemisation 61,62]
83. rich(X0) | patient(X0) [cnf transformation 39]
85. ~happy(X0) | ~patient(X0) [cnf transformation 28]
106. happy(X0) | rich(X0) [cnf transformation 54]
107. ~curious(X0) | happy(X0) [cnf transformation 54]
112. ~wise(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 59]
118. ~rich(sK4) | wise(X1) [cnf transformation 63]
145. curious(susan) [cnf transformation 24]
252. 24 <=> rich(sK4) [avatar definition]
254. ~rich(sK4) <- (~24) [avatar component clause 252]
257. 25 <=> ! [X1] : wise(X1) [avatar definition]
258. wise(X1) <- (25) [avatar component clause 257]
259. 25 | ~24 [avatar split clause 118,252,257]
386. rich(X1) | ~patient(X1) [resolution 106,85]
387. rich(X1) [subsumption resolution 386,83]
388. happy(susan) [resolution 107,145]
391. $false <- (~24) [resolution 387,254]
392. 24 [avatar contradiction clause 391]
460. ~happy(X0) | ~rich(X0) <- (25) [resolution 112,258]
463. ~happy(X0) <- (25) [subsumption resolution 460,387]
484. $false <- (25) [resolution 463,388]
489. ~25 [avatar contradiction clause 484]
490. $false [avatar sat refutation 259,392,489]
% SZS output end Proof for 43225379368591825878327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not brave is both brave and not strong and vice versa.
If mary is either rich or curious then someone is both generous and rich.
Everyone who is wise or not kind is not rich or creative and vice versa.
If someone is both not happy and calm then someone is both not old and humble and vice versa.
Everyone who is brave is not patient or not funny.
If fred is both not tall and quiet then john is both not old and not funny and vice versa.
If fred is not wise then paul is humble and vice versa.
Everyone who is not rich or not creative is not brave or wise.
Everyone who is strong or not old is not brave.
Everyone who is either wise or funny is tall.
If someone is both not brave and calm then lucy is either not tall or not rich.
Everyone who is old or patient is not kind and vice versa.
Everyone who is not strong or tall is either not kind or not curious.
If fred is either happy or not humble then john is either not strong or not brave.
If someone is wise or humble then someone is both not patient and not generous.
Someone is either creative or kind.
Susan is funny or not strong.
Someone is either not generous or tall.
Someone is not humble or not calm.
Someone is either humble or wise. | Fred is not generous. | neutral | (![X]:((~quiet(X)|~brave(X))<=>(brave(X)&~strong(X))))&
(((rich(mary)<~>curious(mary)))=>(?[X]:((generous(X)&rich(X)))))&
(![X]:((wise(X)|~kind(X))<=>(~rich(X)|creative(X))))&
((?[X]:((~happy(X)&calm(X))))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:(brave(X)=>(~patient(X)|~funny(X))))&
(((~tall(fred)&quiet(fred)))<=>((~old(john)&~funny(john))))&
((~wise(fred))<=>(humble(paul)))&
(![X]:((~rich(X)|~creative(X))=>(~brave(X)|wise(X))))&
(![X]:((strong(X)|~old(X))=>~brave(X)))&
(![X]:((wise(X)<~>funny(X))=>tall(X)))&
((?[X]:((~brave(X)&calm(X))))=>((~tall(lucy)<~>~rich(lucy))))&
(![X]:((old(X)|patient(X))<=>~kind(X)))&
(![X]:((~strong(X)|tall(X))=>(~kind(X)<~>~curious(X))))&
(((happy(fred)<~>~humble(fred)))=>((~strong(john)<~>~brave(john))))&
((?[X]:((wise(X)|humble(X))))=>(?[X]:((~patient(X)&~generous(X)))))&
(?[X]:((creative(X)<~>kind(X))))&
((funny(susan)|~strong(susan)))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((humble(X)<~>wise(X)))) | ~generous(fred) | [] | null | 0 |
If someone is either generous or patient then someone is either not tall or tall.
If mary is not quiet then john is both curious and not funny and vice versa.
If someone is not tall then someone is both not kind and rich.
Everyone who is not funny is either generous or tall and vice versa.
Everyone who is either old or not kind is either not patient or funny.
If susan is strong then john is either funny or not brave and vice versa.
If someone is either quiet or not rich then alice is either not kind or quiet and vice versa.
If susan is both quiet and patient then someone is both not patient and wise and vice versa.
Everyone who is patient or not generous is strong and vice versa.
If paul is not rich or funny then paul is either not brave or not creative.
Everyone who is not quiet or not tall is both funny and not funny and vice versa.
Everyone who is wise or not quiet is both not rich and not strong.
Everyone who is patient or strong is strong and vice versa.
If someone is both creative and not happy then someone is not old and vice versa.
If someone is both not humble and quiet then lucy is rich and vice versa.
Everyone who is old is not tall and vice versa.
Someone is strong.
Someone is not brave.
Someone is not humble.
Someone is both not kind and quiet.
John is creative or humble.
Lucy is not creative or generous.
Fred is either strong or calm. | John is generous. | neutral | ((?[X]:((generous(X)<~>patient(X))))=>(?[X]:((~tall(X)<~>tall(X)))))&
((~quiet(mary))<=>((curious(john)&~funny(john))))&
((?[X]:(~tall(X)))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~funny(X)<=>(generous(X)<~>tall(X))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>funny(X))))&
((strong(susan))<=>((funny(john)<~>~brave(john))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>((~kind(alice)<~>quiet(alice))))&
(((quiet(susan)&patient(susan)))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((patient(X)|~generous(X))<=>strong(X)))&
(((~rich(paul)|funny(paul)))=>((~brave(paul)<~>~creative(paul))))&
(![X]:((~quiet(X)|~tall(X))<=>(funny(X)&~funny(X))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&~strong(X))))&
(![X]:((patient(X)|strong(X))<=>strong(X)))&
((?[X]:((creative(X)&~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&quiet(X))))<=>(rich(lucy)))&
(![X]:(old(X)<=>~tall(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~kind(X)&quiet(X))))&
((creative(john)|humble(john)))&
((~creative(lucy)|generous(lucy)))&
((strong(fred)<~>calm(fred))) | generous(john) | [] | null | 0 |
Everyone who is humble or calm is both tall and not funny. If someone is either wise or quiet then someone is generous and vice versa. Everyone who is not calm is funny or not curious and vice versa. If mary is strong or not calm then someone is either strong or not quiet. Everyone who is not patient or creative is not humble and vice versa. Everyone who is either strong or not generous is funny. Everyone who is old is not strong and vice versa. Everyone who is either not humble or not creative is creative. Everyone who is both patient and brave is calm. Everyone who is humble or old is not calm or not quiet and vice versa. If john is both not quiet and wise then lucy is either not old or old and vice versa. If mary is either patient or not calm then susan is either not generous or generous and vice versa. If fred is both old and strong then susan is either not quiet or not rich and vice versa. If mary is generous then mary is either not tall or not wise and vice versa. If alice is creative or not funny then mary is both calm and tall and vice versa. If someone is strong then alice is either generous or not funny. Someone is quiet or not patient. Paul is patient. Alice is not tall. Someone is generous. Someone is not calm or funny. Someone is both funny and quiet. Someone is not patient or not kind. Someone is not strong. | Mary is not calm. | neutral | (![X]:((humble(X)|calm(X))=>(tall(X)&~funny(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:(generous(X))))&
(![X]:(~calm(X)<=>(funny(X)|~curious(X))))&
(((strong(mary)|~calm(mary)))=>(?[X]:((strong(X)<~>~quiet(X)))))&
(![X]:((~patient(X)|creative(X))<=>~humble(X)))&
(![X]:((strong(X)<~>~generous(X))=>funny(X)))&
(![X]:(old(X)<=>~strong(X)))&
(![X]:((~humble(X)<~>~creative(X))=>creative(X)))&
(![X]:((patient(X)&brave(X))=>calm(X)))&
(![X]:((humble(X)|old(X))<=>(~calm(X)|~quiet(X))))&
(((~quiet(john)&wise(john)))<=>((~old(lucy)<~>old(lucy))))&
(((patient(mary)<~>~calm(mary)))<=>((~generous(susan)<~>generous(susan))))&
(((old(fred)&strong(fred)))<=>((~quiet(susan)<~>~rich(susan))))&
((generous(mary))<=>((~tall(mary)<~>~wise(mary))))&
(((creative(alice)|~funny(alice)))<=>((calm(mary)&tall(mary))))&
((?[X]:(strong(X)))=>((generous(alice)<~>~funny(alice))))&
(?[X]:((quiet(X)|~patient(X))))&
(patient(paul))&
(~tall(alice))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)|funny(X))))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:(~strong(X))) | ~calm(mary) | [] | null | 0 |
Everyone who is strong or kind is quiet and vice versa.
Everyone who is strong is not generous or funny and vice versa.
If mary is not generous then someone is not creative.
If someone is rich then someone is both not patient and wise.
Everyone who is both creative and generous is either not happy or not brave.
Everyone who is not patient or wise is not humble and vice versa.
If alice is both patient and not kind then mary is humble and vice versa.
Everyone who is not generous or quiet is both not humble and humble.
Everyone who is either not humble or old is either old or not quiet and vice versa.
If alice is happy or calm then someone is tall or quiet.
If lucy is not kind or not calm then someone is kind or not humble.
If lucy is both tall and funny then someone is either not funny or tall.
Everyone who is not wise is wise.
If fred is not calm then paul is both happy and not creative.
Everyone who is both not strong and not curious is either not creative or not quiet and vice versa.
If someone is not generous or happy then fred is generous or not funny and vice versa.
Someone is funny or curious.
Someone is not creative.
Someone is generous.
Paul is either rich or not patient.
Someone is not patient or quiet.
Someone is tall or humble.
Lucy is not calm. | Alice is patient. | contradiction | (![X]:((strong(X)|kind(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(~generous(X)|funny(X))))&
((~generous(mary))=>(?[X]:(~creative(X))))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((creative(X)&generous(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~patient(X)|wise(X))<=>~humble(X)))&
(((patient(alice)&~kind(alice)))<=>(humble(mary)))&
(![X]:((~generous(X)|quiet(X))=>(~humble(X)&humble(X))))&
(![X]:((~humble(X)<~>old(X))<=>(old(X)<~>~quiet(X))))&
(((happy(alice)|calm(alice)))=>(?[X]:((tall(X)|quiet(X)))))&
(((~kind(lucy)|~calm(lucy)))=>(?[X]:((kind(X)|~humble(X)))))&
(((tall(lucy)&funny(lucy)))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:(~wise(X)=>wise(X)))&
((~calm(fred))=>((happy(paul)&~creative(paul))))&
(![X]:((~strong(X)&~curious(X))<=>(~creative(X)<~>~quiet(X))))&
((?[X]:((~generous(X)|happy(X))))<=>((generous(fred)|~funny(fred))))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
((rich(paul)<~>~patient(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((tall(X)|humble(X))))&
(~calm(lucy)) | patient(alice) | [
"p0",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5604635019826568755474608
% SZS output start Proof for 5604635019826568755474608
1. ! [X0] : ((kind(X0) | strong(X0)) <=> quiet(X0)) [input p0]
7. (~kind(alice) & patient(alice)) <=> humble(mary) [input p6]
8. ! [X0] : ((quiet(X0) | ~generous(X0)) => (humble(X0) & ~humble(X0))) [input p7]
9. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (old(X0) <~> ~quiet(X0))) [input p8]
24. patient(alice) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~humble(X0)) | (~quiet(X0) & generous(X0))) [ennf transformation 8]
37. ! [X0] : (((kind(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~kind(X0) & ~strong(X0)))) [nnf transformation 1]
38. ! [X0] : ((kind(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~kind(X0) & ~strong(X0)))) [flattening 37]
49. ((~kind(alice) & patient(alice)) | ~humble(mary)) & (humble(mary) | (kind(alice) | ~patient(alice))) [nnf transformation 7]
50. ((~kind(alice) & patient(alice)) | ~humble(mary)) & (humble(mary) | kind(alice) | ~patient(alice)) [flattening 49]
51. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 9]
78. ~kind(X0) | quiet(X0) [cnf transformation 38]
91. humble(mary) | kind(alice) | ~patient(alice) [cnf transformation 50]
95. ~humble(X0) | ~quiet(X0) [cnf transformation 30]
97. humble(X0) | ~quiet(X0) [cnf transformation 30]
101. quiet(X0) | ~old(X0) | ~humble(X0) | ~old(X0) [cnf transformation 51]
103. old(X0) | ~humble(X0) | old(X0) | quiet(X0) [cnf transformation 51]
133. patient(alice) [cnf transformation 24]
136. quiet(X0) | ~old(X0) | ~humble(X0) [duplicate literal removal 101]
137. old(X0) | ~humble(X0) | quiet(X0) [duplicate literal removal 103]
162. 6 <=> humble(mary) [avatar definition]
163. humble(mary) <- (6) [avatar component clause 162]
166. 7 <=> kind(alice) [avatar definition]
167. kind(alice) <- (7) [avatar component clause 166]
171. 8 <=> patient(alice) [avatar definition]
175. ~8 | 7 | 6 [avatar split clause 91,162,166,171]
176. ~quiet(X0) [subsumption resolution 95,97]
178. old(X0) | ~humble(X0) [subsumption resolution 137,176]
179. ~old(X0) | ~humble(X0) [subsumption resolution 136,176]
180. ~humble(X0) [subsumption resolution 179,178]
265. 8 [avatar split clause 133,171]
266. $false <- (6) [subsumption resolution 163,180]
267. ~6 [avatar contradiction clause 266]
268. quiet(alice) <- (7) [resolution 78,167]
269. $false <- (7) [subsumption resolution 268,176]
270. ~7 [avatar contradiction clause 269]
271. $false [avatar sat refutation 175,265,267,270]
% SZS output end Proof for 5604635019826568755474608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not patient is either not funny or not strong.
If paul is patient then someone is kind or tall.
If john is curious then paul is both humble and quiet.
Everyone who is either not tall or not happy is either kind or generous and vice versa.
If someone is brave or not kind then someone is either not tall or not quiet and vice versa.
Everyone who is both old and not patient is not old or not creative and vice versa.
Everyone who is either not creative or not tall is calm.
If someone is both not wise and calm then fred is curious or not tall and vice versa.
If mary is both not rich and tall then mary is both not generous and not funny and vice versa.
Everyone who is either funny or not generous is strong.
Everyone who is humble is either creative or not curious.
Everyone who is both tall and patient is both old and creative.
Everyone who is both rich and brave is not humble and vice versa.
If someone is not quiet then paul is either not humble or not quiet.
Everyone who is not strong is curious or kind and vice versa.
If someone is not kind or not calm then john is both not creative and rich.
Fred is not creative.
Paul is not wise.
Fred is both rich and strong.
Fred is old or creative.
Someone is brave or curious.
Someone is not quiet.
Someone is calm. | John is old. | entailment | (![X]:((wise(X)&~patient(X))=>(~funny(X)<~>~strong(X))))&
((patient(paul))=>(?[X]:((kind(X)|tall(X)))))&
((curious(john))=>((humble(paul)&quiet(paul))))&
(![X]:((~tall(X)<~>~happy(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((old(X)&~patient(X))<=>(~old(X)|~creative(X))))&
(![X]:((~creative(X)<~>~tall(X))=>calm(X)))&
((?[X]:((~wise(X)&calm(X))))<=>((curious(fred)|~tall(fred))))&
(((~rich(mary)&tall(mary)))<=>((~generous(mary)&~funny(mary))))&
(![X]:((funny(X)<~>~generous(X))=>strong(X)))&
(![X]:(humble(X)=>(creative(X)<~>~curious(X))))&
(![X]:((tall(X)&patient(X))=>(old(X)&creative(X))))&
(![X]:((rich(X)&brave(X))<=>~humble(X)))&
((?[X]:(~quiet(X)))=>((~humble(paul)<~>~quiet(paul))))&
(![X]:(~strong(X)<=>(curious(X)|kind(X))))&
((?[X]:((~kind(X)|~calm(X))))=>((~creative(john)&rich(john))))&
(~creative(fred))&
(~wise(paul))&
((rich(fred)&strong(fred)))&
((old(fred)|creative(fred)))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X))) | old(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 9026165388309913054350680
% SZS output start Proof for 9026165388309913054350680
6. ! [X0] : ((~patient(X0) & old(X0)) <=> (~creative(X0) | ~old(X0))) [input p5]
24. ~old(john) [input hypothesis]
46. ! [X0] : (((~patient(X0) & old(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (patient(X0) | ~old(X0)))) [nnf transformation 6]
47. ! [X0] : (((~patient(X0) & old(X0)) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | patient(X0) | ~old(X0))) [flattening 46]
89. old(X0) | old(X0) [cnf transformation 47]
130. ~old(john) [cnf transformation 24]
132. old(X0) [duplicate literal removal 89]
268. $false [subsumption resolution 130,132]
% SZS output end Proof for 9026165388309913054350680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not wise. Everyone who is both strong and not creative is not humble. Everyone who is both curious and not funny is curious. Everyone who is either not patient or wise is both not rich and humble. If someone is not rich then someone is both curious and old. Everyone who is both not old and funny is not strong or patient. If lucy is curious or not creative then john is both not calm and not curious and vice versa. If someone is wise then someone is curious or not humble and vice versa. Everyone who is tall or calm is either not humble or funny. Everyone who is either strong or kind is both not generous and not kind. Everyone who is humble or not calm is either not curious or not strong. Everyone who is both not creative and not kind is either tall or happy and vice versa. If fred is both not wise and wise then mary is either wise or not strong and vice versa. Everyone who is wise or old is either rich or tall. Everyone who is patient or old is not patient and vice versa. If someone is both rich and not old then susan is brave and vice versa. Someone is both funny and not creative. Someone is either not wise or not humble. Alice is not generous. Someone is not tall. Fred is not kind. Fred is both not curious and not kind. Someone is not calm. | Fred is strong. | entailment | (![X]:(~strong(X)=>~wise(X)))&
(![X]:((strong(X)&~creative(X))=>~humble(X)))&
(![X]:((curious(X)&~funny(X))=>curious(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~rich(X)&humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)|patient(X))))&
(((curious(lucy)|~creative(lucy)))<=>((~calm(john)&~curious(john))))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((tall(X)|calm(X))=>(~humble(X)<~>funny(X))))&
(![X]:((strong(X)<~>kind(X))=>(~generous(X)&~kind(X))))&
(![X]:((humble(X)|~calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>(tall(X)<~>happy(X))))&
(((~wise(fred)&wise(fred)))<=>((wise(mary)<~>~strong(mary))))&
(![X]:((wise(X)|old(X))=>(rich(X)<~>tall(X))))&
(![X]:((patient(X)|old(X))<=>~patient(X)))&
((?[X]:((rich(X)&~old(X))))<=>(brave(susan)))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(~generous(alice))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~curious(fred)&~kind(fred)))&
(?[X]:(~calm(X))) | strong(fred) | [
"p0",
"p3",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 52405663277170663824045
% SZS output start Proof for 52405663277170663824045
1. ! [X0] : (~strong(X0) => ~wise(X0)) [input p0]
4. ! [X0] : ((~patient(X0) <~> wise(X0)) => (humble(X0) & ~rich(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | humble(X0)) => (~curious(X0) <~> ~strong(X0))) [input p10]
15. ! [X0] : ((old(X0) | patient(X0)) <=> ~patient(X0)) [input p14]
22. ~kind(fred) & ~curious(fred) [input p21]
24. ~strong(fred) [input hypothesis]
29. ! [X0] : (~wise(X0) | strong(X0)) [ennf transformation 1]
34. ! [X0] : ((humble(X0) & ~rich(X0)) | (~patient(X0) <=> wise(X0))) [ennf transformation 4]
40. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 11]
42. ! [X0] : ((humble(X0) & ~rich(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 34]
55. ! [X0] : (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (calm(X0) & ~humble(X0))) [nnf transformation 40]
61. ! [X0] : (((old(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [nnf transformation 15]
62. ! [X0] : ((old(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [flattening 61]
76. ~wise(X0) | strong(X0) [cnf transformation 29]
81. patient(X0) | wise(X0) | humble(X0) [cnf transformation 42]
102. ~humble(X0) | curious(X0) | strong(X0) [cnf transformation 55]
120. ~patient(X0) | ~patient(X0) [cnf transformation 62]
132. ~curious(fred) [cnf transformation 22]
135. ~strong(fred) [cnf transformation 24]
136. ~patient(X0) [duplicate literal removal 120]
258. humble(X0) | wise(X0) [resolution 81,136]
282. curious(X0) | strong(X0) | wise(X0) [resolution 102,258]
283. curious(X0) | strong(X0) [subsumption resolution 282,76]
293. strong(fred) [resolution 283,132]
297. $false [subsumption resolution 293,135]
% SZS output end Proof for 52405663277170663824045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is rich and vice versa. Everyone who is either not wise or not calm is wise or funny and vice versa. Everyone who is not creative or wise is not quiet or not happy. Everyone who is both happy and not calm is both not kind and generous and vice versa. Everyone who is humble or funny is both not wise and creative. If someone is both rich and not patient then susan is rich or not old. If someone is both brave and not brave then mary is not happy. If alice is both not kind and not tall then someone is kind or not calm and vice versa. If someone is not calm then someone is strong or kind and vice versa. If someone is either patient or not old then mary is not kind. If someone is not quiet then someone is patient. Everyone who is brave is both not patient and not tall. If john is patient or not wise then someone is both generous and tall. Everyone who is old is not quiet. If someone is curious then fred is not happy. Someone is not rich. Someone is either old or calm. Lucy is both not calm and old. Someone is either creative or not happy. Paul is wise or not kind. Someone is both not tall and happy. Someone is not generous. | Susan is not curious. | neutral | ((?[X]:(kind(X)))<=>(?[X]:(rich(X))))&
(![X]:((~wise(X)<~>~calm(X))<=>(wise(X)|funny(X))))&
(![X]:((~creative(X)|wise(X))=>(~quiet(X)|~happy(X))))&
(![X]:((happy(X)&~calm(X))<=>(~kind(X)&generous(X))))&
(![X]:((humble(X)|funny(X))=>(~wise(X)&creative(X))))&
((?[X]:((rich(X)&~patient(X))))=>((rich(susan)|~old(susan))))&
((?[X]:((brave(X)&~brave(X))))=>(~happy(mary)))&
(((~kind(alice)&~tall(alice)))<=>(?[X]:((kind(X)|~calm(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((patient(X)<~>~old(X))))=>(~kind(mary)))&
((?[X]:(~quiet(X)))=>(?[X]:(patient(X))))&
(![X]:(brave(X)=>(~patient(X)&~tall(X))))&
(((patient(john)|~wise(john)))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:(old(X)=>~quiet(X)))&
((?[X]:(curious(X)))=>(~happy(fred)))&
(?[X]:(~rich(X)))&
(?[X]:((old(X)<~>calm(X))))&
((~calm(lucy)&old(lucy)))&
(?[X]:((creative(X)<~>~happy(X))))&
((wise(paul)|~kind(paul)))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:(~generous(X))) | ~curious(susan) | [] | null | 0 |
Everyone who is creative or not creative is both not happy and not patient.
If someone is either not wise or curious then alice is either not generous or old and vice versa.
If alice is not strong or not generous then someone is kind or not tall.
If mary is not wise then someone is both not tall and not wise.
Everyone who is old is both not strong and curious and vice versa.
Everyone who is brave is quiet or not generous.
If someone is either not old or curious then someone is both not patient and old and vice versa.
Everyone who is funny or not quiet is not rich.
Everyone who is both not kind and calm is kind and vice versa.
If lucy is not kind then paul is either kind or not rich and vice versa.
Everyone who is not funny or funny is both quiet and generous.
If someone is both tall and not creative then someone is patient.
Everyone who is either not curious or not quiet is both not kind and not wise and vice versa.
Everyone who is both not calm and kind is either calm or not happy.
If susan is happy or quiet then john is both strong and not rich.
If someone is either not happy or not old then someone is either not creative or tall and vice versa.
Mary is either not creative or creative.
Susan is not funny.
Mary is both not funny and not curious.
Susan is either patient or not rich.
Someone is either rich or generous.
Someone is not funny.
Lucy is either curious or funny. | Alice is not generous. | contradiction | (![X]:((creative(X)|~creative(X))=>(~happy(X)&~patient(X))))&
((?[X]:((~wise(X)<~>curious(X))))<=>((~generous(alice)<~>old(alice))))&
(((~strong(alice)|~generous(alice)))=>(?[X]:((kind(X)|~tall(X)))))&
((~wise(mary))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:(old(X)<=>(~strong(X)&curious(X))))&
(![X]:(brave(X)=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)<~>curious(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((funny(X)|~quiet(X))=>~rich(X)))&
(![X]:((~kind(X)&calm(X))<=>kind(X)))&
((~kind(lucy))<=>((kind(paul)<~>~rich(paul))))&
(![X]:((~funny(X)|funny(X))=>(quiet(X)&generous(X))))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(~kind(X)&~wise(X))))&
(![X]:((~calm(X)&kind(X))=>(calm(X)<~>~happy(X))))&
(((happy(susan)|quiet(susan)))=>((strong(john)&~rich(john))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
((~creative(mary)<~>creative(mary)))&
(~funny(susan))&
((~funny(mary)&~curious(mary)))&
((patient(susan)<~>~rich(susan)))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:(~funny(X)))&
((curious(lucy)<~>funny(lucy))) | ~generous(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8000034899989898356605078
% SZS output start Proof for 8000034899989898356605078
11. ! [X0] : ((funny(X0) | ~funny(X0)) => (generous(X0) & quiet(X0))) [input p10]
24. ~generous(alice) [input hypothesis]
33. ! [X0] : ((generous(X0) & quiet(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 11]
111. generous(X0) | funny(X0) [cnf transformation 33]
112. generous(X0) | ~funny(X0) [cnf transformation 33]
146. ~generous(alice) [cnf transformation 24]
237. generous(X0) [subsumption resolution 111,112]
283. $false [subsumption resolution 146,237]
% SZS output end Proof for 8000034899989898356605078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and patient then someone is either humble or not kind and vice versa.
Everyone who is both wise and not quiet is both not strong and not kind.
Everyone who is strong is not brave.
Everyone who is either strong or quiet is not old or not tall and vice versa.
Everyone who is not patient is either happy or patient.
If mary is both humble and not patient then lucy is not creative.
Everyone who is both not wise and not generous is either not calm or generous and vice versa.
Everyone who is both not creative and not curious is rich and vice versa.
Everyone who is not rich or not creative is not rich or not tall and vice versa.
Everyone who is calm is not happy or creative and vice versa.
Everyone who is old or not humble is strong or tall.
If susan is funny then john is humble.
If someone is not strong or quiet then someone is both not wise and happy and vice versa.
If someone is wise then someone is not old or kind and vice versa.
Everyone who is not creative or not brave is not calm or not kind.
Everyone who is wise is rich and vice versa.
Someone is patient or kind.
Someone is either tall or not generous.
Lucy is both patient and not old.
Lucy is not rich.
Mary is not quiet.
Fred is not quiet.
Mary is humble. | Lucy is calm. | contradiction | ((?[X]:((~creative(X)&patient(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((wise(X)&~quiet(X))=>(~strong(X)&~kind(X))))&
(![X]:(strong(X)=>~brave(X)))&
(![X]:((strong(X)<~>quiet(X))<=>(~old(X)|~tall(X))))&
(![X]:(~patient(X)=>(happy(X)<~>patient(X))))&
(((humble(mary)&~patient(mary)))=>(~creative(lucy)))&
(![X]:((~wise(X)&~generous(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((~creative(X)&~curious(X))<=>rich(X)))&
(![X]:((~rich(X)|~creative(X))<=>(~rich(X)|~tall(X))))&
(![X]:(calm(X)<=>(~happy(X)|creative(X))))&
(![X]:((old(X)|~humble(X))=>(strong(X)|tall(X))))&
((funny(susan))=>(humble(john)))&
((?[X]:((~strong(X)|quiet(X))))<=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((~old(X)|kind(X)))))&
(![X]:((~creative(X)|~brave(X))=>(~calm(X)|~kind(X))))&
(![X]:(wise(X)<=>rich(X)))&
(?[X]:((patient(X)|kind(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(lucy)&~old(lucy)))&
(~rich(lucy))&
(~quiet(mary))&
(~quiet(fred))&
(humble(mary)) | calm(lucy) | [
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1483659507940624564135187
% SZS output start Proof for 1483659507940624564135187
7. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (~calm(X0) <~> generous(X0))) [input p6]
16. ! [X0] : (wise(X0) <=> rich(X0)) [input p15]
20. ~rich(lucy) [input p19]
24. calm(lucy) [input hypothesis]
47. ! [X0] : (((~generous(X0) & ~wise(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0)))) & (((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | (generous(X0) | wise(X0)))) [nnf transformation 7]
48. ! [X0] : (((~generous(X0) & ~wise(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0)))) & (((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | generous(X0) | wise(X0))) [flattening 47]
65. ! [X0] : ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))) [nnf transformation 16]
89. generous(X0) | ~calm(X0) | generous(X0) | wise(X0) [cnf transformation 48]
94. ~generous(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 48]
117. ~wise(X0) | rich(X0) [cnf transformation 65]
124. ~rich(lucy) [cnf transformation 20]
128. calm(lucy) [cnf transformation 24]
129. generous(X0) | ~calm(X0) | wise(X0) [duplicate literal removal 89]
130. ~calm(X0) | ~generous(X0) [duplicate literal removal 94]
176. ~calm(X0) | wise(X0) [subsumption resolution 129,130]
258. wise(lucy) [resolution 176,128]
260. rich(lucy) [resolution 258,117]
261. $false [subsumption resolution 260,124]
% SZS output end Proof for 1483659507940624564135187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not humble is not old or brave and vice versa.
If someone is not creative then someone is either not patient or humble and vice versa.
If paul is not humble then someone is not funny or rich and vice versa.
Everyone who is curious or not happy is not kind or not brave.
If someone is both old and not generous then susan is both not old and funny.
If fred is either not rich or not old then someone is either not patient or strong and vice versa.
Everyone who is strong or creative is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Everyone who is either not brave or calm is either rich or not funny.
If paul is both funny and not old then someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise.
Paul is both old and calm.
Someone is rich.
Lucy is both calm and wise.
Paul is both not kind and quiet.
Fred is either quiet or rich. | Paul is curious. | contradiction | (![X]:((wise(X)&~humble(X))<=>(~old(X)|brave(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
((~humble(paul))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((curious(X)|~happy(X))=>(~kind(X)|~brave(X))))&
((?[X]:((old(X)&~generous(X))))=>((~old(susan)&funny(susan))))&
(((~rich(fred)<~>~old(fred)))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((strong(X)|creative(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>calm(X))=>(rich(X)<~>~funny(X))))&
(((funny(paul)&~old(paul)))=>(?[X]:((curious(X)|~calm(X)))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X)))&
((calm(lucy)&wise(lucy)))&
((~kind(paul)&quiet(paul)))&
((quiet(fred)<~>rich(fred))) | curious(paul) | [
"p2",
"p6",
"p11",
"p12",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 685185661454061394096902
% SZS output start Proof for 685185661454061394096902
3. ~humble(paul) <=> ? [X0] : (rich(X0) | ~funny(X0)) [input p2]
7. ! [X0] : ((creative(X0) | strong(X0)) <=> wise(X0)) [input p6]
12. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p11]
13. ! [X0] : ((creative(X0) <~> kind(X0)) <=> curious(X0)) [input p12]
21. ? [X0] : rich(X0) [input p20]
23. quiet(paul) & ~kind(paul) [input p22]
25. curious(paul) [input hypothesis]
45. (~humble(paul) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X0] : (rich(X0) | ~funny(X0)) | humble(paul)) [nnf transformation 3]
46. (~humble(paul) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X1] : (rich(X1) | ~funny(X1)) | humble(paul)) [rectify 45]
47. ? [X1] : (rich(X1) | ~funny(X1)) => (rich(sK2) | ~funny(sK2)) [choice axiom]
48. (~humble(paul) | ! [X0] : (~rich(X0) & funny(X0))) & ((rich(sK2) | ~funny(sK2)) | humble(paul)) [skolemisation 46,47]
53. ! [X0] : (((creative(X0) | strong(X0)) | ~wise(X0)) & (wise(X0) | (~creative(X0) & ~strong(X0)))) [nnf transformation 7]
54. ! [X0] : ((creative(X0) | strong(X0) | ~wise(X0)) & (wise(X0) | (~creative(X0) & ~strong(X0)))) [flattening 53]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 12]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
68. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ~curious(X0)) & (curious(X0) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 13]
81. ? [X0] : rich(X0) => rich(sK11) [choice axiom]
82. rich(sK11) [skolemisation 21,81]
95. ~humble(paul) | ~rich(X0) [cnf transformation 48]
108. ~creative(X0) | wise(X0) [cnf transformation 54]
130. ~wise(X0) | humble(X0) [cnf transformation 67]
133. ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 68]
149. rich(sK11) [cnf transformation 82]
152. ~kind(paul) [cnf transformation 23]
156. curious(paul) [cnf transformation 25]
183. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
184. ~rich(X0) <- (7) [avatar component clause 183]
186. 8 <=> humble(paul) [avatar definition]
189. 7 | ~8 [avatar split clause 95,186,183]
420. creative(paul) | kind(paul) [resolution 133,156]
421. creative(paul) [subsumption resolution 420,152]
451. wise(paul) [resolution 421,108]
518. humble(paul) [resolution 451,130]
522. 8 [avatar split clause 518,186]
523. $false <- (7) [resolution 184,149]
526. ~7 [avatar contradiction clause 523]
527. $false [avatar sat refutation 189,522,526]
% SZS output end Proof for 685185661454061394096902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not kind is creative and vice versa.
Everyone who is both kind and not brave is not creative or brave and vice versa.
If fred is either generous or not calm then john is both kind and generous.
Everyone who is both happy and not generous is not rich.
Everyone who is humble is not wise or patient.
Everyone who is not calm is both quiet and not old and vice versa.
If alice is not calm then someone is both generous and not generous.
If paul is not funny then susan is both funny and strong.
If someone is not patient or humble then mary is both not kind and not curious and vice versa.
Everyone who is either curious or rich is both patient and old and vice versa.
If mary is wise or tall then someone is not kind.
Everyone who is both old and brave is both funny and not calm and vice versa.
Everyone who is either not tall or not happy is both not brave and not creative.
If someone is strong or not creative then fred is both not curious and rich and vice versa.
If susan is funny then john is patient or kind.
If john is not calm or tall then mary is brave.
Someone is strong or generous.
Someone is calm or not humble.
Alice is not quiet or not humble.
Paul is either calm or generous.
Someone is either not strong or curious.
John is either generous or not quiet.
Someone is old or not old.
Someone is either not generous or not funny. | Susan is not strong. | neutral | (![X]:((old(X)&~kind(X))<=>creative(X)))&
(![X]:((kind(X)&~brave(X))<=>(~creative(X)|brave(X))))&
(((generous(fred)<~>~calm(fred)))=>((kind(john)&generous(john))))&
(![X]:((happy(X)&~generous(X))=>~rich(X)))&
(![X]:(humble(X)=>(~wise(X)|patient(X))))&
(![X]:(~calm(X)<=>(quiet(X)&~old(X))))&
((~calm(alice))=>(?[X]:((generous(X)&~generous(X)))))&
((~funny(paul))=>((funny(susan)&strong(susan))))&
((?[X]:((~patient(X)|humble(X))))<=>((~kind(mary)&~curious(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(patient(X)&old(X))))&
(((wise(mary)|tall(mary)))=>(?[X]:(~kind(X))))&
(![X]:((old(X)&brave(X))<=>(funny(X)&~calm(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~brave(X)&~creative(X))))&
((?[X]:((strong(X)|~creative(X))))<=>((~curious(fred)&rich(fred))))&
((funny(susan))=>((patient(john)|kind(john))))&
(((~calm(john)|tall(john)))=>(brave(mary)))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:((calm(X)|~humble(X))))&
((~quiet(alice)|~humble(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:((~strong(X)<~>curious(X))))&
((generous(john)<~>~quiet(john)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~generous(X)<~>~funny(X)))) | ~strong(susan) | [] | null | 0 |
If susan is either not quiet or humble then fred is wise. Everyone who is both kind and not funny is old or brave and vice versa. If someone is not patient then someone is both not kind and curious and vice versa. Everyone who is both not curious and not quiet is both not happy and not calm. Everyone who is not patient is not brave or patient and vice versa. If fred is either tall or not generous then someone is patient and vice versa. If susan is either not tall or wise then someone is not brave or old and vice versa. Everyone who is not old is either not funny or rich. Everyone who is curious or not old is quiet or humble and vice versa. Everyone who is wise or calm is both kind and not wise. Everyone who is both not old and not calm is either not tall or rich and vice versa. Everyone who is not generous is not strong or brave. Everyone who is not humble or not old is both not funny and not humble. Everyone who is rich is creative or tall and vice versa. If lucy is brave or kind then someone is generous or not funny and vice versa. Someone is either not patient or humble. Someone is either generous or tall. Someone is both quiet and not curious. Someone is funny or strong. Someone is strong. Paul is either not rich or curious. Someone is not happy. | Fred is not generous. | contradiction | (((~quiet(susan)<~>humble(susan)))=>(wise(fred)))&
(![X]:((kind(X)&~funny(X))<=>(old(X)|brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((~curious(X)&~quiet(X))=>(~happy(X)&~calm(X))))&
(![X]:(~patient(X)<=>(~brave(X)|patient(X))))&
(((tall(fred)<~>~generous(fred)))<=>(?[X]:(patient(X))))&
(((~tall(susan)<~>wise(susan)))<=>(?[X]:((~brave(X)|old(X)))))&
(![X]:(~old(X)=>(~funny(X)<~>rich(X))))&
(![X]:((curious(X)|~old(X))<=>(quiet(X)|humble(X))))&
(![X]:((wise(X)|calm(X))=>(kind(X)&~wise(X))))&
(![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>rich(X))))&
(![X]:(~generous(X)=>(~strong(X)|brave(X))))&
(![X]:((~humble(X)|~old(X))=>(~funny(X)&~humble(X))))&
(![X]:(rich(X)<=>(creative(X)|tall(X))))&
(((brave(lucy)|kind(lucy)))<=>(?[X]:((generous(X)|~funny(X)))))&
(?[X]:((~patient(X)<~>humble(X))))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((quiet(X)&~curious(X))))&
(?[X]:((funny(X)|strong(X))))&
(?[X]:(strong(X)))&
((~rich(paul)<~>curious(paul)))&
(?[X]:(~happy(X))) | ~generous(fred) | [
"p1",
"p4",
"p5",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3068282245911810459385060
% SZS output start Proof for 3068282245911810459385060
2. ! [X0] : ((~funny(X0) & kind(X0)) <=> (brave(X0) | old(X0))) [input p1]
5. ! [X0] : (~patient(X0) <=> (patient(X0) | ~brave(X0))) [input p4]
6. (tall(fred) <~> ~generous(fred)) <=> ? [X0] : patient(X0) [input p5]
8. ! [X0] : (~old(X0) => (~funny(X0) <~> rich(X0))) [input p7]
11. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> rich(X0))) [input p10]
13. ! [X0] : ((~old(X0) | ~humble(X0)) => (~humble(X0) & ~funny(X0))) [input p12]
14. ! [X0] : (rich(X0) <=> (tall(X0) | creative(X0))) [input p13]
23. ~generous(fred) [input hypothesis]
30. ! [X0] : ((~funny(X0) <~> rich(X0)) | old(X0)) [ennf transformation 8]
34. ! [X0] : ((~humble(X0) & ~funny(X0)) | (old(X0) & humble(X0))) [ennf transformation 13]
36. ! [X0] : (((~funny(X0) & kind(X0)) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | (funny(X0) | ~kind(X0)))) [nnf transformation 2]
37. ! [X0] : (((~funny(X0) & kind(X0)) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | funny(X0) | ~kind(X0))) [flattening 36]
43. ! [X0] : ((~patient(X0) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | patient(X0))) [nnf transformation 5]
44. ! [X0] : ((~patient(X0) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | patient(X0))) [flattening 43]
45. (((generous(fred) | ~tall(fred)) & (~generous(fred) | tall(fred))) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ((tall(fred) | generous(fred)) & (~generous(fred) | ~tall(fred)))) [nnf transformation 6]
46. (((generous(fred) | ~tall(fred)) & (~generous(fred) | tall(fred))) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ((tall(fred) | generous(fred)) & (~generous(fred) | ~tall(fred)))) [rectify 45]
47. ? [X1] : patient(X1) => patient(sK2) [choice axiom]
48. (((generous(fred) | ~tall(fred)) & (~generous(fred) | tall(fred))) | ! [X0] : ~patient(X0)) & (patient(sK2) | ((tall(fred) | generous(fred)) & (~generous(fred) | ~tall(fred)))) [skolemisation 46,47]
53. ! [X0] : (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | old(X0)) [nnf transformation 30]
56. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 11]
57. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 56]
58. ! [X0] : ((rich(X0) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | ~rich(X0))) [nnf transformation 14]
59. ! [X0] : ((rich(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | ~rich(X0))) [flattening 58]
83. ~old(X0) | ~funny(X0) [cnf transformation 37]
91. ~patient(X0) | ~patient(X0) [cnf transformation 44]
93. patient(sK2) | tall(fred) | generous(fred) [cnf transformation 48]
103. ~rich(X0) | funny(X0) | old(X0) [cnf transformation 53]
115. ~rich(X0) | ~tall(X0) | ~old(X0) [cnf transformation 57]
120. ~funny(X0) | old(X0) [cnf transformation 34]
125. ~tall(X0) | rich(X0) [cnf transformation 59]
140. ~generous(fred) [cnf transformation 23]
143. ~patient(X0) [duplicate literal removal 91]
180. tall(fred) | generous(fred) [subsumption resolution 93,143]
182. 9 <=> generous(fred) [avatar definition]
186. 10 <=> tall(fred) [avatar definition]
188. tall(fred) <- (10) [avatar component clause 186]
189. 9 | 10 [avatar split clause 180,186,182]
211. ~funny(X0) [subsumption resolution 120,83]
236. ~9 [avatar split clause 140,182]
239. rich(fred) <- (10) [resolution 125,188]
242. funny(fred) | old(fred) <- (10) [resolution 103,239]
243. old(fred) <- (10) [subsumption resolution 242,211]
285. ~tall(fred) | ~old(fred) <- (10) [resolution 115,239]
286. ~old(fred) <- (10) [subsumption resolution 285,188]
287. $false <- (10) [subsumption resolution 286,243]
288. ~10 [avatar contradiction clause 287]
289. $false [avatar sat refutation 189,236,288]
% SZS output end Proof for 3068282245911810459385060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not creative or not generous and vice versa.
If someone is both creative and brave then someone is both not quiet and rich and vice versa.
Everyone who is both generous and not old is not wise or strong.
Everyone who is not humble or curious is either not calm or not old.
If someone is not brave or rich then lucy is patient and vice versa.
Everyone who is not quiet is either kind or not old and vice versa.
If someone is both not old and creative then mary is happy or not creative.
Everyone who is both calm and wise is not wise or curious and vice versa.
If someone is funny then someone is either funny or not tall.
If mary is not humble then someone is both strong and tall and vice versa.
Everyone who is brave or not tall is both not brave and not quiet and vice versa.
If someone is both not old and not humble then paul is not funny or not quiet.
If lucy is either not kind or calm then susan is both funny and not kind and vice versa.
If someone is either not creative or not brave then someone is not quiet.
Everyone who is either funny or not rich is both not wise and not rich.
Someone is both not brave and not old.
Someone is wise or funny.
John is not quiet or strong.
Fred is either patient or wise.
Someone is tall.
Paul is calm or wise.
Someone is creative or patient. | John is brave. | contradiction | (![X]:(~kind(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((creative(X)&brave(X))))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((generous(X)&~old(X))=>(~wise(X)|strong(X))))&
(![X]:((~humble(X)|curious(X))=>(~calm(X)<~>~old(X))))&
((?[X]:((~brave(X)|rich(X))))<=>(patient(lucy)))&
(![X]:(~quiet(X)<=>(kind(X)<~>~old(X))))&
((?[X]:((~old(X)&creative(X))))=>((happy(mary)|~creative(mary))))&
(![X]:((calm(X)&wise(X))<=>(~wise(X)|curious(X))))&
((?[X]:(funny(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
((~humble(mary))<=>(?[X]:((strong(X)&tall(X)))))&
(![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~old(X)&~humble(X))))=>((~funny(paul)|~quiet(paul))))&
(((~kind(lucy)<~>calm(lucy)))<=>((funny(susan)&~kind(susan))))&
((?[X]:((~creative(X)<~>~brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~rich(X))))&
(?[X]:((~brave(X)&~old(X))))&
(?[X]:((wise(X)|funny(X))))&
((~quiet(john)|strong(john)))&
((patient(fred)<~>wise(fred)))&
(?[X]:(tall(X)))&
((calm(paul)|wise(paul)))&
(?[X]:((creative(X)|patient(X)))) | brave(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6144548446064725724329268
% SZS output start Proof for 6144548446064725724329268
11. ! [X0] : ((~tall(X0) | brave(X0)) <=> (~quiet(X0) & ~brave(X0))) [input p10]
23. brave(john) [input hypothesis]
59. ! [X0] : (((~tall(X0) | brave(X0)) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : ((~tall(X0) | brave(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | (tall(X0) & ~brave(X0)))) [flattening 59]
106. ~brave(X0) | ~brave(X0) [cnf transformation 60]
133. brave(john) [cnf transformation 23]
135. ~brave(X0) [duplicate literal removal 106]
281. $false [subsumption resolution 133,135]
% SZS output end Proof for 6144548446064725724329268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and strong is funny or not quiet. Everyone who is not strong is not quiet or not generous and vice versa. If someone is both not calm and quiet then someone is either happy or tall and vice versa. If someone is strong then lucy is not kind and vice versa. Everyone who is not creative or not funny is both not creative and not happy and vice versa. If paul is not old or happy then john is either not rich or strong and vice versa. Everyone who is curious is either not strong or not calm and vice versa. If someone is either not kind or not generous then someone is not tall or not brave and vice versa. Everyone who is old is either not creative or not calm. Everyone who is both not creative and not wise is both calm and not tall and vice versa. If john is either not generous or generous then someone is either not old or not calm. Everyone who is either brave or not funny is either calm or not brave and vice versa. Everyone who is brave is not patient or not calm. Everyone who is either generous or not creative is not brave and vice versa. Everyone who is both not generous and happy is both patient and not humble and vice versa. Everyone who is both creative and not funny is not creative or not patient. Alice is brave. Paul is both old and not wise. Susan is either calm or not kind. John is rich or not quiet. Lucy is both not quiet and not old. Alice is not wise or not patient. Someone is not generous. Someone is not kind. | Paul is tall. | contradiction | (![X]:((calm(X)&strong(X))=>(funny(X)|~quiet(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((happy(X)<~>tall(X)))))&
((?[X]:(strong(X)))<=>(~kind(lucy)))&
(![X]:((~creative(X)|~funny(X))<=>(~creative(X)&~happy(X))))&
(((~old(paul)|happy(paul)))<=>((~rich(john)<~>strong(john))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(brave(X)=>(~patient(X)|~calm(X))))&
(![X]:((generous(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((~generous(X)&happy(X))<=>(patient(X)&~humble(X))))&
(![X]:((creative(X)&~funny(X))=>(~creative(X)|~patient(X))))&
(brave(alice))&
((old(paul)&~wise(paul)))&
((calm(susan)<~>~kind(susan)))&
((rich(john)|~quiet(john)))&
((~quiet(lucy)&~old(lucy)))&
((~wise(alice)|~patient(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~kind(X))) | tall(paul) | [
"p4",
"p8",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6251529213033184637511011
% SZS output start Proof for 6251529213033184637511011
5. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> (~happy(X0) & ~creative(X0))) [input p4]
9. ! [X0] : (old(X0) => (~creative(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> (~tall(X0) & calm(X0))) [input p9]
12. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p11]
18. ~wise(paul) & old(paul) [input p17]
25. tall(paul) [input hypothesis]
30. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | ~old(X0)) [ennf transformation 9]
47. ! [X0] : (((~funny(X0) | ~creative(X0)) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | (funny(X0) & creative(X0)))) [nnf transformation 5]
48. ! [X0] : ((~funny(X0) | ~creative(X0) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | (funny(X0) & creative(X0)))) [flattening 47]
56. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~old(X0)) [nnf transformation 30]
57. ! [X0] : (((~wise(X0) & ~creative(X0)) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | (wise(X0) | creative(X0)))) [nnf transformation 10]
58. ! [X0] : (((~wise(X0) & ~creative(X0)) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | wise(X0) | creative(X0))) [flattening 57]
62. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 12]
84. ~creative(X0) | funny(X0) [cnf transformation 48]
100. ~old(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 56]
103. ~tall(X0) | wise(X0) | creative(X0) [cnf transformation 58]
110. ~brave(X0) | calm(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 62]
115. ~funny(X0) | brave(X0) | calm(X0) | brave(X0) [cnf transformation 62]
129. old(paul) [cnf transformation 18]
130. ~wise(paul) [cnf transformation 18]
139. tall(paul) [cnf transformation 25]
141. ~brave(X0) | calm(X0) | ~funny(X0) [duplicate literal removal 110]
143. ~funny(X0) | brave(X0) | calm(X0) [duplicate literal removal 115]
202. 13 <=> old(paul) [avatar definition]
203. old(paul) <- (13) [avatar component clause 202]
266. ~funny(X0) | calm(X0) [subsumption resolution 141,143]
267. 13 [avatar split clause 129,202]
303. ~creative(paul) | ~calm(paul) <- (13) [resolution 100,203]
306. 31 <=> calm(paul) [avatar definition]
308. ~calm(paul) <- (~31) [avatar component clause 306]
310. 32 <=> creative(paul) [avatar definition]
311. creative(paul) <- (32) [avatar component clause 310]
313. ~31 | ~32 | ~13 [avatar split clause 303,202,310,306]
319. funny(paul) <- (32) [resolution 311,84]
332. wise(paul) | creative(paul) [resolution 103,139]
368. calm(paul) <- (32) [resolution 319,266]
369. $false <- (~31, 32) [subsumption resolution 368,308]
370. 31 | ~32 [avatar contradiction clause 369]
372. creative(paul) [subsumption resolution 332,130]
373. 32 [avatar split clause 372,310]
375. $false [avatar sat refutation 267,313,370,373]
% SZS output end Proof for 6251529213033184637511011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or creative is not kind and vice versa.
Everyone who is both not brave and funny is either quiet or patient and vice versa.
Everyone who is either not wise or not quiet is not generous or not curious.
Everyone who is not tall is curious and vice versa.
If fred is either tall or kind then someone is either not calm or kind.
Everyone who is either not creative or creative is brave or funny and vice versa.
Everyone who is either not strong or not quiet is both not tall and rich.
Everyone who is not generous is not creative or not happy and vice versa.
Everyone who is not humble or not rich is either not brave or not generous and vice versa.
Everyone who is either not wise or not kind is not old or funny and vice versa.
If someone is not kind then someone is both not creative and generous and vice versa.
Everyone who is either quiet or not brave is either not strong or not quiet and vice versa.
Everyone who is rich or not kind is either not rich or kind.
If lucy is either not curious or not quiet then someone is either strong or happy.
Everyone who is rich or not happy is both tall and old.
Someone is kind or happy.
Someone is not creative or strong.
Lucy is creative or funny.
Susan is wise or not brave.
John is both happy and calm. | Fred is not wise. | entailment | (![X]:((brave(X)|creative(X))<=>~kind(X)))&
(![X]:((~brave(X)&funny(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(~generous(X)|~curious(X))))&
(![X]:(~tall(X)<=>curious(X)))&
(((tall(fred)<~>kind(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)|funny(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(~tall(X)&rich(X))))&
(![X]:(~generous(X)<=>(~creative(X)|~happy(X))))&
(![X]:((~humble(X)|~rich(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(~old(X)|funny(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(~rich(X)<~>kind(X))))&
(((~curious(lucy)<~>~quiet(lucy)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((rich(X)|~happy(X))=>(tall(X)&old(X))))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~creative(X)|strong(X))))&
((creative(lucy)|funny(lucy)))&
((wise(susan)|~brave(susan)))&
((happy(john)&calm(john))) | ~wise(fred) | [
"p0",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3001425604327483981553061
% SZS output start Proof for 3001425604327483981553061
1. ! [X0] : ((creative(X0) | brave(X0)) <=> ~kind(X0)) [input p0]
6. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) | brave(X0))) [input p5]
8. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~creative(X0))) [input p7]
10. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (funny(X0) | ~old(X0))) [input p9]
11. ? [X0] : ~kind(X0) <=> ? [X0] : (generous(X0) & ~creative(X0)) [input p10]
21. wise(fred) [input hypothesis]
22. ? [X0] : ~kind(X0) <=> ? [X1] : (generous(X1) & ~creative(X1)) [rectify 11]
30. ! [X0] : (((creative(X0) | brave(X0)) | kind(X0)) & (~kind(X0) | (~creative(X0) & ~brave(X0)))) [nnf transformation 1]
31. ! [X0] : ((creative(X0) | brave(X0) | kind(X0)) & (~kind(X0) | (~creative(X0) & ~brave(X0)))) [flattening 30]
39. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 6]
40. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 39]
42. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | generous(X0))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | generous(X0))) [flattening 42]
46. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 10]
47. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [flattening 46]
48. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X1] : (generous(X1) & ~creative(X1)) | ! [X0] : kind(X0)) [nnf transformation 22]
49. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X2] : (generous(X2) & ~creative(X2)) | ! [X3] : kind(X3)) [rectify 48]
50. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
51. ? [X2] : (generous(X2) & ~creative(X2)) => (generous(sK2) & ~creative(sK2)) [choice axiom]
52. (~kind(sK1) | ! [X1] : (~generous(X1) | creative(X1))) & ((generous(sK2) & ~creative(sK2)) | ! [X3] : kind(X3)) [skolemisation 49,51,50]
62. ~kind(X0) | ~brave(X0) [cnf transformation 31]
79. funny(X0) | brave(X0) | creative(X0) | creative(X0) [cnf transformation 40]
80. funny(X0) | brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
90. ~generous(X0) | creative(X0) [cnf transformation 43]
101. ~wise(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 47]
104. ~creative(sK2) | kind(X3) [cnf transformation 52]
105. generous(sK2) | kind(X3) [cnf transformation 52]
133. wise(fred) [cnf transformation 21]
140. funny(X0) | brave(X0) | creative(X0) [duplicate literal removal 79]
141. funny(X0) | brave(X0) | ~creative(X0) [duplicate literal removal 80]
162. funny(X0) | brave(X0) [subsumption resolution 140,141]
164. 5 <=> ! [X3] : kind(X3) [avatar definition]
165. kind(X3) <- (5) [avatar component clause 164]
167. 6 <=> generous(sK2) [avatar definition]
169. generous(sK2) <- (6) [avatar component clause 167]
170. 5 | 6 [avatar split clause 105,167,164]
172. 7 <=> creative(sK2) [avatar definition]
175. 5 | ~7 [avatar split clause 104,172,164]
240. creative(sK2) <- (6) [resolution 90,169]
243. 7 | ~6 [avatar split clause 240,167,172]
248. ~brave(X1) <- (5) [resolution 165,62]
286. 22 <=> funny(fred) [avatar definition]
287. ~funny(fred) <- (~22) [avatar component clause 286]
313. ~kind(fred) | ~funny(fred) [resolution 101,133]
314. ~funny(fred) <- (5) [subsumption resolution 313,165]
317. ~22 | ~5 [avatar split clause 314,164,286]
318. brave(fred) <- (~22) [resolution 287,162]
319. $false <- (5, ~22) [subsumption resolution 318,248]
320. ~5 | 22 [avatar contradiction clause 319]
321. $false [avatar sat refutation 170,175,243,317,320]
% SZS output end Proof for 3001425604327483981553061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.046 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not creative is both not patient and not kind and vice versa.
Everyone who is brave is not quiet or not rich.
Everyone who is either quiet or rich is not creative.
Everyone who is both not humble and creative is curious or humble and vice versa.
Everyone who is wise is old or not humble.
Everyone who is happy is strong.
Everyone who is either tall or not kind is not funny.
If mary is quiet then someone is not curious or funny and vice versa.
Everyone who is not rich is not creative or not tall and vice versa.
Everyone who is either generous or kind is not funny.
Everyone who is both not curious and not funny is not calm or patient and vice versa.
Everyone who is happy or wise is both not old and brave.
If paul is both not strong and curious then mary is generous.
Everyone who is not happy or old is tall and vice versa.
If someone is both not kind and not patient then john is both humble and not wise and vice versa.
If someone is either not funny or not kind then someone is either not brave or not tall.
Someone is not tall.
Susan is not rich or funny.
Someone is not strong.
Paul is not rich.
Someone is both not tall and wise.
Someone is either wise or patient.
Susan is either not old or not kind.
Paul is patient or happy. | Paul is not quiet. | entailment | (![X]:((~humble(X)&~creative(X))<=>(~patient(X)&~kind(X))))&
(![X]:(brave(X)=>(~quiet(X)|~rich(X))))&
(![X]:((quiet(X)<~>rich(X))=>~creative(X)))&
(![X]:((~humble(X)&creative(X))<=>(curious(X)|humble(X))))&
(![X]:(wise(X)=>(old(X)|~humble(X))))&
(![X]:(happy(X)=>strong(X)))&
(![X]:((tall(X)<~>~kind(X))=>~funny(X)))&
((quiet(mary))<=>(?[X]:((~curious(X)|funny(X)))))&
(![X]:(~rich(X)<=>(~creative(X)|~tall(X))))&
(![X]:((generous(X)<~>kind(X))=>~funny(X)))&
(![X]:((~curious(X)&~funny(X))<=>(~calm(X)|patient(X))))&
(![X]:((happy(X)|wise(X))=>(~old(X)&brave(X))))&
(((~strong(paul)&curious(paul)))=>(generous(mary)))&
(![X]:((~happy(X)|old(X))<=>tall(X)))&
((?[X]:((~kind(X)&~patient(X))))<=>((humble(john)&~wise(john))))&
((?[X]:((~funny(X)<~>~kind(X))))=>(?[X]:((~brave(X)<~>~tall(X)))))&
(?[X]:(~tall(X)))&
((~rich(susan)|funny(susan)))&
(?[X]:(~strong(X)))&
(~rich(paul))&
(?[X]:((~tall(X)&wise(X))))&
(?[X]:((wise(X)<~>patient(X))))&
((~old(susan)<~>~kind(susan)))&
((patient(paul)|happy(paul))) | ~quiet(paul) | [
"p0",
"p2",
"p3",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8859350079109607780168901
% SZS output start Proof for 8859350079109607780168901
1. ! [X0] : ((~creative(X0) & ~humble(X0)) <=> (~kind(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((quiet(X0) <~> rich(X0)) => ~creative(X0)) [input p2]
4. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (humble(X0) | curious(X0))) [input p3]
15. ? [X0] : (~patient(X0) & ~kind(X0)) <=> (~wise(john) & humble(john)) [input p14]
20. ~rich(paul) [input p19]
25. quiet(paul) [input hypothesis]
29. ! [X0] : (~creative(X0) | (quiet(X0) <=> rich(X0))) [ennf transformation 3]
39. ! [X0] : (((~creative(X0) & ~humble(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (creative(X0) | humble(X0)))) [nnf transformation 1]
40. ! [X0] : (((~creative(X0) & ~humble(X0)) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | creative(X0) | humble(X0))) [flattening 39]
41. ! [X0] : (~creative(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) [nnf transformation 29]
42. ! [X0] : (((creative(X0) & ~humble(X0)) | (~humble(X0) & ~curious(X0))) & ((humble(X0) | curious(X0)) | (~creative(X0) | humble(X0)))) [nnf transformation 4]
43. ! [X0] : (((creative(X0) & ~humble(X0)) | (~humble(X0) & ~curious(X0))) & (humble(X0) | curious(X0) | ~creative(X0) | humble(X0))) [flattening 42]
56. (? [X0] : (~patient(X0) & ~kind(X0)) | (wise(john) | ~humble(john))) & ((~wise(john) & humble(john)) | ! [X0] : (patient(X0) | kind(X0))) [nnf transformation 15]
57. (? [X0] : (~patient(X0) & ~kind(X0)) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X0] : (patient(X0) | kind(X0))) [flattening 56]
58. (? [X0] : (~patient(X0) & ~kind(X0)) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X1] : (patient(X1) | kind(X1))) [rectify 57]
59. ? [X0] : (~patient(X0) & ~kind(X0)) => (~patient(sK1) & ~kind(sK1)) [choice axiom]
60. ((~patient(sK1) & ~kind(sK1)) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X1] : (patient(X1) | kind(X1))) [skolemisation 58,59]
75. ~patient(X0) | creative(X0) | humble(X0) [cnf transformation 40]
76. ~kind(X0) | creative(X0) | humble(X0) [cnf transformation 40]
80. ~quiet(X0) | rich(X0) | ~creative(X0) [cnf transformation 41]
84. ~humble(X0) | ~humble(X0) [cnf transformation 43]
112. humble(john) | patient(X1) | kind(X1) [cnf transformation 60]
123. ~rich(paul) [cnf transformation 20]
131. quiet(paul) [cnf transformation 25]
133. ~humble(X0) [duplicate literal removal 84]
171. 9 <=> ! [X1] : (patient(X1) | kind(X1)) [avatar definition]
172. kind(X1) | patient(X1) <- (9) [avatar component clause 171]
178. patient(X1) | kind(X1) [subsumption resolution 112,133]
179. 9 [avatar split clause 178,171]
259. creative(X0) | humble(X0) | patient(X0) <- (9) [resolution 76,172]
260. patient(X0) | creative(X0) <- (9) [subsumption resolution 259,133]
276. rich(paul) | ~creative(paul) [resolution 80,131]
278. ~creative(paul) [subsumption resolution 276,123]
335. creative(X0) | creative(X0) | humble(X0) <- (9) [resolution 260,75]
339. creative(X0) | humble(X0) <- (9) [duplicate literal removal 335]
340. creative(X0) <- (9) [subsumption resolution 339,133]
352. $false <- (9) [resolution 340,278]
355. ~9 [avatar contradiction clause 352]
357. $false [avatar sat refutation 179,355]
% SZS output end Proof for 8859350079109607780168901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or wise is either funny or old.
If john is both generous and funny then someone is not brave or not tall and vice versa.
If someone is both funny and patient then alice is not calm or not strong and vice versa.
Everyone who is curious is both kind and curious.
If someone is wise then someone is not wise or old.
If someone is not brave then paul is not kind or not curious.
Everyone who is not humble is happy.
If john is both not patient and happy then lucy is either not patient or not old.
Everyone who is not curious or brave is both curious and creative and vice versa.
Everyone who is not calm is not creative or tall and vice versa.
If someone is not humble then susan is either not creative or wise and vice versa.
Everyone who is both kind and brave is not calm or creative.
If someone is generous then someone is either not happy or wise.
If someone is not creative or tall then john is quiet and vice versa.
Everyone who is not generous is humble and vice versa.
If paul is both not calm and not rich then alice is wise or rich and vice versa.
Alice is either curious or not strong.
Someone is both wise and not happy.
Someone is curious or not old.
Someone is not quiet or brave.
Paul is not rich or not tall.
Someone is both not patient and wise.
Someone is either not curious or not calm.
Someone is either tall or not rich. | Paul is not brave. | contradiction | (![X]:((strong(X)<~>wise(X))=>(funny(X)<~>old(X))))&
(((generous(john)&funny(john)))<=>(?[X]:((~brave(X)|~tall(X)))))&
((?[X]:((funny(X)&patient(X))))<=>((~calm(alice)|~strong(alice))))&
(![X]:(curious(X)=>(kind(X)&curious(X))))&
((?[X]:(wise(X)))=>(?[X]:((~wise(X)|old(X)))))&
((?[X]:(~brave(X)))=>((~kind(paul)|~curious(paul))))&
(![X]:(~humble(X)=>happy(X)))&
(((~patient(john)&happy(john)))=>((~patient(lucy)<~>~old(lucy))))&
(![X]:((~curious(X)|brave(X))<=>(curious(X)&creative(X))))&
(![X]:(~calm(X)<=>(~creative(X)|tall(X))))&
((?[X]:(~humble(X)))<=>((~creative(susan)<~>wise(susan))))&
(![X]:((kind(X)&brave(X))=>(~calm(X)|creative(X))))&
((?[X]:(generous(X)))=>(?[X]:((~happy(X)<~>wise(X)))))&
((?[X]:((~creative(X)|tall(X))))<=>(quiet(john)))&
(![X]:(~generous(X)<=>humble(X)))&
(((~calm(paul)&~rich(paul)))<=>((wise(alice)|rich(alice))))&
((curious(alice)<~>~strong(alice)))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~quiet(X)|brave(X))))&
((~rich(paul)|~tall(paul)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((tall(X)<~>~rich(X)))) | ~brave(paul) | [
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3579424308114200419807291
% SZS output start Proof for 3579424308114200419807291
4. ! [X0] : (curious(X0) => (curious(X0) & kind(X0))) [input p3]
6. ? [X0] : ~brave(X0) => (~curious(paul) | ~kind(paul)) [input p5]
9. ! [X0] : ((brave(X0) | ~curious(X0)) <=> (creative(X0) & curious(X0))) [input p8]
25. ~brave(paul) [input hypothesis]
29. ! [X0] : ((curious(X0) & kind(X0)) | ~curious(X0)) [ennf transformation 4]
31. (~curious(paul) | ~kind(paul)) | ! [X0] : brave(X0) [ennf transformation 6]
32. ~curious(paul) | ~kind(paul) | ! [X0] : brave(X0) [flattening 31]
54. ! [X0] : (((brave(X0) | ~curious(X0)) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | (~brave(X0) & curious(X0)))) [nnf transformation 9]
55. ! [X0] : ((brave(X0) | ~curious(X0) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | (~brave(X0) & curious(X0)))) [flattening 54]
102. kind(X0) | ~curious(X0) [cnf transformation 29]
105. ~curious(paul) | ~kind(paul) | brave(X0) [cnf transformation 32]
109. curious(X0) | curious(X0) [cnf transformation 55]
147. ~brave(paul) [cnf transformation 25]
148. curious(X0) [duplicate literal removal 109]
159. 3 <=> ! [X0] : brave(X0) [avatar definition]
160. brave(X0) <- (3) [avatar component clause 159]
213. ~curious(paul) | brave(X0) [subsumption resolution 105,102]
215. 15 <=> curious(paul) [avatar definition]
217. ~curious(paul) <- (~15) [avatar component clause 215]
218. 3 | ~15 [avatar split clause 213,215,159]
338. $false <- (~15) [subsumption resolution 217,148]
339. 15 [avatar contradiction clause 338]
340. $false <- (3) [resolution 160,147]
341. ~3 [avatar contradiction clause 340]
342. $false [avatar sat refutation 218,339,341]
% SZS output end Proof for 3579424308114200419807291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or quiet is tall or not old.
If alice is both quiet and not generous then fred is not funny or not quiet and vice versa.
If susan is either generous or not brave then someone is both not creative and happy and vice versa.
Everyone who is either old or not quiet is not strong.
Everyone who is both not tall and patient is creative or strong and vice versa.
If someone is either creative or not happy then someone is either not patient or strong and vice versa.
Everyone who is both humble and happy is both curious and creative and vice versa.
Everyone who is both creative and not old is either not generous or not rich.
Everyone who is curious or not patient is both not humble and brave and vice versa.
Everyone who is both curious and not rich is old or quiet and vice versa.
Everyone who is funny is either not funny or not old.
Everyone who is strong is either not creative or humble.
If susan is both not quiet and creative then someone is either not brave or not curious.
If alice is both brave and generous then mary is both not patient and humble.
If mary is both happy and funny then paul is generous or not curious.
Fred is not funny or not strong.
Alice is either not strong or kind.
Someone is not kind.
Someone is either old or not kind.
Someone is both not rich and not wise. | Mary is funny. | neutral | (![X]:((~patient(X)|quiet(X))=>(tall(X)|~old(X))))&
(((quiet(alice)&~generous(alice)))<=>((~funny(fred)|~quiet(fred))))&
(((generous(susan)<~>~brave(susan)))<=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((old(X)<~>~quiet(X))=>~strong(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)|strong(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((humble(X)&happy(X))<=>(curious(X)&creative(X))))&
(![X]:((creative(X)&~old(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((curious(X)|~patient(X))<=>(~humble(X)&brave(X))))&
(![X]:((curious(X)&~rich(X))<=>(old(X)|quiet(X))))&
(![X]:(funny(X)=>(~funny(X)<~>~old(X))))&
(![X]:(strong(X)=>(~creative(X)<~>humble(X))))&
(((~quiet(susan)&creative(susan)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(((brave(alice)&generous(alice)))=>((~patient(mary)&humble(mary))))&
(((happy(mary)&funny(mary)))=>((generous(paul)|~curious(paul))))&
((~funny(fred)|~strong(fred)))&
((~strong(alice)<~>kind(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~rich(X)&~wise(X)))) | funny(mary) | [] | null | 0 |
If someone is not calm or not strong then someone is not curious.
If alice is both creative and not old then someone is not brave or funny.
Everyone who is not rich is both not happy and brave.
Everyone who is not humble is either not happy or brave and vice versa.
If someone is patient or rich then someone is either not patient or not quiet.
Everyone who is brave or not strong is either not rich or not patient and vice versa.
If mary is not patient or wise then someone is both not creative and not curious and vice versa.
Everyone who is either humble or not tall is not rich or not tall.
If paul is either not rich or not calm then someone is either kind or tall and vice versa.
Everyone who is both not strong and not funny is not creative or not patient.
Everyone who is calm or strong is not generous or not humble.
If someone is not curious or not quiet then someone is brave or happy and vice versa.
If someone is quiet or kind then alice is both not rich and curious.
Everyone who is either not humble or wise is both not happy and humble.
Everyone who is quiet or patient is not quiet and vice versa.
If someone is tall or patient then someone is either not calm or not brave and vice versa.
Someone is either funny or not quiet.
Alice is creative or not patient.
Someone is wise or not patient.
Someone is both funny and humble.
Someone is either old or not old.
Mary is either not rich or happy.
Someone is not rich.
John is not patient or not humble. | John is wise. | entailment | ((?[X]:((~calm(X)|~strong(X))))=>(?[X]:(~curious(X))))&
(((creative(alice)&~old(alice)))=>(?[X]:((~brave(X)|funny(X)))))&
(![X]:(~rich(X)=>(~happy(X)&brave(X))))&
(![X]:(~humble(X)<=>(~happy(X)<~>brave(X))))&
((?[X]:((patient(X)|rich(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((brave(X)|~strong(X))<=>(~rich(X)<~>~patient(X))))&
(((~patient(mary)|wise(mary)))<=>(?[X]:((~creative(X)&~curious(X)))))&
(![X]:((humble(X)<~>~tall(X))=>(~rich(X)|~tall(X))))&
(((~rich(paul)<~>~calm(paul)))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:((~strong(X)&~funny(X))=>(~creative(X)|~patient(X))))&
(![X]:((calm(X)|strong(X))=>(~generous(X)|~humble(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((quiet(X)|kind(X))))=>((~rich(alice)&curious(alice))))&
(![X]:((~humble(X)<~>wise(X))=>(~happy(X)&humble(X))))&
(![X]:((quiet(X)|patient(X))<=>~quiet(X)))&
((?[X]:((tall(X)|patient(X))))<=>(?[X]:((~calm(X)<~>~brave(X)))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((creative(alice)|~patient(alice)))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((old(X)<~>~old(X))))&
((~rich(mary)<~>happy(mary)))&
(?[X]:(~rich(X)))&
((~patient(john)|~humble(john))) | wise(john) | [
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 9117736184847037592712757
% SZS output start Proof for 9117736184847037592712757
14. ! [X0] : ((~humble(X0) <~> wise(X0)) => (humble(X0) & ~happy(X0))) [input p13]
15. ! [X0] : ((patient(X0) | quiet(X0)) <=> ~quiet(X0)) [input p14]
24. ~humble(john) | ~patient(john) [input p23]
25. ~wise(john) [input hypothesis]
41. ! [X0] : ((humble(X0) & ~happy(X0)) | (~humble(X0) <=> wise(X0))) [ennf transformation 14]
69. ! [X0] : ((humble(X0) & ~happy(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) [nnf transformation 41]
70. ! [X0] : (((patient(X0) | quiet(X0)) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & ~quiet(X0)))) [nnf transformation 15]
71. ! [X0] : ((patient(X0) | quiet(X0) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & ~quiet(X0)))) [flattening 70]
135. humble(X0) | wise(X0) | humble(X0) [cnf transformation 69]
137. ~quiet(X0) | ~quiet(X0) [cnf transformation 71]
139. patient(X0) | quiet(X0) | quiet(X0) [cnf transformation 71]
157. ~humble(john) | ~patient(john) [cnf transformation 24]
158. ~wise(john) [cnf transformation 25]
159. ~quiet(X0) [duplicate literal removal 137]
160. quiet(X0) | patient(X0) [duplicate literal removal 139]
161. wise(X0) | humble(X0) [duplicate literal removal 135]
307. 33 <=> ! [X0] : ~quiet(X0) [avatar definition]
308. ~quiet(X0) <- (33) [avatar component clause 307]
316. 33 [avatar split clause 159,307]
382. 49 <=> patient(john) [avatar definition]
384. ~patient(john) <- (~49) [avatar component clause 382]
386. 50 <=> humble(john) [avatar definition]
389. ~49 | ~50 [avatar split clause 157,386,382]
397. patient(X1) <- (33) [resolution 160,308]
399. humble(john) [resolution 161,158]
400. 50 [avatar split clause 399,386]
416. $false <- (33, ~49) [resolution 397,384]
419. ~33 | 49 [avatar contradiction clause 416]
422. $false [avatar sat refutation 316,389,400,419]
% SZS output end Proof for 9117736184847037592712757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or humble then someone is either not strong or strong.
If susan is either not patient or funny then alice is not old and vice versa.
If fred is either not kind or happy then john is both calm and not kind and vice versa.
Everyone who is both not wise and not humble is both not strong and strong.
Everyone who is curious is both not happy and funny.
Everyone who is both not funny and tall is kind.
Everyone who is either not quiet or calm is happy.
If susan is happy then someone is both not calm and not rich.
If someone is calm then someone is wise or not strong and vice versa.
Everyone who is not kind is old or creative and vice versa.
If fred is either humble or not brave then someone is strong or humble and vice versa.
Everyone who is both wise and kind is not rich and vice versa.
If paul is not patient or old then fred is humble.
Everyone who is not brave or wise is both not quiet and not calm and vice versa.
If paul is either not quiet or wise then someone is both rich and not quiet and vice versa.
Everyone who is not old or tall is both happy and not calm and vice versa.
Someone is both not strong and not kind.
Paul is both brave and not wise.
Someone is strong.
Fred is either not funny or brave.
Someone is creative.
Someone is curious.
Paul is both funny and not happy.
Alice is both creative and tall. | Paul is humble. | entailment | ((?[X]:((~calm(X)|humble(X))))=>(?[X]:((~strong(X)<~>strong(X)))))&
(((~patient(susan)<~>funny(susan)))<=>(~old(alice)))&
(((~kind(fred)<~>happy(fred)))<=>((calm(john)&~kind(john))))&
(![X]:((~wise(X)&~humble(X))=>(~strong(X)&strong(X))))&
(![X]:(curious(X)=>(~happy(X)&funny(X))))&
(![X]:((~funny(X)&tall(X))=>kind(X)))&
(![X]:((~quiet(X)<~>calm(X))=>happy(X)))&
((happy(susan))=>(?[X]:((~calm(X)&~rich(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((wise(X)|~strong(X)))))&
(![X]:(~kind(X)<=>(old(X)|creative(X))))&
(((humble(fred)<~>~brave(fred)))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((wise(X)&kind(X))<=>~rich(X)))&
(((~patient(paul)|old(paul)))=>(humble(fred)))&
(![X]:((~brave(X)|wise(X))<=>(~quiet(X)&~calm(X))))&
(((~quiet(paul)<~>wise(paul)))<=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((~old(X)|tall(X))<=>(happy(X)&~calm(X))))&
(?[X]:((~strong(X)&~kind(X))))&
((brave(paul)&~wise(paul)))&
(?[X]:(strong(X)))&
((~funny(fred)<~>brave(fred)))&
(?[X]:(creative(X)))&
(?[X]:(curious(X)))&
((funny(paul)&~happy(paul)))&
((creative(alice)&tall(alice))) | humble(paul) | [
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3674752574665809145536511
% SZS output start Proof for 3674752574665809145536511
4. ! [X0] : ((~humble(X0) & ~wise(X0)) => (strong(X0) & ~strong(X0))) [input p3]
18. ~wise(paul) & brave(paul) [input p17]
25. ~humble(paul) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~strong(X0)) | (humble(X0) | wise(X0))) [ennf transformation 4]
30. ! [X0] : ((strong(X0) & ~strong(X0)) | humble(X0) | wise(X0)) [flattening 29]
91. ~strong(X0) | humble(X0) | wise(X0) [cnf transformation 30]
92. strong(X0) | humble(X0) | wise(X0) [cnf transformation 30]
136. ~wise(paul) [cnf transformation 18]
146. ~humble(paul) [cnf transformation 25]
185. wise(X0) | humble(X0) [subsumption resolution 91,92]
267. 26 <=> wise(paul) [avatar definition]
269. ~wise(paul) <- (~26) [avatar component clause 267]
287. ~26 [avatar split clause 136,267]
319. humble(paul) <- (~26) [resolution 185,269]
321. $false <- (~26) [subsumption resolution 319,146]
322. 26 [avatar contradiction clause 321]
323. $false [avatar sat refutation 287,322]
% SZS output end Proof for 3674752574665809145536511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and quiet is wise or not old and vice versa.
Everyone who is kind or not old is not happy and vice versa.
If someone is kind then someone is both not humble and not old.
Everyone who is either not strong or rich is not curious or not calm and vice versa.
Everyone who is both kind and wise is wise.
Everyone who is either funny or not happy is not happy and vice versa.
If john is either creative or not humble then someone is tall.
Everyone who is tall is funny.
Everyone who is either not calm or not old is generous.
If fred is kind or not rich then someone is curious.
If alice is either not patient or not funny then someone is both not curious and not creative and vice versa.
Everyone who is happy is generous or quiet and vice versa.
Everyone who is not brave or not strong is either not wise or quiet.
Everyone who is either not humble or patient is both generous and not happy and vice versa.
If alice is either rich or happy then john is either not humble or happy.
Everyone who is calm or not creative is not tall or patient and vice versa.
John is not calm.
Someone is quiet.
Someone is not rich or not brave.
Someone is either not happy or wise.
Someone is both strong and happy.
Someone is not generous or not funny. | John is not kind. | entailment | (![X]:((old(X)&quiet(X))<=>(wise(X)|~old(X))))&
(![X]:((kind(X)|~old(X))<=>~happy(X)))&
((?[X]:(kind(X)))=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~strong(X)<~>rich(X))<=>(~curious(X)|~calm(X))))&
(![X]:((kind(X)&wise(X))=>wise(X)))&
(![X]:((funny(X)<~>~happy(X))<=>~happy(X)))&
(((creative(john)<~>~humble(john)))=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>funny(X)))&
(![X]:((~calm(X)<~>~old(X))=>generous(X)))&
(((kind(fred)|~rich(fred)))=>(?[X]:(curious(X))))&
(((~patient(alice)<~>~funny(alice)))<=>(?[X]:((~curious(X)&~creative(X)))))&
(![X]:(happy(X)<=>(generous(X)|quiet(X))))&
(![X]:((~brave(X)|~strong(X))=>(~wise(X)<~>quiet(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(generous(X)&~happy(X))))&
(((rich(alice)<~>happy(alice)))=>((~humble(john)<~>happy(john))))&
(![X]:((calm(X)|~creative(X))<=>(~tall(X)|patient(X))))&
(~calm(john))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((strong(X)&happy(X))))&
(?[X]:((~generous(X)|~funny(X)))) | ~kind(john) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7218855227064864145810739
% SZS output start Proof for 7218855227064864145810739
1. ! [X0] : ((quiet(X0) & old(X0)) <=> (~old(X0) | wise(X0))) [input p0]
3. ? [X0] : kind(X0) => ? [X0] : (~old(X0) & ~humble(X0)) [input p2]
23. kind(john) [input hypothesis]
24. ? [X0] : kind(X0) => ? [X1] : (~old(X1) & ~humble(X1)) [rectify 3]
25. ? [X1] : (~old(X1) & ~humble(X1)) | ! [X0] : ~kind(X0) [ennf transformation 24]
34. ! [X0] : (((quiet(X0) & old(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (~quiet(X0) | ~old(X0)))) [nnf transformation 1]
35. ! [X0] : (((quiet(X0) & old(X0)) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | ~quiet(X0) | ~old(X0))) [flattening 34]
38. ? [X0] : (~old(X0) & ~humble(X0)) | ! [X1] : ~kind(X1) [rectify 25]
39. ? [X0] : (~old(X0) & ~humble(X0)) => (~old(sK0) & ~humble(sK0)) [choice axiom]
40. (~old(sK0) & ~humble(sK0)) | ! [X1] : ~kind(X1) [skolemisation 38,39]
75. old(X0) | old(X0) [cnf transformation 35]
82. ~old(sK0) | ~kind(X1) [cnf transformation 40]
136. kind(john) [cnf transformation 23]
140. old(X0) [duplicate literal removal 75]
143. ~kind(X1) [subsumption resolution 82,140]
227. $false [subsumption resolution 136,143]
% SZS output end Proof for 7218855227064864145810739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or strong is not brave.
If someone is both not quiet and generous then someone is tall or not wise and vice versa.
If someone is either tall or not generous then someone is both calm and not tall and vice versa.
If someone is either not old or creative then someone is either calm or not curious and vice versa.
Everyone who is curious or not curious is not calm or kind.
If mary is not patient or not quiet then john is both humble and brave.
If someone is curious then paul is both not funny and funny.
If susan is not brave then susan is both patient and strong and vice versa.
If someone is curious or kind then someone is either rich or not strong.
Everyone who is creative is not strong and vice versa.
Everyone who is both calm and quiet is both not quiet and strong and vice versa.
Everyone who is both not creative and rich is not calm and vice versa.
Everyone who is either patient or not kind is not tall and vice versa.
Everyone who is both kind and not humble is rich or funny.
If john is either not generous or not tall then fred is either not brave or tall.
Everyone who is both not funny and not generous is both not wise and funny and vice versa.
John is either not patient or not curious.
Someone is either funny or quiet.
Paul is quiet or patient.
Someone is old or not kind.
Someone is both not creative and not patient.
Mary is either happy or wise.
John is quiet. | Mary is not strong. | contradiction | (![X]:((creative(X)|strong(X))=>~brave(X)))&
((?[X]:((~quiet(X)&generous(X))))<=>(?[X]:((tall(X)|~wise(X)))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((calm(X)&~tall(X)))))&
((?[X]:((~old(X)<~>creative(X))))<=>(?[X]:((calm(X)<~>~curious(X)))))&
(![X]:((curious(X)|~curious(X))=>(~calm(X)|kind(X))))&
(((~patient(mary)|~quiet(mary)))=>((humble(john)&brave(john))))&
((?[X]:(curious(X)))=>((~funny(paul)&funny(paul))))&
((~brave(susan))<=>((patient(susan)&strong(susan))))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
(![X]:((calm(X)&quiet(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~creative(X)&rich(X))<=>~calm(X)))&
(![X]:((patient(X)<~>~kind(X))<=>~tall(X)))&
(![X]:((kind(X)&~humble(X))=>(rich(X)|funny(X))))&
(((~generous(john)<~>~tall(john)))=>((~brave(fred)<~>tall(fred))))&
(![X]:((~funny(X)&~generous(X))<=>(~wise(X)&funny(X))))&
((~patient(john)<~>~curious(john)))&
(?[X]:((funny(X)<~>quiet(X))))&
((quiet(paul)|patient(paul)))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:((~creative(X)&~patient(X))))&
((happy(mary)<~>wise(mary)))&
(quiet(john)) | ~strong(mary) | [
"p0",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 951560537190443202422692
% SZS output start Proof for 951560537190443202422692
1. ! [X0] : ((strong(X0) | creative(X0)) => ~brave(X0)) [input p0]
6. (~quiet(mary) | ~patient(mary)) => (brave(john) & humble(john)) [input p5]
10. ! [X0] : (creative(X0) <=> ~strong(X0)) [input p9]
11. ! [X0] : ((quiet(X0) & calm(X0)) <=> (strong(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : ((rich(X0) & ~creative(X0)) <=> ~calm(X0)) [input p11]
24. ~strong(mary) [input hypothesis]
29. (~quiet(mary) | ~patient(mary)) => brave(john) [pure predicate removal 6]
31. ! [X0] : (~brave(X0) | (~strong(X0) & ~creative(X0))) [ennf transformation 1]
34. brave(john) | (quiet(mary) & patient(mary)) [ennf transformation 29]
59. ! [X0] : ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))) [nnf transformation 10]
60. ! [X0] : (((quiet(X0) & calm(X0)) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | (~quiet(X0) | ~calm(X0)))) [nnf transformation 11]
61. ! [X0] : (((quiet(X0) & calm(X0)) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | ~quiet(X0) | ~calm(X0))) [flattening 60]
62. ! [X0] : (((rich(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) | creative(X0)))) [nnf transformation 12]
63. ! [X0] : (((rich(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | ~rich(X0) | creative(X0))) [flattening 62]
77. ~brave(X0) | ~creative(X0) [cnf transformation 31]
78. ~brave(X0) | ~strong(X0) [cnf transformation 31]
101. brave(john) | quiet(mary) [cnf transformation 34]
112. strong(X0) | creative(X0) [cnf transformation 59]
113. ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 61]
118. ~creative(X0) | calm(X0) [cnf transformation 63]
143. ~strong(mary) [cnf transformation 24]
146. ~calm(X0) | ~quiet(X0) [duplicate literal removal 113]
247. 23 <=> quiet(mary) [avatar definition]
249. quiet(mary) <- (23) [avatar component clause 247]
251. 24 <=> brave(john) [avatar definition]
253. brave(john) <- (24) [avatar component clause 251]
254. 23 | 24 [avatar split clause 101,251,247]
366. ~creative(john) <- (24) [resolution 77,253]
368. ~strong(john) <- (24) [resolution 78,253]
372. creative(mary) [resolution 112,143]
378. creative(john) <- (24) [resolution 368,112]
379. $false <- (24) [subsumption resolution 378,366]
380. ~24 [avatar contradiction clause 379]
381. calm(mary) [resolution 372,118]
396. ~quiet(mary) [resolution 381,146]
397. $false <- (23) [subsumption resolution 396,249]
398. ~23 [avatar contradiction clause 397]
399. $false [avatar sat refutation 254,380,398]
% SZS output end Proof for 951560537190443202422692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either creative or not funny.
Everyone who is wise is either not calm or not strong and vice versa.
If someone is both funny and not rich then someone is not wise.
Everyone who is not quiet is either calm or funny and vice versa.
If mary is either happy or quiet then someone is not quiet or calm and vice versa.
Everyone who is both happy and not old is both not funny and humble.
Everyone who is not calm is curious or not patient and vice versa.
Everyone who is kind or not quiet is not quiet or not kind.
If someone is not calm or not creative then someone is not old or happy and vice versa.
If fred is not kind or funny then susan is both not brave and tall.
Everyone who is not tall or not generous is both not happy and curious.
Everyone who is either not humble or not generous is not patient or not kind and vice versa.
Everyone who is both patient and kind is not tall or not kind and vice versa.
If susan is either patient or calm then someone is both not kind and not patient.
Everyone who is not wise or generous is not calm or not rich and vice versa.
If susan is both patient and not rich then john is not creative.
Someone is not humble or funny.
Someone is strong.
Alice is humble.
Someone is curious.
Mary is not creative or funny.
Lucy is creative or old. | Fred is not patient. | neutral | (![X]:(wise(X)=>(creative(X)<~>~funny(X))))&
(![X]:(wise(X)<=>(~calm(X)<~>~strong(X))))&
((?[X]:((funny(X)&~rich(X))))=>(?[X]:(~wise(X))))&
(![X]:(~quiet(X)<=>(calm(X)<~>funny(X))))&
(((happy(mary)<~>quiet(mary)))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((happy(X)&~old(X))=>(~funny(X)&humble(X))))&
(![X]:(~calm(X)<=>(curious(X)|~patient(X))))&
(![X]:((kind(X)|~quiet(X))=>(~quiet(X)|~kind(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>(?[X]:((~old(X)|happy(X)))))&
(((~kind(fred)|funny(fred)))=>((~brave(susan)&tall(susan))))&
(![X]:((~tall(X)|~generous(X))=>(~happy(X)&curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~patient(X)|~kind(X))))&
(![X]:((patient(X)&kind(X))<=>(~tall(X)|~kind(X))))&
(((patient(susan)<~>calm(susan)))=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~calm(X)|~rich(X))))&
(((patient(susan)&~rich(susan)))=>(~creative(john)))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:(strong(X)))&
(humble(alice))&
(?[X]:(curious(X)))&
((~creative(mary)|funny(mary)))&
((creative(lucy)|old(lucy))) | ~patient(fred) | [] | null | 0 |
If someone is kind then john is not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Lucy is not curious. | entailment | ((?[X]:(kind(X)))<=>((~quiet(john)|humble(john))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | ~curious(lucy) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7390623711888793540612009
% SZS output start Proof for 7390623711888793540612009
6. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X0] : curious(X0) [input p5]
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. curious(lucy) [input hypothesis]
24. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X1] : curious(X1) [rectify 6]
46. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~brave(X0) | ~strong(X0))) [nnf transformation 24]
47. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~brave(X3) | ~strong(X3))) [rectify 46]
48. ? [X0] : (brave(X0) & strong(X0)) => (brave(sK2) & strong(sK2)) [choice axiom]
49. ? [X2] : curious(X2) => curious(sK3) [choice axiom]
50. ((brave(sK2) & strong(sK2)) | ! [X1] : ~curious(X1)) & (curious(sK3) | ! [X3] : (~brave(X3) | ~strong(X3))) [skolemisation 47,49,48]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
61. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 60]
88. brave(sK2) | ~curious(X1) [cnf transformation 50]
112. ~brave(X0) | ~brave(X0) [cnf transformation 61]
124. curious(lucy) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
191. 14 <=> ! [X1] : ~curious(X1) [avatar definition]
192. ~curious(X1) <- (14) [avatar component clause 191]
194. 15 <=> brave(sK2) [avatar definition]
196. brave(sK2) <- (15) [avatar component clause 194]
197. 14 | 15 [avatar split clause 88,194,191]
257. $false <- (15) [subsumption resolution 196,126]
258. ~15 [avatar contradiction clause 257]
263. $false <- (14) [resolution 192,124]
264. ~14 [avatar contradiction clause 263]
265. $false [avatar sat refutation 197,258,264]
% SZS output end Proof for 7390623711888793540612009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or rich is not kind and vice versa.
Everyone who is either old or strong is both not strong and curious.
If someone is either creative or humble then someone is not patient and vice versa.
If someone is not brave then someone is either not calm or generous and vice versa.
Everyone who is not rich is not happy and vice versa.
If someone is both not generous and kind then alice is not calm.
Everyone who is not generous is both not kind and brave and vice versa.
If susan is not quiet or rich then mary is either patient or not wise and vice versa.
Everyone who is both not funny and not wise is both not generous and generous.
Everyone who is either old or not curious is either not strong or curious and vice versa.
Everyone who is kind or rich is both happy and rich.
If paul is either not old or not creative then someone is funny or not rich.
If john is both humble and not quiet then someone is not humble or wise.
Everyone who is not rich or generous is not wise or not humble and vice versa.
Everyone who is rich is not brave or brave and vice versa.
If someone is not quiet then someone is rich.
Fred is either not generous or calm.
Fred is either not wise or not strong.
Someone is not curious.
Paul is both generous and not brave.
Mary is not calm or wise.
Paul is not patient or kind.
Susan is wise or kind. | Alice is old. | neutral | (![X]:((funny(X)|rich(X))<=>~kind(X)))&
(![X]:((old(X)<~>strong(X))=>(~strong(X)&curious(X))))&
((?[X]:((creative(X)<~>humble(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:(~rich(X)<=>~happy(X)))&
((?[X]:((~generous(X)&kind(X))))=>(~calm(alice)))&
(![X]:(~generous(X)<=>(~kind(X)&brave(X))))&
(((~quiet(susan)|rich(susan)))<=>((patient(mary)<~>~wise(mary))))&
(![X]:((~funny(X)&~wise(X))=>(~generous(X)&generous(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((kind(X)|rich(X))=>(happy(X)&rich(X))))&
(((~old(paul)<~>~creative(paul)))=>(?[X]:((funny(X)|~rich(X)))))&
(((humble(john)&~quiet(john)))=>(?[X]:((~humble(X)|wise(X)))))&
(![X]:((~rich(X)|generous(X))<=>(~wise(X)|~humble(X))))&
(![X]:(rich(X)<=>(~brave(X)|brave(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(rich(X))))&
((~generous(fred)<~>calm(fred)))&
((~wise(fred)<~>~strong(fred)))&
(?[X]:(~curious(X)))&
((generous(paul)&~brave(paul)))&
((~calm(mary)|wise(mary)))&
((~patient(paul)|kind(paul)))&
((wise(susan)|kind(susan))) | old(alice) | [] | null | 0 |
Everyone who is wise is not patient and vice versa. If someone is quiet or not patient then john is curious. Everyone who is both strong and not rich is both not strong and not curious. Everyone who is kind or creative is either not happy or not wise. Everyone who is either not quiet or tall is either not creative or creative and vice versa. Everyone who is both not patient and not tall is not happy or patient and vice versa. If mary is brave then someone is both not wise and funny and vice versa. If someone is both not funny and not patient then someone is both quiet and wise and vice versa. Everyone who is strong is either not creative or kind. Everyone who is both curious and not happy is not rich. Everyone who is either not quiet or rich is both calm and not strong. If someone is either kind or not old then alice is kind or not funny. Everyone who is both strong and rich is either not humble or not wise and vice versa. Everyone who is strong or not curious is both not rich and generous and vice versa. If someone is either funny or rich then susan is either not quiet or not brave. Everyone who is not happy is either not creative or not happy and vice versa. Alice is either not calm or not patient. Susan is either calm or not calm. Paul is both not old and not tall. Susan is funny. Fred is both not strong and kind. Someone is both old and not tall. | Fred is not creative. | contradiction | (![X]:(wise(X)<=>~patient(X)))&
((?[X]:((quiet(X)|~patient(X))))=>(curious(john)))&
(![X]:((strong(X)&~rich(X))=>(~strong(X)&~curious(X))))&
(![X]:((kind(X)|creative(X))=>(~happy(X)<~>~wise(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~creative(X)<~>creative(X))))&
(![X]:((~patient(X)&~tall(X))<=>(~happy(X)|patient(X))))&
((brave(mary))<=>(?[X]:((~wise(X)&funny(X)))))&
((?[X]:((~funny(X)&~patient(X))))<=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:(strong(X)=>(~creative(X)<~>kind(X))))&
(![X]:((curious(X)&~happy(X))=>~rich(X)))&
(![X]:((~quiet(X)<~>rich(X))=>(calm(X)&~strong(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((kind(alice)|~funny(alice))))&
(![X]:((strong(X)&rich(X))<=>(~humble(X)<~>~wise(X))))&
(![X]:((strong(X)|~curious(X))<=>(~rich(X)&generous(X))))&
((?[X]:((funny(X)<~>rich(X))))=>((~quiet(susan)<~>~brave(susan))))&
(![X]:(~happy(X)<=>(~creative(X)<~>~happy(X))))&
((~calm(alice)<~>~patient(alice)))&
((calm(susan)<~>~calm(susan)))&
((~old(paul)&~tall(paul)))&
(funny(susan))&
((~strong(fred)&kind(fred)))&
(?[X]:((old(X)&~tall(X)))) | ~creative(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8978398190482767965103947
% SZS output start Proof for 8978398190482767965103947
16. ! [X0] : (~happy(X0) <=> (~creative(X0) <~> ~happy(X0))) [input p15]
23. ~creative(fred) [input hypothesis]
58. ! [X0] : ((~happy(X0) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0)))) & (((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | happy(X0))) [nnf transformation 16]
118. happy(X0) | creative(X0) | happy(X0) [cnf transformation 58]
119. ~happy(X0) | ~happy(X0) | creative(X0) [cnf transformation 58]
132. ~creative(fred) [cnf transformation 23]
133. happy(X0) | creative(X0) [duplicate literal removal 118]
134. ~happy(X0) | creative(X0) [duplicate literal removal 119]
237. creative(X0) [subsumption resolution 133,134]
239. $false [subsumption resolution 132,237]
% SZS output end Proof for 8978398190482767965103947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or humble is not funny and vice versa.
Everyone who is not funny is strong.
If fred is either not old or strong then someone is both not calm and calm.
Everyone who is either not brave or not kind is both not old and not rich and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Everyone who is either happy or not quiet is either wise or happy and vice versa.
If susan is both not humble and not rich then fred is not brave and vice versa.
If mary is not rich or not wise then someone is brave or happy.
Everyone who is either tall or humble is either strong or not creative and vice versa.
Someone is either not tall or tall.
Someone is not generous or not kind.
Fred is both not calm and not kind.
Someone is both not strong and not kind.
Paul is calm or not strong.
Paul is either strong or not happy.
Susan is not happy.
Someone is either not curious or wise. | Fred is happy. | entailment | (![X]:((~creative(X)<~>humble(X))<=>~funny(X)))&
(![X]:(~funny(X)=>strong(X)))&
(((~old(fred)<~>strong(fred)))=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(strong(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((~calm(fred)&~kind(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(paul)|~strong(paul)))&
((strong(paul)<~>~happy(paul)))&
(~happy(susan))&
(?[X]:((~curious(X)<~>wise(X)))) | happy(fred) | [
"p4",
"p5",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2560837339900187172117414
% SZS output start Proof for 2560837339900187172117414
5. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p5]
7. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> ? [X0] : (tall(X0) & ~brave(X0)) [input p6]
19. ~kind(fred) & ~calm(fred) [input p18]
25. ~happy(fred) [input hypothesis]
26. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> ? [X1] : (tall(X1) & ~brave(X1)) [rectify 7]
45. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 5]
46. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 45]
47. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
48. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 47]
49. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ! [X1] : (~tall(X1) | brave(X1))) & (? [X1] : (tall(X1) & ~brave(X1)) | ! [X0] : ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 26]
50. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ! [X1] : (~tall(X1) | brave(X1))) & (? [X2] : (tall(X2) & ~brave(X2)) | ! [X3] : ((happy(X3) | calm(X3)) & (~calm(X3) | ~happy(X3)))) [rectify 49]
51. ? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) => ((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) [choice axiom]
52. ? [X2] : (tall(X2) & ~brave(X2)) => (tall(sK2) & ~brave(sK2)) [choice axiom]
53. (((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) | ! [X1] : (~tall(X1) | brave(X1))) & ((tall(sK2) & ~brave(sK2)) | ! [X3] : ((happy(X3) | calm(X3)) & (~calm(X3) | ~happy(X3)))) [skolemisation 50,52,51]
94. ~tall(X0) | ~quiet(X0) [cnf transformation 46]
98. curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 48]
100. ~tall(X0) | ~curious(X0) | ~curious(X0) | quiet(X0) [cnf transformation 48]
105. tall(sK2) | happy(X3) | calm(X3) [cnf transformation 53]
141. ~calm(fred) [cnf transformation 19]
151. ~happy(fred) [cnf transformation 25]
156. curious(X0) | ~tall(X0) [duplicate literal removal 98]
157. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 100]
174. ~curious(X0) | ~tall(X0) [subsumption resolution 157,94]
175. ~tall(X0) [subsumption resolution 156,174]
177. happy(X3) | calm(X3) [subsumption resolution 105,175]
308. calm(fred) [resolution 177,151]
311. $false [subsumption resolution 308,141]
% SZS output end Proof for 2560837339900187172117414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not patient and not tall then someone is wise and vice versa.
Everyone who is either not calm or not creative is both not strong and not creative.
If someone is both calm and old then alice is either not patient or not creative.
Everyone who is both funny and patient is not strong.
If paul is not strong then someone is both not tall and rich and vice versa.
If john is calm or not patient then fred is both not kind and not rich.
Everyone who is either curious or not calm is both not generous and not brave.
If someone is not brave or brave then lucy is either curious or creative.
If someone is either not patient or creative then someone is both strong and not wise.
If susan is brave or curious then someone is either not brave or not quiet.
Everyone who is either generous or not tall is either not brave or funny.
Everyone who is both funny and strong is both not tall and humble.
Everyone who is both not humble and humble is not happy or generous and vice versa.
Everyone who is both not creative and not wise is both not quiet and not curious.
If john is either not tall or not old then susan is both rich and happy.
Everyone who is either not happy or happy is brave.
Someone is either not wise or happy.
Susan is both not generous and not creative.
Susan is either brave or creative.
Mary is not brave or not curious.
Paul is not curious.
Susan is not generous or not wise.
Someone is not creative or strong.
Someone is humble. | John is not old. | neutral | (((~patient(lucy)&~tall(lucy)))<=>(?[X]:(wise(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(~strong(X)&~creative(X))))&
((?[X]:((calm(X)&old(X))))=>((~patient(alice)<~>~creative(alice))))&
(![X]:((funny(X)&patient(X))=>~strong(X)))&
((~strong(paul))<=>(?[X]:((~tall(X)&rich(X)))))&
(((calm(john)|~patient(john)))=>((~kind(fred)&~rich(fred))))&
(![X]:((curious(X)<~>~calm(X))=>(~generous(X)&~brave(X))))&
((?[X]:((~brave(X)|brave(X))))=>((curious(lucy)<~>creative(lucy))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((strong(X)&~wise(X)))))&
(((brave(susan)|curious(susan)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~brave(X)<~>funny(X))))&
(![X]:((funny(X)&strong(X))=>(~tall(X)&humble(X))))&
(![X]:((~humble(X)&humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((~creative(X)&~wise(X))=>(~quiet(X)&~curious(X))))&
(((~tall(john)<~>~old(john)))=>((rich(susan)&happy(susan))))&
(![X]:((~happy(X)<~>happy(X))=>brave(X)))&
(?[X]:((~wise(X)<~>happy(X))))&
((~generous(susan)&~creative(susan)))&
((brave(susan)<~>creative(susan)))&
((~brave(mary)|~curious(mary)))&
(~curious(paul))&
((~generous(susan)|~wise(susan)))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(humble(X))) | ~old(john) | [] | null | 0 |
If someone is both calm and not curious then someone is either not tall or brave and vice versa.
If paul is brave then john is patient or not strong.
If paul is generous or tall then john is both not creative and not humble.
Everyone who is either not kind or not patient is not humble.
If someone is not patient or kind then susan is either not calm or not wise and vice versa.
Everyone who is either creative or not calm is either not brave or not tall.
If someone is funny then john is not patient or not quiet and vice versa.
Everyone who is not quiet is strong or not calm and vice versa.
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.
Someone is tall.
Someone is creative or not generous.
Paul is either not creative or patient.
Susan is either not brave or not rich.
Someone is not curious.
Someone is not humble. | Paul is not brave. | neutral | ((?[X]:((calm(X)&~curious(X))))<=>(?[X]:((~tall(X)<~>brave(X)))))&
((brave(paul))=>((patient(john)|~strong(john))))&
(((generous(paul)|tall(paul)))=>((~creative(john)&~humble(john))))&
(![X]:((~kind(X)<~>~patient(X))=>~humble(X)))&
((?[X]:((~patient(X)|kind(X))))<=>((~calm(susan)<~>~wise(susan))))&
(![X]:((creative(X)<~>~calm(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![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]:(tall(X)))&
(?[X]:((creative(X)|~generous(X))))&
((~creative(paul)<~>patient(paul)))&
((~brave(susan)<~>~rich(susan)))&
(?[X]:(~curious(X)))&
(?[X]:(~humble(X))) | ~brave(paul) | [] | null | 0 |
Everyone who is either not patient or not curious is not funny.
Everyone who is curious is both brave and not quiet and vice versa.
If someone is wise then someone is humble or calm.
Everyone who is both quiet and generous is not old or strong.
If lucy is both not quiet and calm then someone is both not curious and brave.
If someone is funny then someone is either creative or not quiet and vice versa.
Everyone who is both not kind and humble is not old.
Everyone who is not humble is quiet and vice versa.
If john is creative then john is either not happy or happy.
If someone is either tall or humble then susan is both patient and tall and vice versa.
Everyone who is not humble or humble is tall or wise and vice versa.
Everyone who is either strong or not rich is tall.
Everyone who is either not kind or quiet is curious and vice versa.
Everyone who is both funny and not generous is either not calm or humble and vice versa.
If someone is either curious or not tall then someone is humble and vice versa.
Fred is patient or calm.
Someone is both strong and not rich.
Someone is generous.
Someone is either calm or not calm.
Someone is both not tall and humble.
Paul is both not creative and happy.
John is not wise.
Susan is not happy or not funny. | Susan is tall. | entailment | (![X]:((~patient(X)<~>~curious(X))=>~funny(X)))&
(![X]:(curious(X)<=>(brave(X)&~quiet(X))))&
((?[X]:(wise(X)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((quiet(X)&generous(X))=>(~old(X)|strong(X))))&
(((~quiet(lucy)&calm(lucy)))=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((~kind(X)&humble(X))=>~old(X)))&
(![X]:(~humble(X)<=>quiet(X)))&
((creative(john))=>((~happy(john)<~>happy(john))))&
((?[X]:((tall(X)<~>humble(X))))<=>((patient(susan)&tall(susan))))&
(![X]:((~humble(X)|humble(X))<=>(tall(X)|wise(X))))&
(![X]:((strong(X)<~>~rich(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))<=>curious(X)))&
(![X]:((funny(X)&~generous(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)<~>~tall(X))))<=>(?[X]:(humble(X))))&
((patient(fred)|calm(fred)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((calm(X)<~>~calm(X))))&
(?[X]:((~tall(X)&humble(X))))&
((~creative(paul)&happy(paul)))&
(~wise(john))&
((~happy(susan)|~funny(susan))) | tall(susan) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1074488888982173549414050
% SZS output start Proof for 1074488888982173549414050
10. ? [X0] : (tall(X0) <~> humble(X0)) <=> (tall(susan) & patient(susan)) [input p9]
20. ? [X0] : (humble(X0) & ~tall(X0)) [input p19]
24. ~tall(susan) [input hypothesis]
51. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (~tall(susan) | ~patient(susan))) & ((tall(susan) & patient(susan)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) [nnf transformation 10]
52. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) [flattening 51]
53. (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X1] : ((tall(X1) | ~humble(X1)) & (humble(X1) | ~tall(X1)))) [rectify 52]
54. ? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) => ((~humble(sK4) | ~tall(sK4)) & (humble(sK4) | tall(sK4))) [choice axiom]
55. (((~humble(sK4) | ~tall(sK4)) & (humble(sK4) | tall(sK4))) | ~tall(susan) | ~patient(susan)) & ((tall(susan) & patient(susan)) | ! [X1] : ((tall(X1) | ~humble(X1)) & (humble(X1) | ~tall(X1)))) [skolemisation 53,54]
74. ? [X0] : (humble(X0) & ~tall(X0)) => (humble(sK10) & ~tall(sK10)) [choice axiom]
75. humble(sK10) & ~tall(sK10) [skolemisation 20,74]
95. tall(susan) | tall(X1) | ~humble(X1) [cnf transformation 55]
124. ~tall(sK10) [cnf transformation 75]
125. humble(sK10) [cnf transformation 75]
130. ~tall(susan) [cnf transformation 24]
191. 15 <=> tall(susan) [avatar definition]
205. 18 <=> ! [X1] : (tall(X1) | ~humble(X1)) [avatar definition]
206. ~humble(X1) | tall(X1) <- (18) [avatar component clause 205]
207. 18 | 15 [avatar split clause 95,191,205]
260. ~15 [avatar split clause 130,191]
268. tall(sK10) <- (18) [resolution 206,125]
269. $false <- (18) [subsumption resolution 268,124]
270. ~18 [avatar contradiction clause 269]
271. $false [avatar sat refutation 207,260,270]
% SZS output end Proof for 1074488888982173549414050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not creative or not wise then mary is not happy or not tall. Everyone who is patient or happy is either brave or not calm. Everyone who is old is either not quiet or calm and vice versa. Everyone who is either not creative or generous is funny or generous and vice versa. Everyone who is either not humble or not old is both humble and not humble and vice versa. Everyone who is both generous and not generous is calm or funny and vice versa. If lucy is not rich then someone is either not wise or not strong and vice versa. If someone is either not humble or creative then susan is both generous and calm. Everyone who is not humble or not rich is not old or creative and vice versa. If someone is not humble or curious then paul is either kind or not funny. Everyone who is either not creative or not humble is either creative or not rich and vice versa. If someone is both not brave and brave then someone is strong. If someone is both funny and not quiet then someone is both not curious and not old and vice versa. If alice is both brave and not curious then someone is either not creative or not kind. If mary is rich then someone is not curious or curious and vice versa. Someone is either not kind or old. Someone is not generous or not strong. Alice is either not humble or not creative. Someone is strong or funny. Alice is either not curious or not strong. Someone is either not happy or not creative. Susan is either tall or calm. Someone is both not patient and brave. | Alice is not brave. | neutral | (((~creative(paul)<~>~wise(paul)))=>((~happy(mary)|~tall(mary))))&
(![X]:((patient(X)|happy(X))=>(brave(X)<~>~calm(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(funny(X)|generous(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(humble(X)&~humble(X))))&
(![X]:((generous(X)&~generous(X))<=>(calm(X)|funny(X))))&
((~rich(lucy))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((~humble(X)<~>creative(X))))=>((generous(susan)&calm(susan))))&
(![X]:((~humble(X)|~rich(X))<=>(~old(X)|creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((kind(paul)<~>~funny(paul))))&
(![X]:((~creative(X)<~>~humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(strong(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((~curious(X)&~old(X)))))&
(((brave(alice)&~curious(alice)))=>(?[X]:((~creative(X)<~>~kind(X)))))&
((rich(mary))<=>(?[X]:((~curious(X)|curious(X)))))&
(?[X]:((~kind(X)<~>old(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((~humble(alice)<~>~creative(alice)))&
(?[X]:((strong(X)|funny(X))))&
((~curious(alice)<~>~strong(alice)))&
(?[X]:((~happy(X)<~>~creative(X))))&
((tall(susan)<~>calm(susan)))&
(?[X]:((~patient(X)&brave(X)))) | ~brave(alice) | [] | null | 0 |
If fred is not happy then susan is creative.
If someone is strong or quiet then someone is tall or not strong and vice versa.
If alice is strong or funny then someone is either not funny or generous and vice versa.
Everyone who is both funny and calm is not patient or creative and vice versa.
If someone is either not humble or not curious then someone is both not calm and humble and vice versa.
Everyone who is funny or not rich is either not funny or funny.
If someone is both not generous and not funny then john is not patient or tall.
If alice is both funny and generous then someone is either happy or not generous and vice versa.
If someone is not curious then alice is both curious and quiet.
Everyone who is either wise or strong is not rich or not kind and vice versa.
If john is not funny then someone is either not old or quiet and vice versa.
Everyone who is funny or not calm is not old or happy and vice versa.
If paul is either patient or generous then someone is not strong or creative and vice versa.
Everyone who is old is not patient and vice versa.
Everyone who is happy or generous is not funny.
Everyone who is not humble or kind is both quiet and calm.
Someone is happy.
Mary is either not brave or happy.
Someone is strong.
Someone is not quiet or generous.
Someone is either not happy or old.
Someone is rich.
Someone is not old.
John is both humble and not happy. | Paul is kind. | contradiction | ((~happy(fred))=>(creative(susan)))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((tall(X)|~strong(X)))))&
(((strong(alice)|funny(alice)))<=>(?[X]:((~funny(X)<~>generous(X)))))&
(![X]:((funny(X)&calm(X))<=>(~patient(X)|creative(X))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:((funny(X)|~rich(X))=>(~funny(X)<~>funny(X))))&
((?[X]:((~generous(X)&~funny(X))))=>((~patient(john)|tall(john))))&
(((funny(alice)&generous(alice)))<=>(?[X]:((happy(X)<~>~generous(X)))))&
((?[X]:(~curious(X)))=>((curious(alice)&quiet(alice))))&
(![X]:((wise(X)<~>strong(X))<=>(~rich(X)|~kind(X))))&
((~funny(john))<=>(?[X]:((~old(X)<~>quiet(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~old(X)|happy(X))))&
(((patient(paul)<~>generous(paul)))<=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((happy(X)|generous(X))=>~funny(X)))&
(![X]:((~humble(X)|kind(X))=>(quiet(X)&calm(X))))&
(?[X]:(happy(X)))&
((~brave(mary)<~>happy(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:(rich(X)))&
(?[X]:(~old(X)))&
((humble(john)&~happy(john))) | kind(paul) | [
"p3",
"p7",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 697245270048291122685583
% SZS output start Proof for 697245270048291122685583
4. ! [X0] : ((calm(X0) & funny(X0)) <=> (creative(X0) | ~patient(X0))) [input p3]
8. (generous(alice) & funny(alice)) <=> ? [X0] : (happy(X0) <~> ~generous(X0)) [input p7]
12. ! [X0] : ((~calm(X0) | funny(X0)) <=> (happy(X0) | ~old(X0))) [input p11]
14. ! [X0] : (old(X0) <=> ~patient(X0)) [input p13]
15. ! [X0] : ((generous(X0) | happy(X0)) => ~funny(X0)) [input p14]
16. ! [X0] : ((kind(X0) | ~humble(X0)) => (calm(X0) & quiet(X0))) [input p15]
25. kind(paul) [input hypothesis]
33. ! [X0] : (~funny(X0) | (~generous(X0) & ~happy(X0))) [ennf transformation 15]
34. ! [X0] : ((calm(X0) & quiet(X0)) | (~kind(X0) & humble(X0))) [ennf transformation 16]
45. ! [X0] : (((calm(X0) & funny(X0)) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((calm(X0) & funny(X0)) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | ~calm(X0) | ~funny(X0))) [flattening 45]
53. ((generous(alice) & funny(alice)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~generous(alice) | ~funny(alice))) [nnf transformation 8]
54. ((generous(alice) & funny(alice)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ~generous(alice) | ~funny(alice)) [flattening 53]
55. ((generous(alice) & funny(alice)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (? [X1] : ((generous(X1) | ~happy(X1)) & (~generous(X1) | happy(X1))) | ~generous(alice) | ~funny(alice)) [rectify 54]
56. ? [X1] : ((generous(X1) | ~happy(X1)) & (~generous(X1) | happy(X1))) => ((generous(sK5) | ~happy(sK5)) & (~generous(sK5) | happy(sK5))) [choice axiom]
57. ((generous(alice) & funny(alice)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (((generous(sK5) | ~happy(sK5)) & (~generous(sK5) | happy(sK5))) | ~generous(alice) | ~funny(alice)) [skolemisation 55,56]
64. ! [X0] : (((~calm(X0) | funny(X0)) | (~happy(X0) & old(X0))) & ((happy(X0) | ~old(X0)) | (calm(X0) & ~funny(X0)))) [nnf transformation 12]
65. ! [X0] : ((~calm(X0) | funny(X0) | (~happy(X0) & old(X0))) & (happy(X0) | ~old(X0) | (calm(X0) & ~funny(X0)))) [flattening 64]
70. ! [X0] : ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))) [nnf transformation 14]
97. patient(X0) | funny(X0) [cnf transformation 46]
115. funny(alice) | happy(X0) | generous(X0) [cnf transformation 57]
117. generous(alice) | happy(X0) | generous(X0) [cnf transformation 57]
132. ~calm(X0) | funny(X0) | old(X0) [cnf transformation 65]
140. ~old(X0) | ~patient(X0) [cnf transformation 70]
142. ~funny(X0) | ~happy(X0) [cnf transformation 33]
143. ~funny(X0) | ~generous(X0) [cnf transformation 33]
147. ~kind(X0) | calm(X0) [cnf transformation 34]
159. kind(paul) [cnf transformation 25]
204. 11 <=> ! [X0] : (~funny(X0) | ~generous(X0)) [avatar definition]
205. ~generous(X0) | ~funny(X0) <- (11) [avatar component clause 204]
211. 13 <=> funny(alice) [avatar definition]
213. funny(alice) <- (13) [avatar component clause 211]
272. 26 <=> ! [X0] : (happy(X0) | generous(X0)) [avatar definition]
273. generous(X0) | happy(X0) <- (26) [avatar component clause 272]
275. 27 <=> generous(alice) [avatar definition]
277. generous(alice) <- (27) [avatar component clause 275]
278. 26 | 27 [avatar split clause 117,275,272]
283. 26 | 13 [avatar split clause 115,211,272]
334. 40 <=> patient(paul) [avatar definition]
335. patient(paul) <- (40) [avatar component clause 334]
336. ~patient(paul) <- (~40) [avatar component clause 334]
355. 11 [avatar split clause 143,204]
410. calm(paul) [resolution 147,159]
411. ~funny(alice) <- (11, 27) [resolution 205,277]
412. $false <- (11, 13, 27) [subsumption resolution 411,213]
413. ~11 | ~13 | ~27 [avatar contradiction clause 412]
425. happy(X0) | ~funny(X0) <- (11, 26) [resolution 273,205]
430. ~funny(X0) <- (11, 26) [subsumption resolution 425,142]
446. funny(paul) | old(paul) [resolution 132,410]
448. old(paul) <- (11, 26) [subsumption resolution 446,430]
457. funny(paul) <- (~40) [resolution 336,97]
458. $false <- (11, 26, ~40) [subsumption resolution 457,430]
459. ~11 | ~26 | 40 [avatar contradiction clause 458]
464. ~patient(paul) <- (11, 26) [resolution 448,140]
465. $false <- (11, 26, 40) [subsumption resolution 464,335]
466. ~11 | ~26 | ~40 [avatar contradiction clause 465]
467. $false [avatar sat refutation 278,283,355,413,459,466]
% SZS output end Proof for 697245270048291122685583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is creative then paul is not calm or old and vice versa.
Everyone who is strong is old or kind and vice versa.
If someone is not strong then fred is both rich and quiet.
Everyone who is wise or calm is both happy and brave.
Everyone who is either quiet or brave is both not quiet and not funny and vice versa.
Everyone who is either rich or generous is either happy or not strong.
Everyone who is not funny or wise is generous.
Everyone who is not creative or strong is either tall or rich and vice versa.
Everyone who is either not patient or not creative is either wise or not humble.
Everyone who is not strong or not creative is wise or generous.
If lucy is both creative and tall then susan is both creative and patient and vice versa.
Everyone who is patient is not patient or calm.
Everyone who is funny or old is humble and vice versa.
If alice is both not creative and funny then someone is not calm.
Everyone who is both not kind and not quiet is both humble and curious.
If someone is both curious and funny then someone is not brave.
Someone is not rich.
John is not strong or curious.
Alice is not strong or not kind.
Someone is both brave and happy.
Someone is either rich or not tall.
Someone is not curious or wise.
Mary is not curious or rich.
Someone is humble or not wise. | Fred is rich. | entailment | ((creative(fred))<=>((~calm(paul)|old(paul))))&
(![X]:(strong(X)<=>(old(X)|kind(X))))&
((?[X]:(~strong(X)))=>((rich(fred)&quiet(fred))))&
(![X]:((wise(X)|calm(X))=>(happy(X)&brave(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~quiet(X)&~funny(X))))&
(![X]:((rich(X)<~>generous(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~funny(X)|wise(X))=>generous(X)))&
(![X]:((~creative(X)|strong(X))<=>(tall(X)<~>rich(X))))&
(![X]:((~patient(X)<~>~creative(X))=>(wise(X)<~>~humble(X))))&
(![X]:((~strong(X)|~creative(X))=>(wise(X)|generous(X))))&
(((creative(lucy)&tall(lucy)))<=>((creative(susan)&patient(susan))))&
(![X]:(patient(X)=>(~patient(X)|calm(X))))&
(![X]:((funny(X)|old(X))<=>humble(X)))&
(((~creative(alice)&funny(alice)))=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)&~quiet(X))=>(humble(X)&curious(X))))&
((?[X]:((curious(X)&funny(X))))=>(?[X]:(~brave(X))))&
(?[X]:(~rich(X)))&
((~strong(john)|curious(john)))&
((~strong(alice)|~kind(alice)))&
(?[X]:((brave(X)&happy(X))))&
(?[X]:((rich(X)<~>~tall(X))))&
(?[X]:((~curious(X)|wise(X))))&
((~curious(mary)|rich(mary)))&
(?[X]:((humble(X)|~wise(X)))) | rich(fred) | [
"p2",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6744669284431251461766542
% SZS output start Proof for 6744669284431251461766542
3. ? [X0] : ~strong(X0) => (quiet(fred) & rich(fred)) [input p2]
8. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (tall(X0) <~> rich(X0))) [input p7]
21. ? [X0] : (rich(X0) <~> ~tall(X0)) [input p20]
25. ~rich(fred) [input hypothesis]
27. (quiet(fred) & rich(fred)) | ! [X0] : strong(X0) [ennf transformation 3]
48. ! [X0] : (((strong(X0) | ~creative(X0)) | ((tall(X0) | ~rich(X0)) & (rich(X0) | ~tall(X0)))) & (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 8]
49. ! [X0] : ((strong(X0) | ~creative(X0) | ((tall(X0) | ~rich(X0)) & (rich(X0) | ~tall(X0)))) & (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | (~strong(X0) & creative(X0)))) [flattening 48]
64. ? [X0] : ((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) [nnf transformation 21]
65. ? [X0] : ((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) => ((tall(sK4) | ~rich(sK4)) & (~tall(sK4) | rich(sK4))) [choice axiom]
66. (tall(sK4) | ~rich(sK4)) & (~tall(sK4) | rich(sK4)) [skolemisation 64,65]
77. rich(fred) | strong(X0) [cnf transformation 27]
96. ~strong(X0) | tall(X0) | rich(X0) [cnf transformation 49]
98. ~tall(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 49]
124. ~tall(sK4) | rich(sK4) [cnf transformation 66]
125. tall(sK4) | ~rich(sK4) [cnf transformation 66]
129. ~rich(fred) [cnf transformation 25]
149. 4 <=> ! [X0] : strong(X0) [avatar definition]
150. strong(X0) <- (4) [avatar component clause 149]
157. 6 <=> rich(fred) [avatar definition]
160. 4 | 6 [avatar split clause 77,157,149]
215. 18 <=> rich(sK4) [avatar definition]
216. rich(sK4) <- (18) [avatar component clause 215]
217. ~rich(sK4) <- (~18) [avatar component clause 215]
219. 19 <=> tall(sK4) [avatar definition]
220. ~tall(sK4) <- (~19) [avatar component clause 219]
221. tall(sK4) <- (19) [avatar component clause 219]
222. ~18 | 19 [avatar split clause 125,219,215]
223. 18 | ~19 [avatar split clause 124,219,215]
251. ~6 [avatar split clause 129,157]
267. tall(X0) | rich(X0) <- (4) [resolution 96,150]
268. rich(sK4) <- (4, ~19) [resolution 267,220]
269. $false <- (4, ~18, ~19) [subsumption resolution 268,217]
270. ~4 | 18 | 19 [avatar contradiction clause 269]
282. ~rich(sK4) | ~strong(sK4) <- (19) [resolution 98,221]
283. ~strong(sK4) <- (18, 19) [subsumption resolution 282,216]
284. $false <- (4, 18, 19) [subsumption resolution 283,150]
285. ~4 | ~18 | ~19 [avatar contradiction clause 284]
286. $false [avatar sat refutation 160,222,223,251,270,285]
% SZS output end Proof for 6744669284431251461766542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not humble is not generous and vice versa.
Everyone who is not quiet is kind or tall and vice versa.
Everyone who is either not generous or not creative is either patient or strong and vice versa.
If someone is either not humble or humble then susan is both wise and not old and vice versa.
If someone is either not generous or not happy then lucy is either not strong or not creative.
If john is both strong and not patient then lucy is either curious or not old.
If someone is not brave then fred is not tall or not calm and vice versa.
If someone is both not wise and patient then someone is both not humble and not brave and vice versa.
Everyone who is either not wise or not happy is either humble or kind and vice versa.
Everyone who is funny or humble is both curious and not old.
Everyone who is both not generous and not calm is not kind.
Everyone who is not curious is not tall or calm and vice versa.
If paul is curious or funny then someone is either wise or not tall.
If someone is both humble and calm then lucy is both rich and not old.
Everyone who is either not calm or patient is not strong or kind.
If someone is old then alice is not quiet and vice versa.
Alice is not humble.
Someone is both not tall and brave.
Lucy is brave.
Someone is either not creative or strong.
Someone is both curious and wise.
John is funny.
Someone is either not funny or not patient.
Someone is humble. | Susan is not wise. | contradiction | (![X]:((strong(X)<~>~humble(X))<=>~generous(X)))&
(![X]:(~quiet(X)<=>(kind(X)|tall(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((~humble(X)<~>humble(X))))<=>((wise(susan)&~old(susan))))&
((?[X]:((~generous(X)<~>~happy(X))))=>((~strong(lucy)<~>~creative(lucy))))&
(((strong(john)&~patient(john)))=>((curious(lucy)<~>~old(lucy))))&
((?[X]:(~brave(X)))<=>((~tall(fred)|~calm(fred))))&
((?[X]:((~wise(X)&patient(X))))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)<~>kind(X))))&
(![X]:((funny(X)|humble(X))=>(curious(X)&~old(X))))&
(![X]:((~generous(X)&~calm(X))=>~kind(X)))&
(![X]:(~curious(X)<=>(~tall(X)|calm(X))))&
(((curious(paul)|funny(paul)))=>(?[X]:((wise(X)<~>~tall(X)))))&
((?[X]:((humble(X)&calm(X))))=>((rich(lucy)&~old(lucy))))&
(![X]:((~calm(X)<~>patient(X))=>(~strong(X)|kind(X))))&
((?[X]:(old(X)))<=>(~quiet(alice)))&
(~humble(alice))&
(?[X]:((~tall(X)&brave(X))))&
(brave(lucy))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((curious(X)&wise(X))))&
(funny(john))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:(humble(X))) | ~wise(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6609750437728297560652027
% SZS output start Proof for 6609750437728297560652027
4. ? [X0] : (~humble(X0) <~> humble(X0)) <=> (~old(susan) & wise(susan)) [input p3]
25. ~wise(susan) [input hypothesis]
42. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (old(susan) | ~wise(susan))) & ((~old(susan) & wise(susan)) | ! [X0] : ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 4]
43. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X0] : ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [flattening 42]
44. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X1] : ((~humble(X1) | ~humble(X1)) & (humble(X1) | humble(X1)))) [rectify 43]
45. ? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) => ((~humble(sK0) | humble(sK0)) & (humble(sK0) | ~humble(sK0))) [choice axiom]
46. (((~humble(sK0) | humble(sK0)) & (humble(sK0) | ~humble(sK0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X1] : ((~humble(X1) | ~humble(X1)) & (humble(X1) | humble(X1)))) [skolemisation 44,45]
97. wise(susan) | humble(X1) | humble(X1) [cnf transformation 46]
98. wise(susan) | ~humble(X1) | ~humble(X1) [cnf transformation 46]
153. ~wise(susan) [cnf transformation 25]
154. wise(susan) | humble(X1) [duplicate literal removal 97]
155. wise(susan) | ~humble(X1) [duplicate literal removal 98]
159. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
160. ~humble(X1) <- (1) [avatar component clause 159]
167. 3 <=> ! [X1] : humble(X1) [avatar definition]
168. humble(X1) <- (3) [avatar component clause 167]
171. 4 <=> wise(susan) [avatar definition]
174. 1 | 4 [avatar split clause 155,171,159]
175. 3 | 4 [avatar split clause 154,171,167]
313. ~4 [avatar split clause 153,171]
314. $false <- (1, 3) [subsumption resolution 160,168]
315. ~1 | ~3 [avatar contradiction clause 314]
316. $false [avatar sat refutation 174,175,313,315]
% SZS output end Proof for 6609750437728297560652027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not funny and wise then mary is not curious or funny and vice versa.
If someone is not wise or not curious then someone is either old or calm.
If someone is old or generous then paul is either strong or patient and vice versa.
If susan is both not wise and not brave then alice is quiet or funny.
Everyone who is either not creative or not wise is either strong or rich.
Everyone who is both happy and not tall is both not quiet and not old and vice versa.
Everyone who is generous or old is not funny.
If alice is not curious or not kind then someone is either not tall or curious.
If someone is both not quiet and not creative then someone is not curious or creative.
If someone is both quiet and strong then someone is generous or rich.
Everyone who is not rich is either brave or rich and vice versa.
Everyone who is either not rich or not happy is generous.
If someone is both not humble and strong then someone is rich or not patient.
If fred is both not quiet and wise then john is creative or not wise and vice versa.
Everyone who is either not patient or generous is not old or not wise and vice versa.
Someone is both not patient and strong.
Mary is either not happy or not wise.
Someone is both funny and not humble.
Someone is both patient and not humble.
Lucy is not old.
Lucy is both creative and not rich.
John is either not funny or not wise. | Alice is not humble. | neutral | (((~funny(lucy)&wise(lucy)))<=>((~curious(mary)|funny(mary))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((old(X)|generous(X))))<=>((strong(paul)<~>patient(paul))))&
(((~wise(susan)&~brave(susan)))=>((quiet(alice)|funny(alice))))&
(![X]:((~creative(X)<~>~wise(X))=>(strong(X)<~>rich(X))))&
(![X]:((happy(X)&~tall(X))<=>(~quiet(X)&~old(X))))&
(![X]:((generous(X)|old(X))=>~funny(X)))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:((~curious(X)|creative(X)))))&
((?[X]:((quiet(X)&strong(X))))=>(?[X]:((generous(X)|rich(X)))))&
(![X]:(~rich(X)<=>(brave(X)<~>rich(X))))&
(![X]:((~rich(X)<~>~happy(X))=>generous(X)))&
((?[X]:((~humble(X)&strong(X))))=>(?[X]:((rich(X)|~patient(X)))))&
(((~quiet(fred)&wise(fred)))<=>((creative(john)|~wise(john))))&
(![X]:((~patient(X)<~>generous(X))<=>(~old(X)|~wise(X))))&
(?[X]:((~patient(X)&strong(X))))&
((~happy(mary)<~>~wise(mary)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((patient(X)&~humble(X))))&
(~old(lucy))&
((creative(lucy)&~rich(lucy)))&
((~funny(john)<~>~wise(john))) | ~humble(alice) | [] | null | 0 |
Everyone who is both not quiet and generous is not calm. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. If someone is either calm or curious then someone is both curious and not creative and vice versa. If someone is quiet or old then fred is not funny or not creative and vice versa. If someone is either curious or funny then someone is calm and vice versa. Fred is patient or brave. Someone is strong or not funny. Fred is both generous and funny. Alice is not funny or creative. Someone is either humble or not wise. Someone is not curious or not funny. Someone is generous. | Alice is humble. | neutral | (![X]:((~quiet(X)&generous(X))=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((quiet(X)|old(X))))<=>((~funny(fred)|~creative(fred))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
((patient(fred)|brave(fred)))&
(?[X]:((strong(X)|~funny(X))))&
((generous(fred)&funny(fred)))&
((~funny(alice)|creative(alice)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:(generous(X))) | humble(alice) | [] | null | 0 |
If paul is both generous and not funny then someone is not funny or humble and vice versa.
Everyone who is either funny or brave is both old and humble and vice versa.
Everyone who is either not happy or not funny is both rich and wise and vice versa.
Everyone who is both creative and not creative is both not kind and not quiet and vice versa.
If someone is curious then alice is either not quiet or curious.
If susan is old then someone is not rich and vice versa.
If someone is both not humble and tall then someone is happy or patient.
Everyone who is creative is both not strong and kind.
If someone is both not curious and not strong then susan is both happy and wise.
If paul is either not strong or rich then someone is not tall.
If lucy is both not wise and tall then someone is either not old or tall.
If someone is either calm or not brave then someone is both not patient and not creative and vice versa.
If fred is either brave or not brave then alice is both tall and not brave.
If susan is not curious or happy then someone is not strong or funny.
Everyone who is not old is both calm and not strong and vice versa.
Everyone who is old or quiet is either not rich or creative and vice versa.
Paul is old or not rich.
Someone is not curious.
John is either not tall or strong.
Someone is rich or curious.
Susan is not curious or kind.
Susan is both not calm and not curious.
Paul is either not funny or happy.
Someone is quiet. | Paul is funny. | contradiction | (((generous(paul)&~funny(paul)))<=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:((funny(X)<~>brave(X))<=>(old(X)&humble(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(rich(X)&wise(X))))&
(![X]:((creative(X)&~creative(X))<=>(~kind(X)&~quiet(X))))&
((?[X]:(curious(X)))=>((~quiet(alice)<~>curious(alice))))&
((old(susan))<=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:((happy(X)|patient(X)))))&
(![X]:(creative(X)=>(~strong(X)&kind(X))))&
((?[X]:((~curious(X)&~strong(X))))=>((happy(susan)&wise(susan))))&
(((~strong(paul)<~>rich(paul)))=>(?[X]:(~tall(X))))&
(((~wise(lucy)&tall(lucy)))=>(?[X]:((~old(X)<~>tall(X)))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~patient(X)&~creative(X)))))&
(((brave(fred)<~>~brave(fred)))=>((tall(alice)&~brave(alice))))&
(((~curious(susan)|happy(susan)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:(~old(X)<=>(calm(X)&~strong(X))))&
(![X]:((old(X)|quiet(X))<=>(~rich(X)<~>creative(X))))&
((old(paul)|~rich(paul)))&
(?[X]:(~curious(X)))&
((~tall(john)<~>strong(john)))&
(?[X]:((rich(X)|curious(X))))&
((~curious(susan)|kind(susan)))&
((~calm(susan)&~curious(susan)))&
((~funny(paul)<~>happy(paul)))&
(?[X]:(quiet(X))) | funny(paul) | [
"p0",
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7092441713985443888381150
% SZS output start Proof for 7092441713985443888381150
1. (~funny(paul) & generous(paul)) <=> ? [X0] : (humble(X0) | ~funny(X0)) [input p0]
2. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (humble(X0) & old(X0))) [input p1]
13. (brave(fred) <~> ~brave(fred)) => (~brave(alice) & tall(alice)) [input p12]
25. funny(paul) [input hypothesis]
35. (~brave(alice) & tall(alice)) | (brave(fred) <=> ~brave(fred)) [ennf transformation 13]
37. ((~funny(paul) & generous(paul)) | ! [X0] : (~humble(X0) & funny(X0))) & (? [X0] : (humble(X0) | ~funny(X0)) | (funny(paul) | ~generous(paul))) [nnf transformation 1]
38. ((~funny(paul) & generous(paul)) | ! [X0] : (~humble(X0) & funny(X0))) & (? [X0] : (humble(X0) | ~funny(X0)) | funny(paul) | ~generous(paul)) [flattening 37]
39. ((~funny(paul) & generous(paul)) | ! [X0] : (~humble(X0) & funny(X0))) & (? [X1] : (humble(X1) | ~funny(X1)) | funny(paul) | ~generous(paul)) [rectify 38]
40. ? [X1] : (humble(X1) | ~funny(X1)) => (humble(sK0) | ~funny(sK0)) [choice axiom]
41. ((~funny(paul) & generous(paul)) | ! [X0] : (~humble(X0) & funny(X0))) & ((humble(sK0) | ~funny(sK0)) | funny(paul) | ~generous(paul)) [skolemisation 39,40]
42. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~humble(X0) | ~old(X0))) & ((humble(X0) & old(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 2]
43. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ~humble(X0) | ~old(X0)) & ((humble(X0) & old(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 42]
67. (~brave(alice) & tall(alice)) | ((brave(fred) | brave(fred)) & (~brave(fred) | ~brave(fred))) [nnf transformation 35]
85. ~funny(paul) | funny(X0) [cnf transformation 41]
86. ~funny(paul) | ~humble(X0) [cnf transformation 41]
89. ~funny(X0) | brave(X0) | humble(X0) [cnf transformation 43]
124. ~brave(alice) | ~brave(fred) | ~brave(fred) [cnf transformation 67]
125. ~brave(alice) | brave(fred) | brave(fred) [cnf transformation 67]
148. funny(paul) [cnf transformation 25]
151. ~brave(alice) | ~brave(fred) [duplicate literal removal 124]
152. ~brave(alice) | brave(fred) [duplicate literal removal 125]
154. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
155. ~humble(X0) <- (1) [avatar component clause 154]
157. 2 <=> funny(paul) [avatar definition]
160. 1 | ~2 [avatar split clause 86,157,154]
162. 3 <=> ! [X0] : funny(X0) [avatar definition]
163. funny(X0) <- (3) [avatar component clause 162]
164. 3 | ~2 [avatar split clause 85,157,162]
296. 33 <=> brave(fred) [avatar definition]
300. 34 <=> brave(alice) [avatar definition]
302. ~brave(alice) <- (~34) [avatar component clause 300]
303. 33 | ~34 [avatar split clause 152,300,296]
304. ~33 | ~34 [avatar split clause 151,300,296]
361. 2 [avatar split clause 148,157]
376. brave(X0) | humble(X0) <- (3) [resolution 89,163]
377. brave(X0) <- (1, 3) [subsumption resolution 376,155]
379. $false <- (1, 3, ~34) [resolution 377,302]
381. ~1 | ~3 | 34 [avatar contradiction clause 379]
383. $false [avatar sat refutation 160,164,303,304,361,381]
% SZS output end Proof for 7092441713985443888381150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or happy is both curious and not kind and vice versa.
If john is not brave or not rich then susan is either calm or kind and vice versa.
Everyone who is either brave or quiet is wise or calm and vice versa.
Everyone who is both not happy and not kind is creative or not brave and vice versa.
Everyone who is not curious or creative is calm and vice versa.
Everyone who is both calm and creative is not creative or not old.
Everyone who is both not humble and quiet is patient and vice versa.
Everyone who is strong is patient or not old and vice versa.
If someone is both not tall and happy then alice is rich or strong and vice versa.
Everyone who is not humble is not old or not happy.
If someone is both creative and happy then john is either happy or not curious and vice versa.
If john is brave then someone is not strong or kind.
If someone is both kind and rich then someone is either kind or happy.
Everyone who is both not strong and not tall is either not humble or curious.
If alice is old or rich then someone is rich and vice versa.
Everyone who is funny or not wise is not strong or kind.
Someone is both kind and not funny.
Someone is both old and calm.
Someone is not quiet.
Paul is not rich or not happy.
Susan is not brave or wise.
Someone is either curious or not quiet.
Someone is either not rich or not happy. | John is not creative. | neutral | (![X]:((wise(X)<~>happy(X))<=>(curious(X)&~kind(X))))&
(((~brave(john)|~rich(john)))<=>((calm(susan)<~>kind(susan))))&
(![X]:((brave(X)<~>quiet(X))<=>(wise(X)|calm(X))))&
(![X]:((~happy(X)&~kind(X))<=>(creative(X)|~brave(X))))&
(![X]:((~curious(X)|creative(X))<=>calm(X)))&
(![X]:((calm(X)&creative(X))=>(~creative(X)|~old(X))))&
(![X]:((~humble(X)&quiet(X))<=>patient(X)))&
(![X]:(strong(X)<=>(patient(X)|~old(X))))&
((?[X]:((~tall(X)&happy(X))))<=>((rich(alice)|strong(alice))))&
(![X]:(~humble(X)=>(~old(X)|~happy(X))))&
((?[X]:((creative(X)&happy(X))))<=>((happy(john)<~>~curious(john))))&
((brave(john))=>(?[X]:((~strong(X)|kind(X)))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~strong(X)&~tall(X))=>(~humble(X)<~>curious(X))))&
(((old(alice)|rich(alice)))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)|~wise(X))=>(~strong(X)|kind(X))))&
(?[X]:((kind(X)&~funny(X))))&
(?[X]:((old(X)&calm(X))))&
(?[X]:(~quiet(X)))&
((~rich(paul)|~happy(paul)))&
((~brave(susan)|wise(susan)))&
(?[X]:((curious(X)<~>~quiet(X))))&
(?[X]:((~rich(X)<~>~happy(X)))) | ~creative(john) | [] | null | 0 |
If paul is generous or not humble then someone is not rich.
Everyone who is not wise or not calm is either not happy or calm and vice versa.
Everyone who is not happy is quiet.
If someone is either tall or not calm then alice is both creative and not brave.
If paul is either not old or wise then someone is not strong or kind and vice versa.
If someone is rich then john is either not patient or not calm.
Everyone who is creative or quiet is both not wise and calm.
Everyone who is rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Someone is rich or not curious.
Fred is not humble.
Someone is either brave or not strong.
Fred is either not wise or brave.
Someone is both not wise and not funny.
Mary is either not rich or humble.
Someone is either humble or calm. | Paul is old. | contradiction | (((generous(paul)|~humble(paul)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)|~calm(X))<=>(~happy(X)<~>calm(X))))&
(![X]:(~happy(X)=>quiet(X)))&
((?[X]:((tall(X)<~>~calm(X))))=>((creative(alice)&~brave(alice))))&
(((~old(paul)<~>wise(paul)))<=>(?[X]:((~strong(X)|kind(X)))))&
((?[X]:(rich(X)))=>((~patient(john)<~>~calm(john))))&
(![X]:((creative(X)|quiet(X))=>(~wise(X)&calm(X))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(?[X]:((rich(X)|~curious(X))))&
(~humble(fred))&
(?[X]:((brave(X)<~>~strong(X))))&
((~wise(fred)<~>brave(fred)))&
(?[X]:((~wise(X)&~funny(X))))&
((~rich(mary)<~>humble(mary)))&
(?[X]:((humble(X)<~>calm(X)))) | old(paul) | [
"p4",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 988060432465052159551622
% SZS output start Proof for 988060432465052159551622
5. (~old(paul) <~> wise(paul)) <=> ? [X0] : (kind(X0) | ~strong(X0)) [input p4]
7. ! [X0] : ((quiet(X0) | creative(X0)) => (calm(X0) & ~wise(X0))) [input p6]
15. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (old(X0) <~> ~wise(X0))) [input p14]
16. ! [X0] : ((rich(X0) | strong(X0)) => kind(X0)) [input p15]
24. old(paul) [input hypothesis]
31. ! [X0] : ((calm(X0) & ~wise(X0)) | (~quiet(X0) & ~creative(X0))) [ennf transformation 7]
35. ! [X0] : (kind(X0) | (~rich(X0) & ~strong(X0))) [ennf transformation 16]
41. (((~wise(paul) | old(paul)) & (wise(paul) | ~old(paul))) | ! [X0] : (~kind(X0) & strong(X0))) & (? [X0] : (kind(X0) | ~strong(X0)) | ((~old(paul) | ~wise(paul)) & (wise(paul) | old(paul)))) [nnf transformation 5]
42. (((~wise(paul) | old(paul)) & (wise(paul) | ~old(paul))) | ! [X0] : (~kind(X0) & strong(X0))) & (? [X1] : (kind(X1) | ~strong(X1)) | ((~old(paul) | ~wise(paul)) & (wise(paul) | old(paul)))) [rectify 41]
43. ? [X1] : (kind(X1) | ~strong(X1)) => (kind(sK1) | ~strong(sK1)) [choice axiom]
44. (((~wise(paul) | old(paul)) & (wise(paul) | ~old(paul))) | ! [X0] : (~kind(X0) & strong(X0))) & ((kind(sK1) | ~strong(sK1)) | ((~old(paul) | ~wise(paul)) & (wise(paul) | old(paul)))) [skolemisation 42,43]
64. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 15]
65. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | quiet(X0))) [flattening 64]
92. wise(paul) | ~old(paul) | strong(X0) [cnf transformation 44]
93. wise(paul) | ~old(paul) | ~kind(X0) [cnf transformation 44]
99. ~quiet(X0) | ~wise(X0) [cnf transformation 31]
127. ~wise(X0) | old(X0) | old(X0) | quiet(X0) [cnf transformation 65]
131. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 65]
133. ~strong(X0) | kind(X0) [cnf transformation 35]
147. old(paul) [cnf transformation 24]
148. ~wise(X0) | old(X0) | quiet(X0) [duplicate literal removal 127]
149. ~old(X0) | ~wise(X0) [duplicate literal removal 131]
180. 7 <=> ! [X0] : ~kind(X0) [avatar definition]
181. ~kind(X0) <- (7) [avatar component clause 180]
183. 8 <=> old(paul) [avatar definition]
187. 9 <=> wise(paul) [avatar definition]
188. wise(paul) <- (9) [avatar component clause 187]
192. 10 <=> ! [X0] : strong(X0) [avatar definition]
193. strong(X0) <- (10) [avatar component clause 192]
195. 7 | ~8 | 9 [avatar split clause 93,187,183,180]
196. 10 | ~8 | 9 [avatar split clause 92,187,183,192]
259. 24 <=> ! [X3] : ~wise(X3) [avatar definition]
260. ~wise(X3) <- (24) [avatar component clause 259]
301. ~wise(X0) | quiet(X0) [subsumption resolution 148,149]
302. ~wise(X0) [subsumption resolution 301,99]
303. 24 [avatar split clause 302,259]
349. 8 [avatar split clause 147,183]
350. $false <- (9, 24) [subsumption resolution 188,260]
351. ~9 | ~24 [avatar contradiction clause 350]
367. kind(X0) <- (10) [resolution 133,193]
368. $false <- (7, 10) [subsumption resolution 367,181]
369. ~7 | ~10 [avatar contradiction clause 368]
370. $false [avatar sat refutation 195,196,303,349,351,369]
% SZS output end Proof for 988060432465052159551622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich then someone is either strong or not strong. If alice is either not quiet or old then someone is both wise and not calm and vice versa. Everyone who is generous or not tall is either not calm or not humble and vice versa. Everyone who is either not rich or creative is both brave and creative. If alice is both not humble and curious then someone is both old and strong and vice versa. If someone is both quiet and not funny then someone is calm or wise and vice versa. Everyone who is both not strong and happy is tall. If john is either not old or not kind then fred is not creative and vice versa. Everyone who is either not creative or not tall is calm. Everyone who is wise or calm is either not humble or not happy and vice versa. If someone is tall then someone is creative or not brave and vice versa. Everyone who is either not strong or patient is not creative and vice versa. Everyone who is both not happy and humble is either not strong or brave. If someone is not brave or funny then fred is both funny and humble. Everyone who is both generous and not old is not kind. Everyone who is strong is both not strong and quiet and vice versa. Someone is either kind or brave. Fred is kind or not brave. Someone is not calm or not curious. Someone is not curious or not brave. Paul is humble. Someone is both curious and not rich. | Fred is creative. | entailment | ((?[X]:(rich(X)))=>(?[X]:((strong(X)<~>~strong(X)))))&
(((~quiet(alice)<~>old(alice)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((generous(X)|~tall(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(brave(X)&creative(X))))&
(((~humble(alice)&curious(alice)))<=>(?[X]:((old(X)&strong(X)))))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((~strong(X)&happy(X))=>tall(X)))&
(((~old(john)<~>~kind(john)))<=>(~creative(fred)))&
(![X]:((~creative(X)<~>~tall(X))=>calm(X)))&
(![X]:((wise(X)|calm(X))<=>(~humble(X)<~>~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((creative(X)|~brave(X)))))&
(![X]:((~strong(X)<~>patient(X))<=>~creative(X)))&
(![X]:((~happy(X)&humble(X))=>(~strong(X)<~>brave(X))))&
((?[X]:((~brave(X)|funny(X))))=>((funny(fred)&humble(fred))))&
(![X]:((generous(X)&~old(X))=>~kind(X)))&
(![X]:(strong(X)<=>(~strong(X)&quiet(X))))&
(?[X]:((kind(X)<~>brave(X))))&
((kind(fred)|~brave(fred)))&
(?[X]:((~calm(X)|~curious(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(humble(paul))&
(?[X]:((curious(X)&~rich(X)))) | creative(fred) | [
"p2",
"p5",
"p6",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4529446175683025484780703
% SZS output start Proof for 4529446175683025484780703
3. ! [X0] : ((~tall(X0) | generous(X0)) <=> (~calm(X0) <~> ~humble(X0))) [input p2]
6. ? [X0] : (~funny(X0) & quiet(X0)) <=> ? [X0] : (wise(X0) | calm(X0)) [input p5]
7. ! [X0] : ((happy(X0) & ~strong(X0)) => tall(X0)) [input p6]
9. ! [X0] : ((~creative(X0) <~> ~tall(X0)) => calm(X0)) [input p8]
10. ! [X0] : ((calm(X0) | wise(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p9]
16. ! [X0] : (strong(X0) <=> (quiet(X0) & ~strong(X0))) [input p15]
23. ~creative(fred) [input hypothesis]
25. ? [X0] : (~funny(X0) & quiet(X0)) <=> ? [X1] : (wise(X1) | calm(X1)) [rectify 6]
29. ! [X0] : (tall(X0) | (~happy(X0) | strong(X0))) [ennf transformation 7]
30. ! [X0] : (tall(X0) | ~happy(X0) | strong(X0)) [flattening 29]
31. ! [X0] : (calm(X0) | (~creative(X0) <=> ~tall(X0))) [ennf transformation 9]
45. ! [X0] : (((~tall(X0) | generous(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (tall(X0) & ~generous(X0)))) [nnf transformation 3]
46. ! [X0] : ((~tall(X0) | generous(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (tall(X0) & ~generous(X0)))) [flattening 45]
53. (? [X0] : (~funny(X0) & quiet(X0)) | ! [X1] : (~wise(X1) & ~calm(X1))) & (? [X1] : (wise(X1) | calm(X1)) | ! [X0] : (funny(X0) | ~quiet(X0))) [nnf transformation 25]
54. (? [X0] : (~funny(X0) & quiet(X0)) | ! [X1] : (~wise(X1) & ~calm(X1))) & (? [X2] : (wise(X2) | calm(X2)) | ! [X3] : (funny(X3) | ~quiet(X3))) [rectify 53]
55. ? [X0] : (~funny(X0) & quiet(X0)) => (~funny(sK3) & quiet(sK3)) [choice axiom]
56. ? [X2] : (wise(X2) | calm(X2)) => (wise(sK4) | calm(sK4)) [choice axiom]
57. ((~funny(sK3) & quiet(sK3)) | ! [X1] : (~wise(X1) & ~calm(X1))) & ((wise(sK4) | calm(sK4)) | ! [X3] : (funny(X3) | ~quiet(X3))) [skolemisation 54,56,55]
59. ! [X0] : (calm(X0) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) [nnf transformation 31]
60. ! [X0] : (((calm(X0) | wise(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~calm(X0) & ~wise(X0)))) [nnf transformation 10]
61. ! [X0] : ((calm(X0) | wise(X0) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~calm(X0) & ~wise(X0)))) [flattening 60]
69. ! [X0] : ((strong(X0) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 16]
70. ! [X0] : ((strong(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~strong(X0))) [flattening 69]
91. humble(X0) | calm(X0) | tall(X0) [cnf transformation 46]
103. quiet(sK3) | ~calm(X1) [cnf transformation 57]
104. quiet(sK3) | ~wise(X1) [cnf transformation 57]
107. ~happy(X0) | tall(X0) | strong(X0) [cnf transformation 30]
112. ~tall(X0) | calm(X0) | creative(X0) [cnf transformation 59]
119. ~humble(X0) | wise(X0) | calm(X0) | happy(X0) [cnf transformation 61]
134. ~strong(X0) | ~strong(X0) [cnf transformation 70]
136. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 70]
145. ~creative(fred) [cnf transformation 23]
146. ~strong(X0) [duplicate literal removal 134]
147. ~quiet(X0) | strong(X0) [duplicate literal removal 136]
198. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
199. ~wise(X1) <- (11) [avatar component clause 198]
206. 13 <=> ! [X1] : ~calm(X1) [avatar definition]
207. ~calm(X1) <- (13) [avatar component clause 206]
210. 14 <=> quiet(sK3) [avatar definition]
212. quiet(sK3) <- (14) [avatar component clause 210]
213. 11 | 14 [avatar split clause 104,210,198]
214. 13 | 14 [avatar split clause 103,210,206]
228. 18 <=> creative(fred) [avatar definition]
229. ~creative(fred) <- (~18) [avatar component clause 228]
271. 28 <=> humble(fred) [avatar definition]
272. ~humble(fred) <- (~28) [avatar component clause 271]
273. humble(fred) <- (28) [avatar component clause 271]
319. ~18 [avatar split clause 145,228]
331. strong(sK3) <- (14) [resolution 147,212]
332. $false <- (14) [subsumption resolution 331,146]
333. ~14 [avatar contradiction clause 332]
393. 44 <=> tall(fred) [avatar definition]
394. tall(fred) <- (44) [avatar component clause 393]
395. ~tall(fred) <- (~44) [avatar component clause 393]
406. wise(fred) | calm(fred) | happy(fred) <- (28) [resolution 119,273]
411. calm(fred) | happy(fred) <- (11, 28) [subsumption resolution 406,199]
412. happy(fred) <- (11, 13, 28) [subsumption resolution 411,207]
434. tall(fred) | strong(fred) <- (11, 13, 28) [resolution 412,107]
438. tall(fred) <- (11, 13, 28) [subsumption resolution 434,146]
439. 44 | ~11 | ~13 | ~28 [avatar split clause 438,271,206,198,393]
441. calm(fred) | creative(fred) <- (44) [resolution 394,112]
442. creative(fred) <- (13, 44) [subsumption resolution 441,207]
443. $false <- (13, ~18, 44) [subsumption resolution 442,229]
444. ~13 | 18 | ~44 [avatar contradiction clause 443]
464. calm(fred) | tall(fred) <- (~28) [resolution 272,91]
465. tall(fred) <- (13, ~28) [subsumption resolution 464,207]
466. $false <- (13, ~28, ~44) [subsumption resolution 465,395]
467. ~13 | 28 | 44 [avatar contradiction clause 466]
468. $false [avatar sat refutation 213,214,319,333,439,444,467]
% SZS output end Proof for 4529446175683025484780703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not humble is both kind and not tall and vice versa.
If fred is not old or not tall then someone is either tall or not rich.
Everyone who is either rich or quiet is both kind and quiet.
If someone is both not curious and calm then someone is curious or not generous.
Everyone who is both kind and not rich is both rich and calm.
Everyone who is either tall or not funny is brave or quiet and vice versa.
Everyone who is both not old and not curious is both wise and patient and vice versa.
If someone is either funny or not kind then mary is happy or not old and vice versa.
If someone is tall then mary is not funny and vice versa.
Everyone who is both generous and brave is either happy or not old and vice versa.
If someone is patient or kind then alice is not creative.
If someone is either not funny or not happy then alice is brave.
Everyone who is both not patient and curious is curious or quiet.
If susan is either funny or tall then alice is both patient and not rich and vice versa.
Everyone who is not humble is not humble or not tall.
If lucy is either funny or not kind then someone is humble or not tall and vice versa.
Alice is brave or not rich.
Fred is generous or not quiet.
Someone is rich or not kind.
Mary is both kind and not calm.
Someone is either not wise or quiet. | Alice is rich. | entailment | (![X]:((~rich(X)|~humble(X))<=>(kind(X)&~tall(X))))&
(((~old(fred)|~tall(fred)))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(kind(X)&quiet(X))))&
((?[X]:((~curious(X)&calm(X))))=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((kind(X)&~rich(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)|quiet(X))))&
(![X]:((~old(X)&~curious(X))<=>(wise(X)&patient(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((happy(mary)|~old(mary))))&
((?[X]:(tall(X)))<=>(~funny(mary)))&
(![X]:((generous(X)&brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((patient(X)|kind(X))))=>(~creative(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(brave(alice)))&
(![X]:((~patient(X)&curious(X))=>(curious(X)|quiet(X))))&
(((funny(susan)<~>tall(susan)))<=>((patient(alice)&~rich(alice))))&
(![X]:(~humble(X)=>(~humble(X)|~tall(X))))&
(((funny(lucy)<~>~kind(lucy)))<=>(?[X]:((humble(X)|~tall(X)))))&
((brave(alice)|~rich(alice)))&
((generous(fred)|~quiet(fred)))&
(?[X]:((rich(X)|~kind(X))))&
((kind(mary)&~calm(mary)))&
(?[X]:((~wise(X)<~>quiet(X)))) | rich(alice) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4236677586484320560819267
% SZS output start Proof for 4236677586484320560819267
1. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~tall(X0) & kind(X0))) [input p0]
5. ! [X0] : ((~rich(X0) & kind(X0)) => (calm(X0) & rich(X0))) [input p4]
22. ~rich(alice) [input hypothesis]
28. ! [X0] : ((calm(X0) & rich(X0)) | (rich(X0) | ~kind(X0))) [ennf transformation 5]
29. ! [X0] : ((calm(X0) & rich(X0)) | rich(X0) | ~kind(X0)) [flattening 28]
35. ! [X0] : (((~humble(X0) | ~rich(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 1]
36. ! [X0] : ((~humble(X0) | ~rich(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [flattening 35]
71. kind(X0) | rich(X0) [cnf transformation 36]
85. rich(X0) | rich(X0) | ~kind(X0) [cnf transformation 29]
134. ~rich(alice) [cnf transformation 22]
135. rich(X0) | ~kind(X0) [duplicate literal removal 85]
168. rich(X0) [subsumption resolution 135,71]
279. $false [subsumption resolution 134,168]
% SZS output end Proof for 4236677586484320560819267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not tall is not tall or not humble and vice versa.
Everyone who is either not patient or curious is not old or creative and vice versa.
Everyone who is either not generous or not strong is old and vice versa.
If susan is both not funny and strong then someone is either quiet or not old and vice versa.
Everyone who is not patient or not old is not old or not tall.
If someone is not generous or generous then someone is not strong and vice versa.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
If someone is funny or not kind then someone is both not humble and not rich and vice versa.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is either not old or happy is old and vice versa.
Everyone who is both wise and humble is not strong or wise.
Someone is old.
Someone is both not rich and curious.
Lucy is tall.
Someone is not creative.
Someone is either not wise or quiet.
Mary is brave or not humble.
Someone is not kind or not strong.
Someone is both not funny and wise. | Susan is old. | neutral | (![X]:((old(X)<~>~tall(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~patient(X)<~>curious(X))<=>(~old(X)|creative(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>old(X)))&
(((~funny(susan)&strong(susan)))<=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~patient(X)|~old(X))=>(~old(X)|~tall(X))))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
((?[X]:((funny(X)|~kind(X))))<=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>old(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(?[X]:(old(X)))&
(?[X]:((~rich(X)&curious(X))))&
(tall(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~wise(X)<~>quiet(X))))&
((brave(mary)|~humble(mary)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~funny(X)&wise(X)))) | old(susan) | [] | null | 0 |
Everyone who is either not funny or strong is not old.
Everyone who is either rich or not calm is not funny or not generous.
If someone is both funny and generous then someone is both not kind and quiet.
If fred is both funny and not strong then someone is either brave or not generous and vice versa.
Everyone who is not tall or not calm is either not happy or happy.
Everyone who is tall is either not rich or not funny and vice versa.
Everyone who is both brave and not generous is humble and vice versa.
If lucy is wise or not happy then fred is brave or not kind and vice versa.
Everyone who is strong is both humble and not brave and vice versa.
Everyone who is not generous is not wise or strong and vice versa.
If mary is both brave and not quiet then john is both funny and not kind.
Everyone who is wise is either humble or strong and vice versa.
If lucy is both not quiet and not happy then someone is either wise or not rich and vice versa.
If someone is not kind then john is either not kind or not tall.
If alice is not creative or calm then someone is not rich or old.
Someone is tall.
Someone is not wise.
Lucy is quiet.
John is either tall or calm.
Someone is humble or not curious.
Paul is either not patient or not curious.
Alice is either creative or not creative. | John is not humble. | entailment | (![X]:((~funny(X)<~>strong(X))=>~old(X)))&
(![X]:((rich(X)<~>~calm(X))=>(~funny(X)|~generous(X))))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:((~kind(X)&quiet(X)))))&
(((funny(fred)&~strong(fred)))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~tall(X)|~calm(X))=>(~happy(X)<~>happy(X))))&
(![X]:(tall(X)<=>(~rich(X)<~>~funny(X))))&
(![X]:((brave(X)&~generous(X))<=>humble(X)))&
(((wise(lucy)|~happy(lucy)))<=>((brave(fred)|~kind(fred))))&
(![X]:(strong(X)<=>(humble(X)&~brave(X))))&
(![X]:(~generous(X)<=>(~wise(X)|strong(X))))&
(((brave(mary)&~quiet(mary)))=>((funny(john)&~kind(john))))&
(![X]:(wise(X)<=>(humble(X)<~>strong(X))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))=>((~kind(john)<~>~tall(john))))&
(((~creative(alice)|calm(alice)))=>(?[X]:((~rich(X)|old(X)))))&
(?[X]:(tall(X)))&
(?[X]:(~wise(X)))&
(quiet(lucy))&
((tall(john)<~>calm(john)))&
(?[X]:((humble(X)|~curious(X))))&
((~patient(paul)<~>~curious(paul)))&
((creative(alice)<~>~creative(alice))) | ~humble(john) | [
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 508983714233376966678421
% SZS output start Proof for 508983714233376966678421
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> humble(X0)) [input p6]
9. ! [X0] : (strong(X0) <=> (~brave(X0) & humble(X0))) [input p8]
10. ! [X0] : (~generous(X0) <=> (strong(X0) | ~wise(X0))) [input p9]
12. ! [X0] : (wise(X0) <=> (humble(X0) <~> strong(X0))) [input p11]
23. humble(john) [input hypothesis]
46. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | generous(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((strong(X0) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 9]
51. ! [X0] : ((strong(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [flattening 50]
52. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 10]
53. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | generous(X0))) [flattening 52]
54. ! [X0] : ((wise(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) & (((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | ~wise(X0))) [nnf transformation 12]
93. ~humble(X0) | brave(X0) [cnf transformation 47]
94. ~humble(X0) | ~generous(X0) [cnf transformation 47]
100. ~brave(X0) | ~strong(X0) [cnf transformation 51]
102. ~wise(X0) | strong(X0) | generous(X0) [cnf transformation 53]
109. ~humble(X0) | strong(X0) | wise(X0) [cnf transformation 54]
131. humble(john) [cnf transformation 23]
290. brave(john) [resolution 93,131]
291. ~generous(john) [resolution 94,131]
292. ~strong(john) [resolution 100,290]
379. strong(john) | wise(john) [resolution 109,131]
381. wise(john) [subsumption resolution 379,292]
422. strong(john) | generous(john) [resolution 381,102]
426. generous(john) [subsumption resolution 422,292]
427. $false [subsumption resolution 426,291]
% SZS output end Proof for 508983714233376966678421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both not old and brave. Everyone who is not calm is patient or curious and vice versa. Everyone who is not quiet is kind. Everyone who is funny is either generous or kind and vice versa. Everyone who is not generous or not brave is not funny or not wise and vice versa. If someone is either creative or not brave then susan is tall or not humble. If someone is both wise and humble then someone is not funny. If someone is both not calm and quiet then someone is wise or not strong and vice versa. Everyone who is not strong or rich is not kind and vice versa. Everyone who is either quiet or humble is either not generous or not kind. If alice is both strong and not humble then mary is kind. If fred is both not happy and not humble then susan is not generous or quiet and vice versa. Everyone who is not funny or strong is both rich and not brave. If john is either not tall or not calm then susan is not calm or kind and vice versa. If john is both not kind and old then paul is either quiet or calm and vice versa. If someone is not kind or not wise then lucy is calm or not kind and vice versa. Alice is either not rich or wise. Paul is rich. Someone is both not wise and not brave. Susan is either not generous or not curious. Someone is patient. Paul is either not happy or funny. Someone is not generous. | Mary is kind. | contradiction | (![X]:(~calm(X)=>(~old(X)&brave(X))))&
(![X]:(~calm(X)<=>(patient(X)|curious(X))))&
(![X]:(~quiet(X)=>kind(X)))&
(![X]:(funny(X)<=>(generous(X)<~>kind(X))))&
(![X]:((~generous(X)|~brave(X))<=>(~funny(X)|~wise(X))))&
((?[X]:((creative(X)<~>~brave(X))))=>((tall(susan)|~humble(susan))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((wise(X)|~strong(X)))))&
(![X]:((~strong(X)|rich(X))<=>~kind(X)))&
(![X]:((quiet(X)<~>humble(X))=>(~generous(X)<~>~kind(X))))&
(((strong(alice)&~humble(alice)))=>(kind(mary)))&
(((~happy(fred)&~humble(fred)))<=>((~generous(susan)|quiet(susan))))&
(![X]:((~funny(X)|strong(X))=>(rich(X)&~brave(X))))&
(((~tall(john)<~>~calm(john)))<=>((~calm(susan)|kind(susan))))&
(((~kind(john)&old(john)))<=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~kind(X)|~wise(X))))<=>((calm(lucy)|~kind(lucy))))&
((~rich(alice)<~>wise(alice)))&
(rich(paul))&
(?[X]:((~wise(X)&~brave(X))))&
((~generous(susan)<~>~curious(susan)))&
(?[X]:(patient(X)))&
((~happy(paul)<~>funny(paul)))&
(?[X]:(~generous(X))) | kind(mary) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 37361061002871754594437
% SZS output start Proof for 37361061002871754594437
9. ! [X0] : ((rich(X0) | ~strong(X0)) <=> ~kind(X0)) [input p8]
13. ! [X0] : ((strong(X0) | ~funny(X0)) => (~brave(X0) & rich(X0))) [input p12]
24. kind(mary) [input hypothesis]
35. ! [X0] : ((~brave(X0) & rich(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 13]
50. ! [X0] : (((rich(X0) | ~strong(X0)) | kind(X0)) & (~kind(X0) | (~rich(X0) & strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((rich(X0) | ~strong(X0) | kind(X0)) & (~kind(X0) | (~rich(X0) & strong(X0)))) [flattening 50]
95. ~kind(X0) | strong(X0) [cnf transformation 51]
96. ~rich(X0) | ~kind(X0) [cnf transformation 51]
109. ~strong(X0) | rich(X0) [cnf transformation 35]
139. kind(mary) [cnf transformation 24]
205. 16 <=> kind(mary) [avatar definition]
207. kind(mary) <- (16) [avatar component clause 205]
326. 16 [avatar split clause 139,205]
331. strong(mary) <- (16) [resolution 95,207]
336. rich(mary) <- (16) [resolution 109,331]
343. ~kind(mary) <- (16) [resolution 336,96]
344. $false <- (16) [subsumption resolution 343,207]
345. ~16 [avatar contradiction clause 344]
346. $false [avatar sat refutation 326,345]
% SZS output end Proof for 37361061002871754594437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then fred is patient and vice versa.
If someone is both humble and not patient then someone is both not brave and kind.
If someone is either brave or creative then mary is not brave or not patient and vice versa.
If someone is both not curious and not quiet then someone is calm or not brave and vice versa.
Everyone who is either not patient or not generous is not wise and vice versa.
Everyone who is creative or funny is either humble or creative.
Everyone who is patient or funny is either not quiet or not old and vice versa.
Everyone who is either curious or not quiet is not wise or not creative.
If someone is both generous and quiet then someone is not wise and vice versa.
Everyone who is either patient or old is both wise and not calm.
Everyone who is rich is either not rich or strong and vice versa.
Everyone who is calm or not creative is not strong or happy.
Everyone who is brave or patient is either not wise or not old.
Everyone who is either happy or humble is patient.
Everyone who is not creative or not humble is both not generous and not quiet.
Everyone who is either not brave or not rich is either generous or curious.
Someone is creative.
Fred is tall or calm.
Someone is either rich or kind.
Someone is generous or not rich.
Someone is both wise and not kind. | Mary is calm. | neutral | ((?[X]:(tall(X)))<=>(patient(fred)))&
((?[X]:((humble(X)&~patient(X))))=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>((~brave(mary)|~patient(mary))))&
((?[X]:((~curious(X)&~quiet(X))))<=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~patient(X)<~>~generous(X))<=>~wise(X)))&
(![X]:((creative(X)|funny(X))=>(humble(X)<~>creative(X))))&
(![X]:((patient(X)|funny(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((curious(X)<~>~quiet(X))=>(~wise(X)|~creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((patient(X)<~>old(X))=>(wise(X)&~calm(X))))&
(![X]:(rich(X)<=>(~rich(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))=>(~strong(X)|happy(X))))&
(![X]:((brave(X)|patient(X))=>(~wise(X)<~>~old(X))))&
(![X]:((happy(X)<~>humble(X))=>patient(X)))&
(![X]:((~creative(X)|~humble(X))=>(~generous(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(generous(X)<~>curious(X))))&
(?[X]:(creative(X)))&
((tall(fred)|calm(fred)))&
(?[X]:((rich(X)<~>kind(X))))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((wise(X)&~kind(X)))) | calm(mary) | [] | null | 0 |
Everyone who is either wise or happy is either quiet or creative and vice versa.
If susan is not creative then someone is tall.
Everyone who is not kind is wise or not kind.
Everyone who is either humble or not creative is not brave or not rich.
If paul is either not creative or brave then susan is not curious.
Everyone who is either not generous or calm is both not kind and calm.
Everyone who is both quiet and calm is either not brave or brave and vice versa.
If someone is both patient and not generous then someone is both not wise and tall.
If alice is funny then mary is not brave or rich.
If someone is either calm or not funny then someone is kind or curious and vice versa.
Everyone who is kind is happy or not old.
Everyone who is not curious is either generous or not quiet.
Everyone who is both quiet and strong is not tall or creative.
If lucy is not patient then fred is tall or not generous.
Everyone who is not patient or wise is both not tall and tall and vice versa.
Susan is not humble.
Mary is either not happy or calm.
Paul is both kind and not generous.
Someone is either tall or old.
Someone is brave or creative.
Someone is both not wise and generous. | Susan is tall. | neutral | (![X]:((wise(X)<~>happy(X))<=>(quiet(X)<~>creative(X))))&
((~creative(susan))=>(?[X]:(tall(X))))&
(![X]:(~kind(X)=>(wise(X)|~kind(X))))&
(![X]:((humble(X)<~>~creative(X))=>(~brave(X)|~rich(X))))&
(((~creative(paul)<~>brave(paul)))=>(~curious(susan)))&
(![X]:((~generous(X)<~>calm(X))=>(~kind(X)&calm(X))))&
(![X]:((quiet(X)&calm(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:((patient(X)&~generous(X))))=>(?[X]:((~wise(X)&tall(X)))))&
((funny(alice))=>((~brave(mary)|rich(mary))))&
((?[X]:((calm(X)<~>~funny(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(kind(X)=>(happy(X)|~old(X))))&
(![X]:(~curious(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((quiet(X)&strong(X))=>(~tall(X)|creative(X))))&
((~patient(lucy))=>((tall(fred)|~generous(fred))))&
(![X]:((~patient(X)|wise(X))<=>(~tall(X)&tall(X))))&
(~humble(susan))&
((~happy(mary)<~>calm(mary)))&
((kind(paul)&~generous(paul)))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~wise(X)&generous(X)))) | tall(susan) | [] | null | 0 |
Everyone who is either not quiet or funny is quiet and vice versa. Everyone who is strong is either wise or quiet and vice versa. Everyone who is either rich or not humble is both not old and generous and vice versa. Everyone who is curious or creative is either not generous or funny. If mary is not generous or funny then someone is either rich or old. If paul is curious or not brave then someone is either strong or kind. If someone is either tall or patient then someone is both not happy and wise and vice versa. Everyone who is not kind is both curious and not humble and vice versa. Everyone who is curious is not creative and vice versa. Everyone who is not calm or brave is either curious or generous. Everyone who is either not brave or happy is brave. If john is not happy then someone is not brave or not tall and vice versa. If lucy is not rich or not generous then john is either not kind or not creative and vice versa. Everyone who is either not tall or funny is either quiet or happy. Everyone who is either not old or not generous is kind or not generous. Everyone who is either old or humble is either quiet or not quiet and vice versa. Someone is either strong or humble. Someone is not rich or happy. John is either not quiet or not strong. Someone is brave. Someone is either not curious or not kind. Paul is tall. Someone is either not wise or not old. Lucy is both not quiet and not old. | John is not curious. | entailment | (![X]:((~quiet(X)<~>funny(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>(~old(X)&generous(X))))&
(![X]:((curious(X)|creative(X))=>(~generous(X)<~>funny(X))))&
(((~generous(mary)|funny(mary)))=>(?[X]:((rich(X)<~>old(X)))))&
(((curious(paul)|~brave(paul)))=>(?[X]:((strong(X)<~>kind(X)))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:(~kind(X)<=>(curious(X)&~humble(X))))&
(![X]:(curious(X)<=>~creative(X)))&
(![X]:((~calm(X)|brave(X))=>(curious(X)<~>generous(X))))&
(![X]:((~brave(X)<~>happy(X))=>brave(X)))&
((~happy(john))<=>(?[X]:((~brave(X)|~tall(X)))))&
(((~rich(lucy)|~generous(lucy)))<=>((~kind(john)<~>~creative(john))))&
(![X]:((~tall(X)<~>funny(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)<~>~generous(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)<~>humble(X))<=>(quiet(X)<~>~quiet(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:((~rich(X)|happy(X))))&
((~quiet(john)<~>~strong(john)))&
(?[X]:(brave(X)))&
(?[X]:((~curious(X)<~>~kind(X))))&
(tall(paul))&
(?[X]:((~wise(X)<~>~old(X))))&
((~quiet(lucy)&~old(lucy))) | ~curious(john) | [
"p0",
"p3",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3329889129405820710283845
% SZS output start Proof for 3329889129405820710283845
1. ! [X0] : ((~quiet(X0) <~> funny(X0)) <=> quiet(X0)) [input p0]
4. ! [X0] : ((creative(X0) | curious(X0)) => (~generous(X0) <~> funny(X0))) [input p3]
10. ! [X0] : ((brave(X0) | ~calm(X0)) => (curious(X0) <~> generous(X0))) [input p9]
11. ! [X0] : ((~brave(X0) <~> happy(X0)) => brave(X0)) [input p10]
12. ~happy(john) <=> ? [X0] : (~tall(X0) | ~brave(X0)) [input p11]
25. curious(john) [input hypothesis]
27. ! [X0] : (brave(X0) => (curious(X0) <~> generous(X0))) [pure predicate removal 10]
28. ! [X0] : ((~generous(X0) <~> funny(X0)) | (~creative(X0) & ~curious(X0))) [ennf transformation 4]
31. ! [X0] : ((curious(X0) <~> generous(X0)) | ~brave(X0)) [ennf transformation 27]
32. ! [X0] : (brave(X0) | (~brave(X0) <=> happy(X0))) [ennf transformation 11]
36. ! [X0] : ((((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0))))) [nnf transformation 1]
40. ! [X0] : (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | (~creative(X0) & ~curious(X0))) [nnf transformation 28]
55. ! [X0] : (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ~brave(X0)) [nnf transformation 31]
56. ! [X0] : (brave(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) [nnf transformation 32]
57. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | happy(john)) [nnf transformation 12]
58. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & (? [X1] : (~tall(X1) | ~brave(X1)) | happy(john)) [rectify 57]
59. ? [X1] : (~tall(X1) | ~brave(X1)) => (~tall(sK4) | ~brave(sK4)) [choice axiom]
60. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & ((~tall(sK4) | ~brave(sK4)) | happy(john)) [skolemisation 58,59]
80. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 36]
82. funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 36]
96. ~funny(X0) | generous(X0) | ~curious(X0) [cnf transformation 40]
118. ~generous(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 55]
119. brave(X0) | happy(X0) | brave(X0) [cnf transformation 56]
122. ~happy(john) | brave(X0) [cnf transformation 60]
157. curious(john) [cnf transformation 25]
163. happy(X0) | brave(X0) [duplicate literal removal 119]
164. quiet(X0) | funny(X0) [duplicate literal removal 80]
165. ~quiet(X0) | funny(X0) [duplicate literal removal 82]
166. funny(X0) [subsumption resolution 164,165]
168. ~curious(X0) | generous(X0) [subsumption resolution 96,166]
238. ~brave(X0) | ~curious(X0) [subsumption resolution 118,168]
244. 16 <=> happy(john) [avatar definition]
246. ~happy(john) <- (~16) [avatar component clause 244]
249. 17 <=> ! [X0] : brave(X0) [avatar definition]
250. brave(X0) <- (17) [avatar component clause 249]
251. 17 | ~16 [avatar split clause 122,244,249]
344. brave(john) <- (~16) [resolution 163,246]
355. ~curious(john) <- (~16) [resolution 238,344]
358. $false <- (~16) [subsumption resolution 355,157]
359. 16 [avatar contradiction clause 358]
362. ~curious(X0) <- (17) [resolution 250,238]
368. $false <- (17) [resolution 362,157]
371. ~17 [avatar contradiction clause 368]
372. $false [avatar sat refutation 251,359,371]
% SZS output end Proof for 3329889129405820710283845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not old is either tall or patient. Everyone who is both kind and not humble is kind. If alice is curious or not quiet then mary is either not calm or creative. If lucy is both not curious and not tall then someone is both tall and kind. If someone is kind or not calm then someone is strong or humble and vice versa. Everyone who is generous is both not brave and not creative. Everyone who is both not wise and not calm is both not rich and calm. If susan is both humble and not generous then mary is both generous and not happy. If alice is either quiet or not happy then someone is not tall and vice versa. Everyone who is both not happy and not humble is both not wise and happy and vice versa. If someone is both not creative and not old then fred is not old or happy and vice versa. Everyone who is calm or kind is both not wise and humble. Everyone who is both not kind and calm is not brave or patient and vice versa. Everyone who is calm or brave is both wise and old. If john is not patient then someone is both not calm and old and vice versa. If lucy is both not happy and not curious then lucy is not brave or not curious and vice versa. Someone is both strong and not tall. Mary is either not brave or quiet. Paul is not quiet or tall. Fred is either not wise or creative. Someone is calm or not humble. Someone is both not rich and brave. | Lucy is not brave. | contradiction | (![X]:((generous(X)<~>~old(X))=>(tall(X)<~>patient(X))))&
(![X]:((kind(X)&~humble(X))=>kind(X)))&
(((curious(alice)|~quiet(alice)))=>((~calm(mary)<~>creative(mary))))&
(((~curious(lucy)&~tall(lucy)))=>(?[X]:((tall(X)&kind(X)))))&
((?[X]:((kind(X)|~calm(X))))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
(![X]:((~wise(X)&~calm(X))=>(~rich(X)&calm(X))))&
(((humble(susan)&~generous(susan)))=>((generous(mary)&~happy(mary))))&
(((quiet(alice)<~>~happy(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&~humble(X))<=>(~wise(X)&happy(X))))&
((?[X]:((~creative(X)&~old(X))))<=>((~old(fred)|happy(fred))))&
(![X]:((calm(X)|kind(X))=>(~wise(X)&humble(X))))&
(![X]:((~kind(X)&calm(X))<=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|brave(X))=>(wise(X)&old(X))))&
((~patient(john))<=>(?[X]:((~calm(X)&old(X)))))&
(((~happy(lucy)&~curious(lucy)))<=>((~brave(lucy)|~curious(lucy))))&
(?[X]:((strong(X)&~tall(X))))&
((~brave(mary)<~>quiet(mary)))&
((~quiet(paul)|tall(paul)))&
((~wise(fred)<~>creative(fred)))&
(?[X]:((calm(X)|~humble(X))))&
(?[X]:((~rich(X)&brave(X)))) | ~brave(lucy) | [
"p6",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8862139524442216615580418
% SZS output start Proof for 8862139524442216615580418
7. ! [X0] : ((~calm(X0) & ~wise(X0)) => (calm(X0) & ~rich(X0))) [input p6]
12. ! [X0] : ((kind(X0) | calm(X0)) => (humble(X0) & ~wise(X0))) [input p11]
13. ! [X0] : ((calm(X0) & ~kind(X0)) <=> (patient(X0) | ~brave(X0))) [input p12]
14. ! [X0] : ((brave(X0) | calm(X0)) => (old(X0) & wise(X0))) [input p13]
23. ~brave(lucy) [input hypothesis]
25. ! [X0] : ((~calm(X0) & ~wise(X0)) => calm(X0)) [pure predicate removal 7]
34. ! [X0] : (calm(X0) | (calm(X0) | wise(X0))) [ennf transformation 25]
35. ! [X0] : (calm(X0) | calm(X0) | wise(X0)) [flattening 34]
38. ! [X0] : ((humble(X0) & ~wise(X0)) | (~kind(X0) & ~calm(X0))) [ennf transformation 12]
39. ! [X0] : ((old(X0) & wise(X0)) | (~brave(X0) & ~calm(X0))) [ennf transformation 14]
60. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~calm(X0) | kind(X0)))) [nnf transformation 13]
61. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~calm(X0) | kind(X0))) [flattening 60]
93. calm(X0) | calm(X0) | wise(X0) [cnf transformation 35]
109. ~wise(X0) | ~calm(X0) [cnf transformation 38]
116. brave(X0) | calm(X0) [cnf transformation 61]
118. wise(X0) | ~calm(X0) [cnf transformation 39]
139. ~brave(lucy) [cnf transformation 23]
142. calm(X0) | wise(X0) [duplicate literal removal 93]
270. wise(X0) [subsumption resolution 118,142]
290. 33 <=> brave(lucy) [avatar definition]
291. ~brave(lucy) <- (~33) [avatar component clause 290]
329. ~33 [avatar split clause 139,290]
332. ~calm(X0) [resolution 109,270]
335. calm(lucy) <- (~33) [resolution 116,291]
338. $false <- (~33) [subsumption resolution 335,332]
339. 33 [avatar contradiction clause 338]
343. $false [avatar sat refutation 329,339]
% SZS output end Proof for 8862139524442216615580418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and not funny then someone is both brave and not generous.
If someone is either not patient or not funny then someone is both not strong and not happy and vice versa.
If someone is either brave or not tall then someone is not rich.
Everyone who is both patient and funny is generous and vice versa.
Everyone who is not brave is not creative or not brave.
If mary is either not tall or happy then someone is not rich or not wise.
Everyone who is not old is either creative or not calm.
If someone is either not creative or creative then someone is wise or not tall.
Everyone who is not strong is old or not rich.
If paul is both not generous and calm then someone is either not quiet or old and vice versa.
If lucy is kind or not old then someone is strong or kind.
If fred is creative or curious then susan is not quiet or not tall.
Everyone who is both not curious and old is not calm and vice versa.
Everyone who is creative is quiet and vice versa.
Everyone who is calm is both rich and not rich and vice versa.
Everyone who is either not brave or not rich is both strong and curious.
Someone is either not funny or not patient.
Fred is either not humble or calm.
Lucy is rich or calm.
Someone is funny.
Fred is not rich.
Someone is not kind.
Paul is creative or not humble.
John is either strong or humble. | Paul is not quiet. | entailment | ((?[X]:((~old(X)&~funny(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((~strong(X)&~happy(X)))))&
((?[X]:((brave(X)<~>~tall(X))))=>(?[X]:(~rich(X))))&
(![X]:((patient(X)&funny(X))<=>generous(X)))&
(![X]:(~brave(X)=>(~creative(X)|~brave(X))))&
(((~tall(mary)<~>happy(mary)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~old(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~strong(X)=>(old(X)|~rich(X))))&
(((~generous(paul)&calm(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((kind(lucy)|~old(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(((creative(fred)|curious(fred)))=>((~quiet(susan)|~tall(susan))))&
(![X]:((~curious(X)&old(X))<=>~calm(X)))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:(calm(X)<=>(rich(X)&~rich(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(strong(X)&curious(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
((~humble(fred)<~>calm(fred)))&
((rich(lucy)|calm(lucy)))&
(?[X]:(funny(X)))&
(~rich(fred))&
(?[X]:(~kind(X)))&
((creative(paul)|~humble(paul)))&
((strong(john)<~>humble(john))) | ~quiet(paul) | [
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2702606028376484511834563
% SZS output start Proof for 2702606028376484511834563
10. (calm(paul) & ~generous(paul)) <=> ? [X0] : (~quiet(X0) <~> old(X0)) [input p9]
13. ! [X0] : ((old(X0) & ~curious(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : (calm(X0) <=> (~rich(X0) & rich(X0))) [input p14]
25. quiet(paul) [input hypothesis]
65. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~calm(paul) | generous(paul))) [nnf transformation 10]
66. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~calm(paul) | generous(paul)) [flattening 65]
67. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) | ~calm(paul) | generous(paul)) [rectify 66]
68. ? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) => ((~old(sK6) | quiet(sK6)) & (old(sK6) | ~quiet(sK6))) [choice axiom]
69. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(sK6) | quiet(sK6)) & (old(sK6) | ~quiet(sK6))) | ~calm(paul) | generous(paul)) [skolemisation 67,68]
72. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~old(X0) | curious(X0)))) [nnf transformation 13]
73. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~old(X0) | curious(X0))) [flattening 72]
75. ! [X0] : ((calm(X0) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 15]
76. ! [X0] : ((calm(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [flattening 75]
113. calm(paul) | ~quiet(X0) | ~old(X0) [cnf transformation 69]
120. calm(X0) | old(X0) [cnf transformation 73]
123. rich(X0) | ~calm(X0) [cnf transformation 76]
124. ~calm(X0) | ~rich(X0) [cnf transformation 76]
141. quiet(paul) [cnf transformation 25]
235. 22 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
236. ~quiet(X0) | ~old(X0) <- (22) [avatar component clause 235]
238. 23 <=> calm(paul) [avatar definition]
240. calm(paul) <- (23) [avatar component clause 238]
241. 22 | 23 [avatar split clause 113,238,235]
298. ~calm(X0) [subsumption resolution 123,124]
330. $false <- (23) [subsumption resolution 240,298]
331. ~23 [avatar contradiction clause 330]
332. old(X0) [resolution 120,298]
342. ~old(paul) <- (22) [resolution 236,141]
343. $false <- (22) [subsumption resolution 342,332]
344. ~22 [avatar contradiction clause 343]
345. $false [avatar sat refutation 241,331,344]
% SZS output end Proof for 2702606028376484511834563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
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